Influence of member failure time on dynamic load redistribution in pinned planar trusses

Optimized structures have, by definition, zero redundancy. That is, if a single member were to suddenly fail (through material degradation, or an extreme event such as fire, earthquake, or blast), the load previously carried by that member would be redistributed to neighbouring members, potentially inducing catastrophic progressive collapse. This is somewhat addressed in the area of “fail-safe” optimization, however dynamic effects within the load redistribution phase are generally not considered, thus leading to potentially unsafe designs. This paper begins to address this through an investigation into the influence of non-zero member removal times on dynamic stress amplification (ratio of peak dynamic stress to static stress) in pinned trusses. A force-replacement method was implemented to model non-instantaneous member removal, where the failed element is substituted by equivalent external forces that decay linearly over a defined duration. Dynamic load redistribution is then analysed using a simple time integration method, which is first verified against existing analytical work. Analysis of a simple example structure found that an increase in member removal time led to a reduction in dynamic amplification, the relation of which was linked with the modal time periods of the damaged structure. Investigating the problem for different structures, a series of parametric studies utilising Monte Carlo sampling encompassed sets of 500 individual truss structures with randomly assigned member cross-sectional areas. Dynamic amplification factors were found to follow an approximate log-normal distribution, with a modal average of 1.58 for instantaneous removal, which was reduced to 1.15 when considering removal times greater than 3ms. This research is a promising first step towards comprehensive consideration of dynamic effects in fail-safe truss optimization, with an ultimate view of designing low-carbon, economical structures that are robust and safe.