Engineering Structures 55 (2013) 26–34

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Engineering Structures

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Behavior of reinforced concrete columns under combined effects of axialand blast-induced transverse loads

0141-0296/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.engstruct.2012.12.040

⇑ Corresponding author. Tel.: +1 352 273 0695.E-mail addresses: serdara@ufl.edu (S. Astarlioglu), tedk@ufl.edu (T. Krauthammer),

dave.morency@forces.gc.ca (D. Morency), thien.tran@drdc-rddc.gc.ca (T.P. Tran).

Serdar Astarlioglu a,⇑, Ted Krauthammer a, Dave Morency b, Thien P. Tran c

a Center for Infrastructure Protection and Physical Security (CIPPS), University of Florida, Gainesville, FL 32611, USAb 1st Engineer Support Unit, Moncton, NB, Canadac Force Protection R&D Suffield, Medicine Hat, AL, Canada T1A 8K6

a r t i c l e i n f o a b s t r a c t

Article history:Available online 13 February 2013

Keywords:RC columnsBlast loadsBehaviorSDOF analysisPressure–impulse diagram

The results of numerical studies on the dynamic response of reinforced concrete (RC) columns subjectedto axial and blast-induced transverse loads utilizing an advanced single-degree-of-freedom (SDOF) modelare presented in this paper. The main variables considered in this study were the level of axial force andlongitudinal reinforcement ratio. This work addressed the effect of various levels of axial compressiveload on the resistance function, time-history response, and load–impulse diagram when the columnswere subjected to transverse loads due to blast. The blast loads were idealized as triangular pulses andthe effects of flexural, diagonal shear, and tension membrane behaviors were included in the RC columnresponse. The results from the SDOF analyses were validated using the commercial finite element (FE)program ABAQUS. The results of the parametric study indicated that the level of axial compressive loadhas a significant influence on the behavior of RC columns when subjected to transverse blast-inducedloads.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction axial loads were applied [2]. Furthermore, RC columns may under-

Progressive collapse of a building is typically initiated by anabrupt failure of one or more of the load bearing structural mem-bers, such as columns. Therefore, the endurance of such membersunder severe short duration loads is essential for the survivabilityof the building. The primary objective of this paper is to investigatethe blast response of reinforced concrete columns with various lev-els of axial compressive loads and idealized boundary conditionsusing both fast running nonlinear SDOF and high fidelity contin-uum based finite element approaches, and show how the responseof the column varies as the axial load level is changed usingmoment–curvature, resistance function, and pressure–impulsediagrams. While beams are normally subject only to transverseloads, columns are always exposed to both transverse and axialloads. In practice, it is often assumed that lateral responses arenormally larger than the vertical ones for columns under the abovementioned combined loading conditions, and that the failure ofcolumns are normally caused by transverse, rather than axial, loads[1]. While the failure of the column will most likely be induced bythe transverse loads, the effect of axial loads on the responseshould also be considered. The column resistance may be reduceddue to the axial loads, and the column may fail sooner than if no

go large deformation if the axial load increases enough to create astability failure, and/or the transverse load combined with theaxial load increases enough to cause a flexural failure. If thetransverse deflection is sufficiently large (e.g., larger than thecross-sectional depth) the column may exhibit a tensile membraneresponse that has been observed for RC beams and slabs. Certainconditions must exist for a column to enable tension membranebehavior. The longitudinal steel reinforcement must be continuousthrough the entire length of the column and be well anchored intothe supports. Also, once the transition into a tension membraneoccurs, the axial compressive load acting on the column cannotbe resisted, and it must be redistributed to other structural ele-ments in the building. At that point, although the column no longerhas the capability to carry axial compressive loads, it continues tohave the ability to carry transverse loads. Fig. 1 shows thedeformed shape of an RC column following a blast test in whichthe column exhibited a tension membrane behavior [3]. This capa-bility of the column could be significant for structures that mustprovide protection against various explosively-induced lateralloads [4].

