GATE 2019 ME (ME1) – Question 49
An elastic straight beam of length 10π m has square cross-section of side 5 mm and E = 200 GPa. It is bent so the ends meet, forming a circle of mean radius R. With Euler–Bernoulli bending applicable, find maximum tensile bending stress (MPa).
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Correct answer: 99 to 101
Explanation
The neutral-axis radius is $R=L/(2\pi)=5$ m. Maximum bending strain is $c/R=0.0025/5=0.0005$. Stress is $E c/R=200000(0.0005)=\mathbf{100}$ MPa.