Research ArticleMathematical Model of Hybrid Precast Gravity Frames for SmartConstruction and Engineering

Seon-Chee Park1 Won-Kee Hong1 Sunkuk Kim1 and Xiangyu Wang23

1 Department of Architectural Engineering Kyung Hee University 1732 Deogyeong-daero Giheung-gu Yongin-siGyeonggi-do 446-701 Republic of Korea

2 Australasian Joint Research Centre for Building InformationModelling CurtinUniversity GPOBoxU1987 PerthWA6845 Australia3 Department of Housing and Interior Design Kyung Hee University 1732 Deogyeong-daero Giheung-gu Yongin-siGyeonggi-do 446-701 Republic of Korea

Correspondence should be addressed to Won-Kee Hong hongwkkhuackr

Received 28 February 2014 Revised 4 April 2014 Accepted 1 May 2014 Published 27 August 2014

Academic Editor Changzhi Wu

Copyright copy 2014 Seon-Chee Park et alThis is an open access article distributed under theCreative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The structural stability constructability economic feasibility environmental-friendliness and energy efficiency of hybrid compositeframe systems have been demonstrated by practical application and research A hybrid composite frame system combines theeconomyof precast concrete structureswith the constructability of steel frame structures including erection speedNovel compositeframes will ultimately maximize the efficiency of structural design and facilitate construction This paper presents hybrid precastframes which are precast composite frames based on a simple connection between precast concrete columns and beamsThe hybridprecast frames designed to resist gravity loading consist of PC columns PC beams and steel inserted in the precast members Steelsections located between the precast columns were simply connected to steel inserted at each end of the precast beams Dynamicanalysis of a 15-story building designedwith the proposed composite framewas performed to determine the dynamic characteristicsof a building constructed of hybrid frames including frequencies and mode shapes

1 Introduction

The use of hybrid precast composite frames with hybridprecast beams and columns for gravity loading offers advan-tages of both steel and precast concrete materials Effectiveinteraction between the two materials facilitates a reductionin size of both hybrid precast beams and columnsThe hybridprecast frames are connected by simple connections thatsupport only gravity load

In a previous study Hajjar (2002) demonstrated thebenefits of composite systems relative to more commonsystems [1] Such advantages were determined by comparingthe performance characteristics of beams subjected to ser-vice and ultimate loads Hajjar also analyzed the economicbenefits of composite structures with respect to materialusage and construction costs Fabbrocino et al (2001) useda refined theoretical model to investigate the influence ofsteel reinforcement on the rotational capacity of composite

beams under negative bending [2] This model was validatedthrough experimental testing Yang and Tan (2014) con-ducted a series of experiments to investigate the failuremodesand ductility of composite beam-column joints under amiddle-column-removal scenario and reported the ductilityand load resistances of these five specimens in catenaryaction They found that strengthened web cleat connectionshad a much higher load-carrying capacity than normal webcleat connections because the former could sustain greaterdeformation [3] Tesser and Scotta (2013) studied compositesteel trusses and concrete beams with an inferior precastconcrete base and compared their findings with theoreticalevaluations of typical resistancemechanisms of steel-concretecomposite and reinforced concrete structuresThey discussedthe main qualitative and quantitative features of the compos-ite steel truss and concrete beams [4] Hwang and colleagues(2011) evaluated the seismic resistance of concrete-filled U-shaped steel beam-to-RC column connections and provided

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 916951 14 pageshttpdxdoiorg1011552014916951

2 Mathematical Problems in Engineering

seismic details of concrete-encased U-shaped steel beam-to-RC column connections The specimens exhibited requiredstrength deformation and energy dissipation capacitiesThedeformation capacity exceeded an interstory drift angle of4 which is a requirement for special moment frames [5]Hassan and Khosrow (2011) presented an analytical inves-tigation based on FE models and using ANSYS software toexamine the effectiveness of a precast beam column concreteconnection of a jointed system However this computermodel did not examine the steel section installed in a column-beam joint as discussed in [6] Another study by Ioani andTripa (2012) discussed a new all-precast concrete system usedin Romania to construct a residential building Designed forconstructability a new all-precast concrete system compris-ing columns flat slabs and structural walls were proposedTo validate the structural quality and performance of this typeof structure an extensive program of theoretical analyses andstructural tests (including shake table tests) was conducted[7] This product proposed by Ioani and Tripa differs fromthe one proposed here The structural system developedby the authors is a hybrid composite beam-column framethat demonstrates the structural behaviors of building framesystem We designed hybrid precast composite frames withsimple steel connections inserted between precast concretecolumns and beams to resist only gravity loading The firstobjective of the study by Chou and Uang (2007) was toexamine the effects of the two factors of continuity platesand the amount of transverse reinforcement on the concreteshear strength in the connection regionThe second objectivewas to develop an analytical procedure to quantify theconnection shear force developed in concreteThis continuityplate will be used for the hybrid composite frames of theauthors in later experiments [8] Ju andKim (2005) developedthe technical economical and convenient (TEC) compos-ite beam with experimental investigation using a series ofmonotonic loading tests [9] However this beam is not freefrom the requirement of being fire-proof These studies didnot expand their interests to hybrid composite structures forpractical applications which were covered in this paper Wealso present novel structural systems with dynamic analysisto examine the hybrid behavior of a building which takesadvantage of material structural and construction hybridfeatures and capabilitiesThe hybrid precast composite framesystem shows how material structural and constructionhybridity are established to uniquely provide economy andconstructability making this technology significant to theconstruction industry We also designed hybrid precast com-posite frames with simple steel connections inserted betweenprecast concrete columns and beams to resist only gravityloading The hybrid composite frame system introduced inthis paper is intended to provide the economy of precastconcrete structures with the constructability of steel framestructures Structural design efficiency facilities planningconstruction and buildingmanagement could bemaximizedusing the proposed composite frame system Implementationof integrating augmented reality with building informationmodeling [10ndash13] will help project the schedule and costof construction utilizing smart frame for site engineers andresponses to any demand for changes can be provided in time

We have previously [14 15] investigated dual-frame sys-tems composed of hybrid precast frames The dual-framesystem consists of a moment frame and a bearing wall orbraced frame Seismic forces are distributed in proportionto the lateral stiffness of each frame The moment frame hasto resist at least 25 of the design seismic forces Howeverthe dual frame systems with moment connections includingmuch more complicated construction details require sig-nificant time and costs than simple connections which areused in building frame systems for gravity loadings Buildingframe systems with simple connections are commonly usedwith steel frames to provide fast and easy construction forbuildings In this paper new structural system to providesimplified construction method was presented for buildingframe systems for gravity loadings fabricated with hybridprecast composite frames consisting of simple connectionsbetween columns and beams

The building frame system was designed for the researchthe frames resist gravity loading while the bearingwalls resistlateral forces

2 Precast Composite Structural System(Hybrid Precast Frames)

21 Details of the Frame with Generalized Steel Joints Thehybrid precast frames proposed in this study represent ahybrid composite structural system with the advantages ofboth steel frames and reinforced concrete structures Hybridprecast frames are composed of generalized steel jointsreinforcing steel and precast concrete Apartment build-ings have been outfitted with these hybrid precast framesto resolve problems such as the increase in floor heightwhen constructed with concrete Rahmen These frames canmaintain the same floor height as that of a bearing wall sys-tem providing architectural flexibility and cost-effectiveness[14 15] We developed a precast steel column with steelconnections to effectively erect and assemble the compositeframesThe joints of hybrid precast frames installed to a core-wall were simple connections to support vertical loadingsonly The joints of the gravity frames were not filled withconcrete allowing for pin-joint behavior which enhancesthe constructability and economic feasibility of the gravityframes The construction of the core-walls was followed byconstruction of hybrid precast frames including columnsbeams and slabs Hybrid precast frames were composedof hybrid precast beam units and hybrid precast columnunits with enhanced joint connections capable of resistingvertical loads enablingmore efficient erectionwith structuralstability Specifically the introduction of steel sections forjoint connection makes the construction of hybrid precastframes as timely as that of steel frames Hybrid precast frameconstruction is illustrated in Figure 1

Hybrid precast frames were manufactured either at aplant or on site [16] Hybrid precast beams take advantageof the material properties of both steel and precast concretewithout sacrificing the performance of the composite beamsThe depths of the beam and slab can also be reduced whenslabs are constructed on the edges of precast concrete

Mathematical Problems in Engineering 3

Figure 1 Building construction with hybrid precast frames

Stud bolt

Steel plate

Angle and bolts forsimple connection

(shear tap)

Precast concrete

Cast-in-place concrete

Variable

Simple connection (hinge)

Variable

Steel plate

Figure 2 Detailed information on beam-column joint members

Figure 2 shows the beam-column joint connection ofhybrid precast frames where joint connections are notfilled with concrete (ie pin-joint) Typical hybrid precastbeam-column connections designed for pinned conditions(Figure 2) enable the gravity load to be transferred throughthe joints where the web of steel beams is bolted to the steelsection of the hybrid precast column This type of structuralframe system provides simpler construction with structuralstability to support gravity loads

Figure 3 shows the generalized steel joints configured forgravity loading that are used in the hybrid precast framesAdditional shear taps are installed to provide connectionsbetween the steel sections from both columns and beamsSteel sections inserted into the hybrid precast beams and

columns allow hybrid precast frames to be erected in as manyas three stories at a time Conventional steel joints used inconventional steel construction are utilized as generalizedconnections

Figure 4 shows the construction process used to producethe hybrid precast frames Both the hybrid precast columnand the beam units of the hybrid precast frames weremanufactured as two-story or three-story column units andwere erected in one cycle The main processes of floor workwhich took about four days consisted of marking core wallreinforcement work and form installation installation ofhybrid precast column units and beam units installation ofdeck plates or a PC plate and joint form slab reinforcementwork and pouring

4 Mathematical Problems in Engineering

Column reinforced rebarsSteel plate

Beam units

Simple connection(shear tap)

Cast-in-place concrete

CFTPrecast concrete

Shear tap

Variable

VariableStud bolts

(a) Details of the beam-column joints of the hybrid precast frames

Without CFTShear tap

Stud bolt

With CFTShear tap

(b) Details of the shear tap

CFT Variable Service condition

Stud boltShear tap

(c) Construction details of the column unit

Figure 3 Details of the hybrid precast frame joints

Precast structures cannot be erected as fast as steel struc-tures because beams without slabs lack stability as shown inFigure 5 The hybrid precast frames however can be erectedas quickly as steel structures without slab construction Thehybrid precast frames suggested in this paper are hybridcomposite structures that have the merits of both steel andprecast concrete structures in particular the steel sectionsfunction as erection components This hybrid constructionmethod makes it possible to erect precast concrete frames ina time-frame similar to that of steel frames

22 Structural Stability during Construction The proposedhybrid precast frames with steel joints provide structuralstability during construction In contrast the vertical rein-forcing steel used for vertical splicing in conventional precastapplications is vulnerable to buckling against unexpectedvertical loading before the joints are filled with concretewhich could cause structural instability of the frame underconstruction as shown in Figure 6 In the proposed methodsteel sections are inserted between the upper and lowerprecast columns and are connected to steel sections locatedat both ends of the precast beams and girders or steel sectionsrunning throughout the entire lengths of the precast beamsallowing easy and stable connections

3 Use of Convergence of the HybridPrecast Frames

Because hybrid precast frames can be designed using a widerange of spans and joint designs bearing wall-type apartmentbuildings may be replaced with buildings with hybrid precastframes Structural systems should be optimized with steelconnections which are required to be as small as 20sim25 kgfm2 (about one-tenth that of reinforcing steel) enablingconstructability and assembly time similar to that of steelframes

Figure 7 shows deflections of a composite frame buildingsubjected to wind loads The lateral displacements are withinacceptable limits Displacement along the 119909-axis and 119910-axis was 20 cm (H3910) and 29 cm (H1955) respectivelyAcceptable story drift in response to seismic loading wasalso observed in both directions as shown in Figure 8 Theseresults demonstrate that the optimized structural compositeframes have structural stability

4 Dynamic Analysis of a Building with HybridPrecast Frames

Figure 9 shows a building with 13 stories and two base-ments (total floor area of 6741m2) that was designed with

Mathematical Problems in Engineering 5

Shear tap

Stud bolt

Steel plate

CFT

Cast-in-place concrete

Precast concrete

Shear tap

Figure 4 Hybrid precast frame construction process

+

Critical pathUpwards construction

Figure 5 Reduction of the hybrid precast frame construction period

Rebarconnection

(a)

Rebarconnection

(b)

Figure 6 Conventional precast concrete connections

6 Mathematical Problems in Engineering

X-direction00111 m

(H39099)

Midas genpostprocessordisplacement

resultant

Scale factor =

110700e minus 002100636e minus 002905726e minus 003805090e minus 003704454e minus 003603817e minus 003503181e minus 003402545e minus 003301909e minus 003201272e minus 003100636e minus 003000000e + 000

26266E + 002

(a)

Y-direction00222 m

(H19549)

Midas genpostprocessordisplacement

resultant

Scale factor =

222476e minus 002202251e minus 002182025e minus 002161800e minus 002141575e minus 002121350e minus 002101125e minus 002809002e minus 003606752e minus 003404501e minus 003202251e minus 003000000e + 000

13069E + 002

(b)

Figure 7 Wind displacement

0

0002

0004

0006

0008

001

0012

0014

0016

17F

16F

15F

14F

13F

12F

11F

10F 9F 8F 7F 6F 5F 4F 3F 2F 1F

Story drift ratioAllowable story drift ratio

Story drift ratio (x-axis)

(a)

17F

16F

15F

14F

13F

12F

11F

10F 9F 8F 7F 6F 5F 4F 3F 2F 1F

Story drift ratioAllowable story drift ratio

0

0002

0004

0006

0008

001

0012

0014

0016Story drift ratio (y-axis)

(b)

Figure 8 Story drift

the proposed composite frames and selected for dynamicanalysis The floor plan and elevation with framing usingcomposite columns and beams are also shown The buildingwas designed such that the shear walls were resistant to lateralseismic loadings while the frames resisted only vertical loadsDynamic analysis was performed to investigate the influenceof the design and size of the composite frames on the dynamiccharacteristics of the building

Figure 10 shows a computer model of the building withcomposite frames andwalls in which the steel sections at bothends of the beams are connected to steel inserted betweentwo precast columns Figure 10(a) shows gravity compositeframes attached to shear walls that are responsible for lateralearthquake loading Figure 10(b) shows close connectiondetails of the frames and walls that constitute the building

frame Figure 10(c) shows steel frames and connectionsbetween beams and columns The material structural andconstruction hybrid applications were integrated to combinethe constructability of steel structures with the economy ofconcrete structures

Tables 1 and 2 show modal participation masses andeigenvalue results respectively The fundamental transla-tional mode was found in the third return period the firstand second modes were considered to be mixed translationalmodes with torsion A fundamental translational mode of 15seconds along with a weak 119910-axis was deemed reasonableThe fundamental period and mode shapes for the compositeframe were more similar to those of steel structures thanthose of concrete structures indicating that the structuralbehavior of a building with composite frames and steel

Mathematical Problems in Engineering 7

7400

17750

3500

3500

3500

3500

3500

3500

3000

2400

X

Y

2900

2900

X6

X6

X7

X8

X9

X10

2900

4100

39200

14001400

14600

6300 63002000

PS

PS

PSPS

PSPS

PS

PS PS

PSPS

PS

PS

PS

PSPS

PSPS

PSPS

PS

PSPS

PS

PS

PSPS

PS

PS

PS

PS

PS

PSPS

PS

PS

PS

PS

PS

PS

PS

329

0

4928

3500

3500

3500

3500

3500

3500

6300

1300

1300

5000

5000

6300

14600

X1

X2

X3

2000

25928

350

0

350

03

500

350

03

500

350

03

500

350

03

500

350

03

500

700

07

000

700

07

000

700

0

417

90

PS

PS

PS

PS

PS PS

PSPS

Hal

l

PS

PS

49004900

Y3998400

Y4998400

Y5998400

Y6998400

(a)

Figure 9 Continued

8 Mathematical Problems in Engineering

1447

1500

7200

3600

3600

3800

2900

2900

2900

2900

2900

2900

2900

2900

2900

2900

2900

1

29001400

1500 1

0003600

23003600

3800

2900

2600

1300

3200

1600700

600

2900

2900

2900

2900

2900

2900

2900

2900

2900

2900

29001400

40000

2880

2880

920

5100700061508300 6300

6300 630020002150 4150

5382

1447

2250

2250

2250

2250

2250

2250

2250

2250

2250

2250

2250

2250

3200 2400

2300

1600

GL-1800

GL-6000

510070006150146005382

(b)

Figure 9 Floor plan and elevation

Mathematical Problems in Engineering 9

Table 1 Modal participation masses

Mode number TRAN-119883 TRAN-119884 ROTN-119885Mass () Sum () Mass () Sum () Mass () Sum ()

1 405909 405909 02185 02185 127252 1272522 42570 448478 16208 164265 203361 3306123 40667 489145 328629 492893 82552 4131644 96703 585848 01847 49474 40557 4537215 32088 617935 03965 498705 87600 5413216 03685 621620 158676 657381 05207 546528

(a) (b) (c)

Figure 10 Computer model of the building

Table 2 Eigenvalue analysis (fundamental period)

Mode number Frequency Period Tolerance(radsec) (cyclesec) (sec)

1 34768 05533 34768 00000119890 + 000

2 41078 06538 41078 00000119890 + 000

3 53487 08513 53487 00000119890 + 000

4 138311 22013 138311 45251119890 minus 161

5 178259 28371 178259 28518119890 minus 150

6 236726 37676 236726 15909119890 minus 137

joints against vertical and lateral loadings resembles that ofsteel structures even though the building has an externalappearance of a concrete structure

Figure 11 shows the first translational mode (a) and thoseof two mixed modes ((b) (c)) Figures 11(d) 11(e) and 11(f)show these modes from the top view respectively

5 Reduction of Structural Quantity andEmissions of Environmentally HazardousSubstances and Materials

This study evaluated chromium VI and carbon dioxide emis-sions of the building constructed with the proposed framesand conventional walls Reductions in energy consumptiondue to reduction in material quantity were estimated basedon comparison of an apartment building constructed withhybrid precast frames and that of a conventional bearing-wallbuilding

Original units of major building components (Table 3)which were announced in 2008 by the United Kingdom

Table 3 Emissions and energy usage of major building components[17]

Buildingcomponent

CO2 emissionsper original unit

Energy consumptionper original unit

Concrete 25MPa 3196 kg-CO2m3 23265MJm3

Concrete 35MPa 37835 kg-CO2m3 26555MJm3

Reinforcement 27319 kg-CO2kN 371050MJkNSteel section 28338 kg-CO2kN 375127MJkN

Inventory of Carbon and Energy (ICE) were used to evaluatecarbon dioxide emissions and the energy efficiency of theproposed construction The embodied energy 119864 and carbonemissions per kN for the calculated material quantity areobtained from the University of Bathrsquos ICE database [17 18]The ICE has been structured into 34 main material groupsThe database also provides the embodied energy and carboncoefficients for construction materials Table 3 presents theconverted embodied energy and carbon coefficients for fourbuilding components concrete (25MPa) concrete (35MPa)reinforcement and steel section

Domestic and foreign cement heavymetal analysis results(May 2013) published by the Korea National Institute ofEnvironment Research (NIER) were utilized to evaluatechromium VI emissions (Table 4)

In order to explain how the data that evaluates the gravitysystem presented in this paper in terms of material quantityanalytical approach for the hybrid precast composite beamdesign based on the strain compatibility method was intro-duced Figures 12 and 13 illustrate the side view and cross-section of a hybrid composite beam In order to determine the

10 Mathematical Problems in Engineering

Table 4 Heavy metal content standards in cement [19]

Cr6+ As Cd Cu Hg PbAve (May 2013) 1063mgkg 1287mgkg 102mgkg 8903mgkg 061mgkg 3284mgkg

(a) Fundamental translational mode (b) Mixed mode 1 (c) Mixed mode 2

(d) Fundamental translational mode (e) Mixed mode 1 (f) Mixed mode 2

Figure 11 Mode shapes

Figure 12 Side view of a hybrid composite beam

d

d998400

d998400998400

d998400998400998400

Figure 13 Cross-section of a hybrid composite beam

exact material quantity the hybrid composite beam designwas carried out based on the strain compatibility methodEquations (1) and (2) are the mean stress factor 120572 and thecentroid factor 120574 for any strain 120576

119888119898at the extreme com-

pression fiber calculated based on stress-strain relationshipEquations (3) and (5) represent the equilibrium equations ofcompressive and tensile forces at yield limit and maximumload limit state respectively The nominal moment capacitiesof a hybrid composite beam at yield limit andmaximum loadlimit state are calculated by (4) and (6) respectively Figures14 and 15 represent strain and stress diagram at yield limitand maximum load limit state respectively In both figuresblack color indicates steels and reinforcement rebars wereplasticized (yielded) while white color represents structuralmembers remained elastic The structural quantity requiredby apartment buildings with hybrid composite frames wasobtained from (6) and compared with that of conventionalbuildings with bearing walls as shown in Table 5 These

Mathematical Problems in Engineering 11

Table 5 Evaluation of structural systems

Buildingcomponent System Gross area Building material CO2 emission Energy consumption Cr6+ emission

Concrete(HPF = 35MPaBW = 25MPa)

HPF 9236m2 038m3m2 691(minus309) 1362 kg-CO2m

2 775(minus225) 10060MJm2 786

(minus214) 11062mgm2 689(minus311)

BW 6513m2 055m3m2 1000 1758 kg-CO2m2 1000 12796MJm2 1000 16061mgm2 100

Reinforcements HPF 9236m2 053 kNm2 726(minus274) 1445 kg-CO2m

2 724(minus276) 19314MJm2 713

(minus287) mdash mdash

BW 6513m2 073 kNm2 1000 1996 kg-CO2m2 1000 27107MJm2 1000 mdash mdash

Steel section HPF 9236m2 007 kNm2 1000 206 kg-CO2m2 1000 2721MJm2 1000 mdash mdash

BW 6513m2 mdashkNm2 mdash mdashkg-CO2m2 mdash mdashMJm2 mdash mdash mdash

lowastHPF hybrid precast frames BW bearing wall

400 MPa

301 MPa

1354 mm

120576st = 0001506

120576t = 120576y = 0002

120576c = 000178 f998400c

120576998400t = 000096 120576tEs = 192MPa

Figure 14 Strain and stress diagram at yield limit state

120576tEs = 286MPa

400 MPa

325 MPa

11946 mm

120576st = 000328

120576t = 120576y = 00042

120576c = 0003f998400c

120576998400t = 000143

Figure 15 Strain and stress diagram at maximum load limit state

equations would help engineer estimate precise constructionmaterials and understand how buildings with hybrid com-posite frames behave Consider

120572 = (int

0002

0

119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

119891

1015840

1198881 minus 100 (120576

119888minus 120576

119888119900) 119889120576

119888)

times (119891

1015840

119888120576

119888119898)

minus1

(1)

120574 = 1 minus ((int

0002

0

120576

119888119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

120576

119888119891

1015840

1198881 minus 100 (120576

119888minus 120576

119888119900) 119889120576

119888)

times (120576

119888119898[int

0002

0

119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

119891

1015840

1198881minus100 (120576

119888minus120576

119888119900) 119889120576

119888])

minus1

)

(2)

120572119891

1015840

119888119887119888 + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840) +

1

2

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

= 119860

119904119865

119910+ 119860

119891119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

1

2

119860

119908119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891)

(3)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908= 119905

119908(119889 minus 119888 minus 119889

1015840minus 119905

119891)

119872

119899= 120572119891

1015840

119888119887119888 (119888 minus 120574119888) + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840)

2

+

1

3

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

2

+ 119860

119904119865

119910(119889 minus 119888)

12 Mathematical Problems in Engineering

DayProcess

One floor

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7

Marking

Rebar work (wall)

Wall form installation

Slab form installation

Rebar work (slab) Electrical and mechanical

facilities (slab) Cleaning and pouring

Figure 16 Processes for constructing one floor of a conventional wall-type apartment building [20]

+ 119860

119891119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891) (119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

119905

119891

2

(119889 minus 119888 minus 119889

1015840minus

119905

119891

3

)

+

1

3

119860

119908119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891)

2

(4)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908= 119905

119908(119889 minus 119888 minus 119889

1015840minus 119905

119891)

120572119891

1015840

119888119887119888 + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840) +

1

2

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

= 119860

119904119865

119910+ 119860

119891119865

119910+ 119860

119908119901119865

119910+

1

2

119860

119908119899119910119864

119904120576

119904119910

(5)

where1198601015840119908= 119905

119908(119888minus119889

101584010158401015840)119860119908119901

= 119905

119908(119889minus119888+119889

1015840+119905

119891)+(120576

119904119910120576

119888)119888

119860

119908119899119910= 119905

119908(120576

119904119910120576

119888)119888

119872

119899= 120572119891

1015840

119888119887119888 (119888 minus 120574119888) + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840)

2

+

1

3

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

2

+ 119860

119904119865

119910(119889 minus 119888)

+ 119860

119891119865

119910(119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

1

2

119860

119908119901119865

119910(119889 minus 119888 minus 119889

1015840minus 119905

119891) +

120576

119904119910

120576

119888

119888

+

1

3

119860

119908119899119910119864

119904

(120576

119904119910)

2

120576

119888

119888

(6)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908119901

= 119905

119908119889 minus (119888 + 119889

1015840+ (120576

119904119910120576

119888)119888)

119860

119908119899119910= 119905

119908(120576

119904119910120576

119888)119888

A completed bearing wall apartment building wasselected for this comparison Apartment buildings withhybrid precast frames and bearingwall frameswere evaluatedin terms of building material CO

2emission energy con-

sumption and Cr6+ emission shown in Table 5 Construction

materials per square meters were calculated based on (5) and(6)whichwere then used to calculate the quantities of Table 5

The building materials of concrete and reinforcementsof apartment buildings with hybrid precast frames werereduced by 31 and 27 respectively compared with thatof bearing wall frame buildings The CO

2emission energy

consumption andCr6+ emission of apartment buildings withhybrid precast frames were also decreased compared withbearing wall frame buildings as shown in Table 5 exhibitingthe efficiency of using gravity hybrid precast frames forapartment buildings

6 Reduction in Construction Schedule

Figures 16 and 17 compare the construction time frames basedon the use of conventional bearing walls versus the proposedhybrid frames

The construction time is the sum of each critical path asshown in

119899

sum

119894=1

(CA119894) = CA

1+ CA2+ CA3+ CA4sdot sdot sdot (7)

The critical paths that affect construction time for abearing wall apartment are CA

1(marking 1 day) CA

2(rebar

work wall 1 day) CA3(wall form installation 2 days)

CA4(slab form installation 1 day) CA

5(rebar work slab 1

day) and CA6(cleaning and pouring 1 day) Installation of

electrical and mechanical facilities at the slab is performedwith rebar work of the slab and takes less time than that ofrebar work Electrical and mechanical facilities at the slab aretherefore excluded from the critical path The constructiontime per floor is seven days based on (7) The criticalpaths affecting construction time for an apartment buildingusing hybrid frames are CA

1(rebar work core wall 05

days) CA2(column-beam unit installation (1 day) beam

unit installation (15 days)) CA3(rebar work slab 05 days)

and CA4(cleaning and pouring 05 days) Column-beam

unit installation and beam unit installation are carried outalternately Beams are only installed at every second andthird floor since columns are erected as a three-story unit

Mathematical Problems in Engineering 13

DayProcess

First floor Second floor Third floor

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 Day 10

Rebar work (core wall)

Core wall form installationColumn-beam unit

installation Beam unit installation

Deck plate installation

Joint form installation

Rebar work (slab) Electrical and mechanical

facilities (slab) Cleaning and pouring

Figure 17 Processes for constructing three floors of an apartment building using hybrid frames [20]

Table 6 Comparative analysis of the construction period [20]

Structuraltype

Construction periodComparisonTypical

floor30-story apartment

building

Bearing wall 7 days1 floor 210 Days 1000Hybrid precastframe

10 days3floors 100 Days 476

As a result of the critical paths analysis the constructiontime per floor is four days for the first floor and threedays for the next two floors requiring ten days for theconstruction of three floors utilizing columns of a three-story unit The time for frame erection was reduced by 52when using hybrid frames highlighting their economic andconstruction benefits Erection of structural frames for onefloor using conventional bearing walls involves rebar workand concrete pouring and requires about seven days asshown in Figure 16 In contrast only three days were requiredto install wall and slab forms indicating that the overallconstruction was influenced by form work which is highlydependent on work skill However erection of three floorswith hybrid precast frames required only ten days whenthree-story hybrid precast columns were erected at one liftThe significant reduction in form work contributed to thedecrease in overall construction time obtained when usingthe hybrid precast frames as shown in Figure 17 As shown inTable 6 frame erection of a 30-story building required sevendays per floor or 210 days for the entire building when usingconventional bearing walls However only ten days per threefloors (or 100 days for the entire building) were required forframe erection of the building with hybrid precast frameswhich corresponds to a 524 reduction in frame erectiontime

7 Conclusions

This study described and characterized an optimized hybridprecast composite structural system for gravity systemMajorcontributions are summarized below

(1) Gravity hybrid precast frames were presented Thesehybrid frames consist of precast concrete and steelwhich can be erected at a speed similar to that of steelframes Steel sections inserted in precast columns andbeams are used as erection steel components

(2) Mathematical model of gravity hybrid precast beamwas presented at yield limit state and maximum loadlimit state Neutral axis of postyield state found fromequilibrium equations was used to calculate nominalmoment capacities of a hybrid composite beam atboth limit state

(3) The new building frame systems for gravity load-ings fabricated with hybrid precast composite framesconsisting of simple connections between columnsand beams were proposed in this paper The dualframe systems of moment connections with muchmore complicated construction details required sig-nificant time and costs than that of building framesystems of gravity loadings However the gravityhybrid precast composite structures will provide sim-plified construction method while enhancing econ-omyduring constructionThe reductions of construc-tion resources including concrete and reinforcements(31 reduction of concrete and 27 reduction of rein-forcements) were achieved when apartments were tobe built with hybrid precast frames

(4) The gravity hybrid precast frames use less construc-tion materials than conventional frames and there-fore reduce carbon dioxide and hazardous substanceemissions compared to conventional frames It was

14 Mathematical Problems in Engineering

observed the efficiency of using gravity hybrid precastframes for apartment building which decreased theCO2emission (23 reduction of concrete and 28

reduction of reinforcements) energy consumption(21 reduction of concrete and 29 reduction ofreinforcements) and Cr6+ emission compared withbearing wall frame buildings The use of gravityhybrid precast frames was demonstrated to providebetter solutions for environments and economy thanthat of conventional buildings

(5) Dynamic analysis of a 15-story building designedwith the proposed composite gravity frames was per-formed to characterize frequencies and mode shapesof the building for seismic design purposes

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by Grant from the Kyung HeeUniversity in 2013 (KHU-20130363)

References

[1] J F Hajjar ldquoComposite steel and concrete structural systems forseismic engineeringrdquo Journal of Constructional Steel Researchvol 58 no 5ndash8 pp 703ndash723 2002

[2] G Fabbrocino G Manfredi and E Cosenza ldquoDuctility ofcomposite beams under negative bending an equivalence indexfor reinforcing steel classificationrdquo Journal of ConstructionalSteel Research vol 58 no 2 pp 185ndash202 2001

[3] B Yang and K Tan ldquoBehaviour of composite beam-columnjoints under a middle-column-removal scenario experimentaltestsrdquo Journal of Structural Engineering vol 140 no 2 ArticleID 04013045 2014

[4] L Tesser and R Scotta ldquoFlexural and shear capacity of compos-ite steel truss and concrete beams with inferior precast concretebaserdquo Engineering Structures vol 49 pp 135ndash145 2013

[5] H J Hwang H G Park C H Lee et al ldquoSeismic resistanceof concrete-filled U-shaped steel beam-to-RC column connec-tionsrdquo Journal of Korean Society of Steel Construction vol 23 pp83ndash97 2011

[6] J Hassan and B Khosrow ldquoNonlinear seismic behavior evalua-tion of ductile beam-column connections in precast concreterdquoInternational Journal of Civil and Structural Engineering vol 1pp 445ndash453 2011

[7] A M Ioani and E Tripa ldquoStructural behavior of an innovativeall-precast concrete dual system for residential buildingsrdquo PCIJournal vol 57 no 1 pp 110ndash123 2012

[8] C Chou andCUang ldquoEffects of continuity plate and transversereinforcement on cyclic behavior of SRCmoment connectionsrdquoJournal of Structural Engineering vol 133 no 1 pp 96ndash104 2007

[9] Y K Ju and S D Kim ldquoStructural behavior of alternative lowfloor height system using structural ldquoteerdquo half precast concreteand horizontal studrdquoCanadian Journal of Civil Engineering vol32 no 2 pp 329ndash338 2005

[10] X Wang M Truijens L Hou Y Wang and Y Zhou ldquoInte-grating augmented reality with building informationmodelingonsite construction process controlling for liquefied natural gasindustryrdquoAutomation in Construction vol 40 pp 96ndash105 2014

[11] L Hou Y Wang X Wang et al ldquoCombining photogrammetryand augmented reality towards an integrated facility manage-ment system for the oil industryrdquo Proceedings of the IEEE vol102 no 2 pp 204ndash220 2014

[12] L Hou XWang L Bernold and P E D Love ldquoUsing animatedaugmented reality to cognitively guide assemblyrdquo Journal ofComputing in Civil Engineering vol 27 no 5 pp 439ndash451 2013

[13] YWang XWang JWang P Yung andG Jun ldquoEngagement offacilities management in design stage through BIM frameworkand a case studyrdquo Advances in Civil Engineering vol 2013Article ID 189105 8 pages 2013

[14] W K Hong J M Kim S C Park et al ldquoA new apartmentconstruction technology with effective CO

2emission reduction

capabilitiesrdquo Energy vol 35 no 6 pp 2639ndash2646 2010[15] W Hong S Park J Kim et al ldquoDevelopment of structural

composite hybrid systems and their application with regard tothe reduction of CO

2emissionsrdquo Indoor and Built Environment

vol 19 no 1 pp 151ndash162 2010[16] W Hong S Jeong S Park and J T Kim ldquoExperimental

investigation of an energy-efficient hybrid composite beamduring the construction phaserdquo Energy and Buildings vol 46pp 37ndash47 2012

[17] G P Hammond and C I Jones Inventory of Carbon amp Energy(ICE) Department of Mechanical Engineering University ofBath Bath UK 2008

[18] G P Hammond and C I Jones ldquoEmbodied energy and carbonin construction materialsrdquo Proceedings of Institution of CivilEngineers Energy vol 161 no 2 pp 87ndash98 2008

