The total vertical stretching of a uniform hanging bar due to its own weight is equivalent to the extension caused by a concentrated weight of________________?
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Answer: B. half the weight of bar applied at lower end
Explanation
The distributed weight of a hanging bar creates a triangular load profile along its entire length. Integrating this linear self-weight distribution mathematically results in an effective total elongation factor of one-half. Applying half the total weight as a concentrated load at the lower end produces the exact same total extension. Uniform hanging bars experience maximum axial stress at the fixed upper support and zero stress at the free end. The total elongation formula for a self-weight hanging bar is delta equals the product of specific weight and length squared divided by twice the elastic modulus. Substituting the total weight into this derivation confirms the equivalent concentrated load at the boundary.
Applying the full weight at the lower end would incorrectly overestimate the total vertical stretching by a factor of two. Options C and D introduce incorrect mathematical powers or fractions that contradict standard mechanics of materials derivations. The option stating none of the above is incorrect because option B accurately captures the derived mechanical equivalence.
- Subject
- Engineering
- Category
- Mechanical Engineering
- Topic
- —
- Difficulty
- medium
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