Previously we addressed the problem of a pinned-joint truss in the shape of a regular pentagon that issupported on rollers and loaded by a single vertical force F. We want to determine the loads in themembers and the displacements of the joints.4FYou can assume the following:3Since this is an equilibrium problem, it can be tackled as a virtual work problem. Also, the loads areconstant, so their virtual work can be described as a change in energy. Thus the system is a conservativesystem. Instead of approaching the problem by writing the equilibrium equations, solve it using theminimization of energy.=6-E4(A)², where A = the change in length of theNote that the energy for each truss member ismember, 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 be1.61804L.Also, note that the system is symmetrical about the vertical centerline. You can take advantage of thesymmetry of the problem by using the displacements x, y, z, and w to define all nodal displacements.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 torotation 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. 3 t www 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 U₁-E4(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.

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. 3 t www 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 U₁-E4(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.

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter8: Applications Of Plane Stress (pressure Vessels, Beams, And Combined Loadings)

Section: Chapter Questions

Problem 8.5.32P

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