[19] National Institute of Environment Research (NIER) Domesticand foreign cement heavy metal analysis result (May 2013)NIER 2013 httpwwwniergokrericportalkornfnier-nf-02page

[20] S Kim W Hong J Kim and J T Kim ldquoThe developmentof modularized construction of enhanced precast compositestructural systems (Smart Green frame) and its embeddedenergy efficiencyrdquo Energy and Buildings vol 66 pp 16ndash21 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

2 Mathematical Problems in Engineering

seismic details of concrete-encased U-shaped steel beam-to-RC column connections The specimens exhibited requiredstrength deformation and energy dissipation capacitiesThedeformation capacity exceeded an interstory drift angle of4 which is a requirement for special moment frames [5]Hassan and Khosrow (2011) presented an analytical inves-tigation based on FE models and using ANSYS software toexamine the effectiveness of a precast beam column concreteconnection of a jointed system However this computermodel did not examine the steel section installed in a column-beam joint as discussed in [6] Another study by Ioani andTripa (2012) discussed a new all-precast concrete system usedin Romania to construct a residential building Designed forconstructability a new all-precast concrete system compris-ing columns flat slabs and structural walls were proposedTo validate the structural quality and performance of this typeof structure an extensive program of theoretical analyses andstructural tests (including shake table tests) was conducted[7] This product proposed by Ioani and Tripa differs fromthe one proposed here The structural system developedby the authors is a hybrid composite beam-column framethat demonstrates the structural behaviors of building framesystem We designed hybrid precast composite frames withsimple steel connections inserted between precast concretecolumns and beams to resist only gravity loading The firstobjective of the study by Chou and Uang (2007) was toexamine the effects of the two factors of continuity platesand the amount of transverse reinforcement on the concreteshear strength in the connection regionThe second objectivewas to develop an analytical procedure to quantify theconnection shear force developed in concreteThis continuityplate will be used for the hybrid composite frames of theauthors in later experiments [8] Ju andKim (2005) developedthe technical economical and convenient (TEC) compos-ite beam with experimental investigation using a series ofmonotonic loading tests [9] However this beam is not freefrom the requirement of being fire-proof These studies didnot expand their interests to hybrid composite structures forpractical applications which were covered in this paper Wealso present novel structural systems with dynamic analysisto examine the hybrid behavior of a building which takesadvantage of material structural and construction hybridfeatures and capabilitiesThe hybrid precast composite framesystem shows how material structural and constructionhybridity are established to uniquely provide economy andconstructability making this technology significant to theconstruction industry We also designed hybrid precast com-posite frames with simple steel connections inserted betweenprecast concrete columns and beams to resist only gravityloading The hybrid composite frame system introduced inthis paper is intended to provide the economy of precastconcrete structures with the constructability of steel framestructures Structural design efficiency facilities planningconstruction and buildingmanagement could bemaximizedusing the proposed composite frame system Implementationof integrating augmented reality with building informationmodeling [10ndash13] will help project the schedule and costof construction utilizing smart frame for site engineers andresponses to any demand for changes can be provided in time

We have previously [14 15] investigated dual-frame sys-tems composed of hybrid precast frames The dual-framesystem consists of a moment frame and a bearing wall orbraced frame Seismic forces are distributed in proportionto the lateral stiffness of each frame The moment frame hasto resist at least 25 of the design seismic forces Howeverthe dual frame systems with moment connections includingmuch more complicated construction details require sig-nificant time and costs than simple connections which areused in building frame systems for gravity loadings Buildingframe systems with simple connections are commonly usedwith steel frames to provide fast and easy construction forbuildings In this paper new structural system to providesimplified construction method was presented for buildingframe systems for gravity loadings fabricated with hybridprecast composite frames consisting of simple connectionsbetween columns and beams

The building frame system was designed for the researchthe frames resist gravity loading while the bearingwalls resistlateral forces

2 Precast Composite Structural System(Hybrid Precast Frames)

21 Details of the Frame with Generalized Steel Joints Thehybrid precast frames proposed in this study represent ahybrid composite structural system with the advantages ofboth steel frames and reinforced concrete structures Hybridprecast frames are composed of generalized steel jointsreinforcing steel and precast concrete Apartment build-ings have been outfitted with these hybrid precast framesto resolve problems such as the increase in floor heightwhen constructed with concrete Rahmen These frames canmaintain the same floor height as that of a bearing wall sys-tem providing architectural flexibility and cost-effectiveness[14 15] We developed a precast steel column with steelconnections to effectively erect and assemble the compositeframesThe joints of hybrid precast frames installed to a core-wall were simple connections to support vertical loadingsonly The joints of the gravity frames were not filled withconcrete allowing for pin-joint behavior which enhancesthe constructability and economic feasibility of the gravityframes The construction of the core-walls was followed byconstruction of hybrid precast frames including columnsbeams and slabs Hybrid precast frames were composedof hybrid precast beam units and hybrid precast columnunits with enhanced joint connections capable of resistingvertical loads enablingmore efficient erectionwith structuralstability Specifically the introduction of steel sections forjoint connection makes the construction of hybrid precastframes as timely as that of steel frames Hybrid precast frameconstruction is illustrated in Figure 1

Hybrid precast frames were manufactured either at aplant or on site [16] Hybrid precast beams take advantageof the material properties of both steel and precast concretewithout sacrificing the performance of the composite beamsThe depths of the beam and slab can also be reduced whenslabs are constructed on the edges of precast concrete

Mathematical Problems in Engineering 3

Figure 1 Building construction with hybrid precast frames

Stud bolt

Steel plate

Angle and bolts forsimple connection

(shear tap)

Precast concrete

Cast-in-place concrete

Variable

Simple connection (hinge)

Variable

Steel plate

Figure 2 Detailed information on beam-column joint members

Figure 2 shows the beam-column joint connection ofhybrid precast frames where joint connections are notfilled with concrete (ie pin-joint) Typical hybrid precastbeam-column connections designed for pinned conditions(Figure 2) enable the gravity load to be transferred throughthe joints where the web of steel beams is bolted to the steelsection of the hybrid precast column This type of structuralframe system provides simpler construction with structuralstability to support gravity loads

Figure 3 shows the generalized steel joints configured forgravity loading that are used in the hybrid precast framesAdditional shear taps are installed to provide connectionsbetween the steel sections from both columns and beamsSteel sections inserted into the hybrid precast beams and

columns allow hybrid precast frames to be erected in as manyas three stories at a time Conventional steel joints used inconventional steel construction are utilized as generalizedconnections

Figure 4 shows the construction process used to producethe hybrid precast frames Both the hybrid precast columnand the beam units of the hybrid precast frames weremanufactured as two-story or three-story column units andwere erected in one cycle The main processes of floor workwhich took about four days consisted of marking core wallreinforcement work and form installation installation ofhybrid precast column units and beam units installation ofdeck plates or a PC plate and joint form slab reinforcementwork and pouring

4 Mathematical Problems in Engineering

Column reinforced rebarsSteel plate

Beam units

Simple connection(shear tap)

Cast-in-place concrete

CFTPrecast concrete

Shear tap

Variable

VariableStud bolts

(a) Details of the beam-column joints of the hybrid precast frames

Without CFTShear tap

Stud bolt

With CFTShear tap

(b) Details of the shear tap

CFT Variable Service condition

Stud boltShear tap

(c) Construction details of the column unit

Figure 3 Details of the hybrid precast frame joints

Precast structures cannot be erected as fast as steel struc-tures because beams without slabs lack stability as shown inFigure 5 The hybrid precast frames however can be erectedas quickly as steel structures without slab construction Thehybrid precast frames suggested in this paper are hybridcomposite structures that have the merits of both steel andprecast concrete structures in particular the steel sectionsfunction as erection components This hybrid constructionmethod makes it possible to erect precast concrete frames ina time-frame similar to that of steel frames

22 Structural Stability during Construction The proposedhybrid precast frames with steel joints provide structuralstability during construction In contrast the vertical rein-forcing steel used for vertical splicing in conventional precastapplications is vulnerable to buckling against unexpectedvertical loading before the joints are filled with concretewhich could cause structural instability of the frame underconstruction as shown in Figure 6 In the proposed methodsteel sections are inserted between the upper and lowerprecast columns and are connected to steel sections locatedat both ends of the precast beams and girders or steel sectionsrunning throughout the entire lengths of the precast beamsallowing easy and stable connections

3 Use of Convergence of the HybridPrecast Frames

Because hybrid precast frames can be designed using a widerange of spans and joint designs bearing wall-type apartmentbuildings may be replaced with buildings with hybrid precastframes Structural systems should be optimized with steelconnections which are required to be as small as 20sim25 kgfm2 (about one-tenth that of reinforcing steel) enablingconstructability and assembly time similar to that of steelframes

Figure 7 shows deflections of a composite frame buildingsubjected to wind loads The lateral displacements are withinacceptable limits Displacement along the 119909-axis and 119910-axis was 20 cm (H3910) and 29 cm (H1955) respectivelyAcceptable story drift in response to seismic loading wasalso observed in both directions as shown in Figure 8 Theseresults demonstrate that the optimized structural compositeframes have structural stability

4 Dynamic Analysis of a Building with HybridPrecast Frames

Figure 9 shows a building with 13 stories and two base-ments (total floor area of 6741m2) that was designed with

Mathematical Problems in Engineering 5

Shear tap

Stud bolt

Steel plate

CFT

Cast-in-place concrete

Precast concrete

Shear tap

Figure 4 Hybrid precast frame construction process

+

Critical pathUpwards construction

Figure 5 Reduction of the hybrid precast frame construction period

Rebarconnection

(a)

Rebarconnection

(b)

Figure 6 Conventional precast concrete connections

6 Mathematical Problems in Engineering

X-direction00111 m

(H39099)

Midas genpostprocessordisplacement

resultant

Scale factor =

110700e minus 002100636e minus 002905726e minus 003805090e minus 003704454e minus 003603817e minus 003503181e minus 003402545e minus 003301909e minus 003201272e minus 003100636e minus 003000000e + 000

26266E + 002

(a)

Y-direction00222 m

(H19549)

Midas genpostprocessordisplacement

resultant

Scale factor =

222476e minus 002202251e minus 002182025e minus 002161800e minus 002141575e minus 002121350e minus 002101125e minus 002809002e minus 003606752e minus 003404501e minus 003202251e minus 003000000e + 000

13069E + 002

(b)

Figure 7 Wind displacement

0

0002

0004

0006

0008

001

0012

0014

0016

17F

16F

15F

14F

13F

12F

11F

10F 9F 8F 7F 6F 5F 4F 3F 2F 1F

Story drift ratioAllowable story drift ratio

Story drift ratio (x-axis)

(a)

17F

16F

15F

14F

13F

12F

11F

10F 9F 8F 7F 6F 5F 4F 3F 2F 1F

Story drift ratioAllowable story drift ratio

0

0002

0004

0006

0008

001

0012

0014

0016Story drift ratio (y-axis)

(b)

Figure 8 Story drift

the proposed composite frames and selected for dynamicanalysis The floor plan and elevation with framing usingcomposite columns and beams are also shown The buildingwas designed such that the shear walls were resistant to lateralseismic loadings while the frames resisted only vertical loadsDynamic analysis was performed to investigate the influenceof the design and size of the composite frames on the dynamiccharacteristics of the building

Figure 10 shows a computer model of the building withcomposite frames andwalls in which the steel sections at bothends of the beams are connected to steel inserted betweentwo precast columns Figure 10(a) shows gravity compositeframes attached to shear walls that are responsible for lateralearthquake loading Figure 10(b) shows close connectiondetails of the frames and walls that constitute the building

frame Figure 10(c) shows steel frames and connectionsbetween beams and columns The material structural andconstruction hybrid applications were integrated to combinethe constructability of steel structures with the economy ofconcrete structures

Tables 1 and 2 show modal participation masses andeigenvalue results respectively The fundamental transla-tional mode was found in the third return period the firstand second modes were considered to be mixed translationalmodes with torsion A fundamental translational mode of 15seconds along with a weak 119910-axis was deemed reasonableThe fundamental period and mode shapes for the compositeframe were more similar to those of steel structures thanthose of concrete structures indicating that the structuralbehavior of a building with composite frames and steel

Mathematical Problems in Engineering 7

7400

17750

3500

3500

3500

3500

3500

3500

3000

2400

X

Y

2900

2900

X6

X6

X7

X8

X9

X10

2900

4100

39200

14001400

14600

6300 63002000

PS

PS

PSPS

PSPS

PS

PS PS

PSPS

PS

PS

PS

PSPS

PSPS

PSPS

PS

PSPS

PS

PS

PSPS

PS

PS

PS

PS

PS

PSPS

PS

PS

PS

PS

PS

PS

PS

329

0

4928

3500

3500

3500

3500

3500

3500

6300

1300

1300

5000

5000

6300

14600

X1

X2

X3

2000

25928

350

0

350

03

500

350

03

500

350

03

500

350

03

500

350

03

500

700

07

000

700

07

000

700

0

417

90

PS

PS

PS

PS

PS PS

PSPS

Hal

l

PS

PS

49004900

Y3998400

Y4998400

Y5998400

Y6998400

(a)

Figure 9 Continued

8 Mathematical Problems in Engineering

1447

1500

7200

3600

3600

3800

2900

2900

2900

2900

2900

2900

2900

2900

2900

2900

2900

1

29001400

1500 1

0003600

23003600

3800

2900

2600

1300

3200

1600700

600

2900

2900

2900

2900

2900

2900

2900

2900

2900

2900

29001400

40000

2880

2880

920

5100700061508300 6300

6300 630020002150 4150

5382

1447

2250

2250

2250

2250

2250

2250

2250

2250

2250

2250

2250

2250

3200 2400

2300

1600

GL-1800

GL-6000

510070006150146005382

(b)

Figure 9 Floor plan and elevation

Mathematical Problems in Engineering 9

Table 1 Modal participation masses

Mode number TRAN-119883 TRAN-119884 ROTN-119885Mass () Sum () Mass () Sum () Mass () Sum ()

1 405909 405909 02185 02185 127252 1272522 42570 448478 16208 164265 203361 3306123 40667 489145 328629 492893 82552 4131644 96703 585848 01847 49474 40557 4537215 32088 617935 03965 498705 87600 5413216 03685 621620 158676 657381 05207 546528

(a) (b) (c)

Figure 10 Computer model of the building

Table 2 Eigenvalue analysis (fundamental period)

Mode number Frequency Period Tolerance(radsec) (cyclesec) (sec)

1 34768 05533 34768 00000119890 + 000

2 41078 06538 41078 00000119890 + 000

3 53487 08513 53487 00000119890 + 000

4 138311 22013 138311 45251119890 minus 161

5 178259 28371 178259 28518119890 minus 150

6 236726 37676 236726 15909119890 minus 137

joints against vertical and lateral loadings resembles that ofsteel structures even though the building has an externalappearance of a concrete structure

Figure 11 shows the first translational mode (a) and thoseof two mixed modes ((b) (c)) Figures 11(d) 11(e) and 11(f)show these modes from the top view respectively

5 Reduction of Structural Quantity andEmissions of Environmentally HazardousSubstances and Materials

This study evaluated chromium VI and carbon dioxide emis-sions of the building constructed with the proposed framesand conventional walls Reductions in energy consumptiondue to reduction in material quantity were estimated basedon comparison of an apartment building constructed withhybrid precast frames and that of a conventional bearing-wallbuilding

Original units of major building components (Table 3)which were announced in 2008 by the United Kingdom

Table 3 Emissions and energy usage of major building components[17]

Buildingcomponent

CO2 emissionsper original unit

Energy consumptionper original unit

Concrete 25MPa 3196 kg-CO2m3 23265MJm3

Concrete 35MPa 37835 kg-CO2m3 26555MJm3

Reinforcement 27319 kg-CO2kN 371050MJkNSteel section 28338 kg-CO2kN 375127MJkN

Inventory of Carbon and Energy (ICE) were used to evaluatecarbon dioxide emissions and the energy efficiency of theproposed construction The embodied energy 119864 and carbonemissions per kN for the calculated material quantity areobtained from the University of Bathrsquos ICE database [17 18]The ICE has been structured into 34 main material groupsThe database also provides the embodied energy and carboncoefficients for construction materials Table 3 presents theconverted embodied energy and carbon coefficients for fourbuilding components concrete (25MPa) concrete (35MPa)reinforcement and steel section

Domestic and foreign cement heavymetal analysis results(May 2013) published by the Korea National Institute ofEnvironment Research (NIER) were utilized to evaluatechromium VI emissions (Table 4)

In order to explain how the data that evaluates the gravitysystem presented in this paper in terms of material quantityanalytical approach for the hybrid precast composite beamdesign based on the strain compatibility method was intro-duced Figures 12 and 13 illustrate the side view and cross-section of a hybrid composite beam In order to determine the

10 Mathematical Problems in Engineering

Table 4 Heavy metal content standards in cement [19]

Cr6+ As Cd Cu Hg PbAve (May 2013) 1063mgkg 1287mgkg 102mgkg 8903mgkg 061mgkg 3284mgkg

(a) Fundamental translational mode (b) Mixed mode 1 (c) Mixed mode 2

(d) Fundamental translational mode (e) Mixed mode 1 (f) Mixed mode 2

Figure 11 Mode shapes

Figure 12 Side view of a hybrid composite beam

d

d998400

d998400998400

d998400998400998400

Figure 13 Cross-section of a hybrid composite beam

exact material quantity the hybrid composite beam designwas carried out based on the strain compatibility methodEquations (1) and (2) are the mean stress factor 120572 and thecentroid factor 120574 for any strain 120576

119888119898at the extreme com-

pression fiber calculated based on stress-strain relationshipEquations (3) and (5) represent the equilibrium equations ofcompressive and tensile forces at yield limit and maximumload limit state respectively The nominal moment capacitiesof a hybrid composite beam at yield limit andmaximum loadlimit state are calculated by (4) and (6) respectively Figures14 and 15 represent strain and stress diagram at yield limitand maximum load limit state respectively In both figuresblack color indicates steels and reinforcement rebars wereplasticized (yielded) while white color represents structuralmembers remained elastic The structural quantity requiredby apartment buildings with hybrid composite frames wasobtained from (6) and compared with that of conventionalbuildings with bearing walls as shown in Table 5 These

Mathematical Problems in Engineering 11

Table 5 Evaluation of structural systems

Buildingcomponent System Gross area Building material CO2 emission Energy consumption Cr6+ emission

Concrete(HPF = 35MPaBW = 25MPa)

HPF 9236m2 038m3m2 691(minus309) 1362 kg-CO2m

2 775(minus225) 10060MJm2 786

(minus214) 11062mgm2 689(minus311)

BW 6513m2 055m3m2 1000 1758 kg-CO2m2 1000 12796MJm2 1000 16061mgm2 100

Reinforcements HPF 9236m2 053 kNm2 726(minus274) 1445 kg-CO2m

2 724(minus276) 19314MJm2 713

(minus287) mdash mdash

BW 6513m2 073 kNm2 1000 1996 kg-CO2m2 1000 27107MJm2 1000 mdash mdash

Steel section HPF 9236m2 007 kNm2 1000 206 kg-CO2m2 1000 2721MJm2 1000 mdash mdash

BW 6513m2 mdashkNm2 mdash mdashkg-CO2m2 mdash mdashMJm2 mdash mdash mdash

lowastHPF hybrid precast frames BW bearing wall

400 MPa

301 MPa

1354 mm

120576st = 0001506

120576t = 120576y = 0002

120576c = 000178 f998400c

120576998400t = 000096 120576tEs = 192MPa

Figure 14 Strain and stress diagram at yield limit state

120576tEs = 286MPa

400 MPa

325 MPa

11946 mm

120576st = 000328

120576t = 120576y = 00042

120576c = 0003f998400c

120576998400t = 000143

Figure 15 Strain and stress diagram at maximum load limit state

equations would help engineer estimate precise constructionmaterials and understand how buildings with hybrid com-posite frames behave Consider

120572 = (int

0002

0

119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

119891

1015840

1198881 minus 100 (120576

119888minus 120576

119888119900) 119889120576

119888)

times (119891

1015840

119888120576

119888119898)

minus1

(1)

120574 = 1 minus ((int

0002

0

120576

119888119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

120576

119888119891

1015840

1198881 minus 100 (120576

119888minus 120576

119888119900) 119889120576

119888)

times (120576

119888119898[int

0002

0

119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

119891

1015840

1198881minus100 (120576

119888minus120576

119888119900) 119889120576

119888])

minus1

)

(2)

120572119891

1015840

119888119887119888 + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840) +

1

2

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

= 119860

119904119865

119910+ 119860

119891119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

1

2

119860

119908119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891)

(3)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908= 119905

119908(119889 minus 119888 minus 119889

1015840minus 119905

119891)

119872

119899= 120572119891

1015840

119888119887119888 (119888 minus 120574119888) + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840)

2

+

1

3

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

2

+ 119860

119904119865

119910(119889 minus 119888)

12 Mathematical Problems in Engineering

DayProcess

One floor

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7

Marking

Rebar work (wall)

Wall form installation

Slab form installation

Rebar work (slab) Electrical and mechanical

facilities (slab) Cleaning and pouring

Figure 16 Processes for constructing one floor of a conventional wall-type apartment building [20]

+ 119860

119891119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891) (119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

119905

119891

2

(119889 minus 119888 minus 119889

1015840minus

119905

119891

3

)

+

1

3

119860

119908119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891)

2

(4)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908= 119905

119908(119889 minus 119888 minus 119889

1015840minus 119905

119891)

120572119891

1015840

119888119887119888 + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840) +

1

2

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

= 119860

119904119865

119910+ 119860

119891119865

119910+ 119860

119908119901119865

119910+

1

2

119860

119908119899119910119864

119904120576

119904119910

(5)

where1198601015840119908= 119905

119908(119888minus119889

101584010158401015840)119860119908119901

= 119905

119908(119889minus119888+119889

1015840+119905

119891)+(120576

119904119910120576

119888)119888

119860

119908119899119910= 119905

119908(120576

119904119910120576

119888)119888

119872

119899= 120572119891

1015840

119888119887119888 (119888 minus 120574119888) + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840)

2

+

1

3

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

2

+ 119860

119904119865

119910(119889 minus 119888)

+ 119860

119891119865

119910(119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

1

2

119860

119908119901119865

119910(119889 minus 119888 minus 119889

1015840minus 119905

119891) +

120576

119904119910

120576

119888

119888

+

1

3

119860

119908119899119910119864

119904

(120576

119904119910)

2

120576

119888

119888

(6)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908119901

= 119905

119908119889 minus (119888 + 119889

1015840+ (120576

119904119910120576

119888)119888)

119860

119908119899119910= 119905

119908(120576

119904119910120576

119888)119888

A completed bearing wall apartment building wasselected for this comparison Apartment buildings withhybrid precast frames and bearingwall frameswere evaluatedin terms of building material CO

2emission energy con-

sumption and Cr6+ emission shown in Table 5 Construction

materials per square meters were calculated based on (5) and(6)whichwere then used to calculate the quantities of Table 5

The building materials of concrete and reinforcementsof apartment buildings with hybrid precast frames werereduced by 31 and 27 respectively compared with thatof bearing wall frame buildings The CO

2emission energy

consumption andCr6+ emission of apartment buildings withhybrid precast frames were also decreased compared withbearing wall frame buildings as shown in Table 5 exhibitingthe efficiency of using gravity hybrid precast frames forapartment buildings

6 Reduction in Construction Schedule

Figures 16 and 17 compare the construction time frames basedon the use of conventional bearing walls versus the proposedhybrid frames

The construction time is the sum of each critical path asshown in

119899

sum

119894=1

(CA119894) = CA

1+ CA2+ CA3+ CA4sdot sdot sdot (7)

The critical paths that affect construction time for abearing wall apartment are CA

1(marking 1 day) CA

2(rebar

work wall 1 day) CA3(wall form installation 2 days)

CA4(slab form installation 1 day) CA

5(rebar work slab 1

day) and CA6(cleaning and pouring 1 day) Installation of

electrical and mechanical facilities at the slab is performedwith rebar work of the slab and takes less time than that ofrebar work Electrical and mechanical facilities at the slab aretherefore excluded from the critical path The constructiontime per floor is seven days based on (7) The criticalpaths affecting construction time for an apartment buildingusing hybrid frames are CA

1(rebar work core wall 05

days) CA2(column-beam unit installation (1 day) beam

unit installation (15 days)) CA3(rebar work slab 05 days)

and CA4(cleaning and pouring 05 days) Column-beam

unit installation and beam unit installation are carried outalternately Beams are only installed at every second andthird floor since columns are erected as a three-story unit

Mathematical Problems in Engineering 13

DayProcess

First floor Second floor Third floor

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 Day 10

Rebar work (core wall)

Core wall form installationColumn-beam unit

installation Beam unit installation

Deck plate installation

Joint form installation

Rebar work (slab) Electrical and mechanical

facilities (slab) Cleaning and pouring

Figure 17 Processes for constructing three floors of an apartment building using hybrid frames [20]

Table 6 Comparative analysis of the construction period [20]

Structuraltype

Construction periodComparisonTypical

floor30-story apartment

building

Bearing wall 7 days1 floor 210 Days 1000Hybrid precastframe

10 days3floors 100 Days 476

As a result of the critical paths analysis the constructiontime per floor is four days for the first floor and threedays for the next two floors requiring ten days for theconstruction of three floors utilizing columns of a three-story unit The time for frame erection was reduced by 52when using hybrid frames highlighting their economic andconstruction benefits Erection of structural frames for onefloor using conventional bearing walls involves rebar workand concrete pouring and requires about seven days asshown in Figure 16 In contrast only three days were requiredto install wall and slab forms indicating that the overallconstruction was influenced by form work which is highlydependent on work skill However erection of three floorswith hybrid precast frames required only ten days whenthree-story hybrid precast columns were erected at one liftThe significant reduction in form work contributed to thedecrease in overall construction time obtained when usingthe hybrid precast frames as shown in Figure 17 As shown inTable 6 frame erection of a 30-story building required sevendays per floor or 210 days for the entire building when usingconventional bearing walls However only ten days per threefloors (or 100 days for the entire building) were required forframe erection of the building with hybrid precast frameswhich corresponds to a 524 reduction in frame erectiontime

7 Conclusions

This study described and characterized an optimized hybridprecast composite structural system for gravity systemMajorcontributions are summarized below

(1) Gravity hybrid precast frames were presented Thesehybrid frames consist of precast concrete and steelwhich can be erected at a speed similar to that of steelframes Steel sections inserted in precast columns andbeams are used as erection steel components

(2) Mathematical model of gravity hybrid precast beamwas presented at yield limit state and maximum loadlimit state Neutral axis of postyield state found fromequilibrium equations was used to calculate nominalmoment capacities of a hybrid composite beam atboth limit state

(3) The new building frame systems for gravity load-ings fabricated with hybrid precast composite framesconsisting of simple connections between columnsand beams were proposed in this paper The dualframe systems of moment connections with muchmore complicated construction details required sig-nificant time and costs than that of building framesystems of gravity loadings However the gravityhybrid precast composite structures will provide sim-plified construction method while enhancing econ-omyduring constructionThe reductions of construc-tion resources including concrete and reinforcements(31 reduction of concrete and 27 reduction of rein-forcements) were achieved when apartments were tobe built with hybrid precast frames

(4) The gravity hybrid precast frames use less construc-tion materials than conventional frames and there-fore reduce carbon dioxide and hazardous substanceemissions compared to conventional frames It was

14 Mathematical Problems in Engineering

observed the efficiency of using gravity hybrid precastframes for apartment building which decreased theCO2emission (23 reduction of concrete and 28

reduction of reinforcements) energy consumption(21 reduction of concrete and 29 reduction ofreinforcements) and Cr6+ emission compared withbearing wall frame buildings The use of gravityhybrid precast frames was demonstrated to providebetter solutions for environments and economy thanthat of conventional buildings

(5) Dynamic analysis of a 15-story building designedwith the proposed composite gravity frames was per-formed to characterize frequencies and mode shapesof the building for seismic design purposes

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by Grant from the Kyung HeeUniversity in 2013 (KHU-20130363)

References

[1] J F Hajjar ldquoComposite steel and concrete structural systems forseismic engineeringrdquo Journal of Constructional Steel Researchvol 58 no 5ndash8 pp 703ndash723 2002

[2] G Fabbrocino G Manfredi and E Cosenza ldquoDuctility ofcomposite beams under negative bending an equivalence indexfor reinforcing steel classificationrdquo Journal of ConstructionalSteel Research vol 58 no 2 pp 185ndash202 2001

[3] B Yang and K Tan ldquoBehaviour of composite beam-columnjoints under a middle-column-removal scenario experimentaltestsrdquo Journal of Structural Engineering vol 140 no 2 ArticleID 04013045 2014

[4] L Tesser and R Scotta ldquoFlexural and shear capacity of compos-ite steel truss and concrete beams with inferior precast concretebaserdquo Engineering Structures vol 49 pp 135ndash145 2013

[5] H J Hwang H G Park C H Lee et al ldquoSeismic resistanceof concrete-filled U-shaped steel beam-to-RC column connec-tionsrdquo Journal of Korean Society of Steel Construction vol 23 pp83ndash97 2011

[6] J Hassan and B Khosrow ldquoNonlinear seismic behavior evalua-tion of ductile beam-column connections in precast concreterdquoInternational Journal of Civil and Structural Engineering vol 1pp 445ndash453 2011

[7] A M Ioani and E Tripa ldquoStructural behavior of an innovativeall-precast concrete dual system for residential buildingsrdquo PCIJournal vol 57 no 1 pp 110ndash123 2012

[8] C Chou andCUang ldquoEffects of continuity plate and transversereinforcement on cyclic behavior of SRCmoment connectionsrdquoJournal of Structural Engineering vol 133 no 1 pp 96ndash104 2007

[9] Y K Ju and S D Kim ldquoStructural behavior of alternative lowfloor height system using structural ldquoteerdquo half precast concreteand horizontal studrdquoCanadian Journal of Civil Engineering vol32 no 2 pp 329ndash338 2005

[10] X Wang M Truijens L Hou Y Wang and Y Zhou ldquoInte-grating augmented reality with building informationmodelingonsite construction process controlling for liquefied natural gasindustryrdquoAutomation in Construction vol 40 pp 96ndash105 2014

[11] L Hou Y Wang X Wang et al ldquoCombining photogrammetryand augmented reality towards an integrated facility manage-ment system for the oil industryrdquo Proceedings of the IEEE vol102 no 2 pp 204ndash220 2014

[12] L Hou XWang L Bernold and P E D Love ldquoUsing animatedaugmented reality to cognitively guide assemblyrdquo Journal ofComputing in Civil Engineering vol 27 no 5 pp 439ndash451 2013

[13] YWang XWang JWang P Yung andG Jun ldquoEngagement offacilities management in design stage through BIM frameworkand a case studyrdquo Advances in Civil Engineering vol 2013Article ID 189105 8 pages 2013

[14] W K Hong J M Kim S C Park et al ldquoA new apartmentconstruction technology with effective CO

2emission reduction

capabilitiesrdquo Energy vol 35 no 6 pp 2639ndash2646 2010[15] W Hong S Park J Kim et al ldquoDevelopment of structural

composite hybrid systems and their application with regard tothe reduction of CO

2emissionsrdquo Indoor and Built Environment

vol 19 no 1 pp 151ndash162 2010[16] W Hong S Jeong S Park and J T Kim ldquoExperimental

investigation of an energy-efficient hybrid composite beamduring the construction phaserdquo Energy and Buildings vol 46pp 37ndash47 2012

[17] G P Hammond and C I Jones Inventory of Carbon amp Energy(ICE) Department of Mechanical Engineering University ofBath Bath UK 2008

[18] G P Hammond and C I Jones ldquoEmbodied energy and carbonin construction materialsrdquo Proceedings of Institution of CivilEngineers Energy vol 161 no 2 pp 87ndash98 2008

[19] National Institute of Environment Research (NIER) Domesticand foreign cement heavy metal analysis result (May 2013)NIER 2013 httpwwwniergokrericportalkornfnier-nf-02page

[20] S Kim W Hong J Kim and J T Kim ldquoThe developmentof modularized construction of enhanced precast compositestructural systems (Smart Green frame) and its embeddedenergy efficiencyrdquo Energy and Buildings vol 66 pp 16ndash21 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 3

Figure 1 Building construction with hybrid precast frames

Stud bolt

Steel plate

Angle and bolts forsimple connection

(shear tap)

Precast concrete

Cast-in-place concrete

Variable

Simple connection (hinge)

Variable

Steel plate

Figure 2 Detailed information on beam-column joint members

Figure 2 shows the beam-column joint connection ofhybrid precast frames where joint connections are notfilled with concrete (ie pin-joint) Typical hybrid precastbeam-column connections designed for pinned conditions(Figure 2) enable the gravity load to be transferred throughthe joints where the web of steel beams is bolted to the steelsection of the hybrid precast column This type of structuralframe system provides simpler construction with structuralstability to support gravity loads

Figure 3 shows the generalized steel joints configured forgravity loading that are used in the hybrid precast framesAdditional shear taps are installed to provide connectionsbetween the steel sections from both columns and beamsSteel sections inserted into the hybrid precast beams and

columns allow hybrid precast frames to be erected in as manyas three stories at a time Conventional steel joints used inconventional steel construction are utilized as generalizedconnections

Figure 4 shows the construction process used to producethe hybrid precast frames Both the hybrid precast columnand the beam units of the hybrid precast frames weremanufactured as two-story or three-story column units andwere erected in one cycle The main processes of floor workwhich took about four days consisted of marking core wallreinforcement work and form installation installation ofhybrid precast column units and beam units installation ofdeck plates or a PC plate and joint form slab reinforcementwork and pouring

4 Mathematical Problems in Engineering

Column reinforced rebarsSteel plate

Beam units

Simple connection(shear tap)

Cast-in-place concrete

CFTPrecast concrete

Shear tap

Variable

VariableStud bolts

(a) Details of the beam-column joints of the hybrid precast frames

Without CFTShear tap

Stud bolt

With CFTShear tap

(b) Details of the shear tap

CFT Variable Service condition

Stud boltShear tap

(c) Construction details of the column unit

Figure 3 Details of the hybrid precast frame joints

Precast structures cannot be erected as fast as steel struc-tures because beams without slabs lack stability as shown inFigure 5 The hybrid precast frames however can be erectedas quickly as steel structures without slab construction Thehybrid precast frames suggested in this paper are hybridcomposite structures that have the merits of both steel andprecast concrete structures in particular the steel sectionsfunction as erection components This hybrid constructionmethod makes it possible to erect precast concrete frames ina time-frame similar to that of steel frames

