Probabilistic evaluation of column overdesign factors for frames

In the earthquake resistance design of frame structures, the yielding of all the beams in flexure prior to possible yielding of columns is generally considered to be a preferable mode; this is defined as a beam-hinging pattern in this paper. Structures are therefore generally weak-beam, strong-column designed with a column overdesign factor (COF). In reality however, the designed weak-beam, strong-column structures may not collapse according to the preferable failure mode because of large uncertainties in external loads and member strengths. These uncertainties may change the COF and the structure may collapse according to some unpreferable failure modes such as the weak story mechanisms. The object of this paper is probabilistic evaluation of the target values of COFs for which the occurrence probability of unpreferable failure modes can be limited to within a specific tolerance. A stochastic limit analysis procedure using the linear programming method and the first-order reliability method is developed, and the likely failure modes of weak-beam, strong-column designed structures are investigated using this procedure. The target value of COF is discussed in probabilistic terms. It is found that a much higher value of COF is required in the case of uncertain loads and member strengths than is expected in deterministic cases.