2. Numerical approach

In this study, the Dynamic Structural Analysis Suite (DSAS) isused to perform numerical analysis of RC columns under blastloads. DSAS is a multifunctional dynamic analysis suite, capable

Fig. 1. RC column following a blast test [3].

S. Astarlioglu et al. / Engineering Structures 55 (2013) 26–34 27

of performing time-history analyses of a wide range of structuralcomponents [2,4,5]. DSAS is based on an equivalent SDOF analysisconcept [1], and it utilizes a layered section analysis approach andstrain compatibility to determine the moment–curvature relation-ship of a structural component. Then, a displacement controllednonlinear FE analysis, using Crisfield’s cylindrical arch lengthmethod [6], is carried out to establish the resistance function andthe equivalent load and mass characteristics. The resulting resis-tance function is then used to perform a SDOF time-history analy-sis of the structural component. DSAS is also capable of plottingphysics-based load–impulse diagrams [7]. The details of theapproach used in obtaining the resistance function for differentdegrees of freedoms (DOF) are described below.

2.1. Equivalent SDOF system

In order to perform an SDOF analysis of a structural component,one must establish the relationships that relate the continuoussystem, such as the one shown in Fig. 2, to a simple mass-dampersystem. Furthermore, the load function under consideration shouldbe separable into time dependent and spatial components asshown in Eq. (1), where pt(x) is the load function, kt is the timedependent portion of the load function, and �pðxÞ is the spatial dis-tribution of the load.

ptðxÞ ¼ kt�pðxÞ ð1Þ

The evaluation of the equivalent SDOF properties, including theresistance function, is accomplished by using a static nonlinear

Fig. 2. Continuous structural member.

analysis. The reference displacement for the SDOF system is definedas the displacement of the continuous system at the point of inter-est (e.g., midspan) for each load increment i as shown in Eq. (2). Thenormalized displacement field is defined, as shown in Eq. (3):

uim ¼ ui L

2

� �ð2Þ

uiðxÞ ¼ uiðxÞui

mð3Þ

In which ui(x) is the displacement field at increment i. uim is the mid-

span displacement field at increment i. ui(x) is the normalized dis-placement field at increment i.

The equivalent resistance value for the load increment i can bewritten as shown in Eq. (4), to ensure that the strain energies ofboth the continuous system and the lumped SDOF system areidentical.

Fie ¼

Z L

0piðxÞ �uiðxÞ � dx ð4Þ

In which Fie is the equivalent load at increment i. pi(x) is the load

function at increment i.Similarly, the equivalent mass value for the load increment i is

determined by setting the kinetic energies to both systems equal toeach other and assuming that the acceleration field normalizedwith respect to the midspan acceleration is the same as the nor-malized displacement field. The final equation for the equivalentmass at load increment i, Mi

e, is shown in as follows:

Mie ¼

Z L

0mðxÞ � ½uiðxÞ�2 � dx ð5Þ

In which m(x) is the mass function of the continuous system.Oncethe static analysis is completed and the equivalent SDOF systemproperties are established, the Newmark-Beta method [8] is em-ployed to solve the dynamic equilibrium equation, as shown inEq. (6), and to determine the component’s response time history.

Fte ¼ Mt

e€ut

m þ C _utm þ Rt

e ð6Þ

In which Rte ¼ Reðut

mÞ is the equivalent resistance at time t.

Mte ¼ Meðut

mÞ is the equivalent mass at time t. Fte ¼

FeðutmÞ

kðutmÞ

kt is the

equivalent external force at time t. €utm; _ut

m;utm is the midspan accel-

eration, velocity, and displacement at time t. C is the Dampingcoefficient.

