Reliability of stability of single-layer latticed shells with spatially correlated initial geometric imperfection modeled using conditional autoregressive model

Abstract

Latticed shells are extensively used for large-span structures. Their design is often governed by the global instability requirement stipulated in the Chinese design code for the specified gravity load and initial geometric imperfection (IGI). However, the reliability-basis for the recommended design requirement that a critical load factor of 2 need to be achieved is unknown. In the present study, it is proposed that the spatially varying IGI can be adequately modeled using the conditional autoregressive model. It is shown that this model is sufficiently flexible in modeling spatially varying correlated imperfection and can cope with irregular grid systems. By using this model for IGI and considering global instability, the probability distributions of the load capacity and the failure probabilities of spherical and cylindrical latticed shells designed according to the Chinese design code are evaluated. The evaluation is also carried out by representing the IGI shape using the spatially independent Gaussian model and the first eigen buckling mode (1EBM) that is recommended by the design code. It is shown that the use of the 1EBM to represent the IGI shape does not necessarily lead to conservative estimates of the failure probabilities as compared to those obtained by considering spatially varying stochastic imperfection shapes. The results shown that the estimated failure probability is sensitive to the assumed stochastic model for and standard deviation of the IGI at each joint of the latticed shells. Furthermore, the failure probability of the spherical latticed shell differs from that of the cylindrical latticed shell. The reliability analysis results also indicate that the use of a critical load factor of 2 implemented in the code for design of the latticed shell, in general, lead to an annual failure probability for global instability less than 10−5. A sensitivity analysis indicates that the code recommended critical load factor can be reduced to 1.75 while achieving a target reliability index often adopted for design code calibration.