Discussion
In the plastic analysis of beams, which of the following statements regarding the shape factor (also known as the shape factor for bending) is accurate?
Answer: B
The shape factor is the ratio of the plastic moment capacity to the elastic moment capacity of the section, \(\frac{M_p}{M_y}\). It is always at least 1 (for a rectangle it is 1.5), so the statement that it is less than 1 is wrong. It is not the ratio of the maximum elastic bending stress to the yield stress, and it does not measure ductility, so the second option is the right one.
The shape factor is 1.5 for a rectangular section, about 1.7 for a solid circle and about 1.1 to 1.2 for rolled I-sections, always above 1.
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