Among the different flexure modes for nuclear pipe bends, the out-of-plane bending is the most complex. In this mode, pipe bends are subjected to both bending and torsion. Geometric nonlinearity plays an important role in the collapse behaviour of pipe bends. The ASME B&PV Code Section Ⅲ incorporates these effects of geometric nonlinearity by using stress indices B_1 and B_2 in the general design equation for nuclear pipe bends and elbows. To formulate a reliability-based load and resistance factor design LRFD equation for the design of nuclear pipe bends, it is essential to develop statistical models of these stress indices. The statistical characterisation of primary stress index B_2 for bending of thin-shell stainless steel 90° pipe bends subjected to out-of-plane moment is presented in this paper. The ASME code expression for B_2 is modified and a random variable K is introduced instead of the constant numerator value in this expression to consider geometric uncertainties. A nonlinear finite element analysis is performed to find the collapse moment for a pipe bend. The collapse moment for each specimen is obtained from the maximum moment versus end rotation plot, using the twice-elastic-slope method. B_2 is calculated from this collapse moment. This process is repeated on a Monte Carlo simulation based framework, where the parameters describing the pipe bend geometry are considered to be random variables. The statistics of K are evaluated for various nominal dimensions. The overall mean of K is found to be almost the same as the code specified constant value.
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