GATE ME 2023 Set 1 — Question 24
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Strength of Materials → Beams & Columns → Bending & Shear Stresses
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Question
A beam is undergoing pure bending as shown in the figure. The stress ()-strain () curve for the material is also given. The yield stress of the material is . Which of the option(s) given represent(s) the bending stress distribution at cross-section AA after plastic yielding?
Correct answer
(C) [figure]; (D) [figure]
Solution
In pure bending, the strain distribution across the cross-section remains linear. For an elastic-perfectly plastic material:
1.Initial Yielding: When the strain at the outermost fibers reaches the yield strain , the stress reaches .
2.Elastic-Plastic State: As the bending moment increases further, more fibers from the outside inward reach the yield strain. Because the material is perfectly plastic, the stress in these yielded fibers remains constant at . This results in a trapezoidal stress distribution, as shown in option (D).
3.Fully Plastic State: In the limit, as the moment approaches the plastic moment , the entire cross-section (except the neutral axis) yields. The stress distribution becomes rectangular (constant in tension and compression), as shown in option (C).
Options (A) and (B) show linear distributions with maximum stresses less than , which represent purely elastic states before yielding begins.Continue learning with Success Tracker
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