Evaluation of Fema 356 Models for Reinforced Concrete Columns

EVALUATION OF FEMA 356 MODELS FOR REINFORCED CONCRETE COLUMNS AND BEAM-COLUMN JOINTS

H. Sezen1, and F. Alemdar2

ABSTRACT

This study investigates the accuracy of FEMA 356 shear and flexure modeling procedures for reinforced concrete (RC) columns and beam-column joints with poorly detailed or insufficient reinforcement. Following the FEMA 356 guidelines, generalized flexure and shear force-deformation relations were developed and compared with the experimental data from 26 column specimens and 17 beam-column joint specimens. Specifically, the measured and predicted responses were compared and evaluated: at yield displacement and the corresponding lateral load, lateral load and displacement at ultimate, and at axial load failure. In general, while the FEMA 356 models predict the lateral strength of columns reasonably well, they underestimate the shear strength of beam column joints. The predicted initial stiffness and deformations at both yield and ultimate are conservative for columns.

Introduction This study was initiated to examine the accuracy of the Federal Emergency Management Agency Prestandard, FEMA 356 (2000) models in capturing the behavior of lightly reinforced concrete columns and beam-column joints. This research is timely because a large number of reinforced columns and beam-column joints with insufficient strength or deformation capacity are in use today in seismic regions, placing many structures and people at risk in the event of a major earthquake. Most of these structures were designed and constructed before the seismic code provisions and detailing requirements were changed significantly in the early 1970s. The majority of columns and beam-column joints investigated in this study represents columns and beam-column joints in existing structures, and do not meet the current code requirements. According to the classifications provided in FEMA 356 document, these are the columns and beam-column joints with non-conforming details. The test columns used in this research were chosen from the database compiled by Sezen (2002). The detailed description of damage, failure mechanisms, and digital lateral load-displacement relations were available for the 26 column specimens used in this study. Table 1 identifies key parameters of the test columns, all of which were subjected to cyclic lateral load reversals and had apparent shear distress at failure. The column aspect ratio or shear span-to-depth ratio, La/d varies between 2.0 and 4.0, and the transverse reinforcement index, w fy/ cf varies between 0.01 and 0.12. Columns were tested by shearing a full-length column in double curvature, or by loading one or a double cantilever in single curvature. Three test specimens, 3SLH18, 2SLH18 and 3SMD12 in Table 1, had short lap splices near the bottom of the column. Details of the

1 Assistant Professor, Department of Civil and Environmental Engineering and Geodetic Science, The Ohio State University, 470 Hitchcock Hall, 2070 Neil Ave, Columbus, OH 43210-1275 2 Graduate Student Researcher, Department of Civil and Environmental Engineering and Geodetic Science, The Ohio State University, 470 Hitchcock Hall, 2070 Neil Ave, Columbus, OH 43210

