A horizontal rigid bar of weight W = 7200 lb is supported by three slender circular rods that are equally spaced (see figure). The two outer rods are made of aluminum (E1 = 10 × 106 psi) with diameter d1 = 0.4 in. and length L1 = 40 in. The inner rod is magnesium (E2 = 6.5 × 106 psi) with diameter d2 and length L2. The allowable stresses in the aluminum and magnesium are 24,000 psi and 13,000 psi, respectively.
If it is desired to have all three rods loaded to their maximum allowable values, what should be the diameter d2 and length L2 of the middle rod?

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d2 la W = weight of rigid bar