22 Structural Stability during Construction The proposedhybrid precast frames with steel joints provide structuralstability during construction In contrast the vertical rein-forcing steel used for vertical splicing in conventional precastapplications is vulnerable to buckling against unexpectedvertical loading before the joints are filled with concretewhich could cause structural instability of the frame underconstruction as shown in Figure 6 In the proposed methodsteel sections are inserted between the upper and lowerprecast columns and are connected to steel sections locatedat both ends of the precast beams and girders or steel sectionsrunning throughout the entire lengths of the precast beamsallowing easy and stable connections

3 Use of Convergence of the HybridPrecast Frames

Because hybrid precast frames can be designed using a widerange of spans and joint designs bearing wall-type apartmentbuildings may be replaced with buildings with hybrid precastframes Structural systems should be optimized with steelconnections which are required to be as small as 20sim25 kgfm2 (about one-tenth that of reinforcing steel) enablingconstructability and assembly time similar to that of steelframes

Figure 7 shows deflections of a composite frame buildingsubjected to wind loads The lateral displacements are withinacceptable limits Displacement along the 119909-axis and 119910-axis was 20 cm (H3910) and 29 cm (H1955) respectivelyAcceptable story drift in response to seismic loading wasalso observed in both directions as shown in Figure 8 Theseresults demonstrate that the optimized structural compositeframes have structural stability

4 Dynamic Analysis of a Building with HybridPrecast Frames

Figure 9 shows a building with 13 stories and two base-ments (total floor area of 6741m2) that was designed with

Mathematical Problems in Engineering 5

Shear tap

Stud bolt

Steel plate

CFT

Cast-in-place concrete

Precast concrete

Shear tap

Figure 4 Hybrid precast frame construction process

+

Critical pathUpwards construction

Figure 5 Reduction of the hybrid precast frame construction period

Rebarconnection

(a)

Rebarconnection

(b)

Figure 6 Conventional precast concrete connections

6 Mathematical Problems in Engineering

X-direction00111 m

(H39099)

Midas genpostprocessordisplacement

resultant

Scale factor =

110700e minus 002100636e minus 002905726e minus 003805090e minus 003704454e minus 003603817e minus 003503181e minus 003402545e minus 003301909e minus 003201272e minus 003100636e minus 003000000e + 000

26266E + 002

(a)

Y-direction00222 m

(H19549)

Midas genpostprocessordisplacement

resultant

Scale factor =

222476e minus 002202251e minus 002182025e minus 002161800e minus 002141575e minus 002121350e minus 002101125e minus 002809002e minus 003606752e minus 003404501e minus 003202251e minus 003000000e + 000

13069E + 002

(b)

Figure 7 Wind displacement

0

0002

0004

0006

0008

001

0012

0014

0016

17F

16F

15F

14F

13F

12F

11F

10F 9F 8F 7F 6F 5F 4F 3F 2F 1F

Story drift ratioAllowable story drift ratio

Story drift ratio (x-axis)

(a)

17F

16F

15F

14F

13F

12F

11F

10F 9F 8F 7F 6F 5F 4F 3F 2F 1F

Story drift ratioAllowable story drift ratio

0

0002

0004

0006

0008

001

0012

0014

0016Story drift ratio (y-axis)

(b)

Figure 8 Story drift

the proposed composite frames and selected for dynamicanalysis The floor plan and elevation with framing usingcomposite columns and beams are also shown The buildingwas designed such that the shear walls were resistant to lateralseismic loadings while the frames resisted only vertical loadsDynamic analysis was performed to investigate the influenceof the design and size of the composite frames on the dynamiccharacteristics of the building

Figure 10 shows a computer model of the building withcomposite frames andwalls in which the steel sections at bothends of the beams are connected to steel inserted betweentwo precast columns Figure 10(a) shows gravity compositeframes attached to shear walls that are responsible for lateralearthquake loading Figure 10(b) shows close connectiondetails of the frames and walls that constitute the building

frame Figure 10(c) shows steel frames and connectionsbetween beams and columns The material structural andconstruction hybrid applications were integrated to combinethe constructability of steel structures with the economy ofconcrete structures

Tables 1 and 2 show modal participation masses andeigenvalue results respectively The fundamental transla-tional mode was found in the third return period the firstand second modes were considered to be mixed translationalmodes with torsion A fundamental translational mode of 15seconds along with a weak 119910-axis was deemed reasonableThe fundamental period and mode shapes for the compositeframe were more similar to those of steel structures thanthose of concrete structures indicating that the structuralbehavior of a building with composite frames and steel

Mathematical Problems in Engineering 7

7400

17750

3500

3500

3500

3500

3500

3500

3000

2400

X

Y

2900

2900

X6

X6

X7

X8

X9

X10

2900

4100

39200

14001400

14600

6300 63002000

PS

PS

PSPS

PSPS

PS

PS PS

PSPS

PS

PS

PS

PSPS

PSPS

PSPS

PS

PSPS

PS

PS

PSPS

PS

PS

PS

PS

PS

PSPS

PS

PS

PS

PS

PS

PS

PS

329

0

4928

3500

3500

3500

3500

3500

3500

6300

1300

1300

5000

5000

6300

14600

X1

X2

X3

2000

25928

350

0

350

03

500

350

03

500

350

03

500

350

03

500

350

03

500

700

07

000

700

07

000

700

0

417

90

PS

PS

PS

PS

PS PS

PSPS

Hal

l

PS

PS

49004900

Y3998400

Y4998400

Y5998400

Y6998400

(a)

Figure 9 Continued

8 Mathematical Problems in Engineering

1447

1500

7200

3600

3600

3800

2900

2900

2900

2900

2900

2900

2900

2900

2900

2900

2900

1

29001400

1500 1

0003600

23003600

3800

2900

2600

1300

3200

1600700

600

2900

2900

2900

2900

2900

2900

2900

2900

2900

2900

29001400

40000

2880

2880

920

5100700061508300 6300

6300 630020002150 4150

5382

1447

2250

2250

2250

2250

2250

2250

2250

2250

2250

2250

2250

2250

3200 2400

2300

1600

GL-1800

GL-6000

510070006150146005382

(b)

Figure 9 Floor plan and elevation

Mathematical Problems in Engineering 9

Table 1 Modal participation masses

Mode number TRAN-119883 TRAN-119884 ROTN-119885Mass () Sum () Mass () Sum () Mass () Sum ()

1 405909 405909 02185 02185 127252 1272522 42570 448478 16208 164265 203361 3306123 40667 489145 328629 492893 82552 4131644 96703 585848 01847 49474 40557 4537215 32088 617935 03965 498705 87600 5413216 03685 621620 158676 657381 05207 546528

(a) (b) (c)

Figure 10 Computer model of the building

Table 2 Eigenvalue analysis (fundamental period)

Mode number Frequency Period Tolerance(radsec) (cyclesec) (sec)

1 34768 05533 34768 00000119890 + 000

2 41078 06538 41078 00000119890 + 000

3 53487 08513 53487 00000119890 + 000

4 138311 22013 138311 45251119890 minus 161

5 178259 28371 178259 28518119890 minus 150

6 236726 37676 236726 15909119890 minus 137

joints against vertical and lateral loadings resembles that ofsteel structures even though the building has an externalappearance of a concrete structure

Figure 11 shows the first translational mode (a) and thoseof two mixed modes ((b) (c)) Figures 11(d) 11(e) and 11(f)show these modes from the top view respectively

5 Reduction of Structural Quantity andEmissions of Environmentally HazardousSubstances and Materials

This study evaluated chromium VI and carbon dioxide emis-sions of the building constructed with the proposed framesand conventional walls Reductions in energy consumptiondue to reduction in material quantity were estimated basedon comparison of an apartment building constructed withhybrid precast frames and that of a conventional bearing-wallbuilding

Original units of major building components (Table 3)which were announced in 2008 by the United Kingdom

Table 3 Emissions and energy usage of major building components[17]

Buildingcomponent

CO2 emissionsper original unit

Energy consumptionper original unit

Concrete 25MPa 3196 kg-CO2m3 23265MJm3

Concrete 35MPa 37835 kg-CO2m3 26555MJm3

Reinforcement 27319 kg-CO2kN 371050MJkNSteel section 28338 kg-CO2kN 375127MJkN

Inventory of Carbon and Energy (ICE) were used to evaluatecarbon dioxide emissions and the energy efficiency of theproposed construction The embodied energy 119864 and carbonemissions per kN for the calculated material quantity areobtained from the University of Bathrsquos ICE database [17 18]The ICE has been structured into 34 main material groupsThe database also provides the embodied energy and carboncoefficients for construction materials Table 3 presents theconverted embodied energy and carbon coefficients for fourbuilding components concrete (25MPa) concrete (35MPa)reinforcement and steel section

Domestic and foreign cement heavymetal analysis results(May 2013) published by the Korea National Institute ofEnvironment Research (NIER) were utilized to evaluatechromium VI emissions (Table 4)

In order to explain how the data that evaluates the gravitysystem presented in this paper in terms of material quantityanalytical approach for the hybrid precast composite beamdesign based on the strain compatibility method was intro-duced Figures 12 and 13 illustrate the side view and cross-section of a hybrid composite beam In order to determine the

10 Mathematical Problems in Engineering

Table 4 Heavy metal content standards in cement [19]

Cr6+ As Cd Cu Hg PbAve (May 2013) 1063mgkg 1287mgkg 102mgkg 8903mgkg 061mgkg 3284mgkg

(a) Fundamental translational mode (b) Mixed mode 1 (c) Mixed mode 2

(d) Fundamental translational mode (e) Mixed mode 1 (f) Mixed mode 2

Figure 11 Mode shapes

Figure 12 Side view of a hybrid composite beam

d

d998400

d998400998400

d998400998400998400

Figure 13 Cross-section of a hybrid composite beam

exact material quantity the hybrid composite beam designwas carried out based on the strain compatibility methodEquations (1) and (2) are the mean stress factor 120572 and thecentroid factor 120574 for any strain 120576

119888119898at the extreme com-

pression fiber calculated based on stress-strain relationshipEquations (3) and (5) represent the equilibrium equations ofcompressive and tensile forces at yield limit and maximumload limit state respectively The nominal moment capacitiesof a hybrid composite beam at yield limit andmaximum loadlimit state are calculated by (4) and (6) respectively Figures14 and 15 represent strain and stress diagram at yield limitand maximum load limit state respectively In both figuresblack color indicates steels and reinforcement rebars wereplasticized (yielded) while white color represents structuralmembers remained elastic The structural quantity requiredby apartment buildings with hybrid composite frames wasobtained from (6) and compared with that of conventionalbuildings with bearing walls as shown in Table 5 These

Mathematical Problems in Engineering 11

Table 5 Evaluation of structural systems

Buildingcomponent System Gross area Building material CO2 emission Energy consumption Cr6+ emission

Concrete(HPF = 35MPaBW = 25MPa)

HPF 9236m2 038m3m2 691(minus309) 1362 kg-CO2m

2 775(minus225) 10060MJm2 786

(minus214) 11062mgm2 689(minus311)

BW 6513m2 055m3m2 1000 1758 kg-CO2m2 1000 12796MJm2 1000 16061mgm2 100

Reinforcements HPF 9236m2 053 kNm2 726(minus274) 1445 kg-CO2m

2 724(minus276) 19314MJm2 713

(minus287) mdash mdash

BW 6513m2 073 kNm2 1000 1996 kg-CO2m2 1000 27107MJm2 1000 mdash mdash

Steel section HPF 9236m2 007 kNm2 1000 206 kg-CO2m2 1000 2721MJm2 1000 mdash mdash

BW 6513m2 mdashkNm2 mdash mdashkg-CO2m2 mdash mdashMJm2 mdash mdash mdash

lowastHPF hybrid precast frames BW bearing wall

400 MPa

301 MPa

1354 mm

120576st = 0001506

120576t = 120576y = 0002

120576c = 000178 f998400c

120576998400t = 000096 120576tEs = 192MPa

Figure 14 Strain and stress diagram at yield limit state

120576tEs = 286MPa

400 MPa

325 MPa

11946 mm

120576st = 000328

120576t = 120576y = 00042

120576c = 0003f998400c

120576998400t = 000143

Figure 15 Strain and stress diagram at maximum load limit state

equations would help engineer estimate precise constructionmaterials and understand how buildings with hybrid com-posite frames behave Consider

120572 = (int

0002

0

119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

119891

1015840

1198881 minus 100 (120576

119888minus 120576

119888119900) 119889120576

119888)

times (119891

1015840

119888120576

119888119898)

minus1

(1)

120574 = 1 minus ((int

0002

0

120576

119888119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

120576

119888119891

1015840

1198881 minus 100 (120576

119888minus 120576

119888119900) 119889120576

119888)

times (120576

119888119898[int

0002

0

119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

119891

1015840

1198881minus100 (120576

119888minus120576

119888119900) 119889120576

119888])

minus1

)

(2)

120572119891

1015840

119888119887119888 + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840) +

1

2

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

= 119860

119904119865

119910+ 119860

119891119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

1

2

119860

119908119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891)

(3)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908= 119905

119908(119889 minus 119888 minus 119889

1015840minus 119905

119891)

119872

119899= 120572119891

1015840

119888119887119888 (119888 minus 120574119888) + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840)

2

+

1

3

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

2

+ 119860

119904119865

119910(119889 minus 119888)

12 Mathematical Problems in Engineering

DayProcess

One floor

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7

Marking

Rebar work (wall)

Wall form installation

Slab form installation

Rebar work (slab) Electrical and mechanical

facilities (slab) Cleaning and pouring

Figure 16 Processes for constructing one floor of a conventional wall-type apartment building [20]

+ 119860

119891119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891) (119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

119905

119891

2

(119889 minus 119888 minus 119889

1015840minus

119905

119891

3

)

+

1

3

119860

119908119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891)

2

(4)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908= 119905

119908(119889 minus 119888 minus 119889

1015840minus 119905

119891)

120572119891

1015840

119888119887119888 + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840) +

1

2

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

= 119860

119904119865

119910+ 119860

119891119865

119910+ 119860

119908119901119865

119910+

1

2

119860

119908119899119910119864

119904120576

119904119910

(5)

where1198601015840119908= 119905

119908(119888minus119889

101584010158401015840)119860119908119901

= 119905

119908(119889minus119888+119889

1015840+119905

119891)+(120576

119904119910120576

119888)119888

119860

119908119899119910= 119905

119908(120576

119904119910120576

119888)119888

119872

119899= 120572119891

1015840

119888119887119888 (119888 minus 120574119888) + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840)

2

+

1

3

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

2

+ 119860

119904119865

119910(119889 minus 119888)

+ 119860

119891119865

119910(119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

1

2

119860

119908119901119865

119910(119889 minus 119888 minus 119889

1015840minus 119905

119891) +

120576

119904119910

120576

119888

119888

+

1

3

119860

119908119899119910119864

119904

(120576

119904119910)

2

120576

119888

119888

(6)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908119901

= 119905

119908119889 minus (119888 + 119889

1015840+ (120576

119904119910120576

119888)119888)

119860

119908119899119910= 119905

119908(120576

119904119910120576

119888)119888

A completed bearing wall apartment building wasselected for this comparison Apartment buildings withhybrid precast frames and bearingwall frameswere evaluatedin terms of building material CO

2emission energy con-

sumption and Cr6+ emission shown in Table 5 Construction

materials per square meters were calculated based on (5) and(6)whichwere then used to calculate the quantities of Table 5

The building materials of concrete and reinforcementsof apartment buildings with hybrid precast frames werereduced by 31 and 27 respectively compared with thatof bearing wall frame buildings The CO

2emission energy

consumption andCr6+ emission of apartment buildings withhybrid precast frames were also decreased compared withbearing wall frame buildings as shown in Table 5 exhibitingthe efficiency of using gravity hybrid precast frames forapartment buildings

6 Reduction in Construction Schedule

Figures 16 and 17 compare the construction time frames basedon the use of conventional bearing walls versus the proposedhybrid frames

The construction time is the sum of each critical path asshown in

119899

sum

119894=1

(CA119894) = CA

1+ CA2+ CA3+ CA4sdot sdot sdot (7)

The critical paths that affect construction time for abearing wall apartment are CA

1(marking 1 day) CA

2(rebar

work wall 1 day) CA3(wall form installation 2 days)

CA4(slab form installation 1 day) CA

5(rebar work slab 1

day) and CA6(cleaning and pouring 1 day) Installation of

electrical and mechanical facilities at the slab is performedwith rebar work of the slab and takes less time than that ofrebar work Electrical and mechanical facilities at the slab aretherefore excluded from the critical path The constructiontime per floor is seven days based on (7) The criticalpaths affecting construction time for an apartment buildingusing hybrid frames are CA

1(rebar work core wall 05

days) CA2(column-beam unit installation (1 day) beam

unit installation (15 days)) CA3(rebar work slab 05 days)

and CA4(cleaning and pouring 05 days) Column-beam

unit installation and beam unit installation are carried outalternately Beams are only installed at every second andthird floor since columns are erected as a three-story unit

Mathematical Problems in Engineering 13

DayProcess

First floor Second floor Third floor

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 Day 10

Rebar work (core wall)

Core wall form installationColumn-beam unit

installation Beam unit installation

Deck plate installation

Joint form installation

Rebar work (slab) Electrical and mechanical

facilities (slab) Cleaning and pouring

Figure 17 Processes for constructing three floors of an apartment building using hybrid frames [20]

Table 6 Comparative analysis of the construction period [20]

Structuraltype

Construction periodComparisonTypical

floor30-story apartment

building

Bearing wall 7 days1 floor 210 Days 1000Hybrid precastframe

10 days3floors 100 Days 476

As a result of the critical paths analysis the constructiontime per floor is four days for the first floor and threedays for the next two floors requiring ten days for theconstruction of three floors utilizing columns of a three-story unit The time for frame erection was reduced by 52when using hybrid frames highlighting their economic andconstruction benefits Erection of structural frames for onefloor using conventional bearing walls involves rebar workand concrete pouring and requires about seven days asshown in Figure 16 In contrast only three days were requiredto install wall and slab forms indicating that the overallconstruction was influenced by form work which is highlydependent on work skill However erection of three floorswith hybrid precast frames required only ten days whenthree-story hybrid precast columns were erected at one liftThe significant reduction in form work contributed to thedecrease in overall construction time obtained when usingthe hybrid precast frames as shown in Figure 17 As shown inTable 6 frame erection of a 30-story building required sevendays per floor or 210 days for the entire building when usingconventional bearing walls However only ten days per threefloors (or 100 days for the entire building) were required forframe erection of the building with hybrid precast frameswhich corresponds to a 524 reduction in frame erectiontime

7 Conclusions

This study described and characterized an optimized hybridprecast composite structural system for gravity systemMajorcontributions are summarized below

(1) Gravity hybrid precast frames were presented Thesehybrid frames consist of precast concrete and steelwhich can be erected at a speed similar to that of steelframes Steel sections inserted in precast columns andbeams are used as erection steel components

(2) Mathematical model of gravity hybrid precast beamwas presented at yield limit state and maximum loadlimit state Neutral axis of postyield state found fromequilibrium equations was used to calculate nominalmoment capacities of a hybrid composite beam atboth limit state

(3) The new building frame systems for gravity load-ings fabricated with hybrid precast composite framesconsisting of simple connections between columnsand beams were proposed in this paper The dualframe systems of moment connections with muchmore complicated construction details required sig-nificant time and costs than that of building framesystems of gravity loadings However the gravityhybrid precast composite structures will provide sim-plified construction method while enhancing econ-omyduring constructionThe reductions of construc-tion resources including concrete and reinforcements(31 reduction of concrete and 27 reduction of rein-forcements) were achieved when apartments were tobe built with hybrid precast frames

(4) The gravity hybrid precast frames use less construc-tion materials than conventional frames and there-fore reduce carbon dioxide and hazardous substanceemissions compared to conventional frames It was

14 Mathematical Problems in Engineering

observed the efficiency of using gravity hybrid precastframes for apartment building which decreased theCO2emission (23 reduction of concrete and 28

reduction of reinforcements) energy consumption(21 reduction of concrete and 29 reduction ofreinforcements) and Cr6+ emission compared withbearing wall frame buildings The use of gravityhybrid precast frames was demonstrated to providebetter solutions for environments and economy thanthat of conventional buildings

(5) Dynamic analysis of a 15-story building designedwith the proposed composite gravity frames was per-formed to characterize frequencies and mode shapesof the building for seismic design purposes

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by Grant from the Kyung HeeUniversity in 2013 (KHU-20130363)

References

[1] J F Hajjar ldquoComposite steel and concrete structural systems forseismic engineeringrdquo Journal of Constructional Steel Researchvol 58 no 5ndash8 pp 703ndash723 2002

[2] G Fabbrocino G Manfredi and E Cosenza ldquoDuctility ofcomposite beams under negative bending an equivalence indexfor reinforcing steel classificationrdquo Journal of ConstructionalSteel Research vol 58 no 2 pp 185ndash202 2001

[3] B Yang and K Tan ldquoBehaviour of composite beam-columnjoints under a middle-column-removal scenario experimentaltestsrdquo Journal of Structural Engineering vol 140 no 2 ArticleID 04013045 2014

[4] L Tesser and R Scotta ldquoFlexural and shear capacity of compos-ite steel truss and concrete beams with inferior precast concretebaserdquo Engineering Structures vol 49 pp 135ndash145 2013

[5] H J Hwang H G Park C H Lee et al ldquoSeismic resistanceof concrete-filled U-shaped steel beam-to-RC column connec-tionsrdquo Journal of Korean Society of Steel Construction vol 23 pp83ndash97 2011

[6] J Hassan and B Khosrow ldquoNonlinear seismic behavior evalua-tion of ductile beam-column connections in precast concreterdquoInternational Journal of Civil and Structural Engineering vol 1pp 445ndash453 2011

[7] A M Ioani and E Tripa ldquoStructural behavior of an innovativeall-precast concrete dual system for residential buildingsrdquo PCIJournal vol 57 no 1 pp 110ndash123 2012

[8] C Chou andCUang ldquoEffects of continuity plate and transversereinforcement on cyclic behavior of SRCmoment connectionsrdquoJournal of Structural Engineering vol 133 no 1 pp 96ndash104 2007

[9] Y K Ju and S D Kim ldquoStructural behavior of alternative lowfloor height system using structural ldquoteerdquo half precast concreteand horizontal studrdquoCanadian Journal of Civil Engineering vol32 no 2 pp 329ndash338 2005

[10] X Wang M Truijens L Hou Y Wang and Y Zhou ldquoInte-grating augmented reality with building informationmodelingonsite construction process controlling for liquefied natural gasindustryrdquoAutomation in Construction vol 40 pp 96ndash105 2014

[11] L Hou Y Wang X Wang et al ldquoCombining photogrammetryand augmented reality towards an integrated facility manage-ment system for the oil industryrdquo Proceedings of the IEEE vol102 no 2 pp 204ndash220 2014

[12] L Hou XWang L Bernold and P E D Love ldquoUsing animatedaugmented reality to cognitively guide assemblyrdquo Journal ofComputing in Civil Engineering vol 27 no 5 pp 439ndash451 2013

[13] YWang XWang JWang P Yung andG Jun ldquoEngagement offacilities management in design stage through BIM frameworkand a case studyrdquo Advances in Civil Engineering vol 2013Article ID 189105 8 pages 2013

[14] W K Hong J M Kim S C Park et al ldquoA new apartmentconstruction technology with effective CO

2emission reduction

capabilitiesrdquo Energy vol 35 no 6 pp 2639ndash2646 2010[15] W Hong S Park J Kim et al ldquoDevelopment of structural

composite hybrid systems and their application with regard tothe reduction of CO

2emissionsrdquo Indoor and Built Environment

vol 19 no 1 pp 151ndash162 2010[16] W Hong S Jeong S Park and J T Kim ldquoExperimental

investigation of an energy-efficient hybrid composite beamduring the construction phaserdquo Energy and Buildings vol 46pp 37ndash47 2012

[17] G P Hammond and C I Jones Inventory of Carbon amp Energy(ICE) Department of Mechanical Engineering University ofBath Bath UK 2008

[18] G P Hammond and C I Jones ldquoEmbodied energy and carbonin construction materialsrdquo Proceedings of Institution of CivilEngineers Energy vol 161 no 2 pp 87ndash98 2008

[19] National Institute of Environment Research (NIER) Domesticand foreign cement heavy metal analysis result (May 2013)NIER 2013 httpwwwniergokrericportalkornfnier-nf-02page

[20] S Kim W Hong J Kim and J T Kim ldquoThe developmentof modularized construction of enhanced precast compositestructural systems (Smart Green frame) and its embeddedenergy efficiencyrdquo Energy and Buildings vol 66 pp 16ndash21 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

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Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Mathematical PhysicsAdvances in

Complex AnalysisJournal of

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OptimizationJournal of

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

4 Mathematical Problems in Engineering

Column reinforced rebarsSteel plate

Beam units

Simple connection(shear tap)

Cast-in-place concrete

CFTPrecast concrete

Shear tap

Variable

VariableStud bolts

(a) Details of the beam-column joints of the hybrid precast frames

Without CFTShear tap

Stud bolt

With CFTShear tap

(b) Details of the shear tap

CFT Variable Service condition

Stud boltShear tap

(c) Construction details of the column unit

Figure 3 Details of the hybrid precast frame joints

Precast structures cannot be erected as fast as steel struc-tures because beams without slabs lack stability as shown inFigure 5 The hybrid precast frames however can be erectedas quickly as steel structures without slab construction Thehybrid precast frames suggested in this paper are hybridcomposite structures that have the merits of both steel andprecast concrete structures in particular the steel sectionsfunction as erection components This hybrid constructionmethod makes it possible to erect precast concrete frames ina time-frame similar to that of steel frames

22 Structural Stability during Construction The proposedhybrid precast frames with steel joints provide structuralstability during construction In contrast the vertical rein-forcing steel used for vertical splicing in conventional precastapplications is vulnerable to buckling against unexpectedvertical loading before the joints are filled with concretewhich could cause structural instability of the frame underconstruction as shown in Figure 6 In the proposed methodsteel sections are inserted between the upper and lowerprecast columns and are connected to steel sections locatedat both ends of the precast beams and girders or steel sectionsrunning throughout the entire lengths of the precast beamsallowing easy and stable connections

3 Use of Convergence of the HybridPrecast Frames

Because hybrid precast frames can be designed using a widerange of spans and joint designs bearing wall-type apartmentbuildings may be replaced with buildings with hybrid precastframes Structural systems should be optimized with steelconnections which are required to be as small as 20sim25 kgfm2 (about one-tenth that of reinforcing steel) enablingconstructability and assembly time similar to that of steelframes

Figure 7 shows deflections of a composite frame buildingsubjected to wind loads The lateral displacements are withinacceptable limits Displacement along the 119909-axis and 119910-axis was 20 cm (H3910) and 29 cm (H1955) respectivelyAcceptable story drift in response to seismic loading wasalso observed in both directions as shown in Figure 8 Theseresults demonstrate that the optimized structural compositeframes have structural stability

4 Dynamic Analysis of a Building with HybridPrecast Frames

Figure 9 shows a building with 13 stories and two base-ments (total floor area of 6741m2) that was designed with

Mathematical Problems in Engineering 5

Shear tap

Stud bolt

Steel plate

CFT

Cast-in-place concrete

Precast concrete

Shear tap

Figure 4 Hybrid precast frame construction process

+

Critical pathUpwards construction

Figure 5 Reduction of the hybrid precast frame construction period

Rebarconnection

(a)

Rebarconnection

(b)

Figure 6 Conventional precast concrete connections

6 Mathematical Problems in Engineering

X-direction00111 m

(H39099)

Midas genpostprocessordisplacement

resultant

Scale factor =

110700e minus 002100636e minus 002905726e minus 003805090e minus 003704454e minus 003603817e minus 003503181e minus 003402545e minus 003301909e minus 003201272e minus 003100636e minus 003000000e + 000

26266E + 002

(a)

Y-direction00222 m

(H19549)

Midas genpostprocessordisplacement

resultant

Scale factor =

222476e minus 002202251e minus 002182025e minus 002161800e minus 002141575e minus 002121350e minus 002101125e minus 002809002e minus 003606752e minus 003404501e minus 003202251e minus 003000000e + 000

13069E + 002

(b)

Figure 7 Wind displacement

0

0002

0004

0006

0008

001

0012

0014

0016

17F

16F

15F

14F

13F

12F

11F

10F 9F 8F 7F 6F 5F 4F 3F 2F 1F

Story drift ratioAllowable story drift ratio

Story drift ratio (x-axis)

(a)

17F

16F

15F

14F

13F

12F

11F

10F 9F 8F 7F 6F 5F 4F 3F 2F 1F

Story drift ratioAllowable story drift ratio

0

0002

0004

0006

0008

001

0012

0014

0016Story drift ratio (y-axis)

(b)

Figure 8 Story drift

the proposed composite frames and selected for dynamicanalysis The floor plan and elevation with framing usingcomposite columns and beams are also shown The buildingwas designed such that the shear walls were resistant to lateralseismic loadings while the frames resisted only vertical loadsDynamic analysis was performed to investigate the influenceof the design and size of the composite frames on the dynamiccharacteristics of the building

Figure 10 shows a computer model of the building withcomposite frames andwalls in which the steel sections at bothends of the beams are connected to steel inserted betweentwo precast columns Figure 10(a) shows gravity compositeframes attached to shear walls that are responsible for lateralearthquake loading Figure 10(b) shows close connectiondetails of the frames and walls that constitute the building

frame Figure 10(c) shows steel frames and connectionsbetween beams and columns The material structural andconstruction hybrid applications were integrated to combinethe constructability of steel structures with the economy ofconcrete structures

Tables 1 and 2 show modal participation masses andeigenvalue results respectively The fundamental transla-tional mode was found in the third return period the firstand second modes were considered to be mixed translationalmodes with torsion A fundamental translational mode of 15seconds along with a weak 119910-axis was deemed reasonableThe fundamental period and mode shapes for the compositeframe were more similar to those of steel structures thanthose of concrete structures indicating that the structuralbehavior of a building with composite frames and steel

Mathematical Problems in Engineering 7

7400

17750

3500

3500

3500

3500

3500

3500

3000

2400

X

Y

2900

2900

X6

X6

X7

X8

X9

X10

2900

4100

39200

14001400

14600

6300 63002000

PS

PS

PSPS

PSPS

PS

PS PS

PSPS

PS

PS

PS

PSPS

PSPS

PSPS

PS

PSPS

PS

PS

PSPS

PS

PS

PS

PS

PS

PSPS

PS

PS

PS

PS

PS

PS

PS

329

0

4928

3500

3500

3500

3500

3500

3500

6300

1300

1300

5000

5000

6300

14600

X1

X2

X3

2000

25928

350

0

350

03

500

350

03

500

350

03

500

350

03

500

350

03

500

700

07

000

700

07

000

700

0

417

90

PS

PS

PS

PS

PS PS

PSPS

Hal

l

PS

PS

49004900

Y3998400

Y4998400

Y5998400

Y6998400

(a)

Figure 9 Continued

8 Mathematical Problems in Engineering

1447

1500

7200

3600

3600

3800

2900

2900

2900

2900

2900

2900

2900

2900

2900

2900

2900

1

29001400

1500 1

0003600

23003600

3800

2900

2600

1300

3200

1600700

600

2900

2900

2900

2900

2900

2900

2900

2900

2900

2900

29001400

40000

2880

2880

920

5100700061508300 6300

6300 630020002150 4150

5382

1447

2250

2250

2250

2250

2250

2250

2250

2250

2250

2250

2250

2250

3200 2400

2300

1600

GL-1800

GL-6000

510070006150146005382

(b)

Figure 9 Floor plan and elevation

Mathematical Problems in Engineering 9

Table 1 Modal participation masses

Mode number TRAN-119883 TRAN-119884 ROTN-119885Mass () Sum () Mass () Sum () Mass () Sum ()

1 405909 405909 02185 02185 127252 1272522 42570 448478 16208 164265 203361 3306123 40667 489145 328629 492893 82552 4131644 96703 585848 01847 49474 40557 4537215 32088 617935 03965 498705 87600 5413216 03685 621620 158676 657381 05207 546528

(a) (b) (c)

Figure 10 Computer model of the building

Table 2 Eigenvalue analysis (fundamental period)

Mode number Frequency Period Tolerance(radsec) (cyclesec) (sec)

1 34768 05533 34768 00000119890 + 000

2 41078 06538 41078 00000119890 + 000

3 53487 08513 53487 00000119890 + 000

4 138311 22013 138311 45251119890 minus 161

5 178259 28371 178259 28518119890 minus 150

6 236726 37676 236726 15909119890 minus 137

joints against vertical and lateral loadings resembles that ofsteel structures even though the building has an externalappearance of a concrete structure

Figure 11 shows the first translational mode (a) and thoseof two mixed modes ((b) (c)) Figures 11(d) 11(e) and 11(f)show these modes from the top view respectively

5 Reduction of Structural Quantity andEmissions of Environmentally HazardousSubstances and Materials

This study evaluated chromium VI and carbon dioxide emis-sions of the building constructed with the proposed framesand conventional walls Reductions in energy consumptiondue to reduction in material quantity were estimated basedon comparison of an apartment building constructed withhybrid precast frames and that of a conventional bearing-wallbuilding

Original units of major building components (Table 3)which were announced in 2008 by the United Kingdom

Table 3 Emissions and energy usage of major building components[17]

Buildingcomponent

CO2 emissionsper original unit

Energy consumptionper original unit

Concrete 25MPa 3196 kg-CO2m3 23265MJm3

Concrete 35MPa 37835 kg-CO2m3 26555MJm3

Reinforcement 27319 kg-CO2kN 371050MJkNSteel section 28338 kg-CO2kN 375127MJkN

Inventory of Carbon and Energy (ICE) were used to evaluatecarbon dioxide emissions and the energy efficiency of theproposed construction The embodied energy 119864 and carbonemissions per kN for the calculated material quantity areobtained from the University of Bathrsquos ICE database [17 18]The ICE has been structured into 34 main material groupsThe database also provides the embodied energy and carboncoefficients for construction materials Table 3 presents theconverted embodied energy and carbon coefficients for fourbuilding components concrete (25MPa) concrete (35MPa)reinforcement and steel section

Domestic and foreign cement heavymetal analysis results(May 2013) published by the Korea National Institute ofEnvironment Research (NIER) were utilized to evaluatechromium VI emissions (Table 4)

In order to explain how the data that evaluates the gravitysystem presented in this paper in terms of material quantityanalytical approach for the hybrid precast composite beamdesign based on the strain compatibility method was intro-duced Figures 12 and 13 illustrate the side view and cross-section of a hybrid composite beam In order to determine the

10 Mathematical Problems in Engineering

Table 4 Heavy metal content standards in cement [19]

Cr6+ As Cd Cu Hg PbAve (May 2013) 1063mgkg 1287mgkg 102mgkg 8903mgkg 061mgkg 3284mgkg