specimens, test setups, and reported load-deformation relations can be found in Sezen (2002). The beam-column joint specimens used in this research were chosen from the database compiled by Alemdar (2007). Table 2 identifies the critical test parameters of beam-column joints needed to construct the FEMA response envelopes. The 14 specimens listed in Table 2 are exterior beam-column joints. Three additional interior beam-column joints, SL1, SL2 and SL4 tested by Shin and LaFave (2004), are also used to evaluate the FEMA 356 model. Both exterior and interior beam-column joints used in this study failed in shear. Details of the specimens, test setups, and load-deformation relations can be found in the corresponding references listed in Table 2. FEMA 356 Flexure Model The procedures outlined in the FEMA 356 document provide guidelines to develop nonlinear lateral force-deformation relations for RC members. For columns and beam-column joints with strength limited by flexure, the load-displacement model follows the general relation shown in Fig.1, where lateral force is normalized with respect to the yield force. For a given column or beam-column joint, in order to generate a relationship as shown in Fig. 1, the initial stiffness; the displacement, y or lateral load, Vy at yielding (Point B); and/or the lateral load at flexure failure, Vp (Point C); the plastic rotation angles a and b, and the residual strength ratio, c need to be determined. The initial stiffness or the slope of line AB in Fig. 1 is defined considering flexural and shear deformations for columns. Flexural rigidity, kEcIg is defined equal to 0.5EcIg for P 0.3Agfc, and 0.7EcIg for P 0.5Agfc, with a linear variation in between (Ec = modulus of elasticity of concrete, Ig = gross moment of inertia, and Ag = gross cross sectional area). Shear stiffness for rectangular cross sections is defined as 0.4EcAg. The initial stiffness is not defined for beam-column joints clearly in the FEMA 356 prestandard. The shear rigidity for beam-column joints is assumed to be 0.4EcAg by considering that the shear rigidity for both beams and columns are specified as 0.4EcAg and by assuming that the beam-column joints are part of the columns or beams. The plastic rotation angles a and b depend on the axial load, nominal shear stress, and reinforcement details. The residual strength ratio, c is equal to 0.2. The flexural strength is calculated for expected material strengths (i.e., measured steel and concrete strengths for test specimens) using the procedures outlined in the ACI 318 code (2005). It may be argued that the maximum plastic moment, Mp should be used to define point C, instead of the moment capacity, Mn based on the ACI 318 rectangular compressive stress block assumption. Considering that the purpose of FEMA 356 document is to provide simple guidelines to generate a force-deformation relationship as in Fig. 1, the moment capacity Mn is used in this study. It is also possible to increase Mn by 25% assuming that the longitudinal steel strength can be equal to 1.25fy at ultimate as suggested in Chapter 21 of the ACI 318 code. However, the detailed moment-curvature analysis of the columns included in this study showed that the difference between the ACI moment capacity Mn and the plastic moment capacity Mp was very small, not justifying a 25% increase in Mn. FEMA 356 requires that the slope from point B to C to be zero or 10% of the initial slope. In this study, the slope is assumed to be zero. FEMA 356 Shear Model In the FEMA 356 document, the shear strength of columns is defined by Eq. 1

ggc

cysn A

Af

P

VdM

fk

sdfA

kV 8.06

16

'

'

21

++= (1)

where k1 = 1 for transverse steel spacing less than or equal d/2, k1 = 0.5 for spacing exceeding d/2 but not more than d, k1 = 0 otherwise; k2 = 1 for displacement ductility demand, 2, k2 = 0.7 for 4 with linear variation between these limits (Fig. 2), = 1 for normal-weight concrete; M and V = moment and shear at section of maximum moment; the value of M/Vd (=La/d) is limited to 2 La/d 3. The displacement ductility demand, is defined as the ratio of yield displacement, y (at point B) to ultimate displacement (at point C). The FEMA 356 document recommends Eq. 2 for the calculation of nominal shear strength of beam-column joints according to the general procedures of ACI 318. jcn AfV '= (2) where is the nominal strength coefficient as defined in Table 3, Aj is the effective horizontal joint area defined as the product of the column dimension in the direction of loading and the joint width equal to the smaller of 1) column width, or 2) beam width plus the joint depth, or 3) twice the smaller perpendicular distance from the longitudinal axis of the beam to the column side. Lateral Force-Deformation Relations and Implications Fig. 3 shows the cyclic load-deformation relation for a column specimen with poor reinforcement details (e.g., with 90-degree hooks at the end of the hoops) tested by Sezen (2002). Yielding of the longitudinal reinforcement is evident by a reduction in the lateral load stiffness at a displacement of approximately 25 mm in both loading directions. For the nine columns tested by Saatcioglu and Ozcebe (1989) and Wight and Sozen (1975), no experimental yield displacement was reported. For those columns, the yield displacement is estimated using the procedure illustrated in Fig. 3, where y,test is assumed to occur at the intersection of a horizontal line corresponding to the maximum lateral load with a secant drawn to intersect the lateral load-displacement relation at 70% of the maximum lateral load. For all columns listed in Table 1, the ultimate displacement indicating significant reduction in lateral load resistance, u,test was defined as the maximum measured displacement at which the lateral load drops to 80% of the maximum applied lateral load. Continued deformation cycles typically result in loss of axial-load-carrying capacity at a maximum displacement, ug as identified in Fig. 3. The maximum lateral strength of the column, Vtest reported in Table 4 is defined as the largest lateral force measured in either loading direction. The FEMA 356 flexure and shear models are compared with the experimental data in Figs. 4 and 5 for 12 of the columns considered in this study. The maximum flexure and shear strengths predicted from FEMA 356 models (as reported in Table 4) are based on the observation that the maximum lateral strength is typically reached at a displacement ductility less than 2.0 following the flexural yielding (Figs. 4 and 5). Then, the maximum lateral strength, Vn,FEMA reported in Table 4 is the smaller of Vp,flexure (=Mn,ACI/La) and Vn,shear (from Eq. 1). The mean ratio of measured lateral strength, Vtest to strength predicted by FEMA 356, Vn,FEMA is 1.15. This is an indication that FEMA 356 models can predict the maximum strength of columns reasonably well, if both flexure and shear strengths are evaluated together.

