A Stability-Based Target Displacement for Direct Displacement-Based Design of Bridge Piers

P-Δ effects can cause instability if they are not properly accounted for during the design of bridge piers and other structures. When a bridge pier is designed with the Direct Displacement-Based Design Method, P-Δ effects are evaluated at the end of the design process and compared to the flexural strength of the pier to find a stability index. If the stability index exceeds the specified value, the design must be repeated, iteratively reducing the target design displacement. This article presents a model that when used at the beginning of design (without knowledge of strength) allows the estimation of the maximum lateral displacement that a bridge pier can sustain without exceeding the specified value of the stability index, therefore eliminating the need for iteration. The examples that are presented prove that the model is accurate and very useful for design of extended pile bents.     

Dynamic Stability and Design of C-Bent Columns

Symmetrically reinforced bridge columns with a horizontal cantilever in one direction, called C-bent columns, tend to deform predominantly in the direction of applied moment when subject to strong earthquake shaking. For this reason, the strength in the direction of applied moment is generally increased in design. This article describes the use of inelastic dynamic time history analyses with a suite of ground motion records to quantify the amount of strength increase required to minimize likely peak and permanent displacement demands. It is shown that the strength should be increased by approximately 2.3 times the applied moment in design.     

Optimal Spectral Acceleration-based Intensity Measure for Seismic Collapse Assessment of P-Delta Vulnerable Frame Structures

This study proposes an “optimal” spectral acceleration-based intensity measure (IM) to assess the collapse capacity of highly inelastic frame structures vulnerable to the P-delta effect. The IM is derived from the geometric mean of the spectral pseudo-acceleration over a certain period interval. The lower bound period of the averaging interval is related to the mode in which 95% of the effective modal mass is exceeded. The upper bound period is 1.6 times the fundamental period. This IM provides minimum, or close to the minimum, dispersion for frames with different fundamental periods of vibration, or number of stories.     

Influence of Collapse Definition and Near-Field Effects on Collapse Capacity Spectra

In the present article, the impact of both near fault ground motions and a finite ductility threshold on the collapse capacity is studied. Single-degree-of-freedom systems with non-deteriorating bilinear hysteretic behavior, vulnerable to P-delta effects, are considered. Defining collapse as excessive ductility is investigated, and the difference to collapse associated with instability is elaborated. Medians of individual record dependent collapse capacities are presented as function of the initial structural period for characteristic structural and ground motion parameters. Analytical expressions for influence coefficients, which account for a differing ground motion set, and finite ductility thresholds, respectively, are derived via non-linear regression analysis.