How does a bar's deformation under its own weight compare to that caused by an equivalent external direct load_______________?
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Answer: C. half
Explanation
Deformation of a bar under its own weight equals half that of an equivalent end load. Distributed self-weight creates a varying tensile stress profile along the length of the bar. Integrating this distributed weight results in half the total elongation of a concentrated load. Prismatic bars hanging vertically experience axial tension due to their own distributed weight. Self-weight elongation is proportional to the square of the bar length and material density. Equivalent concentrated loads apply the entire weight force at the free lower end.
Structural engineers calculate self-weight elongation in very tall hanging cables and vertical shafts. Ignoring self-weight can introduce calculation errors in long vertical suspension systems. Materials science formulas account for distributed gravitational loads in hanging tensile members. Saying the deformation is the same ignores the distributed nature of the gravitational load. Double deformation would incorrectly overestimate the effect of distributed self-weight. Four times or one-fourth values represent incorrect mathematical integration results.
- Subject
- Engineering
- Category
- Mechanical Engineering
- Topic
- —
- Difficulty
- medium
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