2.2. Flexural and tension membrane resistance

Most RC components will respond to dynamic lateral loads in aflexural behavior mode. One may determine the equivalent loadand equivalent mass for elastic and plastic ranges using closed formsolutions, as described by Biggs [1]. This, however, may lead to someinaccuracies, since the ratio of the equivalent load to the appliedload, defined as the load factor, and the ratio of the equivalent massto total mass, defined as the mass factor, vary continuously as thenonlinearities in the member progress. In DSAS, a specific purposeFE analysis using structural type elements and a solution algorithmbased on Crisfield’s cylindrical arc-length method [6] are used toevaluate the equivalent resistance and mass values in Eqs. (2) and(3) at each load increment, respectively. Each of the structuralelement’s behaviors is determined from the moment–curvaturerelationship of the section, considering the nonlinear materialbehavior of concrete and reinforcing steel. These material modelsaccount for crushing of concrete layers and fracture of steel layers.The moment–curvature function assigned to each element is de-rived using a layered section analysis and strain compatibility,

Fig. 3. Tension membrane.

Fig. 4. Combined flexural and tension membrane resistance.

28 S. Astarlioglu et al. / Engineering Structures 55 (2013) 26–34

and the material properties are adjusted to account for strain rateeffects and level of confinement. Furthermore, the moment curva-ture relationship is modified by incorporating a shear reduction fac-tor to account for presence of diagonal shear [9].

In addition to flexural behavior, in cases where the longitudinalreinforcement is well anchored in the supports, RC columns canalso exhibit tension membrane behavior, which is quite clearly vis-ible in Fig. 1. In this mode of response, the concrete with its negli-gible tensile strength plays a very little role [10]. Fig. 3 shows thedeflected shape and the support reactions in the tensionmembrane.

The deflected shape of a pure membrane under uniform loadtakes the shape of a parabola:

y ¼ 4um

L2 x2 ð7Þ

The length of the membrane is (origin of the coordinate systemis placed at the lowest point of the curve) using symmetry is:

Larc ¼ 2Z L=2

0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ dy

dx

� �2s

dx ð8Þ

Taking the derivative of Eq. (7) and substituting into Eq. (8):

Larc ¼2a

Z L=2

0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia2 þ x2

pdx� L ð9Þ

where

a ¼ L2

8um¼ T0

pð10Þ

The average strain in the membrane can be calculated as:

e ¼ Larc � LL

¼ Larc

L� 1 ð11Þ

The tension for the membrane at a distance x from the origin:

T ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiT2

0 þ ðpxÞ2q

ð12Þ

In which T0 is the Tension force in the membrane at midspan.The average tension for the cable can be obtained by integrating

Eq. (12) from zero to L/2 and then dividing by L/2 and substitutingthe second part of Eq. (10):

Tave ¼2pL

Z L=2

0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia2 þ x2

pdx ð13Þ

Rearranging the terms in Eq. (13):

p ¼ TaveL2� 1R L=2

0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia2 þ x2p

dxð14Þ

Once the strain in the material is determined for a given midspandisplacement, the average tension force in the steel can be deter-mined using the constitutive relation of the material and thensubstituted into Eq. (14) to estimate the uniform load.

As noted earlier, the tensile membrane response can developonly if the longitudinal reinforcement is well anchored into the sup-ports, and failure will be defined by the tensile capacity of the longi-tudinal reinforcement. Initially, the column will respond in a flexuralresponse mode, and undergo relatively small lateral displacements.However, the column would jump into a tensile membrane behaviorunder specific conditions that will be defined later, herein. A transi-tion into a tensile membrane response also means that the adjacentmembers can take over the gravity loads that the column previouslycarried and withstand the additional axial compression induced bythe tensile forces generated by the membrane in the deformedmember. The switch to tension membrane mode is initiated byeither compression failure of the concrete, buckling of the column,or when the lateral displacement exceeds the effective depth ofthe cross section. Fig. 4 shows the combined flexural and tensionmembrane resistance functions. Instead of simply superimposingthe pure tension membrane curve on top of the flexural resistancecurve, the tension membrane curve was shifted up slightly to ac-count for the existing stresses in the member at the time of the tran-sition from flexure to tensile membrane, as recommended in [11].

