Report - PEER - University of California, Berkeley

The first three modes of vibration of the structure, evaluated considering crackedstiffness properties, are shown in Figure 2, Left to Right. The first mode ispredominantly flexural parallel to axis X ( T = 0. 8s), the second mode ispredominantly flexural parallel to axis Y ( T = 0. 72s), while the third ispredominantly torsional ( T = 0. 64s).Figure 2. First three modal shapes.3.1 Modes of Failure and Definition of CollapseFailure of the structure is defined in terms of the columns failures only. The latter canbe either in flexure or in shear. Failure in flexure is defined as the attainment of theultimate compression strain at the core concrete ε .The shear failure mode capacity is given by the shear strength model suggestedin Kowalsky 2000, which is chosen since it allows evaluation of capacity under biaxialloading. The model considers the shear capacity as the sum of three distinctcomponents:( V )c+ Vs+ Vp⋅εVV = (11)where Vcrepresents the concrete contribution, V sthe transverse steel contribution,and V the axial load contribution to shear resistance, respectively. The expressionspfor the three contributions are given in fib Bull.24, 2003, where the model, originallycalibrated to circular columns, is extensively evaluated finding a mean value of theratio of experimental to calculated results equal to 0.86 for rectangular sections and acorresponding CoV of 26.1%. A model correction term, ε Vis therefore included inEq. (11).Failure of the structure is defined as the series system of the flexural and shearfailure modes of all columns.cc, u226