Concrete Design Term Project

1

East San Diego Pedestrian Bridge

SE 151A

Concrete Mechanics and Design Department of Structural Engineering

University of California, San Diego

Jose Restrepo

Alvin Aguelo

Luke Robinson

Term Project

Fall 2010

2

TABLE OF CONTENTS

I. References ........................................................................................................................................................................ 5

II. Dimensions & Section Properties ............................................................................................................................... 6

III. Design Loads ................................................................................................................................................................ 8

IV. Structural Analysis ........................................................................................................................................................ 9

V. Slab Design ................................................................................................................................................................... 19

VI. Girder Design ............................................................................................................................................................. 20

VII. Development of Longitudinal and Miscellaneous Requirements ..................................................................... 21

VIII. Column Design ....................................................................................................................................................... 22

IX. Drawings ..................................................................................................................................................................... 28

X. Appendix ....................................................................................................................................................................... 33

Appendix 1.1: Calculations for Ag,slab ,Ixx,slab and Se,slab ........................................................................................... 36

Appendix 1.2: Calculations for Ag,column, Ixx,column and Se,column. .............................................................................. 36

Appendix 1.3: Calculations for yb, yt, Ag,girder, Ixx,girder and Se,girder. ......................................................................... 37

Appendix 1.4: Calculations for Slab Design Loads................................................................................................. 38

Appendix 1.5: Calculations for Girder Design Loads. ........................................................................................... 38

Appendix 1.6: Calculations for the Slab Design ...................................................................................................... 39

Appendix 1.7: Calculations for the Positive Girder Design .................................................................................. 41

Appendix 1.8: Calculations for the Negative Girder Design ................................................................................ 44

Appendix 1.9: Calculations for the Shear Design – Slab Section ......................................................................... 47

Appendix 2.0: Calculations for the Shear Design – Girder Section ..................................................................... 48

Appendix 2.1: Bar Development Girder Calculations ........................................................................................... 50

Appendix 2.2 : Column Design Sample Calculation .............................................................................................. 53

Appendix 2.3: MATLAB Program used for Linear Interpolation ....................................................................... 55

XI. Hours Spent per Student .......................................................................................................................................... 56

3

DESIGN PROCESS

ARCHITECTURAL

RENDERINGS

|01

|02

|03

4

5

I. REFERENCES

PURPOSE:

The proposed bridge is designed as a connecting two-span pedestrian path for a park located in

East San Diego County. The proposed geometric layout requires a crossing of a 5 lane low-

volume roadway designed for frequent loading (due to pedestrians). As stated, the bridge will

account for multiple loading cases that are designed to assure public safety (reference accordance

with the American Association of Highway and Transportation Officials (AASHTO)). The

permanent load cases are defined as follows: dead load of structural components (DC, AASHTO

3.3.2) and dead load of wearing surfaces and utilities (DW, AASHTO 3.3.2). Transient loading

are also accounted for and defined as: pedestrian live load (PL, AASHTO 3.3.2).

The preliminary design for the bridge was originally a T-shaped girder cross section which was

re-designed to have a taper of 30 mm depth. This design was primarily chosen for aesthetic basis

and as well as safety purposes. In addition, the slab and overhanging girder depth are designed

with consideration of the minimum code requirements (with specifications from the

client). Column size for the bridge was designed to have a side dimension of 850 mm.

Additional specification for the loading is as follows: the structure shall be designed to support

its own dead weight, the weight of a 50mm asphaltic concrete overlay (unit weight of asphaltic

concrete is 16 kN/m3, a 1 kN/m handrail load at the slab edges, and a live load per AASHTO

LRFD of 4.1 kN/m2. The normal weight of concrete are also considered and defined as 23.5

kN/m3 with a specified compressive strength of fc’ = 38 MPa. The average aggregate size used

in the concrete is 25 millimeters in diameter.

Figure1: Elevation View of Proposed Bridge (Dimensions in mm)

6

Figure 2: Preliminary Cross-Sectional View of Proposed Bridge (Dimensions in mm).

II. DIMENSIONS & SECTION PROPERTIES

A.) Deck Slab:

Analysis of the decking slab and determination of the slab depth was based on idealizing

the T-section as a solid one way cantilevered beam. Checking against ACI Code in Table

9.5(a), to avoid calculating deflections the minimum depth of the fixed end of the

cantilever must be 0.19m or larger. For the proposed bridge a slab depth of 0.20m was

chosen for simplicity.

Figure 3: Cross-Sectional Measurements: Decking Slab measurement in mm.

The proposed slab has the following sectional properties:

Cross-Sectional Properties:

Decking Slab

Ag,slab 0.2 m2

Ixx,slab 6.667e-4 m4

Se,slab 6.667e-3 m3

Table 1: Sectional Properties of Decking Slab (For Calculation See Appendix 1.1)

7

B) Girder:

Analysis of the girder and determination of the girder depth was based on ACI Code for

non-pre-stressed beams. Checking against ACI Code in Table 9.5(a), to avoid calculating

deflections the minimum depth of the non-pre-stressed beam with one end continuous

must be a minimum if 0.95m. For the design proposed a depth of 1m was chosen for

calculation purposes.

Figure 4: Cross-Sectional Measurements: Girder measurement in meters.

