A circular beam of 120mm diameter is simply supported over a span of 10m and carries a uniformly distributed load of 1000N/m. Find maximum bending stress produced.

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written 6.4 years ago by

teamques10 ★ 69k

• modified 5.4 years ago

strength of materials

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written 6.4 years ago by

teamques10 ★ 69k

Given

d = 120 mm, L = 10 m, UDL = 1000 N/m

To Find $\sigma_b = ?$

Solution

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$\frac{E}{R} = \frac{M}{I} = \frac{\sigma_b}{y}........(1)$

$M_{max} = \frac{WL^2}{8} = \frac{1000\hspace{0.05cm}\times\hspace{0.05cm}10^2}{8}\\ \hspace{02cm} = 12500\hspace{0.05cm}Nm\\ \hspace{02cm} = 12500\hspace{0.05cm}\times\hspace{0.05cm}10^3\hspace{0.05cm}Nmm$

$y = \frac{d}{2} = \frac{120}{2} = 60\hspace{0.05cm}mm$

Moment of Inertia (I) = $\frac{\pi}{64}D^4 = 10.17\hspace{0.05cm}\times\hspace{0.05cm}10^6\hspace{0.05cm}mm^4$ …

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