What is the ratio of the self-weight elongation of a prismatic bar (W) to that of an identical bar supporting an extra load (W) _________________?
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Answer: B. 1 : 3
Explanation
The self-weight elongation of a prismatic bar is half that of a bar supporting an added load. Adding an extra load equal to its own weight doubles the total tensile force acting on the bar. Integrating the distributed self-weight stress yields an elongation coefficient factor of one-third relative to full uniform load. Prismatic bars subjected to their own distributed weight experience internal stresses that vary linearly along their length. The total elongation formula for self-weight integrates cross-sectional area, material density, and length squared over twice the rigidity modulus. External axial loads produce uniform stress distributions throughout the entire length of the elastic structural element.
Option A represents half of the correct ratio and fails to account for combined loading. Option C overestimates the denominator by assuming a linear fourfold increase in total elongation. Option D and E offer incorrect fractional ratios that do not satisfy the integration equations for self-weight.
- Subject
- Engineering
- Category
- Mechanical Engineering
- Topic
- —
- Difficulty
- medium
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