The m_β -multiplier method based on Mura's extended variational principles in plasticity relies on a reference stress that is obtained from an entire stress distribution in a structure. The method is relatively insensitive to components that undergo localized plastic action and generates limit load bounds that are better than the classical and m_α-multiplier methods. The multiplier m_β is determined by evaluating a reference parameter β_R , which may be difficult to determine if the stress distribution obtained using elastic modulus adjustment procedures does not converge to a limit type of distribution. In this paper, physical insights relating to the reference parameter β_R are provided by linking the concept of reference volume to the local collapse of the structure. As well, a systematic procedure to identify the converged limit state is presented. The m_β-multiplier method, developed in conjunction with the reference volume concept, is applied to a number of cracked component configurations. The results are compared with the corresponding inelastic finite element analysis.
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