Using the FEMA 356 flexure and shear models for columns, an attempt was made to classify the critical failure mechanism. The failure modes predicted in Table 4 are defined as: 1) flexure dominated, if the flexure strength was significantly lower than the shear capacity; 2) shear dominated, if the shear strength was found to be significantly lower than the flexure capacity; 3) flexure-shear mode, if the shear and flexure strengths were very close. This classification may have a significant impact on determination of expected failure mechanism and the rehabilitation method to be used. The measured yield and maximum shear strength of beam-column joints, Vy,test and Vtest are reported in Table 6. The FEMA 356 models are compared with the experimental data in Figs. 6 and 7 for 9 exterior and 3 interior beam-column joints. The FEMA 356 model overestimates the shear strength of all beam-column joints. The mean ratio of measured shear strength of external beam-column joints, Vn,test to strength predicted by FEMA 356, Vn,FEMA is 1.69 with a standard deviation of 0.32. The mean ratio of measured to predicted yield rotations for the exterior joints listed in Table 6 was 3.55 with a very large deviation. As shown in Table 7, the reported experimental yield and ultimate rotations as well as corresponding simplified FEMA 356 predictions varied widely. The displacements at first yielding, y and at ultimate, u calculated following the guidelines provided in the FEMA 356 document are compared with experimental data in Table 5 for columns. FEMA 356 procedures consistently underestimate both yield and ultimate displacements for columns. The mean ratio of observed displacements to calculated displacements at yield (y,test/y,FEMA) and at ultimate (u,test/u,FEMA) are 2.06 and 3.88, respectively. It appears that both the initial stiffness and plastic rotation angle estimates provided in the FEMA 356 document are conservative for the columns considered in this paper. The discrepancy is probably because the FEMA 356 model does not consider slip of longitudinal reinforcement from the beam-column connections. The FEMA 356 model could be improved by including this additional flexibility. Comparison of test data and models in Figs. 4 and 5 indicate that, in general, the estimated displacements at axial-load-failure (ug in Fig. 3) are also significantly less than the actual apparent values. It should be noted that the models estimate the overall response reasonably for a few columns such as 2CHD12, 2CMH18, and 3CMH18. FEMA 356 flexure and shear models estimate that none of the 12 columns would fail in shear after the flexural capacity is reached (Figs. 4 and 5). In other words, no flexure model crosses the inclined or reduced portion of the shear model, indicating that the columns would either fail in shear (flexure model crosses shear model at a low displacement ductility) or fail in flexure (flexure model does not cross the shear model). If the initial stiffness and deformation models in FEMA 356 are improved, it may be possible to see several columns failing in shear after development of flexural strength as reported by the researchers.

Conclusions The FEMA 356 flexure and shear models were used to predict the behavior of lightly reinforced or poorly detailed 26 RC columns and 17 beam-column joints. Based on the comparison of models and test data, the following can be concluded. The maximum lateral strengths of columns were predicted relatively accurately using the combination of flexure and shear models. The discrepancies between the predicted and measured

strengths will improve if the initial stiffness or the deformation predictions are improved. The predicted failure mechanisms for columns did not compare well with the reported experimental data, partially because of the problems associated with initial stiffness or deformation predictions. In all cases, the initial stiffness and the corresponding yield displacement, and the displacement at ultimate were underestimated for column specimens. The initial stiffness estimates can be improved by including the effect of longitudinal bar slip in the flexure model. The predicted maximum shear strength of exterior beam-column joints were too conservative. The shear strength factor for exterior beam-column joints in ACI 318 code is two times the corresponding values in the FEMA 356 standard for the same type of joints used in this research. ACI 318 shear strength calculations are more accurate by considering the joints investigated in this research (Type 2 joints according to ACI 318). The maximum shear strength of interior beam-column joints are reasonable well predicted by considering the three specimens. Further research should be conducted to evaluate the accurateness of FEMA model for interior beam-column joints since the number of the test specimens is not adequate to have a conclusive remark. The predicted strength degradation (i.e., drop between C and D in Figure 1) do not represent the actual behavior of most beam-column joints considered here. The overall beam-column joint behavior and the associated maximum shear strength and plastic rotations (at yield and ultimate) were predicted poorly. Beam-column joint test data reported by different researchers also varied widely. References ACI 318. 2005. Building Code Requirements for Structural Concrete. ACI Committee 318, American

