A 20 mm diameter steel bar simply supported over a 40 cm span carries a central load, inducing a peak stress capped at N/mm2. The stored bending strain energy is___________________?
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Answer: C. 611 N mm
Explanation
Integrating strain energy due to bending under a central load for a simply supported bar yields 611 N mm. Internal strain energy equals the external work done by the applied load as it gradually deflects the bar. Substituting the bar diameter, span, and peak stress into the strain energy integral calculates this exact numerical result. Strain energy represents the potential energy stored within an elastic material undergoing mechanical deformation. Simply supported bars store bending energy proportional to the square of the internal bending moments. Central loading creates triangular bending moment diagrams along the longitudinal span of the structural bar.
Option A underestimates the stored energy because it uses incorrect integration limits for the central load. Option B contains minor calculation inaccuracies in evaluating the section properties and span dimensions. Option D overestimates the stored bending energy due to an incorrect scaling factor in the strain integral.
- Subject
- Engineering
- Category
- Civil Engineering
- Topic
- —
- Difficulty
- medium
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