2.3. Direct shear resistance

Another type of response that was observed in RC members un-der highly impulsive loads is direct shear. Unlike the flexural andtension membrane responses that can be combined into the sameresistance function, direct shear is different and unrelated to theother two behaviors. It is initiated by the localized through-thick-ness shear failure of the member at geometric or load discontinuityregions (e.g., at the supports), consequently resulting in separationof the member from the supports during the first milliseconds ofthe loading. In DSAS, the ‘‘check’’ for the direct shear type of failureis accomplished using a resistance function for the direct shear re-sponse mode based on the Hawkins model [12]. The equationsused in DSAS for modeling direct shear response are described indetail in Krauthammer et al. [13] and the influence of axial loadon the direct shear response is included by increasing the shearstrength values according to ACI 318 [14] when the member is un-der axial compression.

The overall algorithm in DSAS is shown in Fig. 5. For most anal-yses, a typical DSAS run time is less than one second, which is con-siderably shorter than the amount of time it takes to analyze thesame member using a continuum based FE approach with tens ofthousands of DOF. This allows a large number of cases or a singlecase with different load functions (i.e. to construct a pressureimpulse diagram) to be analyzed rapidly. For example, typical ABA-

Fig. 5. DSAS flowchart.

Fig. 6. Details of the RC beams tested by Feldman and Siess [15].

Table 1Concrete material properties [15].

Beam f 0c (MPa) Ec (MPa) fr (MPa)

1-C 39.1 29,593 6.21-G 42.8 30,970 6.91-H 42.4 30,682 6.41-I 44.8 32,612 5.91-J 42.0 26,821 6.4

S. Astarlioglu et al. / Engineering Structures 55 (2013) 26–34 29

QUS runtimes for the beam cases described in the next sectionwere in the order of six hours. With DSAS, the results wereobtained almost instantaneously.

3. Numerical procedure validation

3.1. Validation using experimental data from impact tests

Five beams tested by Feldman and Siess [15] were used for val-idation of the computer code DSAS. Fig. 6 shows the layout and thereinforcement details of the beams that were tested. Tables 1 and 2

show the concrete material properties and reinforcement materialproperties, respectively. All five beams had identical layouts and

Table 2Reinforcement material properties [15].

Beam Compression reinforcement Tension reinforcement

fy (MPa) Es (MPa) ey (mm/mm) esh (mm/mm) fy (MPa) Es (MPa) ey (mm/mm) esh (mm/mm)

1-C 322 N/A N/A N/A 318 203,533 0.0016 0.01441-G 333 N/A N/A N/A 329 N/A N/A N/A1-H 328 222,563 0.0015 0.0150 325 240,627 0.0014 0.01251-I 331 N/A N/A N/A 324 224,769 0.0014 0.01501-J 337 203,809 0.0016 0.0120 327 N/A N/A N/A

Table 3Comparison of measured and calculated peak midspan displacements.

Beam Experiment (mm) ABAQUS (mm) DSAS (mm)

1-C 76 74 781-G 105 107 1021-H 225 223 2081-I 268 252 2431-J 24 31 21

Fig. 7. Load function for beam 1-C [15].

30 S. Astarlioglu et al. / Engineering Structures 55 (2013) 26–34

closed stirrups except beam 1-C which had open stirrups. Forcomparison purposes, the beams were also modeled with the FEprogram ABAQUS/Explicit [16]. 8-noded brick elements with aModified Drucker–Prager Cap material model were used inABAQUS to model the concrete, and beam elements were used tomodel the reinforcement.

The peak midspan displacements, shown in Table 3, indicatedthat both DSAS and ABAQUS were able to predict the peak midspanresponse of the beams quite accurately, and except for test case 1-J,the results from both programs were within less than 10% from themeasured peak displacements. Figs. 7 and 8 show the loading func-tion and displacement time history for beam 1-C. While bothprograms follow the experimental results closely, the peak dis-placement is reached slightly earlier in DSAS and slightly later inABAQUS, as compared to the test data.

Fig. 8. Beam 1-C midspan displacement time history under impact loading.