The proposed girder has the following sectional properties:


Decking Girder

Ag,girder 1.510 m2

yb 0.701 m

yt 0.299 m

Ixx,girder 0.1254 m4

Sb,girder 0.1788 m3

St,girder 0.420 m3

Table 2: Sectional Properties of Girder (For Calculation See Appendix 1.2)

C) Column:

The design of the column is allowed to be 850mm, 900mm, 950mm. For the proposed

bridge, a slanted square cross section has been chosen with a width of 850mm. The

thinner column has a more aesthetic quality to it and gives an overall more transparent

appearance to the bridge. Should it be found later that the bridge needs a larger column, it

can always be increased easily.

8

The proposed column has the following sectional properties:


Column

Ag,column 0.723 m2

Ixx,column 0.0435 m4

Se,column 0.1024 m3

Table 3: Sectional Properties of Girder (For Calculation See Appendix 1.1)

III. DESIGN LOADS

A) Deck Slab Design Loads: The design loads for the deck slab were determined to be:

Design Loads: Deck Slab

Design Factor

Final Load

Design with

Factors

WDC1,slab 4.70 kN/m 1.25 5.875 kN/m

PDC2,slab 1.00 kN 1.25 1.25 kN

WPL,slab 4.10 kN/m 1.75 7.175 kN/m

WDW,slab 0.80 kN/m 1.50 1.20 kN/m

Table 4: Design Loads for Deck Slab Cantilever (For Calculation See Appendix 1.3)

B) Girder Design Loads:

The design loads for the girder were determined to be:

Design Loads: Girder

WDC1,girder 35.49 kN/m

WDC2,girder 2.000 kN/m

WPL,girder 18.655 kN/m

WDW,girder 3.640 kN/m

Table 5: Design Loads for Deck Slab Cantilever (For Calculation See Appendix 1.4)

9

Table: 6The shear and the moment values for the loads are calculated through SAP and yield:

IV. STRUCTURAL ANALYSIS

A) Slab:

i) Model:

Figure 5: Cross-Sectional View of the idealized model for transverse bending and shear in the slab.

ii) Load Factors and Combinations:

Using ASSHTO Code for structural analysis, limit states STRENGTH I and

STRENGTH III recommend a load factor of 1.75 for pedestrian live loads in Table

3.4.1-1. Referring to Table 3.4.1-2, ASSHTO Code recommends a minimum load

factor of 1.25 for DC Components and 1.50 for DW wearing surfaces. The following

load factors are incorporated in the Design Envelope.

iii & iv) Bending Moment Diagrams & Shear Force Diagrams:

NOTE: The following shear and moment diagrams were modeled for a solid fixed

end one-way cantilever of length 1.9m. The design loads used were according to

Table 4 of this document and did not use ASSHTO design load factors.

WDW, slab

WPL, slab

WDC1, slab

WDC2, slab

Wcomb1, slab

Shear Value 2.28 kN 13.63 kN 11.16 kN 1.25 kN 28.33 kN

Moment Value 2.17 kN-m 12.95 kN-m 10.6 kN-m 2.25 kN-m 27.97 kN-m

10

1) Dead Load WDC1,slab (Dead Load due to Concrete)

Figure 6: Shear Force Diagram (Max Shear: 11.16 kN)

Figure 7: Moment Diagram (Max Moment: -10.60 kN*m)

2) Superimposed Dead Load WDW,slab (due to Overlay)



3) Handrail Road WDC2,slab (due to handrail)



4) Pedestrian Live Load WPL,slab



11

5) Design Envelope: ASSHTO load factors considered.



B.) Girder:

i.) Model:

Figure 16: First-order SAP Model of the proposed bridge. All dimensions are in mm.

12

ii.) Load Combinations and Factors:

The un-factored loads used in the girder design can be found in Table 5. Five load

cases were considered for the proposed bridge to account for moving live loads and

variability in specific gravity of materials used in the construction of Pollo Gigante

Pedestrian Bridge.

Figure 17: Load Case 1 – Live load across entire bridge span with max load factors used in dead weight of

construction materials.

Figure 18: Load Case 2&3 – Live load across half bridge span with min. load factors used in dead weight of


13

Figure 19: Load Case 4&5 – Live load across half bridge span with max load factors used in dead weight of


Design Loads: Girder

Load Case 1 Load Case 2 Load Case 3

Load LF

(γp)

Design Load

(kN/m) Load

LF (γp)

Design Load

(kN/m) Load

LF (γp)

Design Load

(kN/m)

WDC1,girder 1.25 44.36 WDC1,girder 0.9 31.94 WDC1,girder 0.9 31.94

WDC2,girder 1.25 2.500 WDC2,girder 0.9 1.800 WDC2,girder 0.9 1.800

WPL,girder 1.75 32.65 WPL,girder 1.75 32.65 WPL,girder 1.75 32.65

WDW,girder 1.5 5.460 WDW,girder 0.65 2.366 WDW,girder 0.65 2.366

Load Case 4 Load Case 5

Load LF

(γp)

Design Load

(kN/m) Load

LF (γp)

Design Load

(kN/m)

WDC1,girder 1.25 44.36 WDC1,girder 1.25 44.36

WDC2,girder 1.25 2.500 WDC2,girder 1.25 2.500

WPL,girder 1.75 32.65 WPL,girder 1.75 32.65

WDW,girder 1.5 5.46 WDW,girder 1.5 5.46

Table 7: Design Loads and Load factors used for Girder analysis.

