Question 9.P.7: A 4 m length of the I-beam of Problem 9.2 is simply-supporte......
A 4 m length of the I-beam of Problem 9.2 is simply-supported at each end. What maximum central lateral load may be applied if the bending stresses are not to exceed 150 MN/m²?
Step-by-Step
Suppose W is the central load. If this is applied in the plane of the web, then bending takes place about Cx. The maximum bending moment is
M_x = \frac{1}{2}W(2) = W Nm I_x = 1.642 \times 10^{-6} m^4Then, the greatest bending stress is
\sigma = \frac{M_xy_{\max}}{I_x} = \frac{(W)(0.05)}{1.642 \times 10^{-6}}If this is equal to 150 MN/m², then
W = \frac{(150 \times 10^6)(1.642 \times 10^{-6}) }{0.05} = 4920 N
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