3.2. Validation under blast loads using ABAQUS

Since no test data for a beam under a uniform blast load wasavailable, beam 1-C was also used for a comparison between DSASand ABAQUS. In this case, the computer code CONWEP [17] wasused to derive a loading function from an explosive charge at a spe-cific distance from the beam’s midspan, and it was approximatedby a triangular load time history with the peak pressure of12.3 MPa and load duration of 1.28 ms. The corresponding impulsefor this load is defined by the area under the load-time history(0.5 � 12.3 � 1.28 = 7.872 MPa ms). The results computed fromABAQUS and DSAS for beam 1-C are shown in Fig. 9. The differencein the peak displacements was less than two percent. The residualdisplacement calculated by ABAQUS was much bigger, which maybe attributed to the inability of the material model in ABAQUS tocapture the hysteretic behavior of concrete. Since the peak dis-placements are more relevant than residual displacements forassessing damage in protective structures [18], it was concludedthat these results from both programs are acceptable.

In addition to the simply supported beam, the RC column,shown in Fig. 10, was also modeled with ABAQUS. In this case, a406 mm � 406 mm section with a 3.66 m span length and eightUS No. 11 bars as primary longitudinal reinforcement was selected.The section was enclosed in US No. 4 ties spaced at 304 mm. It wasassumed that the column continued 152 mm at each end to prop-erly model the boundary conditions. A steel plate was emplaced atthe top and bottom of the column to properly distribute the axialpoint load onto the surface of the column. Both supports were fixed

in all directions, and the longitudinal reinforcement ends were alsofixed in the vertical direction to ensure the full development of thereinforcement’s tensile capacity.

Fig. 9. Beam 1-C midspan displacement time history under blast loading.

Fig. 10. RC column mesh in ABAQUS.

Fig. 11. Column midspan displacement time history under blast loading.

Fig. 12. Imposed support displacement time histories to simulate axial loads in theABAQUS model.

Table 4Peak midspan displacements of the column under 3559 kN axial load.

Refl. pressure(MPa)

Refl. impulse(MPa-ms)

DSAS(mm)

ABAQUS(mm)

Difference (%)

29.0 19.6 193 228 1532.8 22.8 240 289 1736.3 25.9 287 345 17

S. Astarlioglu et al. / Engineering Structures 55 (2013) 26–34 31

Using the same pressure time history, as for the beam 1-C case,the displacement time histories, shown in Fig. 11, were obtainedwithout axial loads. Similarly to the beam case, there was a differ-ence between the times the peak displacements were reached in

DSAS and ABAQUS, and between the residual displacements. How-ever, the difference in magnitudes of the peak displacementsdetermined from both programs was less than 2%.

In the next phase of validation, the same column configurationwas analyzed under different levels of axial loads. In the ABAQUS

Table 5Peak midspan displacements of the column under 6672 kN axial load.

Refl. pressure(MPa)

Refl. impulse(MPa-ms)

DSAS(mm)

ABAQUS(mm)

Difference(%)

29.0 19.6 218 231 532.8 22.8 266 262 136.3 25.9 311 342 9

Fig. 13. Column interaction diagram when effects of confinement are ignored.

Fig. 14. Column interaction diagram when effects of confinement are included.

Fig. 15. Column moment curvature relationships for different axial load levels.

Fig. 16. Column resistance functions for different axial load levels.

32 S. Astarlioglu et al. / Engineering Structures 55 (2013) 26–34

model, the axial loads were simulated by slowly superimposingsupport displacement until the axial stresses on the column wereat the desired level prior to application of the transverse blast pres-sures, as shown in Fig. 12. Table 4 shows the peak midspan dis-placements obtained with DSAS and ABAQUS under a constant

axial load of 3559 kN, for three different blast loads, denoted bytheir peak reflected pressure and reflected impulse (I defined theimpulse for 1-C) values. Similarly, Table 5 shows the comparisonbetween ABAQUS and DSAS results under a constant axial load of6672 kN.