Load Case 1 is considered to account for the possibility of the bridge being

completely loaded with pedestrians, LC 1 yields a maximum negative moment in the

girder near the column and in the top of the column and also yields maximum shear in the

girders and column. Load Cases 2, 3 were considered for possible maximum positive

bending in the girder, but was not large enough to control the design. Load cases 4 and 5

were also considered to determine maximum positive bending moments in the left and

14

right side of the girder and did control the design. The design loads for the load cases

used in analysis are as follows.

iii.) Bending Moment Diagrams:

Figure 20: Moment Diagram for Load Combination 1 with Max Values units in kN-m.



15



iv.) Shear Force Diagrams:

Figure 25: Shear Diagram for Load Combination 1 with Max Values units in kN.

16





17

v.) Shear and Bending Moment Design Envelopes:

Figure 30: Moment Design Envelope. All Load Combinations with Max Values in kN-m

Figure 31: Shear Design Envelope with All Load Combinations with Max Values in kN

vi.) Girder Analysis Result Table:

The results for the Girder Analysis are shown below. These results are consistent with

those found from the values in the Moment and Shear Diagrams. From the table, we

check for possible design loads:

1. Shear Analysis (Left Girder): The highest positive shear on the left girder (from

nodes 2 & 3) is 918 kN and the highest negative shear to design for is -567 kN.

2. Shear Analyis (Right Girder): The highest positive shear on the right girder

(from nodes 5 & 6) is 629 kN and the highest positive shear to design for is -848

kN.

18

Girder Analysis

Element Nodes 2-3: Girder Left

Pos. M (kN*m)

Loc. (m)

Neg. M (kN*m) Loc.

Pos. V (kN) Loc.

Neg. V (kN) Loc.

LC 1 1664 6.1 -3295 Col. 918 Col. -532 Sup.

LC 2 1576 6.7 -2069 Col. 708 Col. -466 Sup.

LC 3 503 5.5 -2000 Col. 425 Col. -191 Sup.

LC 4 1892 6.7 -2699 Col. 883 Col. -567 Sup.

LC 5 815 5.5 -2630 Col. 599 Col. -293 Sup.

Element Nodes 5-6: Girder Right

Pos. M (kN*m)

Loc. (m)

Neg. M (kN*m) Loc.

Pos. V (kN) Loc.

Neg. V (kN) Loc.

LC 1 2130 9.8 -2102 Col. 602 Sup. -848 Col.

LC 2 741 10.4 -1304 Col. 232 Sup. -384 Col.

LC 3 1901 9.8 -1285 Col. 512 Sup. -662 Col.

LC 4 1147 10.4 -1703 Col. 347 Sup. -546 Col.

LC 5 2309 9.8 -1684 Col. 629 Sup. -824 Col.

Element Nodes 8-9: Column

Pos. M (kN*m) Loc.

Neg. M (kN*m) Loc.

Pos. V (kN) Loc.

Neg. V (kN) Loc.

LC 1 1222 Girder -1863 Ft. 458 Ft. 425 Girder





Table 8: Tabular results of load case analysis. Listed are the maximum and minimum moments and shears

for each load case and their locations on the girder and column. (Col. – Column/Girder Node [3 or 5], Sup. –

Support/Girder Node [2 or 6], Ft. – Footing/Column Node [9], Girder – Column/Girder Node [8]) If Location

is in meters, it is the distance from the left node [2 or 5] of the girder element analyzed.)

19

V. SLAB DESIGN

i.) Slab Flexure

Slab Design – Single Layer Tensile Steel

Bar Size

No. Bars

db (mm) Ab (mm2) As (mm2) smin (mm) s (mm)

4 7 12.7 129 903 60 130.2

d (mm) c (mm) c/d Mn (kN-

m) Mcr (kN-

m) фMn (kN-m)

Mu (kN-m)

144 14.881 0.1 51.59 25.89 46.53 28

c/d<0.42 Mn > 1.85Mcr фMn > Mu

Table 9: This table lists the slab design for multiple spacing. It also includes the checks for each of the bars

recommended.

Figure32: Slab design with reinforcement. Unit in mm.

ii.) Slab Shear

From analysis of the load case for the slab sections, it was determined that the

concrete in the slab has a factored resistance of 79kN. The analysis listed a maximum

demand of 28kN at the base of the cantilevered section. Per ACI-318, when designing for

shear, no shear reinforcement is needed if the factored demand is less than half the

resistance of the concrete. With a factored resistance of more than 3x the demand, no

shear reinforcement was considered for the slab design.

20

VI. GIRDER DESIGN

i.) Girder Flexure Design:

Girder Design - 1 Layer (Critical Positive Moment)

Bar Size No. Bars


11 7 35.81 1006 7042 50.8 62

d (mm) c (mm) c/d Mn (kN-m) Mcr (kN-m) фMn (kN-m) Mu (kN-m)

919 29.38 0.032 265 68 2383 2309


Girder Design - 1 Layer (Critical Negative Moment)

Bar Size No. Bars


17 9 28.65 645 10965 50.8 varies

d (mm) c (mm) c/d Mn (kN-m) Mcr (kN-m) фMn (kN-m) Mu (kN-m)

923 240.44 0.26 3763 485 3387 3295


Table 10: This table provides the chosen design for the girder

Figure 33: Design of Girder cross section for the critical positive moment case. Units in mm.

Figure 34: Design of Girder cross section for the critical negative moment case. Units in mm.

21

II.) ii.) Girder Shear Design:

III.)

