Compared to a solid bar without defects, the peak stress concentration factor in a bar containing a transverse circular hole under static load will be_________________?
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Answer: C. 3 times more
Explanation
Elasticity theory proves that a small circular hole multiplies uniaxial tension by three. Stress lines crowd around the transverse hole creating a peak stress concentration factor. This concentration factor remains independent of the absolute size of the circular hole. Stress concentration factor relates the maximum localized stress to the nominal applied remote stress. Mathematical derivation using complex variable methods solves elasticity equations for plates with holes. Discontinuities disrupt smooth stress flow lines resulting in localized stress gradients within components.
Structural plates containing rivet or bolt holes must account for this threefold stress increase. Aerospace engineers reinforce window cutouts in aircraft fuselages to mitigate high stress concentration factors. Ignoring this factor can lead to premature yielding and structural failure under static loads. A defect-free solid bar experiences uniform stress distribution without any localized stress multiplication. Factors of two or four apply to different geometries such as elliptical holes or notches. Analytical elasticity solutions make stress concentration factors completely predictable for circular holes.
- Subject
- Engineering
- Category
- Mechanical Engineering
- Topic
- —
- Difficulty
- medium
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