Project ForgeA beam is undergoing pure bending. The stress-strain curve for the material is elastic-perfectly-plastic with yield stress σY. Which of the option(s) given represent(s) the bending stress distribution at the cross-section after plastic yielding?
- ATriangular distribution reaching ±σY/√2 at the extreme fibers
- BTriangular distribution reaching ±σY/2 at the extreme fibers
- Rectangular (fully-plastic) blocks of ±σY with a sharp jump at the neutral axis
- Partially-plastic distribution: linear elastic core reaching ±σY, flat at ±σY beyond that
Explanation
Once a cross-section has undergone SOME plastic yielding under an elastic-perfectly-plastic material law, two valid distributions are possible depending on the applied moment: a partially-yielded (elasto-plastic) section with a linear elastic core near the neutral axis and flat ±σY plastic zones at the outer fibers (option D), or a fully-plastic section with a sharp rectangular ±σY jump at the neutral axis once the entire section has yielded (option C). Options A and B show purely linear (fully-elastic, sub-yield) distributions, which contradict the premise that plastic yielding has occurred.
Source: GATE ME 2023 Official Paper (2023)
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