IV.) The shear Design was completed per ACI-318. All calculations may be found in

Appendix 2.0. It was found that the worst case shear dictated a large section of Case 2,

another Case 3 section near the columns and a small case 1 section at mid-span. Due to

seismic loading in California no unreinforced shear sections were designed for. Minimum

reinforcement was used in all sections of the girder up to section 3. Lastly even though

one side of the bridge experienced less loads per analysis, to be safe and make for easier

constructability, the worst case will be mirrored about the centerline at the column.

V.)

Range фVn (kN) Start (mm) End (mm) # sets Rebar Config. s (mm)

Case 4 Not Encountered

Case 3 3фVc<Vu<Vc 1600 50 4690 32 #4 4 leg 135

Case 2 фVc<Vu<0.5Vc 733 4875 17325 35 #3 4leg 400

Table11: design results from shear analysis.

Figure 35a: Shear design near the column. Case 3

Figure 35b: Shear design near mid-span to the supports. Case 2.

22

VII. DEVELOPMENT OF LONGITUDINAL AND MISCELLANEOUS

REQUIREMENTS

A.) Bar development per ACI-381

From the ACI code, all calculations passed the design checks. It was decided that

the negative reinforcement would be cut off from 17#9 bars to 6#9bars more than

3.27m from the column. Then cut off from 6#9 bars to 4#9 bars at more than 5.61m

from the column and continue till the support for shear stirrups.

The positive reinforcement was determined that the 7#11 bars would be cut off to

4#11 bars at a distance greater than 15.29m from the column and less than 4.08m

from the column, taking proper development into account.

The shear calculations per ACI 12.10.5.1 all passed and no design changes were

needed in that regard. The following is the graphs used in the design of the bar

development. For calculations See Appendix2.1 and for more detail see drawings IV

and V in section IX. Drawings.

Graph 1: Shear Design Envelope including factored resistances per the girder shear design and plots of the

shear for the maximum positive moment case and maximum negative moment case.

0

200

400

600

800

1000

1200

1400

1600

1800

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Sh

ear

Fo

rce k

N i

n G

ird

er

Distance x from Column Face (m)

Shear Design Envelope

Positive Moment

Negative Moment

Design Capacity

Case 3:

фVn = 1600kN

Case 2: фVn = 733kN

23

Graph 2: Moment Design Envelope used for designing bar development of the girder section. The graph

includes maximum positive moment demand and maximum negative moment demand, then plotted are the

corresponding cutoff rebar locations and the distances from the column face.

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Mo

men

t k

N-m

in

Gir

der

Distance x from Column Face (m)

Moment Degign Envelope & Bar Cutoffs

Positive Moment

Negative Moment

B-CutOff (+)

B-CutOff (-)

A-CutOff (-)

Max Positive Moment

xA

-=6.0

4m

xB

-=3.2

7m

xB

L+=

4.0

8m

xB

R+=

15.2

9m

24

VIII. COLUMN DESIGN

i. Column Analysis Results

The analysis for the column was performed through the simplification of the bars chosen

for a potential design. The following schematic illustrates the simplification:

Figure 36: Column Reinforcement

The following results were calculated using five cases that determine the

resistance-flexure axial load interaction diagram. These results are then used as the limits

and criteria for determining the amount of #10 bars that will be used in the column

reinforcement. The cover for the stirrups from the edge of the column is considered to be

50 mm while the stirrup used along the reinforcement is a 12 mm bar. The calculations

for the column design can be found in Appendix 2.2.

25

ρ = .01 ρ = .04

Case φPn(MN) φMn(MN-m) φPn(MN) φMn(MN-m)

1 -17 0 -22.3 0

2 2.7 0 10.76 0

3 -2.88 1.81 -0.2 3.36

4 -4.26 2.24 -2.66 4.27

5 -6.34 2.054 -6.08 3.48

Table 12: Design schematic of the cross section of the bridge (girder) with appropriate dimensions

ii. Factored Resistance-Flexure Axial Load Interaction Diagram

Graph 3: This table provides the chosen design for the girder; the graph displays all the maximum values

from the results of the structural analyses are within the red circle. The chosen design is marked by the red

dashed circle.

26

Graph 4: Linear Interpolation Graph

From the linear interpolation of the data from the resistance-flexure axial load interaction

diagram, the value for rho was found to be .0213. This can now determine the

reinforcement that will be used for the

column.

iii. Column Final Design

The final column reinforcement

design is the following:

20 #10 Bars with a 50 mm

cover from the edge of the

column; 12 mm stirrup at 250

o.c.

0.01, 0.875

0.0213, 1.86

0.04, 3.5

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

φM

n

ρg

Linear Interpolation of ρ

Figure 37: Final Column

Reinforcement Design

27

iv. Column Bar Development

For images and Detailed drawings of Bar development for the Column please refer to Section IX.

Drawings.

Bar Development For Column

A development length 0f 1.3m will cause teh rebar to protrude from the decking surface. Use Std hooks.