Concrete Institute, Farmington Hills, Michigan. Alemdar F. 2007. Behavior of Existing Reinforced Concrete Beam-Column Joints. Master Thesis. The

Ohio State University. Clyde, C., Pantelides, C.P., and Reaveley, L.D., July 2000. Performance-Based Evaluation of Exterior

Reinforced Concrete Buildings Joints for Seismic Excitation. PEER Report, No. 2000/05. Pacific Earthquake Engineering Research Center, University of California, Berkeley.

Esaki F., 1996. Reinforcing Effect of Steel Plate Hoops on Ductility of R/C square Columns. Eleventh World Conference on Earthquake Engineering, Pergamon, Elsevier Science Ltd., Paper No. 196.

FEMA 356, 2000. NEHRP Guidelines for the seismic rehabilitation of buildings. Federal Emergency Management Agency. Washington DC.

Hwang, S.J., Lee,H.J., Liao,T.F., Wang, K.C., and Tsai, H.H., 2005. Role of Hoops on Shear Strength of Reinforced Concrete Beam-Column Joints. ACI Structural Journal. Vol.102 No:3, pp.445-453

Lynn, A. C., Moehle J. P., Mahin S. A., and Holmes W. T., 1996. Seismic Evaluation of Existing Reinforced Concrete Columns, Earthquake Spectra, Earthquake Engineering Research Institute, Vol. 12, No. 4, November 1996, 715-739.

Ohue M., Morimoto H., Fujii S., and Morita S., 1985. The Behavior of R.C. Short Columns Failing in Splitting Bond-Shear Under Dynamic Lateral Loading. Transactions of the Japan Concrete Institute. Vol. 7. pp. 293-300

Pantelides, C.P., Hansen, J.,Nadauld, J., and Reaveley, L.D., May 2002. Assessment of Reinforced Concrete Building Exterior Joints with Substandard Details. PEER Report, No. 2002/18. Pacific Earthquake Engineering Research Center, University of California, Berkeley.

Saatcioglu M., and Ozcebe G., 1989. Response of reinforced concrete columns to simulated seismic loading. ACI Structural Journal. Vol. 86, No.1, Jan.-Feb. 1989. pp. 3-12

Sezen H. 2002. Seismic Behavior and modeling of reinforced concrete building columns. Ph.D. Thesis. University of California, Berkeley. http://peer.berkeley.edu/~sezen/Files/thesis/

Sezen H., and Moehle J. P., November-December 2006. Seismic Tests of Concrete Columns with Light Transverse Reinforcement. ACI Structural Journal. Vol. 103, No: 6, pp. 842-849

Shin, M., and Lafave,J.M., 2004. Thirteenth World Conference on Earthquake Engineering, Vancouver, B.C., Canada, Paper No. 0301.

Wight J. K., and Sozen M. A., 1975. Strength decay of RC columns under shear reversals. Journal of the Structural Division, ASCE. Vol. 101, No. ST5, May 1975, pp. 1053-1065

Table 1. Dimensions, material properties and other details for column specimens

b d La s l w fyl fy cf P Specimen Reference mmm mmm mm mmm % % MPaa MPaa MPaa kN

2CLD12 457 394 147 305 2. 0.1 447 469 21.1 667 2CHD12 457 394 147 305 2. 0.1 447 469 21.1 266

2CLD12M

Sezen and Moehle (2006)

457 394 147 305 2. 0.1 447 469 21.8 667 3CLH18 457 381 147 457 3. 0.1 335 400 25.6 503 3SLH18 457 381 147 457 3. 0.1 335 400 25.6 503 2CLH18 457 381 147 457 2. 0.1 335 400 33.1 503 2SLH18 457 381 147 457 2. 0.1 335 400 33.1 503 2CMH18 457 381 147 457 2. 0.1 335 400 25.7 1513CMH18 457 381 147 457 3. 0.1 335 400 27.6 1513CMD12 457 381 147 305 3. 0.1 335 400 27.6 1513SMD12

Lynn and Moehle (1996)

