QUESTION

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1. Consider the beam with overhanging ends loaded by the three concetrated farces shown in figure bellow. The beam is simply supported and is of T-type cross as shown. The material is gray cast iron having an allowable working stress in tension of $35 \mathrm{Mpa}$ and in compression of $150 \mathrm{Mpa}$. a) Draw the shear and bending moment diagram. b) Find some critical points (not just one maximum) and calculate their bending moments. c) Calculate the value of $\mathrm{P}$ at upper and lower side of each critical points (remember, the allowable stress is different between tension and compression). Apply $\sigma=M y / 1$. The moment of inertia of the area about neutral axis passing through the centroid is $40 \times 10^{6} \mathrm{~mm}^{4}$. Then find the maximum allowable value of $P$.

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