Plastic analysis assigns a circular cross-section a shape factor equal to_________________?
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Answer: C. 1.7
Explanation
The correct answer gives the well-established shape factor value of approximately 1.7 for a solid circular cross-section. Shape factor is calculated by dividing the plastic section modulus by the elastic section modulus of the geometry. Circular sections exhibit a gradual transition into full plastic yielding, resulting in a shape factor higher than rectangular shapes. Plastic analysis evaluates structural capacity based on the formation of plastic hinges rather than initial elastic limits. Solid circular geometries have specific geometric distribution properties that yield higher plastic reserves than standard I-beams. The elastic section modulus for a circle is pi times diameter cubed over thirty-two while its plastic modulus uses a different integral.
A shape factor of 1.5 represents the characteristic value for standard rectangular cross-sections rather than circular profiles. Values like 1.6 or 1.75 correspond to different geometric shapes such as triangles or specialized thin-walled tubes. Choosing incorrect shape factors would lead to erroneous estimates of structural collapse loads in plastic design frameworks.
- Subject
- Engineering
- Category
- Civil Engineering
- Topic
- —
- Difficulty
- medium
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