Seismic Response of Nominally Symmetric Systems with Strength Uncertainty
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The two major sources of uncertainty in earthquake engineering are the input motion and the mathematical model of the structural system. The present study focuses on the effects on seismic response and design of two aspects of system uncertainty: uncertainty in the functional form of the restoring force model of the lateral load resisting elements and uncertainty in the parameters of this model. The restoring force models selected for this study are the elastoplastic and the modified-Clough, the latter of which accounts for stiffness degradation. Of the model parameters, only the yield strength is treated as random variable following lognormal distribution. Input is deterministic, consisting of three earthquake records scaled to several peak ground accelerations. Two system types are considered: a simple one-storey structure and a realistic seven--storey building. Both systems are designed according to the 1994 Uniform Building Code. They are nominally symmetric, i.e., they are symmetric in the elastic range but can experience torsional vibrations following yield, because of asymmetry in the element yield strengths caused by uncertainty. The one-storey system consists of a rigid slab supported by two lateral load resisting elements with random yield strengths. The seven--storey system is a regular seven- by three-span frame-shear wall structure. Each structural member is modeled by a set of inelastic springs. Yield strengths of springs modeling shear walls are treated as random variables. The study is based on Monte Carlo simulation. Dissipated energy, interstorey displacement, and the maxima of displacement, ductility, and rotation are used to quantify the sensitivity of the response to strength uncertainty. The total energy dissipated by the system and the maximum rotation are found to be the least and most sensitive. response measure, respectively. Torsion increases the mean of maximum displacements and ductilities. The nondimensionalized ratio of the dynamic torsional moment to the design shear, called dynamic eccentricity, is used for code evaluation. The code accidental eccentricity appears inadequate to account for torsion caused by strength uncertainty, since it is significantly exceeded by the dynamic eccentricity for large fractions of the motion duration. Finally, if the modified-Clough were the correct restoring force model, use of the elasto-plastic instead would not necessarily be conservative, since the latter may underestimate displacements and overestimate energy dissipation.