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Shigley's 10th Example 3-13 Stress Concentration in an Axially Loaded Bar

The effect of stress concentration is examined for an axially loaded bar containing a geometric discontinuity such as a hole, groove, or shoulder. The example begins by calculating the nominal axial stress using the applied load and minimum cross-sectional area.

A stress concentration factor K_t is then obtained from standard design charts based on geometry ratios. This factor is used to determine the maximum local stress, showing how small geometric changes can significantly increase stress beyond the nominal value.

The example demonstrates a core machine design principle: failures usually initiate at stress raisers, not where average stress is calculated, making stress concentration analysis essential for safe component design.

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R. G. Budynas and J. K. Nisbett, Shigley's Mechanical Engineering Design, 10th ed. New York, NY, USA: McGraw-Hill Education, 2015.