ACI 12.5.4 - At the ends of member, in this case the coloumn member, the factor shall be 1.0

(ACI 12.5.3)

db10 32.26mm

ld_col

12 fy t_bottom e 20 fc MPa

db10 1.3m

Factor 1.0

ldh_col max0.02e fy fc MPa

db10 Factor 8 db10 150mm

0.258m

12 db10 0.387m

D10 8 db10 0.258m

R10

D10

20.129m

28

IX. DRAWINGS

I. T

r

a

n

s

v

e

r

s

e

R

e

b

a

r

S

p

a

c

i

n

29

II. L

o

n

g

i

t

u

d

i

n

a

l

R

e

b

a

r

S

p

a

c

i

n

g

a

n

30

III. L

o

n

g

i

t

u

d

i

n

a

l

R

e

b

a

r

S

p

a

c

i

n

g

31

IV. G

i

r

d

e

r

R

e

i

n

f

o

r

c

e

m

e

n

32

V. S

u

p

p

o

r

t

R

e

b

a

r

33

34

35

36

X. APPENDIX

APPENDIX 1.1: CALCULATIONS FOR AG,SLAB ,IXX,SLAB AND SE,SLAB

Ixx_slab

be hf3

12

Se_slab

Ixx_slab

hf

2

m3

Girder Calculations

APPENDIX 1.2: CALCULATIONS FOR AG,COLUMN , IXX,COLUMN AND SE,COLUMN .

Ixx_slab

be hf3

126.667 10

4 m

4

h 1m hf .2m bw .750m be 1.00m

Ag_slab hf be 0.2m2

bc .850m hc .850m

Acolumn bc hc 0.722m2

Ixx_column

bc hc3

120.044m

4

Se_column

Ixx_column

hc

2

0.102m3

37

APPENDIX 1.3: CALCULATIONS FOR YB , YT , AG,GI RDER , IXX,GIRDER AND SE,GI RDER .

h 1m hf .2m bw .750m be 4.55m

hw h hf 0.8m

Agirder1 bw hw 0.6m2

Agirder2 be hf 0.91m2

y1

hw

20.4m

y2 hw

hf

2 0.9m

Ag_girder Agirder1 Agirder2 1.51m2

yb

Agirder1 y1 Agirder2 y2 Ag_girder

0.701m

yt h yb 0.299m

d1 yb y1 0.301m

d2 yb y2 0.199 m

Ixx1

bw hw3

12Agirder1 d1

2 0.086m

4

Ixx2

be hf3

12Agirder2 d2

2 0.039m

4

Ixx_girder Ixx1 Ixx2 0.1254m4

Sb_girder

Ixx_girder

yb

0.1788 m3

St_girder

Ixx_girder

yt

0.42 m3

38

APPENDIX 1.4: CALCULATIONS FOR SLAB DESIGN LOADS.

APPENDIX 1.5: CALCULATIONS FOR GIRDER DESIGN LOADS.

concrete 23.5kN

m3

asphalt 16kN

m3

hasphalt 0.05m

WDC1_slab concrete hf 1 m 4.7kN

m

WDW_slab asphalthasphalt 1 m 0.8kN

m

PDC2_slab 1kN

m

1 m 1kN

WPL_slab 4.1kN

m2

1 m 4.1kN

m

WDC1_girder concrete Ag_girder 35.485kN

m

WDW_girger asphaltbe hasphalt 3.64kN

m

WDC2_girder 2 1kN

m2

kN

m

WPL_girder 4.1kN

m2

be 18.655kN

m

39

APPENDIX 1.6: CALCULATIONS FOR THE SLAB DESIGN

Critical Negative Moment Slab - Flexure Check

Cracking Moment of Section

Internal Compressive and Tensile Forces

Moment Carrying Capacity of Section

Tesile Dominated Section

fc 38MPa fy 414MPa db4 12.7mm d 144mm l 1900mm

hf 200mm h 1000mm bw 1000mm c 14.61mm Mu 28kN m

be 1000mm

1 0.85 0.0538 28( )

7

0.779

a 1 c 11.375 mm

As_min0.25 38 MPa

fy

bw d 536.036 mm2

As 7

db4

2

2

886.738mm2

fr 0.625 38MPa 3.853 106

Pa yt 100mm Ig 6.667 104

m4

Mcr

fr Ig yt

25.686kN m

C 0.85 fc 1 c bw 3.674 105

N

T As fy 3.671 105

N

Error 2C T

C T

100 0.082

Mn T da

2

50.776 kN m

sd c( )

c

.003 0.027 s 0.005

0.9c

d

0.42if

0.65 0.15d

c

1

0.375c

d

0.42if

0c

d

0.42if otherwise

5.5.4.2.1 LRFD( )

0.9

Mn 45.698 kN m

40

AASHTO Code Checks

Mmin min 1.22Mcr 1.33Mu 31.337 kN m

Check1 "PASS" Mn Mminif

"FAIL" Mn Mminif

5.7.3.3.2 LRFD( )

Check2 "PASS" Mn Muif

"FAIL" Mn Muif

Check3 "PASS" 0.42c

dif

"FAIL" 0.42c

dif

5.7.3.3.1 LRFD( )

Check4 "PASS" As As_minif

"FAIL" As As_minif

Check1 "PASS" Check2 "PASS" Check3 "PASS" Check4 "PASS"

41

APPENDIX 1.7: CALCULATIONS FOR THE POSITIVE GIRDER DESIGN

Critical Positive Moment Case:

