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Consider an elastic straight beam of length $L= 10 \pi \: m$, with square cross-section of side $a=5 \: mm$, and Young’s modulus $E=200 \: GPa$. This straight beam was bent in such a way that the two ends meets, to form a circle of mean radius $R$. Assuming that Euler-Bernoulli beam theory is applicable to this bending problem, the maximum tensile bending stress in the bent beam is _____ $MPa$.

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