(a) Fundamental translational mode (b) Mixed mode 1 (c) Mixed mode 2

(d) Fundamental translational mode (e) Mixed mode 1 (f) Mixed mode 2

Figure 11 Mode shapes

Figure 12 Side view of a hybrid composite beam

d

d998400

d998400998400

d998400998400998400

Figure 13 Cross-section of a hybrid composite beam

exact material quantity the hybrid composite beam designwas carried out based on the strain compatibility methodEquations (1) and (2) are the mean stress factor 120572 and thecentroid factor 120574 for any strain 120576

119888119898at the extreme com-

pression fiber calculated based on stress-strain relationshipEquations (3) and (5) represent the equilibrium equations ofcompressive and tensile forces at yield limit and maximumload limit state respectively The nominal moment capacitiesof a hybrid composite beam at yield limit andmaximum loadlimit state are calculated by (4) and (6) respectively Figures14 and 15 represent strain and stress diagram at yield limitand maximum load limit state respectively In both figuresblack color indicates steels and reinforcement rebars wereplasticized (yielded) while white color represents structuralmembers remained elastic The structural quantity requiredby apartment buildings with hybrid composite frames wasobtained from (6) and compared with that of conventionalbuildings with bearing walls as shown in Table 5 These

Mathematical Problems in Engineering 11

Table 5 Evaluation of structural systems

Buildingcomponent System Gross area Building material CO2 emission Energy consumption Cr6+ emission

Concrete(HPF = 35MPaBW = 25MPa)

HPF 9236m2 038m3m2 691(minus309) 1362 kg-CO2m

2 775(minus225) 10060MJm2 786

(minus214) 11062mgm2 689(minus311)

BW 6513m2 055m3m2 1000 1758 kg-CO2m2 1000 12796MJm2 1000 16061mgm2 100

Reinforcements HPF 9236m2 053 kNm2 726(minus274) 1445 kg-CO2m

2 724(minus276) 19314MJm2 713

(minus287) mdash mdash

BW 6513m2 073 kNm2 1000 1996 kg-CO2m2 1000 27107MJm2 1000 mdash mdash

Steel section HPF 9236m2 007 kNm2 1000 206 kg-CO2m2 1000 2721MJm2 1000 mdash mdash

BW 6513m2 mdashkNm2 mdash mdashkg-CO2m2 mdash mdashMJm2 mdash mdash mdash

lowastHPF hybrid precast frames BW bearing wall

400 MPa

301 MPa

1354 mm

120576st = 0001506

120576t = 120576y = 0002

120576c = 000178 f998400c

120576998400t = 000096 120576tEs = 192MPa

Figure 14 Strain and stress diagram at yield limit state

120576tEs = 286MPa

400 MPa

325 MPa

11946 mm

120576st = 000328

120576t = 120576y = 00042

120576c = 0003f998400c

120576998400t = 000143

Figure 15 Strain and stress diagram at maximum load limit state

equations would help engineer estimate precise constructionmaterials and understand how buildings with hybrid com-posite frames behave Consider

120572 = (int

0002

0

119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

119891

1015840

1198881 minus 100 (120576

119888minus 120576

119888119900) 119889120576

119888)

times (119891

1015840

119888120576

119888119898)

minus1

(1)

120574 = 1 minus ((int

0002

0

120576

119888119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

120576

119888119891

1015840

1198881 minus 100 (120576

119888minus 120576

119888119900) 119889120576

119888)

times (120576

119888119898[int

0002

0

119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

119891

1015840

1198881minus100 (120576

119888minus120576

119888119900) 119889120576

119888])

minus1

)

(2)

120572119891

1015840

119888119887119888 + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840) +

1

2

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

= 119860

119904119865

119910+ 119860

119891119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

1

2

119860

119908119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891)

(3)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908= 119905

119908(119889 minus 119888 minus 119889

1015840minus 119905

119891)

119872

119899= 120572119891

1015840

119888119887119888 (119888 minus 120574119888) + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840)

2

+

1

3

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

2

+ 119860

119904119865

119910(119889 minus 119888)

12 Mathematical Problems in Engineering

DayProcess

One floor

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7

Marking

Rebar work (wall)

Wall form installation

Slab form installation

Rebar work (slab) Electrical and mechanical

facilities (slab) Cleaning and pouring

Figure 16 Processes for constructing one floor of a conventional wall-type apartment building [20]

+ 119860

119891119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891) (119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

119905

119891

2

(119889 minus 119888 minus 119889

1015840minus

119905

119891

3

)

+

1

3

119860

119908119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891)

2

(4)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908= 119905

119908(119889 minus 119888 minus 119889

1015840minus 119905

119891)

120572119891

1015840

119888119887119888 + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840) +

1

2

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

= 119860

119904119865

119910+ 119860

119891119865

119910+ 119860

119908119901119865

119910+

1

2

119860

119908119899119910119864

119904120576

119904119910

(5)

where1198601015840119908= 119905

119908(119888minus119889

101584010158401015840)119860119908119901

= 119905

119908(119889minus119888+119889

1015840+119905

119891)+(120576

119904119910120576

119888)119888

119860

119908119899119910= 119905

119908(120576

119904119910120576

119888)119888

119872

119899= 120572119891

1015840

119888119887119888 (119888 minus 120574119888) + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840)

2

+

1

3

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

2

+ 119860

119904119865

119910(119889 minus 119888)

+ 119860

119891119865

119910(119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

1

2

119860

119908119901119865

119910(119889 minus 119888 minus 119889

1015840minus 119905

119891) +

120576

119904119910

120576

119888

119888

+

1

3

119860

119908119899119910119864

119904

(120576

119904119910)

2

120576

119888

119888

(6)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908119901

= 119905

119908119889 minus (119888 + 119889

1015840+ (120576

119904119910120576

119888)119888)

119860

119908119899119910= 119905

119908(120576

119904119910120576

119888)119888

A completed bearing wall apartment building wasselected for this comparison Apartment buildings withhybrid precast frames and bearingwall frameswere evaluatedin terms of building material CO

2emission energy con-

sumption and Cr6+ emission shown in Table 5 Construction

materials per square meters were calculated based on (5) and(6)whichwere then used to calculate the quantities of Table 5

The building materials of concrete and reinforcementsof apartment buildings with hybrid precast frames werereduced by 31 and 27 respectively compared with thatof bearing wall frame buildings The CO

2emission energy

consumption andCr6+ emission of apartment buildings withhybrid precast frames were also decreased compared withbearing wall frame buildings as shown in Table 5 exhibitingthe efficiency of using gravity hybrid precast frames forapartment buildings

6 Reduction in Construction Schedule

Figures 16 and 17 compare the construction time frames basedon the use of conventional bearing walls versus the proposedhybrid frames

The construction time is the sum of each critical path asshown in

119899

sum

119894=1

(CA119894) = CA

1+ CA2+ CA3+ CA4sdot sdot sdot (7)

The critical paths that affect construction time for abearing wall apartment are CA

1(marking 1 day) CA

2(rebar

work wall 1 day) CA3(wall form installation 2 days)

CA4(slab form installation 1 day) CA

5(rebar work slab 1

day) and CA6(cleaning and pouring 1 day) Installation of

electrical and mechanical facilities at the slab is performedwith rebar work of the slab and takes less time than that ofrebar work Electrical and mechanical facilities at the slab aretherefore excluded from the critical path The constructiontime per floor is seven days based on (7) The criticalpaths affecting construction time for an apartment buildingusing hybrid frames are CA

1(rebar work core wall 05

days) CA2(column-beam unit installation (1 day) beam

unit installation (15 days)) CA3(rebar work slab 05 days)

and CA4(cleaning and pouring 05 days) Column-beam

unit installation and beam unit installation are carried outalternately Beams are only installed at every second andthird floor since columns are erected as a three-story unit

Mathematical Problems in Engineering 13

DayProcess

First floor Second floor Third floor

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 Day 10

Rebar work (core wall)

Core wall form installationColumn-beam unit

installation Beam unit installation

Deck plate installation

Joint form installation

Rebar work (slab) Electrical and mechanical

facilities (slab) Cleaning and pouring

Figure 17 Processes for constructing three floors of an apartment building using hybrid frames [20]

Table 6 Comparative analysis of the construction period [20]

Structuraltype

Construction periodComparisonTypical

floor30-story apartment

building

Bearing wall 7 days1 floor 210 Days 1000Hybrid precastframe

10 days3floors 100 Days 476

As a result of the critical paths analysis the constructiontime per floor is four days for the first floor and threedays for the next two floors requiring ten days for theconstruction of three floors utilizing columns of a three-story unit The time for frame erection was reduced by 52when using hybrid frames highlighting their economic andconstruction benefits Erection of structural frames for onefloor using conventional bearing walls involves rebar workand concrete pouring and requires about seven days asshown in Figure 16 In contrast only three days were requiredto install wall and slab forms indicating that the overallconstruction was influenced by form work which is highlydependent on work skill However erection of three floorswith hybrid precast frames required only ten days whenthree-story hybrid precast columns were erected at one liftThe significant reduction in form work contributed to thedecrease in overall construction time obtained when usingthe hybrid precast frames as shown in Figure 17 As shown inTable 6 frame erection of a 30-story building required sevendays per floor or 210 days for the entire building when usingconventional bearing walls However only ten days per threefloors (or 100 days for the entire building) were required forframe erection of the building with hybrid precast frameswhich corresponds to a 524 reduction in frame erectiontime

7 Conclusions

This study described and characterized an optimized hybridprecast composite structural system for gravity systemMajorcontributions are summarized below

(1) Gravity hybrid precast frames were presented Thesehybrid frames consist of precast concrete and steelwhich can be erected at a speed similar to that of steelframes Steel sections inserted in precast columns andbeams are used as erection steel components

(2) Mathematical model of gravity hybrid precast beamwas presented at yield limit state and maximum loadlimit state Neutral axis of postyield state found fromequilibrium equations was used to calculate nominalmoment capacities of a hybrid composite beam atboth limit state

(3) The new building frame systems for gravity load-ings fabricated with hybrid precast composite framesconsisting of simple connections between columnsand beams were proposed in this paper The dualframe systems of moment connections with muchmore complicated construction details required sig-nificant time and costs than that of building framesystems of gravity loadings However the gravityhybrid precast composite structures will provide sim-plified construction method while enhancing econ-omyduring constructionThe reductions of construc-tion resources including concrete and reinforcements(31 reduction of concrete and 27 reduction of rein-forcements) were achieved when apartments were tobe built with hybrid precast frames

(4) The gravity hybrid precast frames use less construc-tion materials than conventional frames and there-fore reduce carbon dioxide and hazardous substanceemissions compared to conventional frames It was

14 Mathematical Problems in Engineering

observed the efficiency of using gravity hybrid precastframes for apartment building which decreased theCO2emission (23 reduction of concrete and 28

reduction of reinforcements) energy consumption(21 reduction of concrete and 29 reduction ofreinforcements) and Cr6+ emission compared withbearing wall frame buildings The use of gravityhybrid precast frames was demonstrated to providebetter solutions for environments and economy thanthat of conventional buildings

(5) Dynamic analysis of a 15-story building designedwith the proposed composite gravity frames was per-formed to characterize frequencies and mode shapesof the building for seismic design purposes

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by Grant from the Kyung HeeUniversity in 2013 (KHU-20130363)

References

[1] J F Hajjar ldquoComposite steel and concrete structural systems forseismic engineeringrdquo Journal of Constructional Steel Researchvol 58 no 5ndash8 pp 703ndash723 2002

[2] G Fabbrocino G Manfredi and E Cosenza ldquoDuctility ofcomposite beams under negative bending an equivalence indexfor reinforcing steel classificationrdquo Journal of ConstructionalSteel Research vol 58 no 2 pp 185ndash202 2001

[3] B Yang and K Tan ldquoBehaviour of composite beam-columnjoints under a middle-column-removal scenario experimentaltestsrdquo Journal of Structural Engineering vol 140 no 2 ArticleID 04013045 2014

[4] L Tesser and R Scotta ldquoFlexural and shear capacity of compos-ite steel truss and concrete beams with inferior precast concretebaserdquo Engineering Structures vol 49 pp 135ndash145 2013

[5] H J Hwang H G Park C H Lee et al ldquoSeismic resistanceof concrete-filled U-shaped steel beam-to-RC column connec-tionsrdquo Journal of Korean Society of Steel Construction vol 23 pp83ndash97 2011

[6] J Hassan and B Khosrow ldquoNonlinear seismic behavior evalua-tion of ductile beam-column connections in precast concreterdquoInternational Journal of Civil and Structural Engineering vol 1pp 445ndash453 2011

[7] A M Ioani and E Tripa ldquoStructural behavior of an innovativeall-precast concrete dual system for residential buildingsrdquo PCIJournal vol 57 no 1 pp 110ndash123 2012

[8] C Chou andCUang ldquoEffects of continuity plate and transversereinforcement on cyclic behavior of SRCmoment connectionsrdquoJournal of Structural Engineering vol 133 no 1 pp 96ndash104 2007

[9] Y K Ju and S D Kim ldquoStructural behavior of alternative lowfloor height system using structural ldquoteerdquo half precast concreteand horizontal studrdquoCanadian Journal of Civil Engineering vol32 no 2 pp 329ndash338 2005

[10] X Wang M Truijens L Hou Y Wang and Y Zhou ldquoInte-grating augmented reality with building informationmodelingonsite construction process controlling for liquefied natural gasindustryrdquoAutomation in Construction vol 40 pp 96ndash105 2014

[11] L Hou Y Wang X Wang et al ldquoCombining photogrammetryand augmented reality towards an integrated facility manage-ment system for the oil industryrdquo Proceedings of the IEEE vol102 no 2 pp 204ndash220 2014

[12] L Hou XWang L Bernold and P E D Love ldquoUsing animatedaugmented reality to cognitively guide assemblyrdquo Journal ofComputing in Civil Engineering vol 27 no 5 pp 439ndash451 2013

[13] YWang XWang JWang P Yung andG Jun ldquoEngagement offacilities management in design stage through BIM frameworkand a case studyrdquo Advances in Civil Engineering vol 2013Article ID 189105 8 pages 2013

[14] W K Hong J M Kim S C Park et al ldquoA new apartmentconstruction technology with effective CO

2emission reduction

capabilitiesrdquo Energy vol 35 no 6 pp 2639ndash2646 2010[15] W Hong S Park J Kim et al ldquoDevelopment of structural

composite hybrid systems and their application with regard tothe reduction of CO

2emissionsrdquo Indoor and Built Environment

vol 19 no 1 pp 151ndash162 2010[16] W Hong S Jeong S Park and J T Kim ldquoExperimental

investigation of an energy-efficient hybrid composite beamduring the construction phaserdquo Energy and Buildings vol 46pp 37ndash47 2012

[17] G P Hammond and C I Jones Inventory of Carbon amp Energy(ICE) Department of Mechanical Engineering University ofBath Bath UK 2008

[18] G P Hammond and C I Jones ldquoEmbodied energy and carbonin construction materialsrdquo Proceedings of Institution of CivilEngineers Energy vol 161 no 2 pp 87ndash98 2008

[19] National Institute of Environment Research (NIER) Domesticand foreign cement heavy metal analysis result (May 2013)NIER 2013 httpwwwniergokrericportalkornfnier-nf-02page

[20] S Kim W Hong J Kim and J T Kim ldquoThe developmentof modularized construction of enhanced precast compositestructural systems (Smart Green frame) and its embeddedenergy efficiencyrdquo Energy and Buildings vol 66 pp 16ndash21 2013

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Mathematical Problems in Engineering

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Differential EquationsInternational Journal of

Volume 2014

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Complex AnalysisJournal of

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OptimizationJournal of

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Operations ResearchAdvances in

Journal of

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Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 5

Shear tap

Stud bolt

Steel plate

CFT

Cast-in-place concrete

Precast concrete

Shear tap

Figure 4 Hybrid precast frame construction process

+

Critical pathUpwards construction

Figure 5 Reduction of the hybrid precast frame construction period

Rebarconnection

(a)

Rebarconnection

(b)

Figure 6 Conventional precast concrete connections

6 Mathematical Problems in Engineering

X-direction00111 m

(H39099)

Midas genpostprocessordisplacement

resultant

Scale factor =

110700e minus 002100636e minus 002905726e minus 003805090e minus 003704454e minus 003603817e minus 003503181e minus 003402545e minus 003301909e minus 003201272e minus 003100636e minus 003000000e + 000

26266E + 002

(a)

Y-direction00222 m

(H19549)

Midas genpostprocessordisplacement

resultant

Scale factor =

222476e minus 002202251e minus 002182025e minus 002161800e minus 002141575e minus 002121350e minus 002101125e minus 002809002e minus 003606752e minus 003404501e minus 003202251e minus 003000000e + 000

13069E + 002

(b)

Figure 7 Wind displacement

0

0002

0004

0006

0008

001

0012

0014

0016

17F

16F

15F

14F

13F

12F

11F

10F 9F 8F 7F 6F 5F 4F 3F 2F 1F

Story drift ratioAllowable story drift ratio

Story drift ratio (x-axis)

(a)

17F

16F

15F

14F

13F

12F

11F

10F 9F 8F 7F 6F 5F 4F 3F 2F 1F

Story drift ratioAllowable story drift ratio

0

0002

0004

0006

0008

001

0012

0014

0016Story drift ratio (y-axis)

(b)

Figure 8 Story drift

the proposed composite frames and selected for dynamicanalysis The floor plan and elevation with framing usingcomposite columns and beams are also shown The buildingwas designed such that the shear walls were resistant to lateralseismic loadings while the frames resisted only vertical loadsDynamic analysis was performed to investigate the influenceof the design and size of the composite frames on the dynamiccharacteristics of the building

Figure 10 shows a computer model of the building withcomposite frames andwalls in which the steel sections at bothends of the beams are connected to steel inserted betweentwo precast columns Figure 10(a) shows gravity compositeframes attached to shear walls that are responsible for lateralearthquake loading Figure 10(b) shows close connectiondetails of the frames and walls that constitute the building

frame Figure 10(c) shows steel frames and connectionsbetween beams and columns The material structural andconstruction hybrid applications were integrated to combinethe constructability of steel structures with the economy ofconcrete structures

Tables 1 and 2 show modal participation masses andeigenvalue results respectively The fundamental transla-tional mode was found in the third return period the firstand second modes were considered to be mixed translationalmodes with torsion A fundamental translational mode of 15seconds along with a weak 119910-axis was deemed reasonableThe fundamental period and mode shapes for the compositeframe were more similar to those of steel structures thanthose of concrete structures indicating that the structuralbehavior of a building with composite frames and steel

Mathematical Problems in Engineering 7

7400

17750

3500

3500

3500

3500

3500

3500

3000

2400

X

Y

2900

2900

X6

X6

X7

X8

X9

X10

2900

4100

39200

14001400

14600

6300 63002000

PS

PS

PSPS

PSPS

PS

PS PS

PSPS

PS

PS

PS

PSPS

PSPS

PSPS

PS

PSPS

PS

PS

PSPS

PS

PS

PS

PS

PS

PSPS

PS

PS

PS

PS

PS

PS

PS

329

0

4928

3500

3500

3500

3500

3500

3500

6300

1300

1300

5000

5000

6300

14600

X1

X2

X3

2000

25928

350

0

350

03

500

350

03

500

350

03

500

350

03

500

350

03

500

700

07

000

700

07

000

700

0

417

90

PS

PS

PS

PS

PS PS

PSPS

Hal

l

PS

PS

49004900

Y3998400

Y4998400

Y5998400

Y6998400

(a)

Figure 9 Continued

8 Mathematical Problems in Engineering

1447

1500

7200

3600

3600

3800

2900

2900

2900

2900

2900

2900

2900

2900

2900

2900

2900

1

29001400

1500 1

0003600

23003600

3800

2900

2600

1300

3200

1600700

600

2900

2900

2900

2900

2900

2900

2900

2900

2900

2900

29001400

40000

2880

2880

920

5100700061508300 6300

6300 630020002150 4150

5382

1447

2250

2250

2250

2250

2250

2250

2250

2250

2250

2250

2250

2250

3200 2400

2300

1600

GL-1800

GL-6000

510070006150146005382

(b)

Figure 9 Floor plan and elevation

Mathematical Problems in Engineering 9

Table 1 Modal participation masses

Mode number TRAN-119883 TRAN-119884 ROTN-119885Mass () Sum () Mass () Sum () Mass () Sum ()

1 405909 405909 02185 02185 127252 1272522 42570 448478 16208 164265 203361 3306123 40667 489145 328629 492893 82552 4131644 96703 585848 01847 49474 40557 4537215 32088 617935 03965 498705 87600 5413216 03685 621620 158676 657381 05207 546528

(a) (b) (c)

Figure 10 Computer model of the building

Table 2 Eigenvalue analysis (fundamental period)

Mode number Frequency Period Tolerance(radsec) (cyclesec) (sec)

1 34768 05533 34768 00000119890 + 000

2 41078 06538 41078 00000119890 + 000

3 53487 08513 53487 00000119890 + 000

4 138311 22013 138311 45251119890 minus 161

5 178259 28371 178259 28518119890 minus 150

6 236726 37676 236726 15909119890 minus 137

joints against vertical and lateral loadings resembles that ofsteel structures even though the building has an externalappearance of a concrete structure

Figure 11 shows the first translational mode (a) and thoseof two mixed modes ((b) (c)) Figures 11(d) 11(e) and 11(f)show these modes from the top view respectively

5 Reduction of Structural Quantity andEmissions of Environmentally HazardousSubstances and Materials

This study evaluated chromium VI and carbon dioxide emis-sions of the building constructed with the proposed framesand conventional walls Reductions in energy consumptiondue to reduction in material quantity were estimated basedon comparison of an apartment building constructed withhybrid precast frames and that of a conventional bearing-wallbuilding

Original units of major building components (Table 3)which were announced in 2008 by the United Kingdom

Table 3 Emissions and energy usage of major building components[17]

Buildingcomponent

CO2 emissionsper original unit

Energy consumptionper original unit

Concrete 25MPa 3196 kg-CO2m3 23265MJm3

Concrete 35MPa 37835 kg-CO2m3 26555MJm3

Reinforcement 27319 kg-CO2kN 371050MJkNSteel section 28338 kg-CO2kN 375127MJkN

Inventory of Carbon and Energy (ICE) were used to evaluatecarbon dioxide emissions and the energy efficiency of theproposed construction The embodied energy 119864 and carbonemissions per kN for the calculated material quantity areobtained from the University of Bathrsquos ICE database [17 18]The ICE has been structured into 34 main material groupsThe database also provides the embodied energy and carboncoefficients for construction materials Table 3 presents theconverted embodied energy and carbon coefficients for fourbuilding components concrete (25MPa) concrete (35MPa)reinforcement and steel section

Domestic and foreign cement heavymetal analysis results(May 2013) published by the Korea National Institute ofEnvironment Research (NIER) were utilized to evaluatechromium VI emissions (Table 4)

In order to explain how the data that evaluates the gravitysystem presented in this paper in terms of material quantityanalytical approach for the hybrid precast composite beamdesign based on the strain compatibility method was intro-duced Figures 12 and 13 illustrate the side view and cross-section of a hybrid composite beam In order to determine the

10 Mathematical Problems in Engineering

Table 4 Heavy metal content standards in cement [19]

Cr6+ As Cd Cu Hg PbAve (May 2013) 1063mgkg 1287mgkg 102mgkg 8903mgkg 061mgkg 3284mgkg

(a) Fundamental translational mode (b) Mixed mode 1 (c) Mixed mode 2

(d) Fundamental translational mode (e) Mixed mode 1 (f) Mixed mode 2

Figure 11 Mode shapes

Figure 12 Side view of a hybrid composite beam

d

d998400

d998400998400

d998400998400998400

Figure 13 Cross-section of a hybrid composite beam

exact material quantity the hybrid composite beam designwas carried out based on the strain compatibility methodEquations (1) and (2) are the mean stress factor 120572 and thecentroid factor 120574 for any strain 120576

119888119898at the extreme com-

pression fiber calculated based on stress-strain relationshipEquations (3) and (5) represent the equilibrium equations ofcompressive and tensile forces at yield limit and maximumload limit state respectively The nominal moment capacitiesof a hybrid composite beam at yield limit andmaximum loadlimit state are calculated by (4) and (6) respectively Figures14 and 15 represent strain and stress diagram at yield limitand maximum load limit state respectively In both figuresblack color indicates steels and reinforcement rebars wereplasticized (yielded) while white color represents structuralmembers remained elastic The structural quantity requiredby apartment buildings with hybrid composite frames wasobtained from (6) and compared with that of conventionalbuildings with bearing walls as shown in Table 5 These

Mathematical Problems in Engineering 11

Table 5 Evaluation of structural systems

Buildingcomponent System Gross area Building material CO2 emission Energy consumption Cr6+ emission

Concrete(HPF = 35MPaBW = 25MPa)

HPF 9236m2 038m3m2 691(minus309) 1362 kg-CO2m

2 775(minus225) 10060MJm2 786

(minus214) 11062mgm2 689(minus311)

BW 6513m2 055m3m2 1000 1758 kg-CO2m2 1000 12796MJm2 1000 16061mgm2 100

Reinforcements HPF 9236m2 053 kNm2 726(minus274) 1445 kg-CO2m

2 724(minus276) 19314MJm2 713

(minus287) mdash mdash

BW 6513m2 073 kNm2 1000 1996 kg-CO2m2 1000 27107MJm2 1000 mdash mdash

Steel section HPF 9236m2 007 kNm2 1000 206 kg-CO2m2 1000 2721MJm2 1000 mdash mdash

BW 6513m2 mdashkNm2 mdash mdashkg-CO2m2 mdash mdashMJm2 mdash mdash mdash

lowastHPF hybrid precast frames BW bearing wall

400 MPa

301 MPa

1354 mm

120576st = 0001506

120576t = 120576y = 0002

120576c = 000178 f998400c

120576998400t = 000096 120576tEs = 192MPa

Figure 14 Strain and stress diagram at yield limit state

120576tEs = 286MPa

400 MPa

325 MPa

11946 mm

120576st = 000328

120576t = 120576y = 00042

120576c = 0003f998400c

120576998400t = 000143

Figure 15 Strain and stress diagram at maximum load limit state

equations would help engineer estimate precise constructionmaterials and understand how buildings with hybrid com-posite frames behave Consider

120572 = (int

0002

0

119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

119891

1015840

1198881 minus 100 (120576

119888minus 120576

119888119900) 119889120576

119888)

times (119891

1015840

119888120576

119888119898)

minus1

(1)

120574 = 1 minus ((int

0002

0

120576

119888119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

120576

119888119891

1015840

1198881 minus 100 (120576

119888minus 120576

119888119900) 119889120576

119888)

times (120576

119888119898[int

0002

0

119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

119891

1015840

1198881minus100 (120576

119888minus120576

119888119900) 119889120576

119888])

minus1

)

(2)

120572119891

1015840

119888119887119888 + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840) +

1

2

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

= 119860

119904119865

119910+ 119860

119891119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

1

2

119860

119908119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891)

(3)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908= 119905

119908(119889 minus 119888 minus 119889

1015840minus 119905

119891)

119872

119899= 120572119891

1015840

119888119887119888 (119888 minus 120574119888) + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840)

2

+

1

3

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

2

+ 119860

119904119865

119910(119889 minus 119888)

12 Mathematical Problems in Engineering

DayProcess

One floor

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7

Marking

Rebar work (wall)

Wall form installation

Slab form installation

Rebar work (slab) Electrical and mechanical

facilities (slab) Cleaning and pouring

Figure 16 Processes for constructing one floor of a conventional wall-type apartment building [20]

+ 119860

119891119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891) (119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

119905

119891

2

(119889 minus 119888 minus 119889

1015840minus

119905

119891

3

)

+

1

3

119860

119908119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891)

2

(4)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908= 119905

119908(119889 minus 119888 minus 119889

1015840minus 119905

119891)

120572119891

1015840

119888119887119888 + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840) +

1

2

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

= 119860

119904119865

119910+ 119860

119891119865

119910+ 119860

119908119901119865

119910+

1

2

119860

119908119899119910119864

119904120576

119904119910

(5)

where1198601015840119908= 119905

119908(119888minus119889

101584010158401015840)119860119908119901

= 119905

119908(119889minus119888+119889

1015840+119905

119891)+(120576

119904119910120576

119888)119888

119860

119908119899119910= 119905

119908(120576

119904119910120576

119888)119888

119872

119899= 120572119891

1015840

119888119887119888 (119888 minus 120574119888) + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840)

2

+

1

3

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

2

+ 119860

119904119865

119910(119889 minus 119888)

+ 119860

119891119865

119910(119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

1

2

119860

119908119901119865

119910(119889 minus 119888 minus 119889

1015840minus 119905

119891) +

120576

119904119910

120576

119888

119888

+

1

3

119860

119908119899119910119864

119904

(120576

119904119910)

2

120576

119888

119888

(6)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908119901

= 119905

119908119889 minus (119888 + 119889

1015840+ (120576

119904119910120576

119888)119888)

119860

119908119899119910= 119905

119908(120576

119904119910120576

119888)119888

A completed bearing wall apartment building wasselected for this comparison Apartment buildings withhybrid precast frames and bearingwall frameswere evaluatedin terms of building material CO

2emission energy con-

sumption and Cr6+ emission shown in Table 5 Construction

materials per square meters were calculated based on (5) and(6)whichwere then used to calculate the quantities of Table 5

The building materials of concrete and reinforcementsof apartment buildings with hybrid precast frames werereduced by 31 and 27 respectively compared with thatof bearing wall frame buildings The CO

2emission energy

consumption andCr6+ emission of apartment buildings withhybrid precast frames were also decreased compared withbearing wall frame buildings as shown in Table 5 exhibitingthe efficiency of using gravity hybrid precast frames forapartment buildings

6 Reduction in Construction Schedule

Figures 16 and 17 compare the construction time frames basedon the use of conventional bearing walls versus the proposedhybrid frames

The construction time is the sum of each critical path asshown in

119899

sum

119894=1

(CA119894) = CA

1+ CA2+ CA3+ CA4sdot sdot sdot (7)

The critical paths that affect construction time for abearing wall apartment are CA

1(marking 1 day) CA

2(rebar

work wall 1 day) CA3(wall form installation 2 days)

CA4(slab form installation 1 day) CA

5(rebar work slab 1

day) and CA6(cleaning and pouring 1 day) Installation of

electrical and mechanical facilities at the slab is performedwith rebar work of the slab and takes less time than that ofrebar work Electrical and mechanical facilities at the slab aretherefore excluded from the critical path The constructiontime per floor is seven days based on (7) The criticalpaths affecting construction time for an apartment buildingusing hybrid frames are CA

1(rebar work core wall 05

days) CA2(column-beam unit installation (1 day) beam

unit installation (15 days)) CA3(rebar work slab 05 days)

and CA4(cleaning and pouring 05 days) Column-beam

unit installation and beam unit installation are carried outalternately Beams are only installed at every second andthird floor since columns are erected as a three-story unit

Mathematical Problems in Engineering 13

DayProcess

First floor Second floor Third floor

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 Day 10

Rebar work (core wall)

Core wall form installationColumn-beam unit

installation Beam unit installation

Deck plate installation

Joint form installation

Rebar work (slab) Electrical and mechanical

facilities (slab) Cleaning and pouring

Figure 17 Processes for constructing three floors of an apartment building using hybrid frames [20]

Table 6 Comparative analysis of the construction period [20]

Structuraltype

Construction periodComparisonTypical

floor30-story apartment

building

Bearing wall 7 days1 floor 210 Days 1000Hybrid precastframe

10 days3floors 100 Days 476

As a result of the critical paths analysis the constructiontime per floor is four days for the first floor and threedays for the next two floors requiring ten days for theconstruction of three floors utilizing columns of a three-story unit The time for frame erection was reduced by 52when using hybrid frames highlighting their economic andconstruction benefits Erection of structural frames for onefloor using conventional bearing walls involves rebar workand concrete pouring and requires about seven days asshown in Figure 16 In contrast only three days were requiredto install wall and slab forms indicating that the overallconstruction was influenced by form work which is highlydependent on work skill However erection of three floorswith hybrid precast frames required only ten days whenthree-story hybrid precast columns were erected at one liftThe significant reduction in form work contributed to thedecrease in overall construction time obtained when usingthe hybrid precast frames as shown in Figure 17 As shown inTable 6 frame erection of a 30-story building required sevendays per floor or 210 days for the entire building when usingconventional bearing walls However only ten days per threefloors (or 100 days for the entire building) were required forframe erection of the building with hybrid precast frameswhich corresponds to a 524 reduction in frame erectiontime

7 Conclusions

This study described and characterized an optimized hybridprecast composite structural system for gravity systemMajorcontributions are summarized below

(1) Gravity hybrid precast frames were presented Thesehybrid frames consist of precast concrete and steelwhich can be erected at a speed similar to that of steelframes Steel sections inserted in precast columns andbeams are used as erection steel components

(2) Mathematical model of gravity hybrid precast beamwas presented at yield limit state and maximum loadlimit state Neutral axis of postyield state found fromequilibrium equations was used to calculate nominalmoment capacities of a hybrid composite beam atboth limit state

(3) The new building frame systems for gravity load-ings fabricated with hybrid precast composite framesconsisting of simple connections between columnsand beams were proposed in this paper The dualframe systems of moment connections with muchmore complicated construction details required sig-nificant time and costs than that of building framesystems of gravity loadings However the gravityhybrid precast composite structures will provide sim-plified construction method while enhancing econ-omyduring constructionThe reductions of construc-tion resources including concrete and reinforcements(31 reduction of concrete and 27 reduction of rein-forcements) were achieved when apartments were tobe built with hybrid precast frames

(4) The gravity hybrid precast frames use less construc-tion materials than conventional frames and there-fore reduce carbon dioxide and hazardous substanceemissions compared to conventional frames It was

14 Mathematical Problems in Engineering

observed the efficiency of using gravity hybrid precastframes for apartment building which decreased theCO2emission (23 reduction of concrete and 28

reduction of reinforcements) energy consumption(21 reduction of concrete and 29 reduction ofreinforcements) and Cr6+ emission compared withbearing wall frame buildings The use of gravityhybrid precast frames was demonstrated to providebetter solutions for environments and economy thanthat of conventional buildings

(5) Dynamic analysis of a 15-story building designedwith the proposed composite gravity frames was per-formed to characterize frequencies and mode shapesof the building for seismic design purposes

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by Grant from the Kyung HeeUniversity in 2013 (KHU-20130363)

References

[1] J F Hajjar ldquoComposite steel and concrete structural systems forseismic engineeringrdquo Journal of Constructional Steel Researchvol 58 no 5ndash8 pp 703ndash723 2002

[2] G Fabbrocino G Manfredi and E Cosenza ldquoDuctility ofcomposite beams under negative bending an equivalence indexfor reinforcing steel classificationrdquo Journal of ConstructionalSteel Research vol 58 no 2 pp 185ndash202 2001