It was noted that there was a better agreement between thepeak displacements calculated by DSAS and ABAQUS in the blastcases which had the bigger level of axial load. While the differencebetween the peak displacements predicted was as high as 17% inthe case of a 3559 kN axial load and a transverse blast loading witha peak pressure of 32.8 MPa and an impulse of 22.8 MPa-ms, theauthors believe that the results obtained from DSAS are reasonablyaccurate.

Fig. 17. Column pressure-impulse diagram for different axial load levels.

S. Astarlioglu et al. / Engineering Structures 55 (2013) 26–34 33

4. Parametric study

In the parametric study, two types of boundary conditions wereconsidered for the RC columns. In the first set, 406 mm �406 mm � 3.66 m RC columns with simply supported boundaryconditions were analyzed, and tension membrane type behaviorwas not included. In the second set, fixed boundary conditionswere considered, and tension membrane behavior was includedin the response.

4.1. Column with simply supported boundary conditions

In this part of the study, the amount of longitudinalreinforcement was selected as the primary variable. Four differentconfigurations were analyzed with reinforcement ratios of 0.0188(8 – No.7), 0.0488 (8 – No.8), 0.0352 (4 – No.14), and 0.0731 (12– No. 11). The specified compressive strength of the concrete was27.6 MPa and the yield strength of the reinforcing steel was413.7 MPa. The interaction curves for the column with the rein-forcement ratio of 0.0188 are shown in Figs. 13 and 14. The inter-action diagram in Fig. 13 was plotted for the case when theinfluence of diagonal shear and the effects of confinement were ig-nored. With the inclusion of ACI 318-08 [14] strength reductions

Table 6Parametric study of a 406 mm � 406 mm � 3.66 m RC column with various amounts of lo

Refl.pressure (MPa)

Refl. impulse(MPa-ms)

Midspan displacement (mm)

8-No.7 8

2224 kN 3559 kN 6672 kN 2

5.1 3.6 10 10 20a 18.2 5.4 21 24a 44a 2

12.3 7.8 54a 54a 85a 414.7 9.3 80a 77a 112a 720.1 12.9 144a 136a 183a 129.0 19.6 F F 329a 232.8 22.8 F F F F36.3 25.9 F F F F

F Indicates direct shear failure.a Indicates tension membrane response.

factors, the curve plotted by DSAS matched well the values pro-vided in Concrete Steel Reinforcing Institute Design Handbook[19], and that served the purpose of further validation of the pro-gram. The second interaction diagram, shown in Fig. 14, was plot-ted for the case where the influence of diagonal shear and theeffects of confinement were included. The axial load levels on thecolumn prior to the application of the blast load were selectedbased on this interaction diagram, as follows: 4448 kN (approxi-mately 80% higher than the balanced axial load), 2491 kN (the bal-anced axial load), 1112 kN (65% less than the balanced axial load),and zero axial load.

Fig. 15 shows the moment–curvature diagrams of the columnwith the reinforcement ratio of 0.0188 under each of the previ-ously-selected axial load levels, and Fig. 16 shows the correspond-ing flexural resistance functions at these levels. As expected, up tothe balance axial load, the strength of the column increased as theaxial load level increased. However, once the axial load level wasgreater than the balance axial load, the strength of the columnstarted to decrease. In all cases, the presence of compressive axialforces on the section reduced the ductility, since the failure modeshifted from a ductile tension type failure in the reinforcement to abrittle compression type failure.

Fig. 17 shows the pressure–impulse diagram of the column withthe reinforcement ratio of 0.0188 under an idealized triangulartransverse load pulse. This diagram was obtained numerically byrunning a large series of SDOF analyses to obtain the thresholdcurves using the approach that was proposed in [7]. For low pres-sure (i.e. 0.42 MPa) and long duration loads (i.e., the quasi-staticdomain), there was very little difference between the thresholdcurves for the different axial load cases, unless the axial load levelwas above the balance axial load level. For high pressure and shortduration loads (i.e., the impulsive domain), the impulsive asymp-tote shifted to the left with each increment in axial load (i.e. lowerimpulse level). This indicated that the column became more vul-nerable to blast loads, as the level of axial load on the columnwas increased.

