Previously we addressed the problem of a pinned-joint truss in the shape of a regular pentagon...

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Previously we addressed the problem of a pinned-joint truss in the shape of a regular pentagon that is supported on rollers and loaded by a single vertical force F. We want to determine the loads in the members and the displacements of the joints. Since this is an equilibrium problem, it can be tackled as a virtual work problem. Also, the loads are constant, so their virtual work can be described as a change in energy. Thus the system is a conservative system. Instead of approaching the problem by writing the equilibrium equations, solve it using the minimization of energy. Note that the energy for each truss member is U, - -EA(A), where A = the change in length of the member, E is the modulus of elasticity for all members and A is the cross sectional area of all members. All outside members are of length L, and the interior members are determined by the geometry to be 1.61804L. Also, note that the system is symmetrical about the vertical centerline. You can take advantage of the symmetry of the problem by using the displacements x, y, z, and w to define all nodal displacements. You can assume the following: There is no friction in the pinned joints. The displacements are small in the sense that the change in length of any truss member due to rotation of the member is negligible. Previously we addressed the problem of a pinned-joint truss in the shape of a regular pentagon that is supported on rollers and loaded by a single vertical force F. We want to determine the loads in the members and the displacements of the joints. Since this is an equilibrium problem, it can be tackled as a virtual work problem. Also, the loads are constant, so their virtual work can be described as a change in energy. Thus the system is a conservative system. Instead of approaching the problem by writing the equilibrium equations, solve it using the minimization of energy. Note that the energy for each truss member is U, - -EA(A), where A = the change in length of the member, E is the modulus of elasticity for all members and A is the cross sectional area of all members. All outside members are of length L, and the interior members are determined by the geometry to be 1.61804L. Also, note that the system is symmetrical about the vertical centerline. You can take advantage of the symmetry of the problem by using the displacements x, y, z, and w to define all nodal displacements. You can assume the following: There is no friction in the pinned joints. The displacements are small in the sense that the change in length of any truss member due to rotation of the member is negligible.