[3] B Yang and K Tan ldquoBehaviour of composite beam-columnjoints under a middle-column-removal scenario experimentaltestsrdquo Journal of Structural Engineering vol 140 no 2 ArticleID 04013045 2014

[4] L Tesser and R Scotta ldquoFlexural and shear capacity of compos-ite steel truss and concrete beams with inferior precast concretebaserdquo Engineering Structures vol 49 pp 135ndash145 2013

[5] H J Hwang H G Park C H Lee et al ldquoSeismic resistanceof concrete-filled U-shaped steel beam-to-RC column connec-tionsrdquo Journal of Korean Society of Steel Construction vol 23 pp83ndash97 2011

[6] J Hassan and B Khosrow ldquoNonlinear seismic behavior evalua-tion of ductile beam-column connections in precast concreterdquoInternational Journal of Civil and Structural Engineering vol 1pp 445ndash453 2011

[7] A M Ioani and E Tripa ldquoStructural behavior of an innovativeall-precast concrete dual system for residential buildingsrdquo PCIJournal vol 57 no 1 pp 110ndash123 2012

[8] C Chou andCUang ldquoEffects of continuity plate and transversereinforcement on cyclic behavior of SRCmoment connectionsrdquoJournal of Structural Engineering vol 133 no 1 pp 96ndash104 2007

[9] Y K Ju and S D Kim ldquoStructural behavior of alternative lowfloor height system using structural ldquoteerdquo half precast concreteand horizontal studrdquoCanadian Journal of Civil Engineering vol32 no 2 pp 329ndash338 2005

[10] X Wang M Truijens L Hou Y Wang and Y Zhou ldquoInte-grating augmented reality with building informationmodelingonsite construction process controlling for liquefied natural gasindustryrdquoAutomation in Construction vol 40 pp 96ndash105 2014

[11] L Hou Y Wang X Wang et al ldquoCombining photogrammetryand augmented reality towards an integrated facility manage-ment system for the oil industryrdquo Proceedings of the IEEE vol102 no 2 pp 204ndash220 2014

[12] L Hou XWang L Bernold and P E D Love ldquoUsing animatedaugmented reality to cognitively guide assemblyrdquo Journal ofComputing in Civil Engineering vol 27 no 5 pp 439ndash451 2013

[13] YWang XWang JWang P Yung andG Jun ldquoEngagement offacilities management in design stage through BIM frameworkand a case studyrdquo Advances in Civil Engineering vol 2013Article ID 189105 8 pages 2013

[14] W K Hong J M Kim S C Park et al ldquoA new apartmentconstruction technology with effective CO

2emission reduction

capabilitiesrdquo Energy vol 35 no 6 pp 2639ndash2646 2010[15] W Hong S Park J Kim et al ldquoDevelopment of structural

composite hybrid systems and their application with regard tothe reduction of CO

2emissionsrdquo Indoor and Built Environment

vol 19 no 1 pp 151ndash162 2010[16] W Hong S Jeong S Park and J T Kim ldquoExperimental

investigation of an energy-efficient hybrid composite beamduring the construction phaserdquo Energy and Buildings vol 46pp 37ndash47 2012

[17] G P Hammond and C I Jones Inventory of Carbon amp Energy(ICE) Department of Mechanical Engineering University ofBath Bath UK 2008

[18] G P Hammond and C I Jones ldquoEmbodied energy and carbonin construction materialsrdquo Proceedings of Institution of CivilEngineers Energy vol 161 no 2 pp 87ndash98 2008

[19] National Institute of Environment Research (NIER) Domesticand foreign cement heavy metal analysis result (May 2013)NIER 2013 httpwwwniergokrericportalkornfnier-nf-02page

[20] S Kim W Hong J Kim and J T Kim ldquoThe developmentof modularized construction of enhanced precast compositestructural systems (Smart Green frame) and its embeddedenergy efficiencyrdquo Energy and Buildings vol 66 pp 16ndash21 2013

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Mathematical Problems in Engineering

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6 Mathematical Problems in Engineering

X-direction00111 m

(H39099)

Midas genpostprocessordisplacement

resultant

Scale factor =

110700e minus 002100636e minus 002905726e minus 003805090e minus 003704454e minus 003603817e minus 003503181e minus 003402545e minus 003301909e minus 003201272e minus 003100636e minus 003000000e + 000

26266E + 002

(a)

Y-direction00222 m

(H19549)

Midas genpostprocessordisplacement

resultant

Scale factor =

222476e minus 002202251e minus 002182025e minus 002161800e minus 002141575e minus 002121350e minus 002101125e minus 002809002e minus 003606752e minus 003404501e minus 003202251e minus 003000000e + 000

13069E + 002

(b)

Figure 7 Wind displacement

0

0002

0004

0006

0008

001

0012

0014

0016

17F

16F

15F

14F

13F

12F

11F

10F 9F 8F 7F 6F 5F 4F 3F 2F 1F

Story drift ratioAllowable story drift ratio

Story drift ratio (x-axis)

(a)

17F

16F

15F

14F

13F

12F

11F

10F 9F 8F 7F 6F 5F 4F 3F 2F 1F

Story drift ratioAllowable story drift ratio

0

0002

0004

0006

0008

001

0012

0014

0016Story drift ratio (y-axis)

(b)

Figure 8 Story drift

the proposed composite frames and selected for dynamicanalysis The floor plan and elevation with framing usingcomposite columns and beams are also shown The buildingwas designed such that the shear walls were resistant to lateralseismic loadings while the frames resisted only vertical loadsDynamic analysis was performed to investigate the influenceof the design and size of the composite frames on the dynamiccharacteristics of the building

Figure 10 shows a computer model of the building withcomposite frames andwalls in which the steel sections at bothends of the beams are connected to steel inserted betweentwo precast columns Figure 10(a) shows gravity compositeframes attached to shear walls that are responsible for lateralearthquake loading Figure 10(b) shows close connectiondetails of the frames and walls that constitute the building

frame Figure 10(c) shows steel frames and connectionsbetween beams and columns The material structural andconstruction hybrid applications were integrated to combinethe constructability of steel structures with the economy ofconcrete structures

Tables 1 and 2 show modal participation masses andeigenvalue results respectively The fundamental transla-tional mode was found in the third return period the firstand second modes were considered to be mixed translationalmodes with torsion A fundamental translational mode of 15seconds along with a weak 119910-axis was deemed reasonableThe fundamental period and mode shapes for the compositeframe were more similar to those of steel structures thanthose of concrete structures indicating that the structuralbehavior of a building with composite frames and steel

Mathematical Problems in Engineering 7

7400

17750

3500

3500

3500

3500

3500

3500

3000

2400

X

Y

2900

2900

X6

X6

X7

X8

X9

X10

2900

4100

39200

14001400

14600

6300 63002000

PS

PS

PSPS

PSPS

PS

PS PS

PSPS

PS

PS

PS

PSPS

PSPS

PSPS

PS

PSPS

PS

PS

PSPS

PS

PS

PS

PS

PS

PSPS

PS

PS

PS

PS

PS

PS

PS

329

0

4928

3500

3500

3500

3500

3500

3500

6300

1300

1300

5000

5000

6300

14600

X1

X2

X3

2000

25928

350

0

350

03

500

350

03

500

350

03

500

350

03

500

350

03

500

700

07

000

700

07

000

700

0

417

90

PS

PS

PS

PS

PS PS

PSPS

Hal

l

PS

PS

49004900

Y3998400

Y4998400

Y5998400

Y6998400

(a)

Figure 9 Continued

8 Mathematical Problems in Engineering

1447

1500

7200

3600

3600

3800

2900

2900

2900

2900

2900

2900

2900

2900

2900

2900

2900

1

29001400

1500 1

0003600

23003600

3800

2900

2600

1300

3200

1600700

600

2900

2900

2900

2900

2900

2900

2900

2900

2900

2900

29001400

40000

2880

2880

920

5100700061508300 6300

6300 630020002150 4150

5382

1447

2250

2250

2250

2250

2250

2250

2250

2250

2250

2250

2250

2250

3200 2400

2300

1600

GL-1800

GL-6000

510070006150146005382

(b)

Figure 9 Floor plan and elevation

Mathematical Problems in Engineering 9

Table 1 Modal participation masses

Mode number TRAN-119883 TRAN-119884 ROTN-119885Mass () Sum () Mass () Sum () Mass () Sum ()

1 405909 405909 02185 02185 127252 1272522 42570 448478 16208 164265 203361 3306123 40667 489145 328629 492893 82552 4131644 96703 585848 01847 49474 40557 4537215 32088 617935 03965 498705 87600 5413216 03685 621620 158676 657381 05207 546528

(a) (b) (c)

Figure 10 Computer model of the building

Table 2 Eigenvalue analysis (fundamental period)

Mode number Frequency Period Tolerance(radsec) (cyclesec) (sec)

1 34768 05533 34768 00000119890 + 000

2 41078 06538 41078 00000119890 + 000

3 53487 08513 53487 00000119890 + 000

4 138311 22013 138311 45251119890 minus 161

5 178259 28371 178259 28518119890 minus 150

6 236726 37676 236726 15909119890 minus 137

joints against vertical and lateral loadings resembles that ofsteel structures even though the building has an externalappearance of a concrete structure

Figure 11 shows the first translational mode (a) and thoseof two mixed modes ((b) (c)) Figures 11(d) 11(e) and 11(f)show these modes from the top view respectively

5 Reduction of Structural Quantity andEmissions of Environmentally HazardousSubstances and Materials

This study evaluated chromium VI and carbon dioxide emis-sions of the building constructed with the proposed framesand conventional walls Reductions in energy consumptiondue to reduction in material quantity were estimated basedon comparison of an apartment building constructed withhybrid precast frames and that of a conventional bearing-wallbuilding

Original units of major building components (Table 3)which were announced in 2008 by the United Kingdom

Table 3 Emissions and energy usage of major building components[17]

Buildingcomponent

CO2 emissionsper original unit

Energy consumptionper original unit

Concrete 25MPa 3196 kg-CO2m3 23265MJm3

Concrete 35MPa 37835 kg-CO2m3 26555MJm3

Reinforcement 27319 kg-CO2kN 371050MJkNSteel section 28338 kg-CO2kN 375127MJkN

Inventory of Carbon and Energy (ICE) were used to evaluatecarbon dioxide emissions and the energy efficiency of theproposed construction The embodied energy 119864 and carbonemissions per kN for the calculated material quantity areobtained from the University of Bathrsquos ICE database [17 18]The ICE has been structured into 34 main material groupsThe database also provides the embodied energy and carboncoefficients for construction materials Table 3 presents theconverted embodied energy and carbon coefficients for fourbuilding components concrete (25MPa) concrete (35MPa)reinforcement and steel section

Domestic and foreign cement heavymetal analysis results(May 2013) published by the Korea National Institute ofEnvironment Research (NIER) were utilized to evaluatechromium VI emissions (Table 4)

In order to explain how the data that evaluates the gravitysystem presented in this paper in terms of material quantityanalytical approach for the hybrid precast composite beamdesign based on the strain compatibility method was intro-duced Figures 12 and 13 illustrate the side view and cross-section of a hybrid composite beam In order to determine the

10 Mathematical Problems in Engineering

Table 4 Heavy metal content standards in cement [19]

Cr6+ As Cd Cu Hg PbAve (May 2013) 1063mgkg 1287mgkg 102mgkg 8903mgkg 061mgkg 3284mgkg

(a) Fundamental translational mode (b) Mixed mode 1 (c) Mixed mode 2

(d) Fundamental translational mode (e) Mixed mode 1 (f) Mixed mode 2

Figure 11 Mode shapes

Figure 12 Side view of a hybrid composite beam

d

d998400

d998400998400

d998400998400998400

Figure 13 Cross-section of a hybrid composite beam

exact material quantity the hybrid composite beam designwas carried out based on the strain compatibility methodEquations (1) and (2) are the mean stress factor 120572 and thecentroid factor 120574 for any strain 120576

119888119898at the extreme com-

pression fiber calculated based on stress-strain relationshipEquations (3) and (5) represent the equilibrium equations ofcompressive and tensile forces at yield limit and maximumload limit state respectively The nominal moment capacitiesof a hybrid composite beam at yield limit andmaximum loadlimit state are calculated by (4) and (6) respectively Figures14 and 15 represent strain and stress diagram at yield limitand maximum load limit state respectively In both figuresblack color indicates steels and reinforcement rebars wereplasticized (yielded) while white color represents structuralmembers remained elastic The structural quantity requiredby apartment buildings with hybrid composite frames wasobtained from (6) and compared with that of conventionalbuildings with bearing walls as shown in Table 5 These

Mathematical Problems in Engineering 11

Table 5 Evaluation of structural systems

Buildingcomponent System Gross area Building material CO2 emission Energy consumption Cr6+ emission

Concrete(HPF = 35MPaBW = 25MPa)

HPF 9236m2 038m3m2 691(minus309) 1362 kg-CO2m

2 775(minus225) 10060MJm2 786

(minus214) 11062mgm2 689(minus311)

BW 6513m2 055m3m2 1000 1758 kg-CO2m2 1000 12796MJm2 1000 16061mgm2 100

Reinforcements HPF 9236m2 053 kNm2 726(minus274) 1445 kg-CO2m

2 724(minus276) 19314MJm2 713

(minus287) mdash mdash

BW 6513m2 073 kNm2 1000 1996 kg-CO2m2 1000 27107MJm2 1000 mdash mdash

Steel section HPF 9236m2 007 kNm2 1000 206 kg-CO2m2 1000 2721MJm2 1000 mdash mdash

BW 6513m2 mdashkNm2 mdash mdashkg-CO2m2 mdash mdashMJm2 mdash mdash mdash

lowastHPF hybrid precast frames BW bearing wall

400 MPa

301 MPa

1354 mm

120576st = 0001506

120576t = 120576y = 0002

120576c = 000178 f998400c

120576998400t = 000096 120576tEs = 192MPa

Figure 14 Strain and stress diagram at yield limit state

120576tEs = 286MPa

400 MPa

325 MPa

11946 mm

120576st = 000328

120576t = 120576y = 00042

120576c = 0003f998400c

120576998400t = 000143

Figure 15 Strain and stress diagram at maximum load limit state

equations would help engineer estimate precise constructionmaterials and understand how buildings with hybrid com-posite frames behave Consider

120572 = (int

0002

0

119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

119891

1015840

1198881 minus 100 (120576

119888minus 120576

119888119900) 119889120576

119888)

times (119891

1015840

119888120576

119888119898)

minus1

(1)

120574 = 1 minus ((int

0002

0

120576

119888119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

120576

119888119891

1015840

1198881 minus 100 (120576

119888minus 120576

119888119900) 119889120576

119888)

times (120576

119888119898[int

0002

0

119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

119891

1015840

1198881minus100 (120576

119888minus120576

119888119900) 119889120576

119888])

minus1

)

(2)

120572119891

1015840

119888119887119888 + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840) +

1

2

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

= 119860

119904119865

119910+ 119860

119891119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

1

2

119860

119908119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891)

(3)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908= 119905

119908(119889 minus 119888 minus 119889

1015840minus 119905

119891)

119872

119899= 120572119891

1015840

119888119887119888 (119888 minus 120574119888) + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840)

2

+

1

3

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

2

+ 119860

119904119865

119910(119889 minus 119888)

12 Mathematical Problems in Engineering

DayProcess

One floor

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7

Marking

Rebar work (wall)

Wall form installation

Slab form installation

Rebar work (slab) Electrical and mechanical

facilities (slab) Cleaning and pouring

Figure 16 Processes for constructing one floor of a conventional wall-type apartment building [20]

+ 119860

119891119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891) (119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

119905

119891

2

(119889 minus 119888 minus 119889

1015840minus

119905

119891

3

)

+

1

3

119860

119908119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891)

2

(4)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908= 119905

119908(119889 minus 119888 minus 119889

1015840minus 119905

119891)

120572119891

1015840

119888119887119888 + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840) +

1

2

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

= 119860

119904119865

119910+ 119860

119891119865

119910+ 119860

119908119901119865

119910+

1

2

119860

119908119899119910119864

119904120576

119904119910

(5)

where1198601015840119908= 119905

119908(119888minus119889

101584010158401015840)119860119908119901

= 119905

119908(119889minus119888+119889

1015840+119905

119891)+(120576

119904119910120576

119888)119888

119860

119908119899119910= 119905

119908(120576

119904119910120576

119888)119888

119872

119899= 120572119891

1015840

119888119887119888 (119888 minus 120574119888) + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840)

2

+

1

3

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

2

+ 119860

119904119865

119910(119889 minus 119888)

+ 119860

119891119865

119910(119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

1

2

119860

119908119901119865

119910(119889 minus 119888 minus 119889

1015840minus 119905

119891) +

120576

119904119910

120576

119888

119888

+

1

3

119860

119908119899119910119864

119904

(120576

119904119910)

2

120576

119888

119888

(6)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908119901

= 119905

119908119889 minus (119888 + 119889

1015840+ (120576

119904119910120576

119888)119888)

119860

119908119899119910= 119905

119908(120576

119904119910120576

119888)119888

A completed bearing wall apartment building wasselected for this comparison Apartment buildings withhybrid precast frames and bearingwall frameswere evaluatedin terms of building material CO

2emission energy con-

sumption and Cr6+ emission shown in Table 5 Construction

materials per square meters were calculated based on (5) and(6)whichwere then used to calculate the quantities of Table 5

The building materials of concrete and reinforcementsof apartment buildings with hybrid precast frames werereduced by 31 and 27 respectively compared with thatof bearing wall frame buildings The CO

2emission energy

consumption andCr6+ emission of apartment buildings withhybrid precast frames were also decreased compared withbearing wall frame buildings as shown in Table 5 exhibitingthe efficiency of using gravity hybrid precast frames forapartment buildings

6 Reduction in Construction Schedule

Figures 16 and 17 compare the construction time frames basedon the use of conventional bearing walls versus the proposedhybrid frames

The construction time is the sum of each critical path asshown in

119899

sum

119894=1

(CA119894) = CA

1+ CA2+ CA3+ CA4sdot sdot sdot (7)

The critical paths that affect construction time for abearing wall apartment are CA

1(marking 1 day) CA

2(rebar

work wall 1 day) CA3(wall form installation 2 days)

CA4(slab form installation 1 day) CA

5(rebar work slab 1

day) and CA6(cleaning and pouring 1 day) Installation of

electrical and mechanical facilities at the slab is performedwith rebar work of the slab and takes less time than that ofrebar work Electrical and mechanical facilities at the slab aretherefore excluded from the critical path The constructiontime per floor is seven days based on (7) The criticalpaths affecting construction time for an apartment buildingusing hybrid frames are CA

1(rebar work core wall 05

days) CA2(column-beam unit installation (1 day) beam

unit installation (15 days)) CA3(rebar work slab 05 days)

and CA4(cleaning and pouring 05 days) Column-beam

unit installation and beam unit installation are carried outalternately Beams are only installed at every second andthird floor since columns are erected as a three-story unit

Mathematical Problems in Engineering 13

DayProcess

First floor Second floor Third floor

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 Day 10

Rebar work (core wall)

Core wall form installationColumn-beam unit

installation Beam unit installation

Deck plate installation

Joint form installation

Rebar work (slab) Electrical and mechanical

facilities (slab) Cleaning and pouring

Figure 17 Processes for constructing three floors of an apartment building using hybrid frames [20]

Table 6 Comparative analysis of the construction period [20]

Structuraltype

Construction periodComparisonTypical

floor30-story apartment

building

Bearing wall 7 days1 floor 210 Days 1000Hybrid precastframe

10 days3floors 100 Days 476

As a result of the critical paths analysis the constructiontime per floor is four days for the first floor and threedays for the next two floors requiring ten days for theconstruction of three floors utilizing columns of a three-story unit The time for frame erection was reduced by 52when using hybrid frames highlighting their economic andconstruction benefits Erection of structural frames for onefloor using conventional bearing walls involves rebar workand concrete pouring and requires about seven days asshown in Figure 16 In contrast only three days were requiredto install wall and slab forms indicating that the overallconstruction was influenced by form work which is highlydependent on work skill However erection of three floorswith hybrid precast frames required only ten days whenthree-story hybrid precast columns were erected at one liftThe significant reduction in form work contributed to thedecrease in overall construction time obtained when usingthe hybrid precast frames as shown in Figure 17 As shown inTable 6 frame erection of a 30-story building required sevendays per floor or 210 days for the entire building when usingconventional bearing walls However only ten days per threefloors (or 100 days for the entire building) were required forframe erection of the building with hybrid precast frameswhich corresponds to a 524 reduction in frame erectiontime

7 Conclusions

This study described and characterized an optimized hybridprecast composite structural system for gravity systemMajorcontributions are summarized below

(1) Gravity hybrid precast frames were presented Thesehybrid frames consist of precast concrete and steelwhich can be erected at a speed similar to that of steelframes Steel sections inserted in precast columns andbeams are used as erection steel components

(2) Mathematical model of gravity hybrid precast beamwas presented at yield limit state and maximum loadlimit state Neutral axis of postyield state found fromequilibrium equations was used to calculate nominalmoment capacities of a hybrid composite beam atboth limit state

(3) The new building frame systems for gravity load-ings fabricated with hybrid precast composite framesconsisting of simple connections between columnsand beams were proposed in this paper The dualframe systems of moment connections with muchmore complicated construction details required sig-nificant time and costs than that of building framesystems of gravity loadings However the gravityhybrid precast composite structures will provide sim-plified construction method while enhancing econ-omyduring constructionThe reductions of construc-tion resources including concrete and reinforcements(31 reduction of concrete and 27 reduction of rein-forcements) were achieved when apartments were tobe built with hybrid precast frames

(4) The gravity hybrid precast frames use less construc-tion materials than conventional frames and there-fore reduce carbon dioxide and hazardous substanceemissions compared to conventional frames It was

14 Mathematical Problems in Engineering

observed the efficiency of using gravity hybrid precastframes for apartment building which decreased theCO2emission (23 reduction of concrete and 28

reduction of reinforcements) energy consumption(21 reduction of concrete and 29 reduction ofreinforcements) and Cr6+ emission compared withbearing wall frame buildings The use of gravityhybrid precast frames was demonstrated to providebetter solutions for environments and economy thanthat of conventional buildings

(5) Dynamic analysis of a 15-story building designedwith the proposed composite gravity frames was per-formed to characterize frequencies and mode shapesof the building for seismic design purposes

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by Grant from the Kyung HeeUniversity in 2013 (KHU-20130363)

References

[1] J F Hajjar ldquoComposite steel and concrete structural systems forseismic engineeringrdquo Journal of Constructional Steel Researchvol 58 no 5ndash8 pp 703ndash723 2002

[2] G Fabbrocino G Manfredi and E Cosenza ldquoDuctility ofcomposite beams under negative bending an equivalence indexfor reinforcing steel classificationrdquo Journal of ConstructionalSteel Research vol 58 no 2 pp 185ndash202 2001

[3] B Yang and K Tan ldquoBehaviour of composite beam-columnjoints under a middle-column-removal scenario experimentaltestsrdquo Journal of Structural Engineering vol 140 no 2 ArticleID 04013045 2014

[4] L Tesser and R Scotta ldquoFlexural and shear capacity of compos-ite steel truss and concrete beams with inferior precast concretebaserdquo Engineering Structures vol 49 pp 135ndash145 2013

[5] H J Hwang H G Park C H Lee et al ldquoSeismic resistanceof concrete-filled U-shaped steel beam-to-RC column connec-tionsrdquo Journal of Korean Society of Steel Construction vol 23 pp83ndash97 2011

[6] J Hassan and B Khosrow ldquoNonlinear seismic behavior evalua-tion of ductile beam-column connections in precast concreterdquoInternational Journal of Civil and Structural Engineering vol 1pp 445ndash453 2011

[7] A M Ioani and E Tripa ldquoStructural behavior of an innovativeall-precast concrete dual system for residential buildingsrdquo PCIJournal vol 57 no 1 pp 110ndash123 2012

[8] C Chou andCUang ldquoEffects of continuity plate and transversereinforcement on cyclic behavior of SRCmoment connectionsrdquoJournal of Structural Engineering vol 133 no 1 pp 96ndash104 2007

[9] Y K Ju and S D Kim ldquoStructural behavior of alternative lowfloor height system using structural ldquoteerdquo half precast concreteand horizontal studrdquoCanadian Journal of Civil Engineering vol32 no 2 pp 329ndash338 2005

[10] X Wang M Truijens L Hou Y Wang and Y Zhou ldquoInte-grating augmented reality with building informationmodelingonsite construction process controlling for liquefied natural gasindustryrdquoAutomation in Construction vol 40 pp 96ndash105 2014

[11] L Hou Y Wang X Wang et al ldquoCombining photogrammetryand augmented reality towards an integrated facility manage-ment system for the oil industryrdquo Proceedings of the IEEE vol102 no 2 pp 204ndash220 2014

[12] L Hou XWang L Bernold and P E D Love ldquoUsing animatedaugmented reality to cognitively guide assemblyrdquo Journal ofComputing in Civil Engineering vol 27 no 5 pp 439ndash451 2013

[13] YWang XWang JWang P Yung andG Jun ldquoEngagement offacilities management in design stage through BIM frameworkand a case studyrdquo Advances in Civil Engineering vol 2013Article ID 189105 8 pages 2013

[14] W K Hong J M Kim S C Park et al ldquoA new apartmentconstruction technology with effective CO

2emission reduction

capabilitiesrdquo Energy vol 35 no 6 pp 2639ndash2646 2010[15] W Hong S Park J Kim et al ldquoDevelopment of structural

composite hybrid systems and their application with regard tothe reduction of CO

2emissionsrdquo Indoor and Built Environment

vol 19 no 1 pp 151ndash162 2010[16] W Hong S Jeong S Park and J T Kim ldquoExperimental

investigation of an energy-efficient hybrid composite beamduring the construction phaserdquo Energy and Buildings vol 46pp 37ndash47 2012

[17] G P Hammond and C I Jones Inventory of Carbon amp Energy(ICE) Department of Mechanical Engineering University ofBath Bath UK 2008

[18] G P Hammond and C I Jones ldquoEmbodied energy and carbonin construction materialsrdquo Proceedings of Institution of CivilEngineers Energy vol 161 no 2 pp 87ndash98 2008

[19] National Institute of Environment Research (NIER) Domesticand foreign cement heavy metal analysis result (May 2013)NIER 2013 httpwwwniergokrericportalkornfnier-nf-02page

[20] S Kim W Hong J Kim and J T Kim ldquoThe developmentof modularized construction of enhanced precast compositestructural systems (Smart Green frame) and its embeddedenergy efficiencyrdquo Energy and Buildings vol 66 pp 16ndash21 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 7

7400

17750

3500

3500

3500

3500

3500

3500

3000

2400

X

Y

2900

2900

X6

X6

X7

X8

X9

X10

2900

4100

39200

14001400

14600

6300 63002000

PS

PS

PSPS

PSPS

PS

PS PS

PSPS

PS

PS

PS

PSPS

PSPS

PSPS

PS

PSPS

PS

PS

PSPS

PS

PS

PS

PS

PS

PSPS

PS

PS

PS

PS

PS

PS

PS

329

0

4928

3500

3500

3500

3500

3500

3500

6300

1300

1300

5000

5000

6300

14600

X1

X2

X3

2000

25928

350

0

350

03

500

350

03

500

350

03

500

350

03

500

350

03

500

700

07

000

700

07

000

700

0

417

90

PS

PS

PS

PS

PS PS

PSPS

Hal

l

PS

PS

49004900

Y3998400

Y4998400

Y5998400

Y6998400

(a)

Figure 9 Continued

8 Mathematical Problems in Engineering

1447

1500

7200

3600

3600

3800

2900

2900

2900

2900

2900

2900

2900

2900

2900

2900

2900

1

29001400

1500 1

0003600

23003600

3800

2900

2600

1300

3200

1600700

600

2900

2900

2900

2900

2900

2900

2900

2900

2900

2900

29001400

40000

2880

2880

920

5100700061508300 6300

6300 630020002150 4150

5382

1447

2250

2250

2250

2250

2250

2250

2250

2250

2250

2250

2250

2250

3200 2400

2300

1600

GL-1800

GL-6000

510070006150146005382

(b)

Figure 9 Floor plan and elevation

Mathematical Problems in Engineering 9

Table 1 Modal participation masses

Mode number TRAN-119883 TRAN-119884 ROTN-119885Mass () Sum () Mass () Sum () Mass () Sum ()

1 405909 405909 02185 02185 127252 1272522 42570 448478 16208 164265 203361 3306123 40667 489145 328629 492893 82552 4131644 96703 585848 01847 49474 40557 4537215 32088 617935 03965 498705 87600 5413216 03685 621620 158676 657381 05207 546528

(a) (b) (c)

Figure 10 Computer model of the building

Table 2 Eigenvalue analysis (fundamental period)

Mode number Frequency Period Tolerance(radsec) (cyclesec) (sec)

1 34768 05533 34768 00000119890 + 000

2 41078 06538 41078 00000119890 + 000

3 53487 08513 53487 00000119890 + 000

4 138311 22013 138311 45251119890 minus 161

5 178259 28371 178259 28518119890 minus 150

6 236726 37676 236726 15909119890 minus 137

joints against vertical and lateral loadings resembles that ofsteel structures even though the building has an externalappearance of a concrete structure

Figure 11 shows the first translational mode (a) and thoseof two mixed modes ((b) (c)) Figures 11(d) 11(e) and 11(f)show these modes from the top view respectively

5 Reduction of Structural Quantity andEmissions of Environmentally HazardousSubstances and Materials

This study evaluated chromium VI and carbon dioxide emis-sions of the building constructed with the proposed framesand conventional walls Reductions in energy consumptiondue to reduction in material quantity were estimated basedon comparison of an apartment building constructed withhybrid precast frames and that of a conventional bearing-wallbuilding

Original units of major building components (Table 3)which were announced in 2008 by the United Kingdom

Table 3 Emissions and energy usage of major building components[17]

Buildingcomponent

CO2 emissionsper original unit

Energy consumptionper original unit

Concrete 25MPa 3196 kg-CO2m3 23265MJm3

Concrete 35MPa 37835 kg-CO2m3 26555MJm3

Reinforcement 27319 kg-CO2kN 371050MJkNSteel section 28338 kg-CO2kN 375127MJkN

Inventory of Carbon and Energy (ICE) were used to evaluatecarbon dioxide emissions and the energy efficiency of theproposed construction The embodied energy 119864 and carbonemissions per kN for the calculated material quantity areobtained from the University of Bathrsquos ICE database [17 18]The ICE has been structured into 34 main material groupsThe database also provides the embodied energy and carboncoefficients for construction materials Table 3 presents theconverted embodied energy and carbon coefficients for fourbuilding components concrete (25MPa) concrete (35MPa)reinforcement and steel section

Domestic and foreign cement heavymetal analysis results(May 2013) published by the Korea National Institute ofEnvironment Research (NIER) were utilized to evaluatechromium VI emissions (Table 4)

In order to explain how the data that evaluates the gravitysystem presented in this paper in terms of material quantityanalytical approach for the hybrid precast composite beamdesign based on the strain compatibility method was intro-duced Figures 12 and 13 illustrate the side view and cross-section of a hybrid composite beam In order to determine the

10 Mathematical Problems in Engineering

Table 4 Heavy metal content standards in cement [19]

Cr6+ As Cd Cu Hg PbAve (May 2013) 1063mgkg 1287mgkg 102mgkg 8903mgkg 061mgkg 3284mgkg

(a) Fundamental translational mode (b) Mixed mode 1 (c) Mixed mode 2

(d) Fundamental translational mode (e) Mixed mode 1 (f) Mixed mode 2

Figure 11 Mode shapes

Figure 12 Side view of a hybrid composite beam

d

d998400

d998400998400

d998400998400998400

Figure 13 Cross-section of a hybrid composite beam

exact material quantity the hybrid composite beam designwas carried out based on the strain compatibility methodEquations (1) and (2) are the mean stress factor 120572 and thecentroid factor 120574 for any strain 120576

119888119898at the extreme com-

pression fiber calculated based on stress-strain relationshipEquations (3) and (5) represent the equilibrium equations ofcompressive and tensile forces at yield limit and maximumload limit state respectively The nominal moment capacitiesof a hybrid composite beam at yield limit andmaximum loadlimit state are calculated by (4) and (6) respectively Figures14 and 15 represent strain and stress diagram at yield limitand maximum load limit state respectively In both figuresblack color indicates steels and reinforcement rebars wereplasticized (yielded) while white color represents structuralmembers remained elastic The structural quantity requiredby apartment buildings with hybrid composite frames wasobtained from (6) and compared with that of conventionalbuildings with bearing walls as shown in Table 5 These

Mathematical Problems in Engineering 11

Table 5 Evaluation of structural systems

Buildingcomponent System Gross area Building material CO2 emission Energy consumption Cr6+ emission

Concrete(HPF = 35MPaBW = 25MPa)

HPF 9236m2 038m3m2 691(minus309) 1362 kg-CO2m

2 775(minus225) 10060MJm2 786

(minus214) 11062mgm2 689(minus311)

BW 6513m2 055m3m2 1000 1758 kg-CO2m2 1000 12796MJm2 1000 16061mgm2 100

Reinforcements HPF 9236m2 053 kNm2 726(minus274) 1445 kg-CO2m

2 724(minus276) 19314MJm2 713

(minus287) mdash mdash

BW 6513m2 073 kNm2 1000 1996 kg-CO2m2 1000 27107MJm2 1000 mdash mdash

Steel section HPF 9236m2 007 kNm2 1000 206 kg-CO2m2 1000 2721MJm2 1000 mdash mdash

BW 6513m2 mdashkNm2 mdash mdashkg-CO2m2 mdash mdashMJm2 mdash mdash mdash

lowastHPF hybrid precast frames BW bearing wall

400 MPa

301 MPa

1354 mm

120576st = 0001506

120576t = 120576y = 0002

120576c = 000178 f998400c

120576998400t = 000096 120576tEs = 192MPa

Figure 14 Strain and stress diagram at yield limit state

120576tEs = 286MPa

400 MPa

325 MPa

11946 mm

120576st = 000328

120576t = 120576y = 00042

120576c = 0003f998400c

120576998400t = 000143

Figure 15 Strain and stress diagram at maximum load limit state

equations would help engineer estimate precise constructionmaterials and understand how buildings with hybrid com-posite frames behave Consider

120572 = (int

0002

0

119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

119891

1015840

1198881 minus 100 (120576

119888minus 120576

119888119900) 119889120576

119888)

times (119891

1015840

119888120576

119888119898)

minus1

(1)