Assuming No.4 Stirrup and No.11 Flexural Rebar to get a rough As (design)

and a strength reduction factor of 0.9

Assuming Number 4 stirrup

fc 38MPa fy 414MPa be 3950mm dclear 50mm db 35.81mm dstr 12.7mm

d 1000mm dclear dstrdb

2 919.395mm

Mu 2309kNm .9

a1

fy2

2 .85 fc be 671.693

1

mMPa b1 fy d 380630

1

mkN c1

Mu

2566kN m

b1 b12

4 a1 c1

2 a1559849mm

2

b1 b12

4 a1 c1

2 a16822mm

2

smin 50.8mm bw 750mm dNo9 28.65mm dNo10 32.26mm dNo11 35.81mm

ANo9 645mm2

ANo10 819mm2

ANo11 1006mm2

NNo9

bw 2 dstr 2 dclear smin dNo9 smin

8.501 ANo9_max 8 ANo9 5160mm2

NNo10


8.131 ANo10_max 8 ANo10 6552mm2

NNo11


7.798 ANo11_max 7 ANo11 7042mm2

42

Critical Positive Moment Girder - Flexure Check




Tensile Dominated Section

fc 38MPa fy 414MPa db11 35.84mm d 919mm l 17500mm

hf 200mm h 1000m bw 750mm c 29.41mm Mu 2309kNm

be min bw 2 8 hfl

4

3.95 103

mm

1 0.85 0.0538 28( )

7

0.779

a 1 c 0.023m

As_min0.25 38 MPa

fy

bw d 2.566 103

mm2

As 7

db11

2

2

7.062 103

m2

fr 0.625 38MPa 3.853 106

Pa yt 701mm Ig 0.1254m4

Mcr

fr Ig yt

689.21kN m

C 0.85fc 1 c be 2.921 106

N

T As fy 2.924 106

N

Error 2C T

C T

100 0.076

Mn T da

2

2.653 103

kN m

sd c( )

c

.003 0.091 s 0.005

0.9c

d

0.42if

0.65 0.15d

c

1

0.375c

d

0.42if

0c

d

0.42if otherwise

5.5.4.2.1 LRFD( )

0.9

Mn 2.388 103

kN m

43

AASHTO Code Checks

Mmin min1.22Mcr 1.33Mu 840.836kNm


"FAIL" Mn Mminif

5.7.3.3.2 LRFD( )


"FAIL" Mn Muif

Check3 "PASS" 0.42c

dif

"FAIL" 0.42c

dif

5.7.3.3.1 LRFD( )


"FAIL" As As_minif


44

APPENDIX 1.8: CALCULATIONS FOR THE NEGATIVE GIRDER DESIGN

Critical Negative Moment Case:

Assuming No.4 Stirrup and No.11 Flexural Rebar to get a rough As (design)

and a strength reduction factor of 0.9

Assuming Number 4 stirrup Max number of flexural rebar and Max areas.

Use 17 No.9 bars for critical negative moment

fc 38MPa fy 414MPa be 750mm dclear 50mm db 35.81mm dstr 12.7mm

d 1000mm dclear dstrdb

2 919.395mm

Mu 3295kNm .9

a1

fy2

2 .85 fc be 3.538 10

3

1

mMPa b1 fy d 380630

1

mkN c1

Mu

3661kN m

As_design1

b1 b12

4 a1 c1

2 a196918mm

2 As_design2

b1 b12

4 a1 c1

2 a110678mm

2

smin 50.8mm bw 3950mm dNo9 28.65mm dNo10 32.26mm dNo11 35.81mm

ANo9 645mm2

ANo10 819mm2

ANo11 1006mm2

NNo9


48.778 ANo9_max 48 ANo9 30960mm2

NNo10


46.658 ANo10_max 46 ANo10 37674mm2

NNo11


44.745 ANo11_max 44 ANo11 44264mm2

NNo.9design

As_design2

ANo9

16.556

45

Critical Negative Moment Girder - Flexure Check




Tensile Dominated Section

fc 38MPa fy 414MPa db9 28.7mm d 923mm

hf 200mm h 1000mm bw 750mm c 240mm Mu 3295kNm

be 3950mm

1 0.85 0.0538 28( )

7

0.779

a 1 c 186.857mm

As_min0.25 38 MPa

fy

bw d 2.577 103

mm2

As 17

db9

2

2

1.1 104

mm2

fr 0.625 38MPa 3.853 106

Pa yt 299mm Ig 0.1254m4

Mcr

fr Ig yt

1.616 103

kN m

C 0.85fc 1 c bw 4.527 106

N

T As fy 4.553 106

N

Error 2C T

C T

100 0.582

Mn T da

2

3.777 103

kN m

sd c( )

c

.003 0.009 s 0.005

0.9c

d

0.42if

0.65 0.15d

c

1

0.375c

d

0.42if

0c

d

0.42if otherwise

5.5.4.2.1 LRFD( )

0.9

Mn 3.399 103

kN m

46

AASHTO Code Checks

Mmin min 1.22Mcr 1.33Mu 1.971 103

kN m


"FAIL" Mn Mminif

5.7.3.3.2 LRFD( )


"FAIL" Mn Muif

Check3 "PASS" 0.42c

dif

"FAIL" 0.42c

dif

5.7.3.3.1 LRFD( )


"FAIL" As As_minif


47

APPENDIX 1.9: CALCULATIONS FOR THE SHEAR DESIGN – SLAB SECTION

bw 1000mm d 144mm Vu 28kN fc 38MPa 0.75

Vc1

6

38 MPa bw d 147.946kN

Case "Case 1 - No Required Reinforcement" Vu Vc

2if

"Needs Reinforcement" Vu Vc

2if

Case "Case 1 - No Required Reinforcement"

48

APPENDIX 2.0: CALCULATIONS FOR THE SHEAR DESIGN – GIRDER SECTION

Shear Design per ACI-318

Due To seismic loads native to California Case 1 will be ignored and considered Case2

Case 2: Minimum Shear Reinforcement

Design using 4#3 @ 400mm o.c.

