## 3 Predicting Capacities of Shear-Critical Columns Using the AASHTO Procedures  
To determine the accuracy of the Simplified and General Procedures for seismic shear design, the predicted shear strengths are compared with the shear strengths of reinforced concrete columns that failed in shear and were subjected to reversed-cyclic loading. Experimental results for columns failing in shear [6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17] were obtained from the PEER Structural Performance Database [18]. These column tests were supplemented with additional results for columns failing in shear from the literature [19; 20; 21; 22; 23; 24; 25]. The experimental results had a wide range of variables including: circular, octagonal, and rectangular columns; cross-sectional dimensions from 152 to 914 mm, axial compressive load level, \(P/A_{g}f_{c}^{\prime}\) from zero to 0.506; concrete strengths from 16.0 to 56.2 MPa; yield stress of the longitudinal (\(f_{yl}\)) and transverse reinforcement (\(f_{ye}\)) from 249 to 496 MPa; transverse reinforcement ratio, \(\rho_{v}=A_{v}/(b_{v}s)\), from zero to 0.761%; longitudinal reinforcement ratio, \(\rho_{l}=A_{st}/A_{g}\) from 0.992 to 7.15%, and shear span-to-depth ratios, \(a/D\) or \(a/h\), from 1.09 to 3.22. The effective web width, \(b_{v}\), for circular columns was taken as the diameter and the effective web width for the octagonal columns was taken as the flat-to-flat dimension of the column. The transverse reinforcement typically consists of hoops and seismic crossties in rectangular columns and spirals or circular hoops in circular or octagonal columns. In the application of the Simplified and General Procedures for circular and octagonal columns, the area of shear reinforcement, \(A_{v}\), within distance \(s\) was taken as twice the cross-sectional area of the spiral or circular hoop reinforcement. The cross-sectional dimensions and reinforcement details are given in Figure 1 and Table 1 for the circular and octagonal columns, and Figure 2 and Table 2 for the rectangular columns. Tables 1 and 2 as well as Figures 3 and 4 compare the shear strength predictions using the AASHTO Simplified (\(V_{sim}\)) and General Procedures (\(V_{gen}\)) with the experimentally obtained shear capacities (\(V_{exp}\)) for shear-critical rectangular and circular/octagonal columns. Tables 1 and 2 as well as Figures 3a and 4a include the reduction in \(V_{c}\) for low axial load levels required in the AASHTO Specifications while Figures 3b and 4b do not include this reduction for low axial load levels. The shear strength predictions using the AASHTO Simplified Procedure resulted in average \(V_{exp}/V_{sim}\) of 2.96 (SD = 2.12) and 2.51 (SD = 1.36) for the circular/octagonal and rectangular columns, respectively. The AASHTO General Procedure is more accurate and resulted in an average \(V_{exp}/V_{gen}\) of 1.85 (SD = 1.18) for the circular and octagonal columns, and 1.54 (SD = 0.72) for the rectangular columns. If the reduction in \(V_{c}\) is neglected, the Simplified Procedure results in average \(V_{exp}/V_{sim}\) ratios of 1.89 (SD = 0.58) and 2.05 (SD = 0.75) for the circular/octagonal and rectangular columns, respectively. If the reduction in \(V_{c}\) is neglected, the General Procedure results in average \(V_{exp}/V_{gen}\) ratios of 1.30 (SD = 0.20), and 1.30 (SD = 0.26) for the circular/octagonal and rectangular columns, respectively. It is clear from Figures 3 and 4 that excluding the reduction factor on \(V_{c}\) results in generally conservative and more accurate predictions, with the General Procedure giving the best predictions. By accounting for the combined effects of moment, shear, and axial load, and the amount of longitudinal reinforcement, the General Procedure provides better strength predictions over a wider range of variables. As expected, increasing the axial compression or the amount of longitudinal reinforcement increases the predicted shear capacity.