120574 = 1 minus ((int

0002

0

120576

119888119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

120576

119888119891

1015840

1198881 minus 100 (120576

119888minus 120576

119888119900) 119889120576

119888)

times (120576

119888119898[int

0002

0

119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

119891

1015840

1198881minus100 (120576

119888minus120576

119888119900) 119889120576

119888])

minus1

)

(2)

120572119891

1015840

119888119887119888 + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840) +

1

2

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

= 119860

119904119865

119910+ 119860

119891119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

1

2

119860

119908119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891)

(3)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908= 119905

119908(119889 minus 119888 minus 119889

1015840minus 119905

119891)

119872

119899= 120572119891

1015840

119888119887119888 (119888 minus 120574119888) + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840)

2

+

1

3

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

2

+ 119860

119904119865

119910(119889 minus 119888)

12 Mathematical Problems in Engineering

DayProcess

One floor

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7

Marking

Rebar work (wall)

Wall form installation

Slab form installation

Rebar work (slab) Electrical and mechanical

facilities (slab) Cleaning and pouring

Figure 16 Processes for constructing one floor of a conventional wall-type apartment building [20]

+ 119860

119891119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891) (119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

119905

119891

2

(119889 minus 119888 minus 119889

1015840minus

119905

119891

3

)

+

1

3

119860

119908119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891)

2

(4)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908= 119905

119908(119889 minus 119888 minus 119889

1015840minus 119905

119891)

120572119891

1015840

119888119887119888 + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840) +

1

2

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

= 119860

119904119865

119910+ 119860

119891119865

119910+ 119860

119908119901119865

119910+

1

2

119860

119908119899119910119864

119904120576

119904119910

(5)

where1198601015840119908= 119905

119908(119888minus119889

101584010158401015840)119860119908119901

= 119905

119908(119889minus119888+119889

1015840+119905

119891)+(120576

119904119910120576

119888)119888

119860

119908119899119910= 119905

119908(120576

119904119910120576

119888)119888

119872

119899= 120572119891

1015840

119888119887119888 (119888 minus 120574119888) + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840)

2

+

1

3

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

2

+ 119860

119904119865

119910(119889 minus 119888)

+ 119860

119891119865

119910(119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

1

2

119860

119908119901119865

119910(119889 minus 119888 minus 119889

1015840minus 119905

119891) +

120576

119904119910

120576

119888

119888

+

1

3

119860

119908119899119910119864

119904

(120576

119904119910)

2

120576

119888

119888

(6)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908119901

= 119905

119908119889 minus (119888 + 119889

1015840+ (120576

119904119910120576

119888)119888)

119860

119908119899119910= 119905

119908(120576

119904119910120576

119888)119888

A completed bearing wall apartment building wasselected for this comparison Apartment buildings withhybrid precast frames and bearingwall frameswere evaluatedin terms of building material CO

2emission energy con-

sumption and Cr6+ emission shown in Table 5 Construction

materials per square meters were calculated based on (5) and(6)whichwere then used to calculate the quantities of Table 5

The building materials of concrete and reinforcementsof apartment buildings with hybrid precast frames werereduced by 31 and 27 respectively compared with thatof bearing wall frame buildings The CO

2emission energy

consumption andCr6+ emission of apartment buildings withhybrid precast frames were also decreased compared withbearing wall frame buildings as shown in Table 5 exhibitingthe efficiency of using gravity hybrid precast frames forapartment buildings

6 Reduction in Construction Schedule

Figures 16 and 17 compare the construction time frames basedon the use of conventional bearing walls versus the proposedhybrid frames

The construction time is the sum of each critical path asshown in

119899

sum

119894=1

(CA119894) = CA

1+ CA2+ CA3+ CA4sdot sdot sdot (7)

The critical paths that affect construction time for abearing wall apartment are CA

1(marking 1 day) CA

2(rebar

work wall 1 day) CA3(wall form installation 2 days)

CA4(slab form installation 1 day) CA

5(rebar work slab 1

day) and CA6(cleaning and pouring 1 day) Installation of

electrical and mechanical facilities at the slab is performedwith rebar work of the slab and takes less time than that ofrebar work Electrical and mechanical facilities at the slab aretherefore excluded from the critical path The constructiontime per floor is seven days based on (7) The criticalpaths affecting construction time for an apartment buildingusing hybrid frames are CA

1(rebar work core wall 05

days) CA2(column-beam unit installation (1 day) beam

unit installation (15 days)) CA3(rebar work slab 05 days)

and CA4(cleaning and pouring 05 days) Column-beam

unit installation and beam unit installation are carried outalternately Beams are only installed at every second andthird floor since columns are erected as a three-story unit

Mathematical Problems in Engineering 13

DayProcess

First floor Second floor Third floor

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 Day 10

Rebar work (core wall)

Core wall form installationColumn-beam unit

installation Beam unit installation

Deck plate installation

Joint form installation

Rebar work (slab) Electrical and mechanical

facilities (slab) Cleaning and pouring

Figure 17 Processes for constructing three floors of an apartment building using hybrid frames [20]

Table 6 Comparative analysis of the construction period [20]

Structuraltype

Construction periodComparisonTypical

floor30-story apartment

building

Bearing wall 7 days1 floor 210 Days 1000Hybrid precastframe

10 days3floors 100 Days 476

As a result of the critical paths analysis the constructiontime per floor is four days for the first floor and threedays for the next two floors requiring ten days for theconstruction of three floors utilizing columns of a three-story unit The time for frame erection was reduced by 52when using hybrid frames highlighting their economic andconstruction benefits Erection of structural frames for onefloor using conventional bearing walls involves rebar workand concrete pouring and requires about seven days asshown in Figure 16 In contrast only three days were requiredto install wall and slab forms indicating that the overallconstruction was influenced by form work which is highlydependent on work skill However erection of three floorswith hybrid precast frames required only ten days whenthree-story hybrid precast columns were erected at one liftThe significant reduction in form work contributed to thedecrease in overall construction time obtained when usingthe hybrid precast frames as shown in Figure 17 As shown inTable 6 frame erection of a 30-story building required sevendays per floor or 210 days for the entire building when usingconventional bearing walls However only ten days per threefloors (or 100 days for the entire building) were required forframe erection of the building with hybrid precast frameswhich corresponds to a 524 reduction in frame erectiontime

7 Conclusions

This study described and characterized an optimized hybridprecast composite structural system for gravity systemMajorcontributions are summarized below

(1) Gravity hybrid precast frames were presented Thesehybrid frames consist of precast concrete and steelwhich can be erected at a speed similar to that of steelframes Steel sections inserted in precast columns andbeams are used as erection steel components

(2) Mathematical model of gravity hybrid precast beamwas presented at yield limit state and maximum loadlimit state Neutral axis of postyield state found fromequilibrium equations was used to calculate nominalmoment capacities of a hybrid composite beam atboth limit state

(3) The new building frame systems for gravity load-ings fabricated with hybrid precast composite framesconsisting of simple connections between columnsand beams were proposed in this paper The dualframe systems of moment connections with muchmore complicated construction details required sig-nificant time and costs than that of building framesystems of gravity loadings However the gravityhybrid precast composite structures will provide sim-plified construction method while enhancing econ-omyduring constructionThe reductions of construc-tion resources including concrete and reinforcements(31 reduction of concrete and 27 reduction of rein-forcements) were achieved when apartments were tobe built with hybrid precast frames

(4) The gravity hybrid precast frames use less construc-tion materials than conventional frames and there-fore reduce carbon dioxide and hazardous substanceemissions compared to conventional frames It was

14 Mathematical Problems in Engineering

observed the efficiency of using gravity hybrid precastframes for apartment building which decreased theCO2emission (23 reduction of concrete and 28

reduction of reinforcements) energy consumption(21 reduction of concrete and 29 reduction ofreinforcements) and Cr6+ emission compared withbearing wall frame buildings The use of gravityhybrid precast frames was demonstrated to providebetter solutions for environments and economy thanthat of conventional buildings

(5) Dynamic analysis of a 15-story building designedwith the proposed composite gravity frames was per-formed to characterize frequencies and mode shapesof the building for seismic design purposes

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by Grant from the Kyung HeeUniversity in 2013 (KHU-20130363)

References

[1] J F Hajjar ldquoComposite steel and concrete structural systems forseismic engineeringrdquo Journal of Constructional Steel Researchvol 58 no 5ndash8 pp 703ndash723 2002

[2] G Fabbrocino G Manfredi and E Cosenza ldquoDuctility ofcomposite beams under negative bending an equivalence indexfor reinforcing steel classificationrdquo Journal of ConstructionalSteel Research vol 58 no 2 pp 185ndash202 2001

[3] B Yang and K Tan ldquoBehaviour of composite beam-columnjoints under a middle-column-removal scenario experimentaltestsrdquo Journal of Structural Engineering vol 140 no 2 ArticleID 04013045 2014

[4] L Tesser and R Scotta ldquoFlexural and shear capacity of compos-ite steel truss and concrete beams with inferior precast concretebaserdquo Engineering Structures vol 49 pp 135ndash145 2013

[5] H J Hwang H G Park C H Lee et al ldquoSeismic resistanceof concrete-filled U-shaped steel beam-to-RC column connec-tionsrdquo Journal of Korean Society of Steel Construction vol 23 pp83ndash97 2011

[6] J Hassan and B Khosrow ldquoNonlinear seismic behavior evalua-tion of ductile beam-column connections in precast concreterdquoInternational Journal of Civil and Structural Engineering vol 1pp 445ndash453 2011

[7] A M Ioani and E Tripa ldquoStructural behavior of an innovativeall-precast concrete dual system for residential buildingsrdquo PCIJournal vol 57 no 1 pp 110ndash123 2012

[8] C Chou andCUang ldquoEffects of continuity plate and transversereinforcement on cyclic behavior of SRCmoment connectionsrdquoJournal of Structural Engineering vol 133 no 1 pp 96ndash104 2007

[9] Y K Ju and S D Kim ldquoStructural behavior of alternative lowfloor height system using structural ldquoteerdquo half precast concreteand horizontal studrdquoCanadian Journal of Civil Engineering vol32 no 2 pp 329ndash338 2005

[10] X Wang M Truijens L Hou Y Wang and Y Zhou ldquoInte-grating augmented reality with building informationmodelingonsite construction process controlling for liquefied natural gasindustryrdquoAutomation in Construction vol 40 pp 96ndash105 2014

[11] L Hou Y Wang X Wang et al ldquoCombining photogrammetryand augmented reality towards an integrated facility manage-ment system for the oil industryrdquo Proceedings of the IEEE vol102 no 2 pp 204ndash220 2014

[12] L Hou XWang L Bernold and P E D Love ldquoUsing animatedaugmented reality to cognitively guide assemblyrdquo Journal ofComputing in Civil Engineering vol 27 no 5 pp 439ndash451 2013

[13] YWang XWang JWang P Yung andG Jun ldquoEngagement offacilities management in design stage through BIM frameworkand a case studyrdquo Advances in Civil Engineering vol 2013Article ID 189105 8 pages 2013

[14] W K Hong J M Kim S C Park et al ldquoA new apartmentconstruction technology with effective CO

2emission reduction

capabilitiesrdquo Energy vol 35 no 6 pp 2639ndash2646 2010[15] W Hong S Park J Kim et al ldquoDevelopment of structural

composite hybrid systems and their application with regard tothe reduction of CO

2emissionsrdquo Indoor and Built Environment

vol 19 no 1 pp 151ndash162 2010[16] W Hong S Jeong S Park and J T Kim ldquoExperimental

investigation of an energy-efficient hybrid composite beamduring the construction phaserdquo Energy and Buildings vol 46pp 37ndash47 2012

[17] G P Hammond and C I Jones Inventory of Carbon amp Energy(ICE) Department of Mechanical Engineering University ofBath Bath UK 2008

[18] G P Hammond and C I Jones ldquoEmbodied energy and carbonin construction materialsrdquo Proceedings of Institution of CivilEngineers Energy vol 161 no 2 pp 87ndash98 2008

[19] National Institute of Environment Research (NIER) Domesticand foreign cement heavy metal analysis result (May 2013)NIER 2013 httpwwwniergokrericportalkornfnier-nf-02page

[20] S Kim W Hong J Kim and J T Kim ldquoThe developmentof modularized construction of enhanced precast compositestructural systems (Smart Green frame) and its embeddedenergy efficiencyrdquo Energy and Buildings vol 66 pp 16ndash21 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

8 Mathematical Problems in Engineering

1447

1500

7200

3600

3600

3800

2900

2900

2900

2900

2900

2900

2900

2900

2900

2900

2900

1

29001400

1500 1

0003600

23003600

3800

2900

2600

1300

3200

1600700

600

2900

2900

2900

2900

2900

2900

2900

2900

2900

2900

29001400

40000

2880

2880

920

5100700061508300 6300

6300 630020002150 4150

5382

1447

2250

2250

2250

2250

2250

2250

2250

2250

2250

2250

2250

2250

3200 2400

2300

1600

GL-1800

GL-6000

510070006150146005382

(b)

Figure 9 Floor plan and elevation

Mathematical Problems in Engineering 9

Table 1 Modal participation masses

Mode number TRAN-119883 TRAN-119884 ROTN-119885Mass () Sum () Mass () Sum () Mass () Sum ()

1 405909 405909 02185 02185 127252 1272522 42570 448478 16208 164265 203361 3306123 40667 489145 328629 492893 82552 4131644 96703 585848 01847 49474 40557 4537215 32088 617935 03965 498705 87600 5413216 03685 621620 158676 657381 05207 546528

(a) (b) (c)

Figure 10 Computer model of the building

Table 2 Eigenvalue analysis (fundamental period)

Mode number Frequency Period Tolerance(radsec) (cyclesec) (sec)

1 34768 05533 34768 00000119890 + 000

2 41078 06538 41078 00000119890 + 000

3 53487 08513 53487 00000119890 + 000

4 138311 22013 138311 45251119890 minus 161

5 178259 28371 178259 28518119890 minus 150

6 236726 37676 236726 15909119890 minus 137

joints against vertical and lateral loadings resembles that ofsteel structures even though the building has an externalappearance of a concrete structure

Figure 11 shows the first translational mode (a) and thoseof two mixed modes ((b) (c)) Figures 11(d) 11(e) and 11(f)show these modes from the top view respectively

5 Reduction of Structural Quantity andEmissions of Environmentally HazardousSubstances and Materials

This study evaluated chromium VI and carbon dioxide emis-sions of the building constructed with the proposed framesand conventional walls Reductions in energy consumptiondue to reduction in material quantity were estimated basedon comparison of an apartment building constructed withhybrid precast frames and that of a conventional bearing-wallbuilding

Original units of major building components (Table 3)which were announced in 2008 by the United Kingdom

Table 3 Emissions and energy usage of major building components[17]

Buildingcomponent

CO2 emissionsper original unit

Energy consumptionper original unit

Concrete 25MPa 3196 kg-CO2m3 23265MJm3

Concrete 35MPa 37835 kg-CO2m3 26555MJm3

Reinforcement 27319 kg-CO2kN 371050MJkNSteel section 28338 kg-CO2kN 375127MJkN

Inventory of Carbon and Energy (ICE) were used to evaluatecarbon dioxide emissions and the energy efficiency of theproposed construction The embodied energy 119864 and carbonemissions per kN for the calculated material quantity areobtained from the University of Bathrsquos ICE database [17 18]The ICE has been structured into 34 main material groupsThe database also provides the embodied energy and carboncoefficients for construction materials Table 3 presents theconverted embodied energy and carbon coefficients for fourbuilding components concrete (25MPa) concrete (35MPa)reinforcement and steel section

Domestic and foreign cement heavymetal analysis results(May 2013) published by the Korea National Institute ofEnvironment Research (NIER) were utilized to evaluatechromium VI emissions (Table 4)

In order to explain how the data that evaluates the gravitysystem presented in this paper in terms of material quantityanalytical approach for the hybrid precast composite beamdesign based on the strain compatibility method was intro-duced Figures 12 and 13 illustrate the side view and cross-section of a hybrid composite beam In order to determine the

10 Mathematical Problems in Engineering

Table 4 Heavy metal content standards in cement [19]

Cr6+ As Cd Cu Hg PbAve (May 2013) 1063mgkg 1287mgkg 102mgkg 8903mgkg 061mgkg 3284mgkg

(a) Fundamental translational mode (b) Mixed mode 1 (c) Mixed mode 2

(d) Fundamental translational mode (e) Mixed mode 1 (f) Mixed mode 2

Figure 11 Mode shapes

Figure 12 Side view of a hybrid composite beam

d

d998400

d998400998400

d998400998400998400

Figure 13 Cross-section of a hybrid composite beam

exact material quantity the hybrid composite beam designwas carried out based on the strain compatibility methodEquations (1) and (2) are the mean stress factor 120572 and thecentroid factor 120574 for any strain 120576

119888119898at the extreme com-

pression fiber calculated based on stress-strain relationshipEquations (3) and (5) represent the equilibrium equations ofcompressive and tensile forces at yield limit and maximumload limit state respectively The nominal moment capacitiesof a hybrid composite beam at yield limit andmaximum loadlimit state are calculated by (4) and (6) respectively Figures14 and 15 represent strain and stress diagram at yield limitand maximum load limit state respectively In both figuresblack color indicates steels and reinforcement rebars wereplasticized (yielded) while white color represents structuralmembers remained elastic The structural quantity requiredby apartment buildings with hybrid composite frames wasobtained from (6) and compared with that of conventionalbuildings with bearing walls as shown in Table 5 These

Mathematical Problems in Engineering 11

Table 5 Evaluation of structural systems

Buildingcomponent System Gross area Building material CO2 emission Energy consumption Cr6+ emission

Concrete(HPF = 35MPaBW = 25MPa)

HPF 9236m2 038m3m2 691(minus309) 1362 kg-CO2m

2 775(minus225) 10060MJm2 786

(minus214) 11062mgm2 689(minus311)

BW 6513m2 055m3m2 1000 1758 kg-CO2m2 1000 12796MJm2 1000 16061mgm2 100

Reinforcements HPF 9236m2 053 kNm2 726(minus274) 1445 kg-CO2m

2 724(minus276) 19314MJm2 713

(minus287) mdash mdash

BW 6513m2 073 kNm2 1000 1996 kg-CO2m2 1000 27107MJm2 1000 mdash mdash

Steel section HPF 9236m2 007 kNm2 1000 206 kg-CO2m2 1000 2721MJm2 1000 mdash mdash

BW 6513m2 mdashkNm2 mdash mdashkg-CO2m2 mdash mdashMJm2 mdash mdash mdash

lowastHPF hybrid precast frames BW bearing wall

400 MPa

301 MPa

1354 mm

120576st = 0001506

120576t = 120576y = 0002

120576c = 000178 f998400c

120576998400t = 000096 120576tEs = 192MPa

Figure 14 Strain and stress diagram at yield limit state

120576tEs = 286MPa

400 MPa

325 MPa

11946 mm

120576st = 000328

120576t = 120576y = 00042

120576c = 0003f998400c

120576998400t = 000143

Figure 15 Strain and stress diagram at maximum load limit state

equations would help engineer estimate precise constructionmaterials and understand how buildings with hybrid com-posite frames behave Consider

120572 = (int

0002

0

119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

119891

1015840

1198881 minus 100 (120576

119888minus 120576

119888119900) 119889120576

119888)

times (119891

1015840

119888120576

119888119898)

minus1

(1)

120574 = 1 minus ((int

0002

0

120576

119888119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

120576

119888119891

1015840

1198881 minus 100 (120576

119888minus 120576

119888119900) 119889120576

119888)

times (120576

119888119898[int

0002

0

119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

119891

1015840

1198881minus100 (120576

119888minus120576

119888119900) 119889120576

119888])

minus1

)

(2)

120572119891

1015840

119888119887119888 + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840) +

1

2

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

= 119860

119904119865

119910+ 119860

119891119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

1

2

119860

119908119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891)

(3)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908= 119905

119908(119889 minus 119888 minus 119889

1015840minus 119905

119891)

119872

119899= 120572119891

1015840

119888119887119888 (119888 minus 120574119888) + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840)

2

+

1

3

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

2

+ 119860

119904119865

119910(119889 minus 119888)

12 Mathematical Problems in Engineering

DayProcess

One floor

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7

Marking

Rebar work (wall)

Wall form installation

Slab form installation

Rebar work (slab) Electrical and mechanical

facilities (slab) Cleaning and pouring

Figure 16 Processes for constructing one floor of a conventional wall-type apartment building [20]

+ 119860

119891119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891) (119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

119905

119891

2

(119889 minus 119888 minus 119889

1015840minus

119905

119891

3

)

+

1

3

119860

119908119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891)

2

(4)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908= 119905

119908(119889 minus 119888 minus 119889

1015840minus 119905

119891)

120572119891

1015840

119888119887119888 + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840) +

1

2

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

= 119860

119904119865

119910+ 119860

119891119865

119910+ 119860

119908119901119865

119910+

1

2

119860

119908119899119910119864

119904120576

119904119910

(5)

where1198601015840119908= 119905

119908(119888minus119889

101584010158401015840)119860119908119901

= 119905

119908(119889minus119888+119889

1015840+119905

119891)+(120576

119904119910120576

119888)119888

119860

119908119899119910= 119905

119908(120576

119904119910120576

119888)119888

119872

119899= 120572119891

1015840

119888119887119888 (119888 minus 120574119888) + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840)

2

+

1

3

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

2

+ 119860

119904119865

119910(119889 minus 119888)

+ 119860

119891119865

119910(119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

1

2

119860

119908119901119865

119910(119889 minus 119888 minus 119889

1015840minus 119905

119891) +

120576

119904119910

120576

119888

119888

+

1

3

119860

119908119899119910119864

119904

(120576

119904119910)

2

120576

119888

119888

(6)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908119901

= 119905

119908119889 minus (119888 + 119889

1015840+ (120576

119904119910120576

119888)119888)

119860

119908119899119910= 119905

119908(120576

119904119910120576

119888)119888

A completed bearing wall apartment building wasselected for this comparison Apartment buildings withhybrid precast frames and bearingwall frameswere evaluatedin terms of building material CO

2emission energy con-

sumption and Cr6+ emission shown in Table 5 Construction

materials per square meters were calculated based on (5) and(6)whichwere then used to calculate the quantities of Table 5

The building materials of concrete and reinforcementsof apartment buildings with hybrid precast frames werereduced by 31 and 27 respectively compared with thatof bearing wall frame buildings The CO

2emission energy

consumption andCr6+ emission of apartment buildings withhybrid precast frames were also decreased compared withbearing wall frame buildings as shown in Table 5 exhibitingthe efficiency of using gravity hybrid precast frames forapartment buildings

6 Reduction in Construction Schedule

Figures 16 and 17 compare the construction time frames basedon the use of conventional bearing walls versus the proposedhybrid frames

The construction time is the sum of each critical path asshown in

119899

sum

119894=1

(CA119894) = CA

1+ CA2+ CA3+ CA4sdot sdot sdot (7)

The critical paths that affect construction time for abearing wall apartment are CA

1(marking 1 day) CA

2(rebar

work wall 1 day) CA3(wall form installation 2 days)

CA4(slab form installation 1 day) CA

5(rebar work slab 1

day) and CA6(cleaning and pouring 1 day) Installation of

electrical and mechanical facilities at the slab is performedwith rebar work of the slab and takes less time than that ofrebar work Electrical and mechanical facilities at the slab aretherefore excluded from the critical path The constructiontime per floor is seven days based on (7) The criticalpaths affecting construction time for an apartment buildingusing hybrid frames are CA

1(rebar work core wall 05

days) CA2(column-beam unit installation (1 day) beam

unit installation (15 days)) CA3(rebar work slab 05 days)

and CA4(cleaning and pouring 05 days) Column-beam

unit installation and beam unit installation are carried outalternately Beams are only installed at every second andthird floor since columns are erected as a three-story unit

Mathematical Problems in Engineering 13

DayProcess

First floor Second floor Third floor

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 Day 10

Rebar work (core wall)

Core wall form installationColumn-beam unit

installation Beam unit installation

Deck plate installation

Joint form installation

Rebar work (slab) Electrical and mechanical

facilities (slab) Cleaning and pouring

Figure 17 Processes for constructing three floors of an apartment building using hybrid frames [20]

Table 6 Comparative analysis of the construction period [20]

Structuraltype

Construction periodComparisonTypical

floor30-story apartment

building

Bearing wall 7 days1 floor 210 Days 1000Hybrid precastframe

10 days3floors 100 Days 476

As a result of the critical paths analysis the constructiontime per floor is four days for the first floor and threedays for the next two floors requiring ten days for theconstruction of three floors utilizing columns of a three-story unit The time for frame erection was reduced by 52when using hybrid frames highlighting their economic andconstruction benefits Erection of structural frames for onefloor using conventional bearing walls involves rebar workand concrete pouring and requires about seven days asshown in Figure 16 In contrast only three days were requiredto install wall and slab forms indicating that the overallconstruction was influenced by form work which is highlydependent on work skill However erection of three floorswith hybrid precast frames required only ten days whenthree-story hybrid precast columns were erected at one liftThe significant reduction in form work contributed to thedecrease in overall construction time obtained when usingthe hybrid precast frames as shown in Figure 17 As shown inTable 6 frame erection of a 30-story building required sevendays per floor or 210 days for the entire building when usingconventional bearing walls However only ten days per threefloors (or 100 days for the entire building) were required forframe erection of the building with hybrid precast frameswhich corresponds to a 524 reduction in frame erectiontime

7 Conclusions

This study described and characterized an optimized hybridprecast composite structural system for gravity systemMajorcontributions are summarized below

(1) Gravity hybrid precast frames were presented Thesehybrid frames consist of precast concrete and steelwhich can be erected at a speed similar to that of steelframes Steel sections inserted in precast columns andbeams are used as erection steel components

(2) Mathematical model of gravity hybrid precast beamwas presented at yield limit state and maximum loadlimit state Neutral axis of postyield state found fromequilibrium equations was used to calculate nominalmoment capacities of a hybrid composite beam atboth limit state

(3) The new building frame systems for gravity load-ings fabricated with hybrid precast composite framesconsisting of simple connections between columnsand beams were proposed in this paper The dualframe systems of moment connections with muchmore complicated construction details required sig-nificant time and costs than that of building framesystems of gravity loadings However the gravityhybrid precast composite structures will provide sim-plified construction method while enhancing econ-omyduring constructionThe reductions of construc-tion resources including concrete and reinforcements(31 reduction of concrete and 27 reduction of rein-forcements) were achieved when apartments were tobe built with hybrid precast frames

(4) The gravity hybrid precast frames use less construc-tion materials than conventional frames and there-fore reduce carbon dioxide and hazardous substanceemissions compared to conventional frames It was

14 Mathematical Problems in Engineering

observed the efficiency of using gravity hybrid precastframes for apartment building which decreased theCO2emission (23 reduction of concrete and 28

reduction of reinforcements) energy consumption(21 reduction of concrete and 29 reduction ofreinforcements) and Cr6+ emission compared withbearing wall frame buildings The use of gravityhybrid precast frames was demonstrated to providebetter solutions for environments and economy thanthat of conventional buildings

(5) Dynamic analysis of a 15-story building designedwith the proposed composite gravity frames was per-formed to characterize frequencies and mode shapesof the building for seismic design purposes

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by Grant from the Kyung HeeUniversity in 2013 (KHU-20130363)

References

[1] J F Hajjar ldquoComposite steel and concrete structural systems forseismic engineeringrdquo Journal of Constructional Steel Researchvol 58 no 5ndash8 pp 703ndash723 2002

[2] G Fabbrocino G Manfredi and E Cosenza ldquoDuctility ofcomposite beams under negative bending an equivalence indexfor reinforcing steel classificationrdquo Journal of ConstructionalSteel Research vol 58 no 2 pp 185ndash202 2001

[3] B Yang and K Tan ldquoBehaviour of composite beam-columnjoints under a middle-column-removal scenario experimentaltestsrdquo Journal of Structural Engineering vol 140 no 2 ArticleID 04013045 2014

[4] L Tesser and R Scotta ldquoFlexural and shear capacity of compos-ite steel truss and concrete beams with inferior precast concretebaserdquo Engineering Structures vol 49 pp 135ndash145 2013

[5] H J Hwang H G Park C H Lee et al ldquoSeismic resistanceof concrete-filled U-shaped steel beam-to-RC column connec-tionsrdquo Journal of Korean Society of Steel Construction vol 23 pp83ndash97 2011

[6] J Hassan and B Khosrow ldquoNonlinear seismic behavior evalua-tion of ductile beam-column connections in precast concreterdquoInternational Journal of Civil and Structural Engineering vol 1pp 445ndash453 2011

[7] A M Ioani and E Tripa ldquoStructural behavior of an innovativeall-precast concrete dual system for residential buildingsrdquo PCIJournal vol 57 no 1 pp 110ndash123 2012

[8] C Chou andCUang ldquoEffects of continuity plate and transversereinforcement on cyclic behavior of SRCmoment connectionsrdquoJournal of Structural Engineering vol 133 no 1 pp 96ndash104 2007

[9] Y K Ju and S D Kim ldquoStructural behavior of alternative lowfloor height system using structural ldquoteerdquo half precast concreteand horizontal studrdquoCanadian Journal of Civil Engineering vol32 no 2 pp 329ndash338 2005

[10] X Wang M Truijens L Hou Y Wang and Y Zhou ldquoInte-grating augmented reality with building informationmodelingonsite construction process controlling for liquefied natural gasindustryrdquoAutomation in Construction vol 40 pp 96ndash105 2014

[11] L Hou Y Wang X Wang et al ldquoCombining photogrammetryand augmented reality towards an integrated facility manage-ment system for the oil industryrdquo Proceedings of the IEEE vol102 no 2 pp 204ndash220 2014

[12] L Hou XWang L Bernold and P E D Love ldquoUsing animatedaugmented reality to cognitively guide assemblyrdquo Journal ofComputing in Civil Engineering vol 27 no 5 pp 439ndash451 2013

[13] YWang XWang JWang P Yung andG Jun ldquoEngagement offacilities management in design stage through BIM frameworkand a case studyrdquo Advances in Civil Engineering vol 2013Article ID 189105 8 pages 2013

[14] W K Hong J M Kim S C Park et al ldquoA new apartmentconstruction technology with effective CO

2emission reduction

capabilitiesrdquo Energy vol 35 no 6 pp 2639ndash2646 2010[15] W Hong S Park J Kim et al ldquoDevelopment of structural

composite hybrid systems and their application with regard tothe reduction of CO

2emissionsrdquo Indoor and Built Environment

vol 19 no 1 pp 151ndash162 2010[16] W Hong S Jeong S Park and J T Kim ldquoExperimental

investigation of an energy-efficient hybrid composite beamduring the construction phaserdquo Energy and Buildings vol 46pp 37ndash47 2012

[17] G P Hammond and C I Jones Inventory of Carbon amp Energy(ICE) Department of Mechanical Engineering University ofBath Bath UK 2008

[18] G P Hammond and C I Jones ldquoEmbodied energy and carbonin construction materialsrdquo Proceedings of Institution of CivilEngineers Energy vol 161 no 2 pp 87ndash98 2008

[19] National Institute of Environment Research (NIER) Domesticand foreign cement heavy metal analysis result (May 2013)NIER 2013 httpwwwniergokrericportalkornfnier-nf-02page

[20] S Kim W Hong J Kim and J T Kim ldquoThe developmentof modularized construction of enhanced precast compositestructural systems (Smart Green frame) and its embeddedenergy efficiencyrdquo Energy and Buildings vol 66 pp 16ndash21 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 9

Table 1 Modal participation masses

Mode number TRAN-119883 TRAN-119884 ROTN-119885Mass () Sum () Mass () Sum () Mass () Sum ()

1 405909 405909 02185 02185 127252 1272522 42570 448478 16208 164265 203361 3306123 40667 489145 328629 492893 82552 4131644 96703 585848 01847 49474 40557 4537215 32088 617935 03965 498705 87600 5413216 03685 621620 158676 657381 05207 546528

(a) (b) (c)

Figure 10 Computer model of the building

Table 2 Eigenvalue analysis (fundamental period)

Mode number Frequency Period Tolerance(radsec) (cyclesec) (sec)

1 34768 05533 34768 00000119890 + 000

2 41078 06538 41078 00000119890 + 000

3 53487 08513 53487 00000119890 + 000

4 138311 22013 138311 45251119890 minus 161

5 178259 28371 178259 28518119890 minus 150

6 236726 37676 236726 15909119890 minus 137

joints against vertical and lateral loadings resembles that ofsteel structures even though the building has an externalappearance of a concrete structure

Figure 11 shows the first translational mode (a) and thoseof two mixed modes ((b) (c)) Figures 11(d) 11(e) and 11(f)show these modes from the top view respectively

5 Reduction of Structural Quantity andEmissions of Environmentally HazardousSubstances and Materials

This study evaluated chromium VI and carbon dioxide emis-sions of the building constructed with the proposed framesand conventional walls Reductions in energy consumptiondue to reduction in material quantity were estimated basedon comparison of an apartment building constructed withhybrid precast frames and that of a conventional bearing-wallbuilding

Original units of major building components (Table 3)which were announced in 2008 by the United Kingdom

Table 3 Emissions and energy usage of major building components[17]

Buildingcomponent

CO2 emissionsper original unit

Energy consumptionper original unit

Concrete 25MPa 3196 kg-CO2m3 23265MJm3

Concrete 35MPa 37835 kg-CO2m3 26555MJm3

Reinforcement 27319 kg-CO2kN 371050MJkNSteel section 28338 kg-CO2kN 375127MJkN

Inventory of Carbon and Energy (ICE) were used to evaluatecarbon dioxide emissions and the energy efficiency of theproposed construction The embodied energy 119864 and carbonemissions per kN for the calculated material quantity areobtained from the University of Bathrsquos ICE database [17 18]The ICE has been structured into 34 main material groupsThe database also provides the embodied energy and carboncoefficients for construction materials Table 3 presents theconverted embodied energy and carbon coefficients for fourbuilding components concrete (25MPa) concrete (35MPa)reinforcement and steel section

Domestic and foreign cement heavymetal analysis results(May 2013) published by the Korea National Institute ofEnvironment Research (NIER) were utilized to evaluatechromium VI emissions (Table 4)

In order to explain how the data that evaluates the gravitysystem presented in this paper in terms of material quantityanalytical approach for the hybrid precast composite beamdesign based on the strain compatibility method was intro-duced Figures 12 and 13 illustrate the side view and cross-section of a hybrid composite beam In order to determine the

10 Mathematical Problems in Engineering

Table 4 Heavy metal content standards in cement [19]

Cr6+ As Cd Cu Hg PbAve (May 2013) 1063mgkg 1287mgkg 102mgkg 8903mgkg 061mgkg 3284mgkg