Case 3: Shear Reinforcement

Design using 4#4 @ 400mm o.c.

bw 750mm d 919mm fc 38MPa fy 414MPa 0.75

Vc1

6

38 MPa bw d 708.137kN

Case1max Vc

2 265.551kN

Case2max Vc 531.103kN

Case3max 3 Vc 1.593 103

kN

Case4max 5 Vc 2.656 103

kN

Vul567kN

6.677m

6.677m d( ) 4.89 105

N

Vur 918kN

10.810m

10.810m d( ) 8.4 105

N

s2max mind

2

600mm

0.46m

s2 400mm

Av_min maxbw s2 3 414( )

38MPa bw s2 16 fy

279.185mm2

db3 9.525mm

Av2 4db3

2

2

285.023mm2

s3max mind

2

600mm

0.46m

s3 135mm

Av3min

3 Vc

Vc

1

fy

s3

d

502.534mm2

db4 12.7mm

Av3 4db4

2

2

506.707mm2

49

Case 4&5: Shear Reinforcement

Does not occur in Design

Locations and # Sets for Cases in Girder

Per the Shear Envelope - Designing for Critical Case 3 and Using Case 2 everywhere else.

Case 3 must be designed for at 4557m from the column or more.

Use 35 sets of Case 3 - Stirrups

Case 2 - starting at 50mm of clear cover from the end of the girder at the support

Use 32 sets of Case 2 - Stirrups

x3min531kN 10.810 m 918kN 10.810 m( )

918 kN4557.157mm

n3min4557mm 50mm( )

135mm

1 34.385

n3 35

x3 50mm n3 1 135 mm 4640mm

n2max17375mm 2 50 mm 4640mm( )

400mm

1 32.587

n2 32

x2 50mm n2 1 400 mm 12450mm

dx 17375mm 2 50 mm x2 x3 185mm

50

APPENDIX 2.1: BAR DEVELOPMENT GIRDER CALCULATIONS

Bar Development per ACI-318

Bar Cutoff per ACI-318

Development Length

(1) Negative Bar Cutoff

Bars Cutting off 11#9 bars- 10 in the flanges and one in the web

Determined Via MATLAB

Extrapolated From Graph

Vu_neg x( ) 9181450

17.075

x kN Mu_neg x( )1450

34.15

x2

918x 3295

kN m

Vu_pos x( )1453

17.075

x 824 kN Mu_pos x( )1453

34.15

x2

824x 1684

kN m

fc 38 MPa fy 414MPa bw 750mm d max 919mm923mm( ) lr 17.075m

As_min max 0.25 fc MPa 1.4MPa bw d

fy

2.577 103

mm2

10.5.1 ACI( )

t_top 1.3 t_bottom 1.0 e 1.0 s 1

1 db11 35.81mm db9 28.65mm

ld_neg

12 fy t_top e 20 fc MPa

db9 1.501m Top Bars: Negative Moment

ld_pos

12 fy t_bottom e 20 fc MPa

db11 1.443m Bottom Bars: Positive Moment

AsA1 6db9

2

2

3.868 103

m2

AsB1 11db9

2

2

7.091 103

m2

Mn A1 1283kNm

xtrB1 2.475m

xrB1 maxxtrB1 maxd 12db9 ld_neg 3.398m

Vu_neg 3.398( ) 6.294 105

N

51

Negative moment ends @ xp1r

Vc1

6

fc MPa bw d 7.112 105

N

Av2 279.185mm2

Av3 502.534mm2

s2 400mm s3 135mm

Vs2 Av2 fyd

s2

2.667 105

N Vs3 Av3 fyd

s3

1.422 106

N

V n x( ) 0.75 Vc Vs3 x 4.690if

0.75 Vc Vs2 x 4.690if

V n 3.398( ) 1.6 106

N

Check1neg "PASS" AsA1 As_minif

"FAIL" AsA1 As_minif

10.5.1 ACI( )

Check1neg "PASS"

Check2neg "PASS" AsA1

AsA1 AsB1 3

if

"FAIL" AsA1

AsA1 AsB1 3

if

12.12.3 ACI( )

Check2neg "PASS"

Check3neg "PASS"Vu_neg 3.398( )

V n 3.398( )

2

3if

"FAIL"Vu_neg 3.398( )

V n 3.398( )

2

3if

12.10.51 ACI( )

Check3neg "PASS"

xpir 4.54m

xrAmin max xpir max d 12 db9lr

16

xpir ld_neg

6.041m

52

(2) Positive Bar Cutoff

Bars Cutting off 3#11 bars, every very other in the in the web

Determined Via MATLAB

Extrapolated From Graph

By Symmetry: x.l2 will pass the same checks so no calculations shown.

Bars A per (10.5.1-ACI) & (12.11.1-ACI) need to be embedded 150mm into column.