457 381 147 305 3. 0.1 335 400 25.7 1512D16RS 200 175 400 50 2. 0.5 376 322 32.1 183 4D13RS

Ohue et al. (1985) 200 175 400 50 2. 0.5 377 322 29.9 183

H-2-1/5 200 175 400 50 2. 0.5 363 370 23.0 161 HT-2-1/5 200 175 400 75 2. 0.5 363 370 20.2 161 H-2-1/3 200 175 400 40 2. 0.6 363 370 23.0 269

HT-2-1/3

Esaki (1996)

200 175 400 60 2. 0.6 363 370 20.2 236 U-7 400 375 100 120 2. 0.4 581 382 29.0 464 U-8 400 375 100 120 2. 0.5 581 382 33.5 107U-9

Saatcioglu & Ozcebe (1989) 400 375 100 120 2. 0.5 581 382 34.1 163

40.033aE 152 254 876 127 2. 0.3 496 344 34.7 189 40.033E 152 254 876 127 2. 0.3 496 344 33.6 178 25.033E 152 254 876 127 2. 0.3 496 344 33.6 111 00.033E 152 254 876 127 2. 0.3 496 344 32.0 0 40.048W 152 254 876 89 2. 0.4 496 344 26.1 178 00.048W

Wight and Sozen (1975)

152 254 876 89 2. 0.4 496 344 25.9 0 Notation: b = column width, d = depth to centerline of tension reinforcement, La = shear span (= length, L for cantilevers; =L/2 for double curvature columns), s = hoop spacing, l = longitudinal steel ratio, w = transverse steel ratio, fyl = longitudinal steel yield strength, fy = transverse steel yield strength, cf = concrete strength, P = applied axial load

Table 2. Dimensions, material properties and other test parameters for beam-column joints

cf Joint Joint rein. Specimen MPa gc Af

P*'

bj (mm) hj (mm) s (mm)

#2 46.2 0.10 457 305 - #4 41.0 0.25 457 305 - #5 37.0 0.25 457 305 -

Clyde et al.

#6 40.1 0.10 457 305 - 1 33.1 0.10 406 406 - 3 34.0 0.10 406 406 - 4 31.6 0.25 406 406 - 5 31.7 0.10 406 406 -

Pantelides

et al. 6 31.0 0.25 406 406 -

SST-0 67.3 0.017 420 420 - 01-B8 61.8 0.018 420 420 -

SST-3T3 69.0 0.016 420 420 97 SST-2T4 71.0 0.016 420 420 146

Hwang et al.

SST-1T44 72.8 0.015 420 420 293 Notation: cf = concrete strength, P = applied axial load, Ag = column area where the axial load is applied, bj = joint width, hj = joint depth, s =joint reinforcement spacing Table 3. FEMA 356 values for joint shear calculation

Value of "

Interior joints with

transverse beams

Interior joint without

transverse beams

Exterior joint with transverse

beams

Exterior joint

without transverse

beams

Knee joint

< 0.003 12 10 8 6 4 003.0 20 15 15 12 8

" = volumetric ratio of horizontal confinement reinforcement in the joint, knee joint = self-descriptive (with transverse beams or not)

Table 4. Comparison of observed and predicted failure modes and shear strengths of columns

Failure mode* Specimen Observed** Predicted

Vtest (kN)

Vp,flexure (kN)

Vn,shear (kN)

Vn,FEMA (kN)

Vtest /Vn,FEMA

2CLD12 3 3 315 297 271 271 1.17 2CHD12 3 1 359 285 400 285 1.26

2CLD12M 3 3 294 299 271 271 1.08 3CLH18 2 2 271 290 196 196 1.38 3SLH18 2 2 267 290 196 196 1.36 2CLH18 3 3 240 216 217 216 1.11 2SLH18 3 3 231 216 217 216 1.07 2CMH18 3 3 316 268 277 268 1.18 3CMH18 2 3 338 342 283 283 1.19 3CMD12 2 3 356 342 344 342 1.04 3SMD12 3 3 378 333 336 333 1.14 2D16RS 3 1 102 87 127 87 1.17 4D13RS 3 3 111 104 126 104 1.07 H-2-1/5 1 1 103 86 121 86 1.20

