Global Seismic Damage Evolution And Collapse Margin Of Large-span Space Structures

Hazards induced by strong earthquakes took place in the past decade had made people more concerned than ever about seismic performance of civil infrastructures. Large-span structures are very popular nowadays in the field of transportation, culture, sports etc. due to their excellent architectural aesthetics and desirable economic efficiency with respect to accommodation. In China, these spatial structures are required to act as refuges for people evacuated from neighboring houses or apartments in this event. Thus, it is crucial to reasonably assess damage evolution and collapse safety of these structures subjected to strong earthquakes. It will be useful to the developing and perfecting of seismic design method for large-span spatial structures, concluding the reinforcement of exiting large-span structures. Because large-span spatial structure is sensitive to changes in shape of structure, initial defect will have great influence on its seismic performance, and even affect the failure mode under strong earthquake. How to distinguish failure mode of large-span spatial structure combined with suggestted damage model and assess the influence of initial imperfection are all important problems. According to the above problems, this paper has done the following works:(1) A physics-based macroscopic global seismic damage model is developed for lattice shell structures excited by strong earthquakes. Global seismic damage is generated from modal damage defined as the loss ratio of potential energy stored in structures before and after earthquakes with the combination rule based on the assumption of in-series independencies among modal damages involved. The minimum number of lower modes required in the combination is determined by the suggested procedures using the maximum nodal displacement as a key response quantity. The issue of modal match arises from the modal shift phenomenon commonly exists in aseismic lattice shells is solved by the linear assurance criteria (LMAC) approach. The case study indicates that predicts result from the proposed model exhibit a desirable correlation with the maximum nodal displacement time history response and a good tendency in damage evolution as more modes involved. The global damage curves can comply with a typical five-segment positive S-type damage evolution curve. The proposed model can be regarded as an extension to the final softening model proposed by Disasquale and Cakmak.(2) Through the multi-modal global damage model for reticulated shells, initial defect damage has been quantitatively evaluated, finding initial defect damage has significant multi-modal characteristics. Combined with qualitative dimensional analysis method, the quadratic function relationship between initial defect damage index and defect amplitude is derived. Various initial defect shape, like first modal shape, random defects and deformation under gravity load, is applied to Kiewitt and Schwedler lattice shell to verify this quadratic relationship, finding the Schwedler shell shows more sensitivity to initial geometrical imperfection than the Kiewitt shell. As far as earthquake resistance concerned, the influence of initial imperfection is not always unfavorable. Initial geometrical imperfections with small amplitude may make shells being stronger for earthquake resistance. After that, the damage model is recommended to determine the failure modes of reticulated shells. If structure collapses after the damage index is more than 0.98, which is to experience the A4-A5 part, the failure mode belongs to the strength collapse; if the overall damage index is less than 0.98, but when we slightly increase the intensity of earthquake ground motion, the global damage index reaches 1.0 or computing is not convergent, the failure mode belongs to instability failure. We also found initial defect will change the type of failure mode, so it is suggested to control the initial defect size reasonably in the design and construction process.(3) Using the proposed model to distinguish the collapse point, a collapse safety margin analytical method is proposed for large-span lattice shells with the concept of consistent collapse probability. With the assumed standard normal distribution for collapse probability density function and the assumed exponential distribution for seismic hazard function, the limit of 50-year consistent collapse probability for large-span lattice shells is acquired from the product of collapse probability density function and seismic hazard function with the assumed collapse probability of 10 percent for great earthquakes. Such limit turns out to 0.68%, lower than that suggested for ordinary building structures by Luco et al. The consistent collapse probability of large-span lattice shells is introduced to modify the pre-defined intensity of great earthquakes. According to this amended intensity, the new collapse safety margin analytical method is recommended. Progressive resistant design combined with this treatment can account for earthquake intensities with all various probability of exceedance. And, large-span lattice shells can have a guaranteed unified limit of collapse probability with different seismic fortification intensities. Possible spectral correction is also required in the proposal for the determination of collapse safety margin ratio of large-span lattice shells. The results also indicate an over-conservative 50-year collapse probability of 0.37%for the example lattice shell designed by the static procedures with safety factor of 2.0.