AsA2 4db11

2

2

4.029 103

m2

AsB2 3db11

2

2

3.021 103

m2

Mn A2 1371kNm

xtl2 4.9967m

xlB2 maxxtl2 maxd 12db11 ld_pos 5.92m

Vu_pos 5.623( ) 3.455 105

N

V n 9.7 5.623( ) 1.6 106

N

Check1pos "PASS" AsA2 As_minif

"FAIL" AsA2 As_minif

10.5.1 ACI( )

Check1pos "PASS"

Check2pos "PASS" AsA2

AsA2 AsB2 3

if

"FAIL" AsA2

AsA2 AsB2 3

if

12.12.3 ACI( )

Check2pos "PASS"

Check3pos "PASS"Vu_neg 5.623( )

V n 5.623( )

2

3if

"FAIL"Vu_neg 5.623( )

V n 5.623( )

2

3if

12.10.51 ACI( )

Check3pos "PASS"

53

APPENDIX 2.2 : COLUMN DESIGN SAMPLE CALCULATION

Using AASHTO code for Design:

Column Schematic (Idealized version):

(Calculation of the distance from L1 fiber to L3 fiber)

Column Analysis (Case 1):

Strength Reduction Factor ϕ


Strength Reduction Factor ϕ


Assumed the value of c at .23*h of the column

since the yield ε s1 is less greater than .005

h 850mm

b 850mm

gh h 2 5 1232.3

2

gh 693.7mm

g .01 g .04

Ast g Ag 7225mm2

28900mm2

Pn Ast fy Ag Ast .85 fprime_c 26.09 MN 34.37 MN

Mn 0MN 0MN 0MN

.65 .65

Pn Ast fy 2.99MN 11.96MN

Mn 0MN 0MN 0MN

.90 .90

ccolumn .23h

a 1 c .779 195.5.5mm( ) .90

a 195.5mm

c

c1.535 10

5 dh

21 g( ) 772mm

54

Layer (1)

Layer (2):

Layer (3):

Summing the Forces:

Summing the Moments:

s1 d c( ) .0085

s1 0 fs1 minEs s1 fy fs1 414MPa

s2 h

2c

.0035

s2 0 fs2 minEs s2 fy fs2 414MPa

s3 h

21 g( ) c

.0018

s3 0 ah

21 g( ) c

fs3 maxs3 fy 0.85fprime_c fs3 327.7 MPa

g .01 g .04

Fs13

8Ast fs1 1122kN 4487kN

748kN 2991kNFs2

2

8Ast fs2

889 kN 3551 kN

Fs33

8Ast fs3

4181 kN 4181 kNCc .85 fprime_c a b

Pn 3200 kN 253 kN

Mn Fs1 x1 Fs3 x3 Cc xc 2.01MN m 3.73MN m

x1gh

23.468 x3

gh

23.468

xch

2

a

2

348.9

55

APPENDIX 2.3: MATLAB PROGRAM USED FOR LINEAR INTERPOLATION

The linear interpolation of the actual graph was determined through the use of MATLAB code.

clc;

clear;

y1 = input ('y1 value=');

y0 = input ('y0 value=');

x1 = input ('x1 value=');

x0 = input ('x0 value=');

y = input ('y value=');

% x = input ('x value=');

x = x0+(y-y0)*((x1-x0)/(y1-y0))

% y = y0+(x-x0)*((y1-y0)/(x1-x0))

Results with Reduction Factors



P n M n 2.88 MN 1.81MN m( ) .2 MN 3.36MN m( )

ccolumn3

8d 289.43mm

a 1 c 194.3mm

.003

289.431.037 10

5

ccolumn

cu

cu y d 463.2mm

a 1 c 360.83mm

b.003

463.2

The Calculations for these cases

is similar to Case 3.

56

XI. HOURS SPENT PER STUDENT

Hours Spent

Luke Robinson

Alvin Aguelo

1. References

0 0.5

2. Dimensions & Section Properties

a. Slab 1 1

b. Girder 1 1

c. Column 1 1

3. Design Loads

a. slab 0 0

i. Dead Load 1 1

ii. Superimposed Dead Load 1 1

iii. Live Load 1 1

b. Girder

i. Dead Load 2 2

ii. Superimposed Dead Load 2 2

iii. Live Load 2 2

4. Structural Analysis

a. Slab 0 0

i. Model 1 1

ii. Load Combinations 1 1

iii. Bending Moment Diagrams of Load Combinations 1 1

iv. Shear Force Diagrams of Load Combinations 1 1

v. Design Envelopes 1 1

b. Girder

i. Model

ii. Load Combinations and Factors 2 2

iii. Bending Moment Diagrams of Load Combinations 2 2

iv. Shear Force Diagrams of Load Combinations 2 2

v. Design Envelopes 2 2

5. Slab Design

a. Flexure Design of Critical Section 0 4

b. Design for Shear 0.25 0

6. Girder Design

a. Flexure Design of Critical Section 1 0

i. Negative Moment 1 0

ii. Positive Moment 1 0

b. Design for Shear 1 0

57

7. Development of Longitudinal Reinforcement and Miscellaneous Requirements

a. Slab reinforcement 2 0

i. Longitudinal Bar Development 2 0

ii. Shrinkage and Temperature 2 0

iii. Cross Section Sketches 2 0

b. Girder Reinforcement 2 0

i. Longitudinal Bar Development 2 0

ii. Cross Section Sketches 2 0

8. Column Design

a. Interaction diagrams 0 2

b. Pn, Mu combinations 0 2

c. Design for Shear 0 2

d. Longitudinal Bar Development 0 2

9. Handrail Base Design

0 0

10. Drawings

1 1

10. Editing/Formatting Report

15 25

Total Hours Spent

Luke Robinson 59.25

Alvin Aguelo 58.5

Documents

Concrete Design Term Project