GATE ME 2019 Set 1 — Question 49
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Strength of Materials → Beams & Columns → Bending & Shear Stresses
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Question
Consider an elastic straight beam of length m, with square cross-section of side mm, and Young's modulus GPa. This straight beam was bent in such a way that the two ends meet, to form a circle of mean radius . Assuming that Euler-Bernoulli beam theory is applicable to this bending problem, the maximum tensile bending stress in the bent beam is ______ MPa.
Correct answer
99 to 101
Solution
1.Determine the radius of curvature ():
The beam of length is bent into a full circle. The circumference of this circle is equal to the length of the beam:Given m:
2.Apply the bending stress formula:
According to the Euler-Bernoulli bending equation:where is the bending stress, is the distance from the neutral axis, is Young's modulus, and is the radius of curvature.
3.Calculate the maximum tensile stress:
The maximum tensile stress occurs at the fiber furthest from the neutral axis (). For a square cross-section of side mm:Given GPa MPa:
Therefore, the maximum tensile bending stress is 100 MPa.
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