4.2. Column with fixed boundary conditions

In this part, a column with the same dimensions and materialproperties as the one described in the previous section was used.Three different longitudinal reinforcement ratios of 0.0247 (8 –No.8), 0.0313 (8 – No.9), and 0.0488 (8 – No.11) were applied.The axial stresses in the columns were slowly increased to13.5 MPa (2224 kN), 21.5 MPa (3559 kN), and 40.4 MPa (6672 kN)before the columns were subjected to blast loads, as shown inFig. 12. Eight different blast loads, ranging from the least severecase of a 5.1 MPa peak reflected pressure and a duration of1.43 ms (reflected impulse = 3.6 MPa-ms) to the most severe case

ngitudinal reinforcing subjected to different blast pressures and axial loads.

-No.9 8-No.11

224 kN 3559 kN 6672 kN 2224 kN 3559 kN 6672 kN

1 11 20a 10 10 142 23 41a 19 18 31a

7a 54a 78a 36 39a 64a

2a 76a 101a 52 60a 85a

30a 131a 160a 102a 107a 130a

50a 246a 281a 199a 193a 218a

F 336a 248a 240a 266a

F 385a F 287a 311a

34 S. Astarlioglu et al. / Engineering Structures 55 (2013) 26–34

of a 36.3 MPa peak pressure and a duration of 1.43 ms (reflectedimpulse = 25.9 MPa-ms) were used. A total of 72 cases wereanalyzed.

Table 6 shows both the loading characteristics and the peak dis-placements calculated for the columns under these loads. In mostof the loading cases, the columns behaved in the tension mem-brane mode. This type of response was expected since the axialload levels on the columns in this part of the study were selectedto be relatively high to cause an early compressive failure thatwould force the columns to enter the tension membrane mode.For more intensive loads, the columns failed in the direct shearmode. It is interesting to note that the columns with the highestaxial load level of 6672 kN started to exhibit a tension membranebehavior even under relatively small blast loads. This is a conse-quence of the addition of flexural stresses caused by the blast loadto the already existing high levels of compressive stresses in thesection. The columns with lower levels of axial load behaved inflexure up to moderate levels of blast loads. In more severe blastload cases, failures due to direct shear were observed. Based onthe results of the parametric study, it is apparent that the columnswith the highest reinforcement ratio and axial load are more resis-tant to blast loads, and the column with 8 – No. 11 bars and6672 kN axial load survived the most severe blast load.

5. Conclusions

The comparisons and results provided in this study indicatedthat advanced SDOF based models can be used to study blastloaded RC column behavior efficiently with acceptable accuracy.When compared with experimental results from impact tests onRC beams, DSAS results were within 2–11% of the measured valuesWhen compared with ABAQUS results for blast loading cases, thedifference was between 1% and 17%. Nevertheless, further valida-tion with results from actual tests of RC columns is needed to bet-ter define the accuracies of both computational approaches.

The results from the parametric study indicated that the level ofaxial compressive load had a significant effect on the response of aRC column and should not be ignored. Even if the actual axial loadon the column is less than half of its balance axial load, it resultedin a significant reduction of its ability to withstand the impulsedelivered by the blast, as compared to its capacity under pure flex-ure. This is contrary to the response of columns under combinedflexural and axial loads when subjected to quasi-static loads, asindicated by the pressure–impulse diagram. For columns withfixed boundary conditions and continuous reinforcement, a ten-sion membrane type of behavior provided a considerable reservecapacity to resist blast loads and to avoid failure. However, whenthe column switched to a tension membrane, it indicated that

the column lost its ability to carry axial compressive loads. If theadjacent load bearing members are not able to redistribute theloads, this condition may initiate a progressive collapse. Finally,it was observed that for blast loads with very high peak pressures,the columns were prone to direct shear type failures.

Acknowledgement

The authors wish to acknowledge the support provided by USArmy Corps of Engineers – Engineering Research and DevelopmentCenter (ERDC), and the Canadian Forces.

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