HT-2-1/5 1 1 102 81 117 81 1.26 H-2-1/3 1 1 121 92 149 92 1.32

HT-2-1/3 1 1 112 87 143 87 1.29 U1 1 3 275 233 258 233 1.18 U2 1 3 270 287 300 287 0.94 U3 1 1 268 279 459 279 0.96

40.033aE 3 3 96 92 122 92 1.04 40.033E 3 3 97 91 120 91 1.07 25.033E 2 3 87 84 114 84 1.04 00.033E 2 3 81 72 101 72 1.13 40.048W 3 1 95 88 114 89 1.07 00.048W 2 1 86 70 95 70 1.23

*: 1) flexure; 2) shear; 3) flexure-shear **: Failure modes from PEER column database (http://maximus.ce.washington.edu/~peera1)

Table 5. Comparison of measured and calculated displacements of column specimens

Yield displacement (mm) Ultimate displacement (mm) Specimen y,test y,FEMA y,test/y,FEMA u,test u,FEMA u,test/u,FEMA

2CLD12 26.16 16.45 1.59 75.44 24.00 3.14 2CHD12 20.07 11.43 1.76 25.91 19.14 1.35

2CLD12M 26.92 16.32 1.65 84.58 23.90 3.54 3CLH18 19.05 14.60 1.30 30.48 22.50 1.35 3SLH18 15.75 14.60 1.08 29.21 22.50 1.30 2CLH18 14.99 9.56 1.57 76.20 18.40 4.14 2SLH18 12.95 9.56 1.35 60.96 18.40 3.31 2CMH18 16.51 13.44 1.23 30.48 21.65 1.41 3CMH18 22.61 16.57 1.35 30.48 23.94 1.27 3CMD12 19.56 16.57 1.18 45.72 23.94 1.91 3SMD12 22.61 16.72 1.35 45.72 24.05 1.90 2D16RS 7.87 2.23 3.53 27.43 4.01 6.84 4D13RS 6.10 2.75 2.22 14.73 4.34 3.39 H-2-1/5 4.06 2.59 1.57 20.07 4.19 4.79

HT-2-1/5 4.83 2.62 1.84 20.83 4.21 4.95 H-2-1/3 3.56 2.79 1.28 16.00 4.38 3.65

HT-2-1/3 4.83 2.79 1.73 20.07 4.39 4.57 U-7 17.02 4.11 4.14 53.09 9.79 5.42 U-8 14.99 6.08 2.47 42.93 8.12 5.29 U-9 16.00 5.51 2.90 44.96 7.73 5.82

40.033aE 7.62 4.26 1.79 31.75 6.35 5.00 40.033E 12.19 4.28 2.85 43.94 6.36 6.91 25.033E 11.94 3.95 3.02 31.50 6.14 5.13 00.033E 7.62 3.47 2.20 27.94 8.45 3.31 40.048W 14.48 4.73 3.06 48.51 6.67 7.27 00.048W 13.46 3.77 3.57 33.02 8.65 3.82

Table 6. Comparison of observed and predicted shear strengths of beam-column joints

Table 7. Comparison of measured and calculated displacements of beam column joints

Yield strength (kN) Maximum strength (kN) Specimen Vy,FEMA Vy,test Vy,test/Vy,FEMA Vn,FEMA Vn,test Vn,test/Vn,FEMA

#2 472 229 0.49 472 847 1.80 #4 444 346 0.78 444 881 1.98 #5 422 229 0.54 422 841 1.99

Clyde et al.

#6 440 244 0.55 440 828 1.88 1 473 363 0.77 473 424 0.90 3 480 408 0.85 480 836 1.74 4 480 376 0.78 480 952 1.98 5 463 679 1.47 463 872 1.88

Pantelides

et al.

6 463 378 0.82 463 888 1.92 SST-0 721 724 1.00 721 997 1.38 01-B8 691 964 1.39 691 1255 1.82

SST-3T3 730 855 1.17 730 1131 1.55 SST-2T4 741 862 1.16 741 1078 1.45

Hwang et al.

SST-1T44 750 837 1.12 750 1032 1.38

Yield rotation (rad) Ultimate rotation (rad) Specimen y,FEMA y,test y,test

/y,FEMA u,FEMA. u,test u,test

/u,FEMA 2 0.000287 0.000109 0.38 0.00529 0.00511 0.97 4 0.000263 0.000256 0.97 0.00526 0.01425 2.71 5 0.000263 0.000498 1.89 0.00526 0.00475 0.90

Clyde et al.

