An approximate method of dynamic amplification factor for alternate load path in redundancy and progressive collapse linear static analysis for steel truss bridges

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دسته: , تاریخ انتشار: 30 فروردین 1400تعداد بازدید: 293
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scopus – master journals – JCR

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۴٫۲۷۶ در سال ۲۰۲۰

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An approximate method of dynamic amplification factor for alternate load path in redundancy and progressive collapse linear static analysis for steel truss bridges

فهرست مطالب مقاله:


Linear static analysis with an alternate load path using dynamic amplification factor (DAF) is  often used for  redundancy and progressive collapse analysis of  steel truss bridges to avoid using the more time-consuming dynamic analysis. This  study presents an empirical equation to calculate the DAF for  this type of analysis against the initial sudden member fracture. Currently, this analysis employs an approximate model with a single degree of freedom to calculate the DAF. With a 5% damping ratio, the constant DAF of 1.854 is used for  all  types of steel truss bridges. However, this approach is inaccurate because the DAF varies between bridges and with the location of the fractured members as well. Considering some of the approaches developed for building structures but adapting them to steel truss bridges, this paper proposes an empirical equation that allows for  the computation of the DAF from the maximum norm stress   is / iy  in static linear elastic analysis of the damaged model with a member removal. A total of 30  illustrative cases for  two typical steel truss bridges are investigated to obtain the data points for the empirical equation. The proposed empirical equation is the enveloped line offset from the best fit line for  the data points in illustrative cases.

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  1. Introduction

Progressive collapse is the spread of an  initial local  failure from element to  element, member to  member, eventually resulting in  the collapse of a part, entire structures or  a disproportionately large part [1].  A sudden member failure is a dynamic event in which the structural motion is initiated by energy released by the sudden loss  of a load-carrying member. Four  methods, including linear static analysis, nonlinear static, linear dynamic and nonlinear dynamic methodologies, are available for redundancy and progressive collapse analysis of structures for the sudden fracture of a member or component [2,3].  The  event of a sudden member fracture relates to  both the primary loading, which causes the initial fracture, and impact loading, which causes structural motions after the initial fracture. The dynamic method is a direct solution to address impact loading and the dissipation procedure of the energy induced by the initial member fracture. This approach is accurate, but it requires much intensive computation with time-history transient analysis. Static analysis with an alternate load path,

which amplifies the primary loading with a dynamic amplification factor (DAF) to form the impact loading, is an alternative approach for analysis without using dynamic analysis.

Currently, linear redundancy and progressive collapse linear static analysis of steel truss bridges have employed a single degree of freedom (SDOF) model to conventionally calculate the DAF [4,5]. With a 5% damping ratio, the conventional DAF is 1.854, constant for all bridges. This approach is conservative because the bridge system acts as multiple degrees of freedom instead of a single degree of freedom. The DAF varies between bridges and with the location of the fractured members, as well. To consider a model with multiple degrees of freedom, Goto  et al. propose the root mean square mode combination method to approximate the DAF [6]. This approach is moderately accurate and requires some correction factors. Although no  other studies have yet  been published about the approximation of the DAF for bridge systems, such approaches by Liu [7], McKay  et al. [8], DoD, U.S. [9], and Stevens et al. [10]  that approximate DAF in a building system are  valuable. McKay et al., DoD, U.S., and Stevens et al. propose different linear functions of norm rotation, which is the ratio of the total member rotation to the member-yield rotation, to compute the DAF of steel buildings. On the other hand, Liu computes the DAF by using the function of max(Mu /Mp ), where the max operator is applied to  all affected beams that are  directly adjacent to and above the removed column. Mu  and Mp  are  the factored moment demand under the original unamplified static gravity loads and the factored plastic moment capacity, respectively, of an affected beam. These approaches may be limited to only one building system because the norm rotation and Mu /Mp are  critical parameters for the behavior of a building system. In a steel truss bridge system, when a member fractures, in addition to  axial force, the members are  also  subject to  bending moments. Considering this behavior, this study proposed the DAF as a function of the maximum norm stress   is / iy , where  is  and  iy  are  stress in a static analysis and the yield stress of bridge members. In this paper, a total of 30 illustrative cases are  investigated in 3D models. The empirical equation to  calculate the DAF was defined as the enveloped line  offset from the best fit line  for the data points from illustrative cases.

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