1.6:* A truss, consisting of two pin-connected rods AB and AC (each made of the same...

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1.6:* A truss, consisting of two pin-connected rods AB and AC (each made of the same material whose density is p (N/m) and each having different cross-sectional area A), supports a force P as shown in Fig. (1P.6). The truss is to be designed such that lal, the maximum allowable normal stresses (in absolute value), are the same in each member. (a) Show that under these conditions, the weight W of the truss is W= A PPL 1 2 + tan B sin 2 (b) Assuming that P is much greater than the total weight W of the truss, determine the angle & for which the truss has minimum weight, thus yielding an optimal design. What is the minimum weight Wexpressed non-dimensionally as PP? W P Figure 1P.6 3 L B 1.6:* A truss, consisting of two pin-connected rods AB and AC (each made of the same material whose density is p (N/m) and each having different cross-sectional area A), supports a force P as shown in Fig. (1P.6). The truss is to be designed such that lal, the maximum allowable normal stresses (in absolute value), are the same in each member. (a) Show that under these conditions, the weight W of the truss is W= A PPL 1 2 + tan B sin 2 (b) Assuming that P is much greater than the total weight W of the truss, determine the angle & for which the truss has minimum weight, thus yielding an optimal design. What is the minimum weight Wexpressed non-dimensionally as PP? W P Figure 1P.6 3 L B

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The problem presented is a classic optimization problem in structural engineering combining concepts from statics material science and calculus to determine the optimal design for a truss system with ... View the full answer