(a) Fundamental translational mode (b) Mixed mode 1 (c) Mixed mode 2

(d) Fundamental translational mode (e) Mixed mode 1 (f) Mixed mode 2

Figure 11 Mode shapes

Figure 12 Side view of a hybrid composite beam

d

d998400

d998400998400

d998400998400998400

Figure 13 Cross-section of a hybrid composite beam

exact material quantity the hybrid composite beam designwas carried out based on the strain compatibility methodEquations (1) and (2) are the mean stress factor 120572 and thecentroid factor 120574 for any strain 120576

119888119898at the extreme com-

pression fiber calculated based on stress-strain relationshipEquations (3) and (5) represent the equilibrium equations ofcompressive and tensile forces at yield limit and maximumload limit state respectively The nominal moment capacitiesof a hybrid composite beam at yield limit andmaximum loadlimit state are calculated by (4) and (6) respectively Figures14 and 15 represent strain and stress diagram at yield limitand maximum load limit state respectively In both figuresblack color indicates steels and reinforcement rebars wereplasticized (yielded) while white color represents structuralmembers remained elastic The structural quantity requiredby apartment buildings with hybrid composite frames wasobtained from (6) and compared with that of conventionalbuildings with bearing walls as shown in Table 5 These

Mathematical Problems in Engineering 11

Table 5 Evaluation of structural systems

Buildingcomponent System Gross area Building material CO2 emission Energy consumption Cr6+ emission

Concrete(HPF = 35MPaBW = 25MPa)

HPF 9236m2 038m3m2 691(minus309) 1362 kg-CO2m

2 775(minus225) 10060MJm2 786

(minus214) 11062mgm2 689(minus311)

BW 6513m2 055m3m2 1000 1758 kg-CO2m2 1000 12796MJm2 1000 16061mgm2 100

Reinforcements HPF 9236m2 053 kNm2 726(minus274) 1445 kg-CO2m

2 724(minus276) 19314MJm2 713

(minus287) mdash mdash

BW 6513m2 073 kNm2 1000 1996 kg-CO2m2 1000 27107MJm2 1000 mdash mdash

Steel section HPF 9236m2 007 kNm2 1000 206 kg-CO2m2 1000 2721MJm2 1000 mdash mdash

BW 6513m2 mdashkNm2 mdash mdashkg-CO2m2 mdash mdashMJm2 mdash mdash mdash

lowastHPF hybrid precast frames BW bearing wall

400 MPa

301 MPa

1354 mm

120576st = 0001506

120576t = 120576y = 0002

120576c = 000178 f998400c

120576998400t = 000096 120576tEs = 192MPa

Figure 14 Strain and stress diagram at yield limit state

120576tEs = 286MPa

400 MPa

325 MPa

11946 mm

120576st = 000328

120576t = 120576y = 00042

120576c = 0003f998400c

120576998400t = 000143

Figure 15 Strain and stress diagram at maximum load limit state

equations would help engineer estimate precise constructionmaterials and understand how buildings with hybrid com-posite frames behave Consider

120572 = (int

0002

0

119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

119891

1015840

1198881 minus 100 (120576

119888minus 120576

119888119900) 119889120576

119888)

times (119891

1015840

119888120576

119888119898)

minus1

(1)

120574 = 1 minus ((int

0002

0

120576

119888119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

120576

119888119891

1015840

1198881 minus 100 (120576

119888minus 120576

119888119900) 119889120576

119888)

times (120576

119888119898[int

0002

0

119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

119891

1015840

1198881minus100 (120576

119888minus120576

119888119900) 119889120576

119888])

minus1

)

(2)

120572119891

1015840

119888119887119888 + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840) +

1

2

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

= 119860

119904119865

119910+ 119860

119891119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

1

2

119860

119908119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891)

(3)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908= 119905

119908(119889 minus 119888 minus 119889

1015840minus 119905

119891)

119872

119899= 120572119891

1015840

119888119887119888 (119888 minus 120574119888) + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840)

2

+

1

3

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

2

+ 119860

119904119865

119910(119889 minus 119888)

12 Mathematical Problems in Engineering

DayProcess

One floor

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7

Marking

Rebar work (wall)

Wall form installation

Slab form installation

Rebar work (slab) Electrical and mechanical

facilities (slab) Cleaning and pouring

Figure 16 Processes for constructing one floor of a conventional wall-type apartment building [20]

+ 119860

119891119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891) (119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

119905

119891

2

(119889 minus 119888 minus 119889

1015840minus

119905

119891

3

)

+

1

3

119860

119908119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891)

2

(4)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908= 119905

119908(119889 minus 119888 minus 119889

1015840minus 119905

119891)

120572119891

1015840

119888119887119888 + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840) +

1

2

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

= 119860

119904119865

119910+ 119860

119891119865

119910+ 119860

119908119901119865

119910+

1

2

119860

119908119899119910119864

119904120576

119904119910

(5)

where1198601015840119908= 119905

119908(119888minus119889

101584010158401015840)119860119908119901

= 119905

119908(119889minus119888+119889

1015840+119905

119891)+(120576

119904119910120576

119888)119888

119860

119908119899119910= 119905

119908(120576

119904119910120576

119888)119888

119872

119899= 120572119891

1015840

119888119887119888 (119888 minus 120574119888) + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840)

2

+

1

3

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

2

+ 119860

119904119865

119910(119889 minus 119888)

+ 119860

119891119865

119910(119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

1

2

119860

119908119901119865

119910(119889 minus 119888 minus 119889

1015840minus 119905

119891) +

120576

119904119910

120576

119888

119888

+

1

3

119860

119908119899119910119864

119904

(120576

119904119910)

2

120576

119888

119888

(6)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908119901

= 119905

119908119889 minus (119888 + 119889

1015840+ (120576

119904119910120576

119888)119888)

119860

119908119899119910= 119905

119908(120576

119904119910120576

119888)119888

A completed bearing wall apartment building wasselected for this comparison Apartment buildings withhybrid precast frames and bearingwall frameswere evaluatedin terms of building material CO

2emission energy con-

sumption and Cr6+ emission shown in Table 5 Construction

materials per square meters were calculated based on (5) and(6)whichwere then used to calculate the quantities of Table 5

The building materials of concrete and reinforcementsof apartment buildings with hybrid precast frames werereduced by 31 and 27 respectively compared with thatof bearing wall frame buildings The CO

2emission energy

consumption andCr6+ emission of apartment buildings withhybrid precast frames were also decreased compared withbearing wall frame buildings as shown in Table 5 exhibitingthe efficiency of using gravity hybrid precast frames forapartment buildings

6 Reduction in Construction Schedule

Figures 16 and 17 compare the construction time frames basedon the use of conventional bearing walls versus the proposedhybrid frames

The construction time is the sum of each critical path asshown in

119899

sum

119894=1

(CA119894) = CA

1+ CA2+ CA3+ CA4sdot sdot sdot (7)

The critical paths that affect construction time for abearing wall apartment are CA

1(marking 1 day) CA

2(rebar

work wall 1 day) CA3(wall form installation 2 days)

CA4(slab form installation 1 day) CA

5(rebar work slab 1

day) and CA6(cleaning and pouring 1 day) Installation of

electrical and mechanical facilities at the slab is performedwith rebar work of the slab and takes less time than that ofrebar work Electrical and mechanical facilities at the slab aretherefore excluded from the critical path The constructiontime per floor is seven days based on (7) The criticalpaths affecting construction time for an apartment buildingusing hybrid frames are CA

1(rebar work core wall 05

days) CA2(column-beam unit installation (1 day) beam

unit installation (15 days)) CA3(rebar work slab 05 days)

and CA4(cleaning and pouring 05 days) Column-beam

unit installation and beam unit installation are carried outalternately Beams are only installed at every second andthird floor since columns are erected as a three-story unit

Mathematical Problems in Engineering 13

DayProcess

First floor Second floor Third floor

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 Day 10

Rebar work (core wall)

Core wall form installationColumn-beam unit

installation Beam unit installation

Deck plate installation

Joint form installation

Rebar work (slab) Electrical and mechanical

facilities (slab) Cleaning and pouring

Figure 17 Processes for constructing three floors of an apartment building using hybrid frames [20]

Table 6 Comparative analysis of the construction period [20]

Structuraltype

Construction periodComparisonTypical

floor30-story apartment

building

Bearing wall 7 days1 floor 210 Days 1000Hybrid precastframe

10 days3floors 100 Days 476

As a result of the critical paths analysis the constructiontime per floor is four days for the first floor and threedays for the next two floors requiring ten days for theconstruction of three floors utilizing columns of a three-story unit The time for frame erection was reduced by 52when using hybrid frames highlighting their economic andconstruction benefits Erection of structural frames for onefloor using conventional bearing walls involves rebar workand concrete pouring and requires about seven days asshown in Figure 16 In contrast only three days were requiredto install wall and slab forms indicating that the overallconstruction was influenced by form work which is highlydependent on work skill However erection of three floorswith hybrid precast frames required only ten days whenthree-story hybrid precast columns were erected at one liftThe significant reduction in form work contributed to thedecrease in overall construction time obtained when usingthe hybrid precast frames as shown in Figure 17 As shown inTable 6 frame erection of a 30-story building required sevendays per floor or 210 days for the entire building when usingconventional bearing walls However only ten days per threefloors (or 100 days for the entire building) were required forframe erection of the building with hybrid precast frameswhich corresponds to a 524 reduction in frame erectiontime

7 Conclusions

This study described and characterized an optimized hybridprecast composite structural system for gravity systemMajorcontributions are summarized below

(1) Gravity hybrid precast frames were presented Thesehybrid frames consist of precast concrete and steelwhich can be erected at a speed similar to that of steelframes Steel sections inserted in precast columns andbeams are used as erection steel components

(2) Mathematical model of gravity hybrid precast beamwas presented at yield limit state and maximum loadlimit state Neutral axis of postyield state found fromequilibrium equations was used to calculate nominalmoment capacities of a hybrid composite beam atboth limit state

(3) The new building frame systems for gravity load-ings fabricated with hybrid precast composite framesconsisting of simple connections between columnsand beams were proposed in this paper The dualframe systems of moment connections with muchmore complicated construction details required sig-nificant time and costs than that of building framesystems of gravity loadings However the gravityhybrid precast composite structures will provide sim-plified construction method while enhancing econ-omyduring constructionThe reductions of construc-tion resources including concrete and reinforcements(31 reduction of concrete and 27 reduction of rein-forcements) were achieved when apartments were tobe built with hybrid precast frames

(4) The gravity hybrid precast frames use less construc-tion materials than conventional frames and there-fore reduce carbon dioxide and hazardous substanceemissions compared to conventional frames It was

14 Mathematical Problems in Engineering

observed the efficiency of using gravity hybrid precastframes for apartment building which decreased theCO2emission (23 reduction of concrete and 28

reduction of reinforcements) energy consumption(21 reduction of concrete and 29 reduction ofreinforcements) and Cr6+ emission compared withbearing wall frame buildings The use of gravityhybrid precast frames was demonstrated to providebetter solutions for environments and economy thanthat of conventional buildings

(5) Dynamic analysis of a 15-story building designedwith the proposed composite gravity frames was per-formed to characterize frequencies and mode shapesof the building for seismic design purposes

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by Grant from the Kyung HeeUniversity in 2013 (KHU-20130363)

References

[1] J F Hajjar ldquoComposite steel and concrete structural systems forseismic engineeringrdquo Journal of Constructional Steel Researchvol 58 no 5ndash8 pp 703ndash723 2002

[2] G Fabbrocino G Manfredi and E Cosenza ldquoDuctility ofcomposite beams under negative bending an equivalence indexfor reinforcing steel classificationrdquo Journal of ConstructionalSteel Research vol 58 no 2 pp 185ndash202 2001

[3] B Yang and K Tan ldquoBehaviour of composite beam-columnjoints under a middle-column-removal scenario experimentaltestsrdquo Journal of Structural Engineering vol 140 no 2 ArticleID 04013045 2014

[4] L Tesser and R Scotta ldquoFlexural and shear capacity of compos-ite steel truss and concrete beams with inferior precast concretebaserdquo Engineering Structures vol 49 pp 135ndash145 2013

[5] H J Hwang H G Park C H Lee et al ldquoSeismic resistanceof concrete-filled U-shaped steel beam-to-RC column connec-tionsrdquo Journal of Korean Society of Steel Construction vol 23 pp83ndash97 2011

[6] J Hassan and B Khosrow ldquoNonlinear seismic behavior evalua-tion of ductile beam-column connections in precast concreterdquoInternational Journal of Civil and Structural Engineering vol 1pp 445ndash453 2011

[7] A M Ioani and E Tripa ldquoStructural behavior of an innovativeall-precast concrete dual system for residential buildingsrdquo PCIJournal vol 57 no 1 pp 110ndash123 2012

[8] C Chou andCUang ldquoEffects of continuity plate and transversereinforcement on cyclic behavior of SRCmoment connectionsrdquoJournal of Structural Engineering vol 133 no 1 pp 96ndash104 2007

[9] Y K Ju and S D Kim ldquoStructural behavior of alternative lowfloor height system using structural ldquoteerdquo half precast concreteand horizontal studrdquoCanadian Journal of Civil Engineering vol32 no 2 pp 329ndash338 2005

[10] X Wang M Truijens L Hou Y Wang and Y Zhou ldquoInte-grating augmented reality with building informationmodelingonsite construction process controlling for liquefied natural gasindustryrdquoAutomation in Construction vol 40 pp 96ndash105 2014

[11] L Hou Y Wang X Wang et al ldquoCombining photogrammetryand augmented reality towards an integrated facility manage-ment system for the oil industryrdquo Proceedings of the IEEE vol102 no 2 pp 204ndash220 2014

[12] L Hou XWang L Bernold and P E D Love ldquoUsing animatedaugmented reality to cognitively guide assemblyrdquo Journal ofComputing in Civil Engineering vol 27 no 5 pp 439ndash451 2013

[13] YWang XWang JWang P Yung andG Jun ldquoEngagement offacilities management in design stage through BIM frameworkand a case studyrdquo Advances in Civil Engineering vol 2013Article ID 189105 8 pages 2013

[14] W K Hong J M Kim S C Park et al ldquoA new apartmentconstruction technology with effective CO

2emission reduction

capabilitiesrdquo Energy vol 35 no 6 pp 2639ndash2646 2010[15] W Hong S Park J Kim et al ldquoDevelopment of structural

composite hybrid systems and their application with regard tothe reduction of CO

2emissionsrdquo Indoor and Built Environment

vol 19 no 1 pp 151ndash162 2010[16] W Hong S Jeong S Park and J T Kim ldquoExperimental

investigation of an energy-efficient hybrid composite beamduring the construction phaserdquo Energy and Buildings vol 46pp 37ndash47 2012

[17] G P Hammond and C I Jones Inventory of Carbon amp Energy(ICE) Department of Mechanical Engineering University ofBath Bath UK 2008

[18] G P Hammond and C I Jones ldquoEmbodied energy and carbonin construction materialsrdquo Proceedings of Institution of CivilEngineers Energy vol 161 no 2 pp 87ndash98 2008

[19] National Institute of Environment Research (NIER) Domesticand foreign cement heavy metal analysis result (May 2013)NIER 2013 httpwwwniergokrericportalkornfnier-nf-02page

[20] S Kim W Hong J Kim and J T Kim ldquoThe developmentof modularized construction of enhanced precast compositestructural systems (Smart Green frame) and its embeddedenergy efficiencyrdquo Energy and Buildings vol 66 pp 16ndash21 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

10 Mathematical Problems in Engineering

Table 4 Heavy metal content standards in cement [19]

Cr6+ As Cd Cu Hg PbAve (May 2013) 1063mgkg 1287mgkg 102mgkg 8903mgkg 061mgkg 3284mgkg

(a) Fundamental translational mode (b) Mixed mode 1 (c) Mixed mode 2

(d) Fundamental translational mode (e) Mixed mode 1 (f) Mixed mode 2

Figure 11 Mode shapes

Figure 12 Side view of a hybrid composite beam

d

d998400

d998400998400

d998400998400998400

Figure 13 Cross-section of a hybrid composite beam

exact material quantity the hybrid composite beam designwas carried out based on the strain compatibility methodEquations (1) and (2) are the mean stress factor 120572 and thecentroid factor 120574 for any strain 120576

119888119898at the extreme com-

pression fiber calculated based on stress-strain relationshipEquations (3) and (5) represent the equilibrium equations ofcompressive and tensile forces at yield limit and maximumload limit state respectively The nominal moment capacitiesof a hybrid composite beam at yield limit andmaximum loadlimit state are calculated by (4) and (6) respectively Figures14 and 15 represent strain and stress diagram at yield limitand maximum load limit state respectively In both figuresblack color indicates steels and reinforcement rebars wereplasticized (yielded) while white color represents structuralmembers remained elastic The structural quantity requiredby apartment buildings with hybrid composite frames wasobtained from (6) and compared with that of conventionalbuildings with bearing walls as shown in Table 5 These

Mathematical Problems in Engineering 11

Table 5 Evaluation of structural systems

Buildingcomponent System Gross area Building material CO2 emission Energy consumption Cr6+ emission

Concrete(HPF = 35MPaBW = 25MPa)

HPF 9236m2 038m3m2 691(minus309) 1362 kg-CO2m

2 775(minus225) 10060MJm2 786

(minus214) 11062mgm2 689(minus311)

BW 6513m2 055m3m2 1000 1758 kg-CO2m2 1000 12796MJm2 1000 16061mgm2 100

Reinforcements HPF 9236m2 053 kNm2 726(minus274) 1445 kg-CO2m

2 724(minus276) 19314MJm2 713

(minus287) mdash mdash

BW 6513m2 073 kNm2 1000 1996 kg-CO2m2 1000 27107MJm2 1000 mdash mdash

Steel section HPF 9236m2 007 kNm2 1000 206 kg-CO2m2 1000 2721MJm2 1000 mdash mdash

BW 6513m2 mdashkNm2 mdash mdashkg-CO2m2 mdash mdashMJm2 mdash mdash mdash

lowastHPF hybrid precast frames BW bearing wall

400 MPa

301 MPa

1354 mm

120576st = 0001506

120576t = 120576y = 0002

120576c = 000178 f998400c

120576998400t = 000096 120576tEs = 192MPa

Figure 14 Strain and stress diagram at yield limit state

120576tEs = 286MPa

400 MPa

325 MPa

11946 mm

120576st = 000328

120576t = 120576y = 00042

120576c = 0003f998400c

120576998400t = 000143

Figure 15 Strain and stress diagram at maximum load limit state

equations would help engineer estimate precise constructionmaterials and understand how buildings with hybrid com-posite frames behave Consider

120572 = (int

0002

0

119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

119891

1015840

1198881 minus 100 (120576

119888minus 120576

119888119900) 119889120576

119888)

times (119891

1015840

119888120576

119888119898)

minus1

(1)

120574 = 1 minus ((int

0002

0

120576

119888119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

120576

119888119891

1015840

1198881 minus 100 (120576

119888minus 120576

119888119900) 119889120576

119888)

times (120576

119888119898[int

0002

0

119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

119891

1015840

1198881minus100 (120576

119888minus120576

119888119900) 119889120576

119888])

minus1

)

(2)

120572119891

1015840

119888119887119888 + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840) +

1

2

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

= 119860

119904119865

119910+ 119860

119891119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

1

2

119860

119908119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891)

(3)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908= 119905

119908(119889 minus 119888 minus 119889

1015840minus 119905

119891)

119872

119899= 120572119891

1015840

119888119887119888 (119888 minus 120574119888) + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840)

2

+

1

3

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

2

+ 119860

119904119865

119910(119889 minus 119888)

12 Mathematical Problems in Engineering

DayProcess

One floor

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7

Marking

Rebar work (wall)

Wall form installation

Slab form installation

Rebar work (slab) Electrical and mechanical

facilities (slab) Cleaning and pouring

Figure 16 Processes for constructing one floor of a conventional wall-type apartment building [20]

+ 119860

119891119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891) (119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

119905

119891

2

(119889 minus 119888 minus 119889

1015840minus

119905

119891

3

)

+

1

3

119860

119908119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891)

2

(4)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908= 119905

119908(119889 minus 119888 minus 119889

1015840minus 119905

119891)

120572119891

1015840

119888119887119888 + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840) +

1

2

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

= 119860

119904119865

119910+ 119860

119891119865

119910+ 119860

119908119901119865

119910+

1

2

119860

119908119899119910119864

119904120576

119904119910

(5)

where1198601015840119908= 119905

119908(119888minus119889

101584010158401015840)119860119908119901

= 119905

119908(119889minus119888+119889

1015840+119905

119891)+(120576

119904119910120576

119888)119888

119860

119908119899119910= 119905

119908(120576

119904119910120576

119888)119888

119872

119899= 120572119891

1015840

119888119887119888 (119888 minus 120574119888) + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840)

2

+

1

3

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

2

+ 119860

119904119865

119910(119889 minus 119888)

+ 119860

119891119865

119910(119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

1

2

119860

119908119901119865

119910(119889 minus 119888 minus 119889

1015840minus 119905

119891) +

120576

119904119910

120576

119888

119888

+

1

3

119860

119908119899119910119864

119904

(120576

119904119910)

2

120576

119888

119888

(6)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908119901

= 119905

119908119889 minus (119888 + 119889

1015840+ (120576

119904119910120576

119888)119888)

119860

119908119899119910= 119905

119908(120576

119904119910120576

119888)119888

A completed bearing wall apartment building wasselected for this comparison Apartment buildings withhybrid precast frames and bearingwall frameswere evaluatedin terms of building material CO

2emission energy con-

sumption and Cr6+ emission shown in Table 5 Construction

materials per square meters were calculated based on (5) and(6)whichwere then used to calculate the quantities of Table 5

The building materials of concrete and reinforcementsof apartment buildings with hybrid precast frames werereduced by 31 and 27 respectively compared with thatof bearing wall frame buildings The CO

2emission energy

consumption andCr6+ emission of apartment buildings withhybrid precast frames were also decreased compared withbearing wall frame buildings as shown in Table 5 exhibitingthe efficiency of using gravity hybrid precast frames forapartment buildings

6 Reduction in Construction Schedule

Figures 16 and 17 compare the construction time frames basedon the use of conventional bearing walls versus the proposedhybrid frames

The construction time is the sum of each critical path asshown in

119899

sum

119894=1

(CA119894) = CA

1+ CA2+ CA3+ CA4sdot sdot sdot (7)

The critical paths that affect construction time for abearing wall apartment are CA

1(marking 1 day) CA

2(rebar

work wall 1 day) CA3(wall form installation 2 days)

CA4(slab form installation 1 day) CA

5(rebar work slab 1

day) and CA6(cleaning and pouring 1 day) Installation of

electrical and mechanical facilities at the slab is performedwith rebar work of the slab and takes less time than that ofrebar work Electrical and mechanical facilities at the slab aretherefore excluded from the critical path The constructiontime per floor is seven days based on (7) The criticalpaths affecting construction time for an apartment buildingusing hybrid frames are CA

1(rebar work core wall 05

days) CA2(column-beam unit installation (1 day) beam

unit installation (15 days)) CA3(rebar work slab 05 days)

and CA4(cleaning and pouring 05 days) Column-beam

unit installation and beam unit installation are carried outalternately Beams are only installed at every second andthird floor since columns are erected as a three-story unit

Mathematical Problems in Engineering 13

DayProcess

First floor Second floor Third floor

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 Day 10

Rebar work (core wall)

Core wall form installationColumn-beam unit

installation Beam unit installation

Deck plate installation

Joint form installation

Rebar work (slab) Electrical and mechanical

facilities (slab) Cleaning and pouring

Figure 17 Processes for constructing three floors of an apartment building using hybrid frames [20]

Table 6 Comparative analysis of the construction period [20]

Structuraltype

Construction periodComparisonTypical

floor30-story apartment

building

Bearing wall 7 days1 floor 210 Days 1000Hybrid precastframe

10 days3floors 100 Days 476

As a result of the critical paths analysis the constructiontime per floor is four days for the first floor and threedays for the next two floors requiring ten days for theconstruction of three floors utilizing columns of a three-story unit The time for frame erection was reduced by 52when using hybrid frames highlighting their economic andconstruction benefits Erection of structural frames for onefloor using conventional bearing walls involves rebar workand concrete pouring and requires about seven days asshown in Figure 16 In contrast only three days were requiredto install wall and slab forms indicating that the overallconstruction was influenced by form work which is highlydependent on work skill However erection of three floorswith hybrid precast frames required only ten days whenthree-story hybrid precast columns were erected at one liftThe significant reduction in form work contributed to thedecrease in overall construction time obtained when usingthe hybrid precast frames as shown in Figure 17 As shown inTable 6 frame erection of a 30-story building required sevendays per floor or 210 days for the entire building when usingconventional bearing walls However only ten days per threefloors (or 100 days for the entire building) were required forframe erection of the building with hybrid precast frameswhich corresponds to a 524 reduction in frame erectiontime

7 Conclusions

This study described and characterized an optimized hybridprecast composite structural system for gravity systemMajorcontributions are summarized below

(1) Gravity hybrid precast frames were presented Thesehybrid frames consist of precast concrete and steelwhich can be erected at a speed similar to that of steelframes Steel sections inserted in precast columns andbeams are used as erection steel components

(2) Mathematical model of gravity hybrid precast beamwas presented at yield limit state and maximum loadlimit state Neutral axis of postyield state found fromequilibrium equations was used to calculate nominalmoment capacities of a hybrid composite beam atboth limit state

(3) The new building frame systems for gravity load-ings fabricated with hybrid precast composite framesconsisting of simple connections between columnsand beams were proposed in this paper The dualframe systems of moment connections with muchmore complicated construction details required sig-nificant time and costs than that of building framesystems of gravity loadings However the gravityhybrid precast composite structures will provide sim-plified construction method while enhancing econ-omyduring constructionThe reductions of construc-tion resources including concrete and reinforcements(31 reduction of concrete and 27 reduction of rein-forcements) were achieved when apartments were tobe built with hybrid precast frames

(4) The gravity hybrid precast frames use less construc-tion materials than conventional frames and there-fore reduce carbon dioxide and hazardous substanceemissions compared to conventional frames It was

14 Mathematical Problems in Engineering

observed the efficiency of using gravity hybrid precastframes for apartment building which decreased theCO2emission (23 reduction of concrete and 28

reduction of reinforcements) energy consumption(21 reduction of concrete and 29 reduction ofreinforcements) and Cr6+ emission compared withbearing wall frame buildings The use of gravityhybrid precast frames was demonstrated to providebetter solutions for environments and economy thanthat of conventional buildings

(5) Dynamic analysis of a 15-story building designedwith the proposed composite gravity frames was per-formed to characterize frequencies and mode shapesof the building for seismic design purposes

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by Grant from the Kyung HeeUniversity in 2013 (KHU-20130363)

References

[1] J F Hajjar ldquoComposite steel and concrete structural systems forseismic engineeringrdquo Journal of Constructional Steel Researchvol 58 no 5ndash8 pp 703ndash723 2002

[2] G Fabbrocino G Manfredi and E Cosenza ldquoDuctility ofcomposite beams under negative bending an equivalence indexfor reinforcing steel classificationrdquo Journal of ConstructionalSteel Research vol 58 no 2 pp 185ndash202 2001

[3] B Yang and K Tan ldquoBehaviour of composite beam-columnjoints under a middle-column-removal scenario experimentaltestsrdquo Journal of Structural Engineering vol 140 no 2 ArticleID 04013045 2014

[4] L Tesser and R Scotta ldquoFlexural and shear capacity of compos-ite steel truss and concrete beams with inferior precast concretebaserdquo Engineering Structures vol 49 pp 135ndash145 2013

[5] H J Hwang H G Park C H Lee et al ldquoSeismic resistanceof concrete-filled U-shaped steel beam-to-RC column connec-tionsrdquo Journal of Korean Society of Steel Construction vol 23 pp83ndash97 2011

[6] J Hassan and B Khosrow ldquoNonlinear seismic behavior evalua-tion of ductile beam-column connections in precast concreterdquoInternational Journal of Civil and Structural Engineering vol 1pp 445ndash453 2011

[7] A M Ioani and E Tripa ldquoStructural behavior of an innovativeall-precast concrete dual system for residential buildingsrdquo PCIJournal vol 57 no 1 pp 110ndash123 2012

[8] C Chou andCUang ldquoEffects of continuity plate and transversereinforcement on cyclic behavior of SRCmoment connectionsrdquoJournal of Structural Engineering vol 133 no 1 pp 96ndash104 2007

[9] Y K Ju and S D Kim ldquoStructural behavior of alternative lowfloor height system using structural ldquoteerdquo half precast concreteand horizontal studrdquoCanadian Journal of Civil Engineering vol32 no 2 pp 329ndash338 2005

[10] X Wang M Truijens L Hou Y Wang and Y Zhou ldquoInte-grating augmented reality with building informationmodelingonsite construction process controlling for liquefied natural gasindustryrdquoAutomation in Construction vol 40 pp 96ndash105 2014

[11] L Hou Y Wang X Wang et al ldquoCombining photogrammetryand augmented reality towards an integrated facility manage-ment system for the oil industryrdquo Proceedings of the IEEE vol102 no 2 pp 204ndash220 2014

[12] L Hou XWang L Bernold and P E D Love ldquoUsing animatedaugmented reality to cognitively guide assemblyrdquo Journal ofComputing in Civil Engineering vol 27 no 5 pp 439ndash451 2013

[13] YWang XWang JWang P Yung andG Jun ldquoEngagement offacilities management in design stage through BIM frameworkand a case studyrdquo Advances in Civil Engineering vol 2013Article ID 189105 8 pages 2013

[14] W K Hong J M Kim S C Park et al ldquoA new apartmentconstruction technology with effective CO

2emission reduction

capabilitiesrdquo Energy vol 35 no 6 pp 2639ndash2646 2010[15] W Hong S Park J Kim et al ldquoDevelopment of structural

composite hybrid systems and their application with regard tothe reduction of CO

2emissionsrdquo Indoor and Built Environment

vol 19 no 1 pp 151ndash162 2010[16] W Hong S Jeong S Park and J T Kim ldquoExperimental

investigation of an energy-efficient hybrid composite beamduring the construction phaserdquo Energy and Buildings vol 46pp 37ndash47 2012

[17] G P Hammond and C I Jones Inventory of Carbon amp Energy(ICE) Department of Mechanical Engineering University ofBath Bath UK 2008

[18] G P Hammond and C I Jones ldquoEmbodied energy and carbonin construction materialsrdquo Proceedings of Institution of CivilEngineers Energy vol 161 no 2 pp 87ndash98 2008

[19] National Institute of Environment Research (NIER) Domesticand foreign cement heavy metal analysis result (May 2013)NIER 2013 httpwwwniergokrericportalkornfnier-nf-02page

[20] S Kim W Hong J Kim and J T Kim ldquoThe developmentof modularized construction of enhanced precast compositestructural systems (Smart Green frame) and its embeddedenergy efficiencyrdquo Energy and Buildings vol 66 pp 16ndash21 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 11

Table 5 Evaluation of structural systems

Buildingcomponent System Gross area Building material CO2 emission Energy consumption Cr6+ emission

Concrete(HPF = 35MPaBW = 25MPa)

HPF 9236m2 038m3m2 691(minus309) 1362 kg-CO2m

2 775(minus225) 10060MJm2 786

(minus214) 11062mgm2 689(minus311)

BW 6513m2 055m3m2 1000 1758 kg-CO2m2 1000 12796MJm2 1000 16061mgm2 100

Reinforcements HPF 9236m2 053 kNm2 726(minus274) 1445 kg-CO2m

2 724(minus276) 19314MJm2 713

(minus287) mdash mdash

BW 6513m2 073 kNm2 1000 1996 kg-CO2m2 1000 27107MJm2 1000 mdash mdash

Steel section HPF 9236m2 007 kNm2 1000 206 kg-CO2m2 1000 2721MJm2 1000 mdash mdash

BW 6513m2 mdashkNm2 mdash mdashkg-CO2m2 mdash mdashMJm2 mdash mdash mdash

lowastHPF hybrid precast frames BW bearing wall

400 MPa

301 MPa

1354 mm

120576st = 0001506

120576t = 120576y = 0002

120576c = 000178 f998400c

120576998400t = 000096 120576tEs = 192MPa

Figure 14 Strain and stress diagram at yield limit state

120576tEs = 286MPa

400 MPa

325 MPa

11946 mm

120576st = 000328

120576t = 120576y = 00042

120576c = 0003f998400c

120576998400t = 000143

Figure 15 Strain and stress diagram at maximum load limit state

equations would help engineer estimate precise constructionmaterials and understand how buildings with hybrid com-posite frames behave Consider

120572 = (int

0002

0

119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

119891

1015840

1198881 minus 100 (120576

119888minus 120576

119888119900) 119889120576

119888)

times (119891

1015840

119888120576

119888119898)

minus1

(1)

120574 = 1 minus ((int

0002

0

120576

119888119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

120576

119888119891

1015840

1198881 minus 100 (120576

119888minus 120576

119888119900) 119889120576

119888)

times (120576

119888119898[int

0002

0

119891

1015840

119888

2120576

119888

120576

119888119900

minus (

120576

119888

120576

119888119900

)

2

119889120576

119888

+ int

0003

0002

119891

1015840

1198881minus100 (120576

119888minus120576

119888119900) 119889120576

119888])

minus1

)

(2)

120572119891

1015840

119888119887119888 + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840) +

1

2

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

= 119860

119904119865

119910+ 119860

119891119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

1

2

119860

119908119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891)

(3)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908= 119905

119908(119889 minus 119888 minus 119889

1015840minus 119905

119891)

119872

119899= 120572119891

1015840

119888119887119888 (119888 minus 120574119888) + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840)

2

+

1

3

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

2

+ 119860

119904119865

119910(119889 minus 119888)

12 Mathematical Problems in Engineering

DayProcess

One floor

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7

Marking

Rebar work (wall)

Wall form installation

Slab form installation

Rebar work (slab) Electrical and mechanical

facilities (slab) Cleaning and pouring

Figure 16 Processes for constructing one floor of a conventional wall-type apartment building [20]

+ 119860

119891119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891) (119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

119905

119891

2

(119889 minus 119888 minus 119889

1015840minus

119905

119891

3

)

+

1

3

119860

119908119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891)

2

(4)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908= 119905

119908(119889 minus 119888 minus 119889

1015840minus 119905

119891)

120572119891

1015840

119888119887119888 + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840) +

1

2

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

= 119860

119904119865

119910+ 119860

119891119865

119910+ 119860

119908119901119865

119910+

1

2

119860

119908119899119910119864

119904120576

119904119910

(5)

where1198601015840119908= 119905

119908(119888minus119889

101584010158401015840)119860119908119901

= 119905

119908(119889minus119888+119889

1015840+119905

119891)+(120576

119904119910120576

119888)119888

119860

119908119899119910= 119905

119908(120576

119904119910120576

119888)119888

119872

119899= 120572119891

1015840

119888119887119888 (119888 minus 120574119888) + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840)

