Reliability-Based Dynamic Amplification Factor on Stress Ranges for Fatigue Design of Existing Bridges

Abstract

A dynamic amplification factor (DAF) or a dynamic load allowance (IM) is typically used in bridge design specifications to include dynamic effects from vehicles on bridges. The calculated live-load stress ranges may not be correct because of varied dynamic amplification effects in different regions along the bridge, different road roughness conditions, and multiple stress-range cycles generated for one vehicle passage on the bridge. In this study, a reliability-based dynamic amplification factor on stress ranges (DAFS) for fatigue design is proposed to include the fatigue damage from multiple stress-range cycles resulting from each vehicle passage at varied speeds under various road conditions on the bridge’s life cycle. A numerical simulation toward solving a coupled vehicle-bridge system, including a three-dimensional (3D) suspension-vehicle model and a 3D dynamic bridge model, is used to obtain the revised equivalent stress range. The revised equivalent stress range is defined on an equivalent fatigue-damage basis; namely, the fatigue damage from multiple stress ranges with varied amplitudes is equivalent to the fatigue damage from one stress cycle of the revised equivalent stress range. Dynamic amplification factor on stress ranges is then defined as the ratio of the nominal live-load stress range and the maximum static stress range. A parametric study on DAFS was carried out to analyze the effect from multiple variables on the bridge’s life cycle, for instance, faulting days in each year, vehicle speed limit and its coefficient of variance, vehicle type distribution, and annual traffic increase. To appreciate the difference between the proposed DAFS and the traditional DAF, the calculated fatigue lives from the six approaches related to DAFS or DAF are compared with each other. Similar to DAF for dynamic response on displacements, DAFS is proposed to obtain dynamic stress ranges for fatigue design. As a result, once the DAFS values are available, the dynamic stress ranges for fatigue design can be easily obtained by multiplying the maximum static stress range and the DAFS, which helps to preserve both the accuracy and simplicity of bridge fatigue design.