6 0.000263 0.000315 1.20 0.00526 0.00725 1.38 1 0.000263 0.002000 7.60 0.00526 0.00200 0.38 3 0.000263 0.000400 1.52 0.00526 0.00600 1.14 4 0.000263 - - 0.00526 0.00725 1.38 5 0.000263 0.004000 15.21 0.00526 0.01750 3.33

Pantelides

et al.

6 0.000263 - - 0.00526 0.00833 1.58 SST-0 0.000299 0.000208 0.70 0.00530 0.00750 1.42 01-B8 0.000297 0.001422 4.79 0.00530 0.00666 1.26

SST-3T3 0.000300 0.001208 4.03 0.00530 0.01100 2.08 SST-2T4 0.000300 0.000250 0.83 0.00530 0.00287 0.54

Hwang et al.

SST-1T44 0.000302 0.001083 3.59 0.00530 0.00772 1.46

Figure 1. Generalized force-deformation relationship in FEMA 356.

displacement ductility, 2.0

k

high ductility demand

4.0

1

1.0

moderate ductility demand

lowductility demand

0.7

Figure 2. Concrete contribution to shear strength as a function of displacement ductility

150 100 50 0 50 100 150

300

200

100

0

100

200

300 Vtest

0.7Vtest

0.8Vtest

y

u

ug

lateral displacement (mm)

late

ral l

oad

(kN

)

Figure 3. Experimental lateral load-displacement relation (Specimen 2CLD12 in Table 1)

Deformation

NormalizedForce

Deformation

NormalizedForce

150 100 50 0 50 100 150

200

0

200

Lateral displacement (mm)

Late

ral L

oad

(kN

)

2CLD12

50 0 50400

200

0

200

400

Lateral displacement (mm)

Late

ral L

oad

(kN

) 2CHD12

50 0 50 100 150300

200

100

0

100

200

300

Lateral displacement (mm)

Late

ral L

oad

(kN

)

2CLD12M

100 50 0 50 100300

200

100

0

100

200

300

Lateral displacement (mm)

Late

ral L

oad

(kN

)

3CLH18

100 50 0 50 100300

200

100

0

100

200

300

Lateral displacement (mm)

Late

ral L

oad

(kN

)

2CLH18

50 0 50 100300

200

100

0

100

200

300

Lateral displacement (mm)

Late

ral L

oad

(kN

)

2CMH18

Test dataFEMA 356 flexureFEMA 356 shear

100 50 0 50 100400

200

0

200

400

Lateral displacement (mm)

Late

ral L

oad

(kN

)

3CMH18

100 50 0 50 100400

200

0

200

400

Lateral displacement (mm)

Late

ral L

oad

(kN

)

3CMD12

Figure 4. Comparison of FEMA 356 column flexure and shear models with test data

100 50 0 50 100400

200

0

200

400

Lateral displacement (mm)

Late

ral L

oad

(kN

)3CMH18

100 50 0 50 100400

200

0

200

400

Lateral displacement (mm)

Late

ral L

oad

(kN

)

3CMD12

100 50 0 50 100400

200

0

200

400

Lateral displacement (mm)

Late

ral L

oad

(kN

)

3SMD12

30 20 10 0 10 20 30150

100

50

0

50

100

150

Lateral displacement (mm)

Late

ral L

oad

(kN

)

4D13RS

300

Figure 5. Comparison of FEMA 356 column flexure and shear models with test data

Figure 6. Comparison of FEMA 356 models with beam-column joint test data (Clyde et al. 2000)

20000 10000 0 100001000

0

1000 SST0

10000 0 100002000

0

200001B8

10000 0 100001000

0

1000

2000

J

oint

She

ar F

orce

(kN

)

SST3T3

10000 0 100001000

0

1000

2000

J

oint

She

ar F

orce

(kN

)

SST2T4

10000 0 100001000

0

1000

2000SST1T44

30000 10000 0 10000 300001000

500

0

500

1000SL1

20000 0 20000 400001000

500

0

500

1000

Joint Shear Strain (rad)

J

oint

She

ar F

orce

(kN

)

SL2

20000 0 20000 600001000

500

0

500

1000

Joint Shear Strain (rad)

Join

t Sh

ear

For

ce (

kN)

SL4

test data FEMA 356 shear

Figure 7. Comparison of FEMA 356 models with beam-column joint test data