2

+

1

3

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

2

+ 119860

119904119865

119910(119889 minus 119888)

+ 119860

119891119865

119910(119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

1

2

119860

119908119901119865

119910(119889 minus 119888 minus 119889

1015840minus 119905

119891) +

120576

119904119910

120576

119888

119888

+

1

3

119860

119908119899119910119864

119904

(120576

119904119910)

2

120576

119888

119888

(6)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908119901

= 119905

119908119889 minus (119888 + 119889

1015840+ (120576

119904119910120576

119888)119888)

119860

119908119899119910= 119905

119908(120576

119904119910120576

119888)119888

A completed bearing wall apartment building wasselected for this comparison Apartment buildings withhybrid precast frames and bearingwall frameswere evaluatedin terms of building material CO

2emission energy con-

sumption and Cr6+ emission shown in Table 5 Construction

materials per square meters were calculated based on (5) and(6)whichwere then used to calculate the quantities of Table 5

The building materials of concrete and reinforcementsof apartment buildings with hybrid precast frames werereduced by 31 and 27 respectively compared with thatof bearing wall frame buildings The CO

2emission energy

consumption andCr6+ emission of apartment buildings withhybrid precast frames were also decreased compared withbearing wall frame buildings as shown in Table 5 exhibitingthe efficiency of using gravity hybrid precast frames forapartment buildings

6 Reduction in Construction Schedule

Figures 16 and 17 compare the construction time frames basedon the use of conventional bearing walls versus the proposedhybrid frames

The construction time is the sum of each critical path asshown in

119899

sum

119894=1

(CA119894) = CA

1+ CA2+ CA3+ CA4sdot sdot sdot (7)

The critical paths that affect construction time for abearing wall apartment are CA

1(marking 1 day) CA

2(rebar

work wall 1 day) CA3(wall form installation 2 days)

CA4(slab form installation 1 day) CA

5(rebar work slab 1

day) and CA6(cleaning and pouring 1 day) Installation of

electrical and mechanical facilities at the slab is performedwith rebar work of the slab and takes less time than that ofrebar work Electrical and mechanical facilities at the slab aretherefore excluded from the critical path The constructiontime per floor is seven days based on (7) The criticalpaths affecting construction time for an apartment buildingusing hybrid frames are CA

1(rebar work core wall 05

days) CA2(column-beam unit installation (1 day) beam

unit installation (15 days)) CA3(rebar work slab 05 days)

and CA4(cleaning and pouring 05 days) Column-beam

unit installation and beam unit installation are carried outalternately Beams are only installed at every second andthird floor since columns are erected as a three-story unit

Mathematical Problems in Engineering 13

DayProcess

First floor Second floor Third floor

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 Day 10

Rebar work (core wall)

Core wall form installationColumn-beam unit

installation Beam unit installation

Deck plate installation

Joint form installation

Rebar work (slab) Electrical and mechanical

facilities (slab) Cleaning and pouring

Figure 17 Processes for constructing three floors of an apartment building using hybrid frames [20]

Table 6 Comparative analysis of the construction period [20]

Structuraltype

Construction periodComparisonTypical

floor30-story apartment

building

Bearing wall 7 days1 floor 210 Days 1000Hybrid precastframe

10 days3floors 100 Days 476

As a result of the critical paths analysis the constructiontime per floor is four days for the first floor and threedays for the next two floors requiring ten days for theconstruction of three floors utilizing columns of a three-story unit The time for frame erection was reduced by 52when using hybrid frames highlighting their economic andconstruction benefits Erection of structural frames for onefloor using conventional bearing walls involves rebar workand concrete pouring and requires about seven days asshown in Figure 16 In contrast only three days were requiredto install wall and slab forms indicating that the overallconstruction was influenced by form work which is highlydependent on work skill However erection of three floorswith hybrid precast frames required only ten days whenthree-story hybrid precast columns were erected at one liftThe significant reduction in form work contributed to thedecrease in overall construction time obtained when usingthe hybrid precast frames as shown in Figure 17 As shown inTable 6 frame erection of a 30-story building required sevendays per floor or 210 days for the entire building when usingconventional bearing walls However only ten days per threefloors (or 100 days for the entire building) were required forframe erection of the building with hybrid precast frameswhich corresponds to a 524 reduction in frame erectiontime

7 Conclusions

This study described and characterized an optimized hybridprecast composite structural system for gravity systemMajorcontributions are summarized below

(1) Gravity hybrid precast frames were presented Thesehybrid frames consist of precast concrete and steelwhich can be erected at a speed similar to that of steelframes Steel sections inserted in precast columns andbeams are used as erection steel components

(2) Mathematical model of gravity hybrid precast beamwas presented at yield limit state and maximum loadlimit state Neutral axis of postyield state found fromequilibrium equations was used to calculate nominalmoment capacities of a hybrid composite beam atboth limit state

(3) The new building frame systems for gravity load-ings fabricated with hybrid precast composite framesconsisting of simple connections between columnsand beams were proposed in this paper The dualframe systems of moment connections with muchmore complicated construction details required sig-nificant time and costs than that of building framesystems of gravity loadings However the gravityhybrid precast composite structures will provide sim-plified construction method while enhancing econ-omyduring constructionThe reductions of construc-tion resources including concrete and reinforcements(31 reduction of concrete and 27 reduction of rein-forcements) were achieved when apartments were tobe built with hybrid precast frames

(4) The gravity hybrid precast frames use less construc-tion materials than conventional frames and there-fore reduce carbon dioxide and hazardous substanceemissions compared to conventional frames It was

14 Mathematical Problems in Engineering

observed the efficiency of using gravity hybrid precastframes for apartment building which decreased theCO2emission (23 reduction of concrete and 28

reduction of reinforcements) energy consumption(21 reduction of concrete and 29 reduction ofreinforcements) and Cr6+ emission compared withbearing wall frame buildings The use of gravityhybrid precast frames was demonstrated to providebetter solutions for environments and economy thanthat of conventional buildings

(5) Dynamic analysis of a 15-story building designedwith the proposed composite gravity frames was per-formed to characterize frequencies and mode shapesof the building for seismic design purposes

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by Grant from the Kyung HeeUniversity in 2013 (KHU-20130363)

References

[1] J F Hajjar ldquoComposite steel and concrete structural systems forseismic engineeringrdquo Journal of Constructional Steel Researchvol 58 no 5ndash8 pp 703ndash723 2002

[2] G Fabbrocino G Manfredi and E Cosenza ldquoDuctility ofcomposite beams under negative bending an equivalence indexfor reinforcing steel classificationrdquo Journal of ConstructionalSteel Research vol 58 no 2 pp 185ndash202 2001

[3] B Yang and K Tan ldquoBehaviour of composite beam-columnjoints under a middle-column-removal scenario experimentaltestsrdquo Journal of Structural Engineering vol 140 no 2 ArticleID 04013045 2014

[4] L Tesser and R Scotta ldquoFlexural and shear capacity of compos-ite steel truss and concrete beams with inferior precast concretebaserdquo Engineering Structures vol 49 pp 135ndash145 2013

[5] H J Hwang H G Park C H Lee et al ldquoSeismic resistanceof concrete-filled U-shaped steel beam-to-RC column connec-tionsrdquo Journal of Korean Society of Steel Construction vol 23 pp83ndash97 2011

[6] J Hassan and B Khosrow ldquoNonlinear seismic behavior evalua-tion of ductile beam-column connections in precast concreterdquoInternational Journal of Civil and Structural Engineering vol 1pp 445ndash453 2011

[7] A M Ioani and E Tripa ldquoStructural behavior of an innovativeall-precast concrete dual system for residential buildingsrdquo PCIJournal vol 57 no 1 pp 110ndash123 2012

[8] C Chou andCUang ldquoEffects of continuity plate and transversereinforcement on cyclic behavior of SRCmoment connectionsrdquoJournal of Structural Engineering vol 133 no 1 pp 96ndash104 2007

[9] Y K Ju and S D Kim ldquoStructural behavior of alternative lowfloor height system using structural ldquoteerdquo half precast concreteand horizontal studrdquoCanadian Journal of Civil Engineering vol32 no 2 pp 329ndash338 2005

[10] X Wang M Truijens L Hou Y Wang and Y Zhou ldquoInte-grating augmented reality with building informationmodelingonsite construction process controlling for liquefied natural gasindustryrdquoAutomation in Construction vol 40 pp 96ndash105 2014

[11] L Hou Y Wang X Wang et al ldquoCombining photogrammetryand augmented reality towards an integrated facility manage-ment system for the oil industryrdquo Proceedings of the IEEE vol102 no 2 pp 204ndash220 2014

[12] L Hou XWang L Bernold and P E D Love ldquoUsing animatedaugmented reality to cognitively guide assemblyrdquo Journal ofComputing in Civil Engineering vol 27 no 5 pp 439ndash451 2013

[13] YWang XWang JWang P Yung andG Jun ldquoEngagement offacilities management in design stage through BIM frameworkand a case studyrdquo Advances in Civil Engineering vol 2013Article ID 189105 8 pages 2013

[14] W K Hong J M Kim S C Park et al ldquoA new apartmentconstruction technology with effective CO

2emission reduction

capabilitiesrdquo Energy vol 35 no 6 pp 2639ndash2646 2010[15] W Hong S Park J Kim et al ldquoDevelopment of structural

composite hybrid systems and their application with regard tothe reduction of CO

2emissionsrdquo Indoor and Built Environment

vol 19 no 1 pp 151ndash162 2010[16] W Hong S Jeong S Park and J T Kim ldquoExperimental

investigation of an energy-efficient hybrid composite beamduring the construction phaserdquo Energy and Buildings vol 46pp 37ndash47 2012

[17] G P Hammond and C I Jones Inventory of Carbon amp Energy(ICE) Department of Mechanical Engineering University ofBath Bath UK 2008

[18] G P Hammond and C I Jones ldquoEmbodied energy and carbonin construction materialsrdquo Proceedings of Institution of CivilEngineers Energy vol 161 no 2 pp 87ndash98 2008

[19] National Institute of Environment Research (NIER) Domesticand foreign cement heavy metal analysis result (May 2013)NIER 2013 httpwwwniergokrericportalkornfnier-nf-02page

[20] S Kim W Hong J Kim and J T Kim ldquoThe developmentof modularized construction of enhanced precast compositestructural systems (Smart Green frame) and its embeddedenergy efficiencyrdquo Energy and Buildings vol 66 pp 16ndash21 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

12 Mathematical Problems in Engineering

DayProcess

One floor

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7

Marking

Rebar work (wall)

Wall form installation

Slab form installation

Rebar work (slab) Electrical and mechanical

facilities (slab) Cleaning and pouring

Figure 16 Processes for constructing one floor of a conventional wall-type apartment building [20]

+ 119860

119891119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891) (119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

119905

119891

2

(119889 minus 119888 minus 119889

1015840minus

119905

119891

3

)

+

1

3

119860

119908119864

119904

120576

119888

119888

(119889 minus 119888 minus 119889

1015840minus 119905

119891)

2

(4)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908= 119905

119908(119889 minus 119888 minus 119889

1015840minus 119905

119891)

120572119891

1015840

119888119887119888 + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840) +

1

2

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

= 119860

119904119865

119910+ 119860

119891119865

119910+ 119860

119908119901119865

119910+

1

2

119860

119908119899119910119864

119904120576

119904119910

(5)

where1198601015840119908= 119905

119908(119888minus119889

101584010158401015840)119860119908119901

= 119905

119908(119889minus119888+119889

1015840+119905

119891)+(120576

119904119910120576

119888)119888

119860

119908119899119910= 119905

119908(120576

119904119910120576

119888)119888

119872

119899= 120572119891

1015840

119888119887119888 (119888 minus 120574119888) + 119860

1015840

119904119864

119904

120576

119888

119888

(119888 minus 119889

10158401015840)

2

+

1

3

119860

1015840

119908119864

119904

120576

119888

119888

(119888 minus 119889

101584010158401015840)

2

+ 119860

119904119865

119910(119889 minus 119888)

+ 119860

119891119865

119910(119889 minus 119888 minus 119889

1015840minus

119905

119891

2

)

+

1

2

119860

119908119901119865

119910(119889 minus 119888 minus 119889

1015840minus 119905

119891) +

120576

119904119910

120576

119888

119888

+

1

3

119860

119908119899119910119864

119904

(120576

119904119910)

2

120576

119888

119888

(6)

where 1198601015840119908= 119905

119908(119888 minus 119889

101584010158401015840) 119860119908119901

= 119905

119908119889 minus (119888 + 119889

1015840+ (120576

119904119910120576

119888)119888)

119860

119908119899119910= 119905

119908(120576

119904119910120576

119888)119888

A completed bearing wall apartment building wasselected for this comparison Apartment buildings withhybrid precast frames and bearingwall frameswere evaluatedin terms of building material CO

2emission energy con-

sumption and Cr6+ emission shown in Table 5 Construction

materials per square meters were calculated based on (5) and(6)whichwere then used to calculate the quantities of Table 5

The building materials of concrete and reinforcementsof apartment buildings with hybrid precast frames werereduced by 31 and 27 respectively compared with thatof bearing wall frame buildings The CO

2emission energy

consumption andCr6+ emission of apartment buildings withhybrid precast frames were also decreased compared withbearing wall frame buildings as shown in Table 5 exhibitingthe efficiency of using gravity hybrid precast frames forapartment buildings

6 Reduction in Construction Schedule

Figures 16 and 17 compare the construction time frames basedon the use of conventional bearing walls versus the proposedhybrid frames

The construction time is the sum of each critical path asshown in

119899

sum

119894=1

(CA119894) = CA

1+ CA2+ CA3+ CA4sdot sdot sdot (7)

The critical paths that affect construction time for abearing wall apartment are CA

1(marking 1 day) CA

2(rebar

work wall 1 day) CA3(wall form installation 2 days)

CA4(slab form installation 1 day) CA

5(rebar work slab 1

day) and CA6(cleaning and pouring 1 day) Installation of

electrical and mechanical facilities at the slab is performedwith rebar work of the slab and takes less time than that ofrebar work Electrical and mechanical facilities at the slab aretherefore excluded from the critical path The constructiontime per floor is seven days based on (7) The criticalpaths affecting construction time for an apartment buildingusing hybrid frames are CA

1(rebar work core wall 05

days) CA2(column-beam unit installation (1 day) beam

unit installation (15 days)) CA3(rebar work slab 05 days)

and CA4(cleaning and pouring 05 days) Column-beam

unit installation and beam unit installation are carried outalternately Beams are only installed at every second andthird floor since columns are erected as a three-story unit

Mathematical Problems in Engineering 13

DayProcess

First floor Second floor Third floor

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 Day 10

Rebar work (core wall)

Core wall form installationColumn-beam unit

installation Beam unit installation

Deck plate installation

Joint form installation

Rebar work (slab) Electrical and mechanical

facilities (slab) Cleaning and pouring

Figure 17 Processes for constructing three floors of an apartment building using hybrid frames [20]

Table 6 Comparative analysis of the construction period [20]

Structuraltype

Construction periodComparisonTypical

floor30-story apartment

building

Bearing wall 7 days1 floor 210 Days 1000Hybrid precastframe

10 days3floors 100 Days 476

As a result of the critical paths analysis the constructiontime per floor is four days for the first floor and threedays for the next two floors requiring ten days for theconstruction of three floors utilizing columns of a three-story unit The time for frame erection was reduced by 52when using hybrid frames highlighting their economic andconstruction benefits Erection of structural frames for onefloor using conventional bearing walls involves rebar workand concrete pouring and requires about seven days asshown in Figure 16 In contrast only three days were requiredto install wall and slab forms indicating that the overallconstruction was influenced by form work which is highlydependent on work skill However erection of three floorswith hybrid precast frames required only ten days whenthree-story hybrid precast columns were erected at one liftThe significant reduction in form work contributed to thedecrease in overall construction time obtained when usingthe hybrid precast frames as shown in Figure 17 As shown inTable 6 frame erection of a 30-story building required sevendays per floor or 210 days for the entire building when usingconventional bearing walls However only ten days per threefloors (or 100 days for the entire building) were required forframe erection of the building with hybrid precast frameswhich corresponds to a 524 reduction in frame erectiontime

7 Conclusions

This study described and characterized an optimized hybridprecast composite structural system for gravity systemMajorcontributions are summarized below

(1) Gravity hybrid precast frames were presented Thesehybrid frames consist of precast concrete and steelwhich can be erected at a speed similar to that of steelframes Steel sections inserted in precast columns andbeams are used as erection steel components

(2) Mathematical model of gravity hybrid precast beamwas presented at yield limit state and maximum loadlimit state Neutral axis of postyield state found fromequilibrium equations was used to calculate nominalmoment capacities of a hybrid composite beam atboth limit state

(3) The new building frame systems for gravity load-ings fabricated with hybrid precast composite framesconsisting of simple connections between columnsand beams were proposed in this paper The dualframe systems of moment connections with muchmore complicated construction details required sig-nificant time and costs than that of building framesystems of gravity loadings However the gravityhybrid precast composite structures will provide sim-plified construction method while enhancing econ-omyduring constructionThe reductions of construc-tion resources including concrete and reinforcements(31 reduction of concrete and 27 reduction of rein-forcements) were achieved when apartments were tobe built with hybrid precast frames

(4) The gravity hybrid precast frames use less construc-tion materials than conventional frames and there-fore reduce carbon dioxide and hazardous substanceemissions compared to conventional frames It was

14 Mathematical Problems in Engineering

observed the efficiency of using gravity hybrid precastframes for apartment building which decreased theCO2emission (23 reduction of concrete and 28

reduction of reinforcements) energy consumption(21 reduction of concrete and 29 reduction ofreinforcements) and Cr6+ emission compared withbearing wall frame buildings The use of gravityhybrid precast frames was demonstrated to providebetter solutions for environments and economy thanthat of conventional buildings

(5) Dynamic analysis of a 15-story building designedwith the proposed composite gravity frames was per-formed to characterize frequencies and mode shapesof the building for seismic design purposes

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by Grant from the Kyung HeeUniversity in 2013 (KHU-20130363)

References

[1] J F Hajjar ldquoComposite steel and concrete structural systems forseismic engineeringrdquo Journal of Constructional Steel Researchvol 58 no 5ndash8 pp 703ndash723 2002

[2] G Fabbrocino G Manfredi and E Cosenza ldquoDuctility ofcomposite beams under negative bending an equivalence indexfor reinforcing steel classificationrdquo Journal of ConstructionalSteel Research vol 58 no 2 pp 185ndash202 2001

[3] B Yang and K Tan ldquoBehaviour of composite beam-columnjoints under a middle-column-removal scenario experimentaltestsrdquo Journal of Structural Engineering vol 140 no 2 ArticleID 04013045 2014

[4] L Tesser and R Scotta ldquoFlexural and shear capacity of compos-ite steel truss and concrete beams with inferior precast concretebaserdquo Engineering Structures vol 49 pp 135ndash145 2013

[5] H J Hwang H G Park C H Lee et al ldquoSeismic resistanceof concrete-filled U-shaped steel beam-to-RC column connec-tionsrdquo Journal of Korean Society of Steel Construction vol 23 pp83ndash97 2011

[6] J Hassan and B Khosrow ldquoNonlinear seismic behavior evalua-tion of ductile beam-column connections in precast concreterdquoInternational Journal of Civil and Structural Engineering vol 1pp 445ndash453 2011

[7] A M Ioani and E Tripa ldquoStructural behavior of an innovativeall-precast concrete dual system for residential buildingsrdquo PCIJournal vol 57 no 1 pp 110ndash123 2012

[8] C Chou andCUang ldquoEffects of continuity plate and transversereinforcement on cyclic behavior of SRCmoment connectionsrdquoJournal of Structural Engineering vol 133 no 1 pp 96ndash104 2007

[9] Y K Ju and S D Kim ldquoStructural behavior of alternative lowfloor height system using structural ldquoteerdquo half precast concreteand horizontal studrdquoCanadian Journal of Civil Engineering vol32 no 2 pp 329ndash338 2005

[10] X Wang M Truijens L Hou Y Wang and Y Zhou ldquoInte-grating augmented reality with building informationmodelingonsite construction process controlling for liquefied natural gasindustryrdquoAutomation in Construction vol 40 pp 96ndash105 2014

[11] L Hou Y Wang X Wang et al ldquoCombining photogrammetryand augmented reality towards an integrated facility manage-ment system for the oil industryrdquo Proceedings of the IEEE vol102 no 2 pp 204ndash220 2014

[12] L Hou XWang L Bernold and P E D Love ldquoUsing animatedaugmented reality to cognitively guide assemblyrdquo Journal ofComputing in Civil Engineering vol 27 no 5 pp 439ndash451 2013

[13] YWang XWang JWang P Yung andG Jun ldquoEngagement offacilities management in design stage through BIM frameworkand a case studyrdquo Advances in Civil Engineering vol 2013Article ID 189105 8 pages 2013

[14] W K Hong J M Kim S C Park et al ldquoA new apartmentconstruction technology with effective CO

2emission reduction

capabilitiesrdquo Energy vol 35 no 6 pp 2639ndash2646 2010[15] W Hong S Park J Kim et al ldquoDevelopment of structural

composite hybrid systems and their application with regard tothe reduction of CO

2emissionsrdquo Indoor and Built Environment

vol 19 no 1 pp 151ndash162 2010[16] W Hong S Jeong S Park and J T Kim ldquoExperimental

investigation of an energy-efficient hybrid composite beamduring the construction phaserdquo Energy and Buildings vol 46pp 37ndash47 2012

[17] G P Hammond and C I Jones Inventory of Carbon amp Energy(ICE) Department of Mechanical Engineering University ofBath Bath UK 2008

[18] G P Hammond and C I Jones ldquoEmbodied energy and carbonin construction materialsrdquo Proceedings of Institution of CivilEngineers Energy vol 161 no 2 pp 87ndash98 2008

[19] National Institute of Environment Research (NIER) Domesticand foreign cement heavy metal analysis result (May 2013)NIER 2013 httpwwwniergokrericportalkornfnier-nf-02page

[20] S Kim W Hong J Kim and J T Kim ldquoThe developmentof modularized construction of enhanced precast compositestructural systems (Smart Green frame) and its embeddedenergy efficiencyrdquo Energy and Buildings vol 66 pp 16ndash21 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 13

DayProcess

First floor Second floor Third floor

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 Day 10

Rebar work (core wall)

Core wall form installationColumn-beam unit

installation Beam unit installation

Deck plate installation

Joint form installation

Rebar work (slab) Electrical and mechanical

facilities (slab) Cleaning and pouring

Figure 17 Processes for constructing three floors of an apartment building using hybrid frames [20]

Table 6 Comparative analysis of the construction period [20]

Structuraltype

Construction periodComparisonTypical

floor30-story apartment

building

Bearing wall 7 days1 floor 210 Days 1000Hybrid precastframe

10 days3floors 100 Days 476

As a result of the critical paths analysis the constructiontime per floor is four days for the first floor and threedays for the next two floors requiring ten days for theconstruction of three floors utilizing columns of a three-story unit The time for frame erection was reduced by 52when using hybrid frames highlighting their economic andconstruction benefits Erection of structural frames for onefloor using conventional bearing walls involves rebar workand concrete pouring and requires about seven days asshown in Figure 16 In contrast only three days were requiredto install wall and slab forms indicating that the overallconstruction was influenced by form work which is highlydependent on work skill However erection of three floorswith hybrid precast frames required only ten days whenthree-story hybrid precast columns were erected at one liftThe significant reduction in form work contributed to thedecrease in overall construction time obtained when usingthe hybrid precast frames as shown in Figure 17 As shown inTable 6 frame erection of a 30-story building required sevendays per floor or 210 days for the entire building when usingconventional bearing walls However only ten days per threefloors (or 100 days for the entire building) were required forframe erection of the building with hybrid precast frameswhich corresponds to a 524 reduction in frame erectiontime

7 Conclusions

This study described and characterized an optimized hybridprecast composite structural system for gravity systemMajorcontributions are summarized below

(1) Gravity hybrid precast frames were presented Thesehybrid frames consist of precast concrete and steelwhich can be erected at a speed similar to that of steelframes Steel sections inserted in precast columns andbeams are used as erection steel components

(2) Mathematical model of gravity hybrid precast beamwas presented at yield limit state and maximum loadlimit state Neutral axis of postyield state found fromequilibrium equations was used to calculate nominalmoment capacities of a hybrid composite beam atboth limit state

(3) The new building frame systems for gravity load-ings fabricated with hybrid precast composite framesconsisting of simple connections between columnsand beams were proposed in this paper The dualframe systems of moment connections with muchmore complicated construction details required sig-nificant time and costs than that of building framesystems of gravity loadings However the gravityhybrid precast composite structures will provide sim-plified construction method while enhancing econ-omyduring constructionThe reductions of construc-tion resources including concrete and reinforcements(31 reduction of concrete and 27 reduction of rein-forcements) were achieved when apartments were tobe built with hybrid precast frames

(4) The gravity hybrid precast frames use less construc-tion materials than conventional frames and there-fore reduce carbon dioxide and hazardous substanceemissions compared to conventional frames It was

14 Mathematical Problems in Engineering

observed the efficiency of using gravity hybrid precastframes for apartment building which decreased theCO2emission (23 reduction of concrete and 28

reduction of reinforcements) energy consumption(21 reduction of concrete and 29 reduction ofreinforcements) and Cr6+ emission compared withbearing wall frame buildings The use of gravityhybrid precast frames was demonstrated to providebetter solutions for environments and economy thanthat of conventional buildings

(5) Dynamic analysis of a 15-story building designedwith the proposed composite gravity frames was per-formed to characterize frequencies and mode shapesof the building for seismic design purposes

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by Grant from the Kyung HeeUniversity in 2013 (KHU-20130363)

References

[1] J F Hajjar ldquoComposite steel and concrete structural systems forseismic engineeringrdquo Journal of Constructional Steel Researchvol 58 no 5ndash8 pp 703ndash723 2002

[2] G Fabbrocino G Manfredi and E Cosenza ldquoDuctility ofcomposite beams under negative bending an equivalence indexfor reinforcing steel classificationrdquo Journal of ConstructionalSteel Research vol 58 no 2 pp 185ndash202 2001

[3] B Yang and K Tan ldquoBehaviour of composite beam-columnjoints under a middle-column-removal scenario experimentaltestsrdquo Journal of Structural Engineering vol 140 no 2 ArticleID 04013045 2014

[4] L Tesser and R Scotta ldquoFlexural and shear capacity of compos-ite steel truss and concrete beams with inferior precast concretebaserdquo Engineering Structures vol 49 pp 135ndash145 2013

[5] H J Hwang H G Park C H Lee et al ldquoSeismic resistanceof concrete-filled U-shaped steel beam-to-RC column connec-tionsrdquo Journal of Korean Society of Steel Construction vol 23 pp83ndash97 2011

[6] J Hassan and B Khosrow ldquoNonlinear seismic behavior evalua-tion of ductile beam-column connections in precast concreterdquoInternational Journal of Civil and Structural Engineering vol 1pp 445ndash453 2011

[7] A M Ioani and E Tripa ldquoStructural behavior of an innovativeall-precast concrete dual system for residential buildingsrdquo PCIJournal vol 57 no 1 pp 110ndash123 2012

[8] C Chou andCUang ldquoEffects of continuity plate and transversereinforcement on cyclic behavior of SRCmoment connectionsrdquoJournal of Structural Engineering vol 133 no 1 pp 96ndash104 2007

[9] Y K Ju and S D Kim ldquoStructural behavior of alternative lowfloor height system using structural ldquoteerdquo half precast concreteand horizontal studrdquoCanadian Journal of Civil Engineering vol32 no 2 pp 329ndash338 2005

[10] X Wang M Truijens L Hou Y Wang and Y Zhou ldquoInte-grating augmented reality with building informationmodelingonsite construction process controlling for liquefied natural gasindustryrdquoAutomation in Construction vol 40 pp 96ndash105 2014

[11] L Hou Y Wang X Wang et al ldquoCombining photogrammetryand augmented reality towards an integrated facility manage-ment system for the oil industryrdquo Proceedings of the IEEE vol102 no 2 pp 204ndash220 2014

[12] L Hou XWang L Bernold and P E D Love ldquoUsing animatedaugmented reality to cognitively guide assemblyrdquo Journal ofComputing in Civil Engineering vol 27 no 5 pp 439ndash451 2013

[13] YWang XWang JWang P Yung andG Jun ldquoEngagement offacilities management in design stage through BIM frameworkand a case studyrdquo Advances in Civil Engineering vol 2013Article ID 189105 8 pages 2013

[14] W K Hong J M Kim S C Park et al ldquoA new apartmentconstruction technology with effective CO

2emission reduction

capabilitiesrdquo Energy vol 35 no 6 pp 2639ndash2646 2010[15] W Hong S Park J Kim et al ldquoDevelopment of structural

composite hybrid systems and their application with regard tothe reduction of CO

2emissionsrdquo Indoor and Built Environment

vol 19 no 1 pp 151ndash162 2010[16] W Hong S Jeong S Park and J T Kim ldquoExperimental

investigation of an energy-efficient hybrid composite beamduring the construction phaserdquo Energy and Buildings vol 46pp 37ndash47 2012

[17] G P Hammond and C I Jones Inventory of Carbon amp Energy(ICE) Department of Mechanical Engineering University ofBath Bath UK 2008

[18] G P Hammond and C I Jones ldquoEmbodied energy and carbonin construction materialsrdquo Proceedings of Institution of CivilEngineers Energy vol 161 no 2 pp 87ndash98 2008

[19] National Institute of Environment Research (NIER) Domesticand foreign cement heavy metal analysis result (May 2013)NIER 2013 httpwwwniergokrericportalkornfnier-nf-02page

[20] S Kim W Hong J Kim and J T Kim ldquoThe developmentof modularized construction of enhanced precast compositestructural systems (Smart Green frame) and its embeddedenergy efficiencyrdquo Energy and Buildings vol 66 pp 16ndash21 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

14 Mathematical Problems in Engineering

observed the efficiency of using gravity hybrid precastframes for apartment building which decreased theCO2emission (23 reduction of concrete and 28

reduction of reinforcements) energy consumption(21 reduction of concrete and 29 reduction ofreinforcements) and Cr6+ emission compared withbearing wall frame buildings The use of gravityhybrid precast frames was demonstrated to providebetter solutions for environments and economy thanthat of conventional buildings

(5) Dynamic analysis of a 15-story building designedwith the proposed composite gravity frames was per-formed to characterize frequencies and mode shapesof the building for seismic design purposes

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by Grant from the Kyung HeeUniversity in 2013 (KHU-20130363)

References

[1] J F Hajjar ldquoComposite steel and concrete structural systems forseismic engineeringrdquo Journal of Constructional Steel Researchvol 58 no 5ndash8 pp 703ndash723 2002

[2] G Fabbrocino G Manfredi and E Cosenza ldquoDuctility ofcomposite beams under negative bending an equivalence indexfor reinforcing steel classificationrdquo Journal of ConstructionalSteel Research vol 58 no 2 pp 185ndash202 2001

[3] B Yang and K Tan ldquoBehaviour of composite beam-columnjoints under a middle-column-removal scenario experimentaltestsrdquo Journal of Structural Engineering vol 140 no 2 ArticleID 04013045 2014

[4] L Tesser and R Scotta ldquoFlexural and shear capacity of compos-ite steel truss and concrete beams with inferior precast concretebaserdquo Engineering Structures vol 49 pp 135ndash145 2013

[5] H J Hwang H G Park C H Lee et al ldquoSeismic resistanceof concrete-filled U-shaped steel beam-to-RC column connec-tionsrdquo Journal of Korean Society of Steel Construction vol 23 pp83ndash97 2011

[6] J Hassan and B Khosrow ldquoNonlinear seismic behavior evalua-tion of ductile beam-column connections in precast concreterdquoInternational Journal of Civil and Structural Engineering vol 1pp 445ndash453 2011

[7] A M Ioani and E Tripa ldquoStructural behavior of an innovativeall-precast concrete dual system for residential buildingsrdquo PCIJournal vol 57 no 1 pp 110ndash123 2012

[8] C Chou andCUang ldquoEffects of continuity plate and transversereinforcement on cyclic behavior of SRCmoment connectionsrdquoJournal of Structural Engineering vol 133 no 1 pp 96ndash104 2007

[9] Y K Ju and S D Kim ldquoStructural behavior of alternative lowfloor height system using structural ldquoteerdquo half precast concreteand horizontal studrdquoCanadian Journal of Civil Engineering vol32 no 2 pp 329ndash338 2005

[10] X Wang M Truijens L Hou Y Wang and Y Zhou ldquoInte-grating augmented reality with building informationmodelingonsite construction process controlling for liquefied natural gasindustryrdquoAutomation in Construction vol 40 pp 96ndash105 2014

[11] L Hou Y Wang X Wang et al ldquoCombining photogrammetryand augmented reality towards an integrated facility manage-ment system for the oil industryrdquo Proceedings of the IEEE vol102 no 2 pp 204ndash220 2014

[12] L Hou XWang L Bernold and P E D Love ldquoUsing animatedaugmented reality to cognitively guide assemblyrdquo Journal ofComputing in Civil Engineering vol 27 no 5 pp 439ndash451 2013

[13] YWang XWang JWang P Yung andG Jun ldquoEngagement offacilities management in design stage through BIM frameworkand a case studyrdquo Advances in Civil Engineering vol 2013Article ID 189105 8 pages 2013

[14] W K Hong J M Kim S C Park et al ldquoA new apartmentconstruction technology with effective CO

2emission reduction

capabilitiesrdquo Energy vol 35 no 6 pp 2639ndash2646 2010[15] W Hong S Park J Kim et al ldquoDevelopment of structural

composite hybrid systems and their application with regard tothe reduction of CO

2emissionsrdquo Indoor and Built Environment

vol 19 no 1 pp 151ndash162 2010[16] W Hong S Jeong S Park and J T Kim ldquoExperimental

investigation of an energy-efficient hybrid composite beamduring the construction phaserdquo Energy and Buildings vol 46pp 37ndash47 2012

[17] G P Hammond and C I Jones Inventory of Carbon amp Energy(ICE) Department of Mechanical Engineering University ofBath Bath UK 2008

[18] G P Hammond and C I Jones ldquoEmbodied energy and carbonin construction materialsrdquo Proceedings of Institution of CivilEngineers Energy vol 161 no 2 pp 87ndash98 2008

[19] National Institute of Environment Research (NIER) Domesticand foreign cement heavy metal analysis result (May 2013)NIER 2013 httpwwwniergokrericportalkornfnier-nf-02page

[20] S Kim W Hong J Kim and J T Kim ldquoThe developmentof modularized construction of enhanced precast compositestructural systems (Smart Green frame) and its embeddedenergy efficiencyrdquo Energy and Buildings vol 66 pp 16ndash21 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of