Consider the truss made of 2 bars with lengths 1 m, orientated in the structure shown in Figure 1. The two bars have the same cross-sectional areas A = 5·10-4 m² and modulus of elasticity E = 2·10¹¹ N/m². 10 kN is applied in the x-direction at node 1. A force of F1,x = 850 P 2 = 90° 2 AE L 1 1m 3 1m F1,x = 10KN Figure 1: Truss assembly formed of two bars. Nodes and bars are numbered, with bars numbered with underlines. X a) Using the numbering system of nodes and bars shown in Figure 1, state the 2 local stiffness matrices for each bar and combine these into a global stiffness system for all nodal displacements of the truss. Use the matrix system given in Eq. 1 below relating the local displacements of a single bar to the local forces applied to its nodes. fix fiy fjx fjy Here C = cos(0) and S = sin(0), where is the angle of orientation of the bar. CS -C² -CS C² CS S² -CS -S² -C² -CS C² -CS -S² CS CS S² R Wi Vi U j (1) What is the force required on node 1 for the displacement of the node 1 to be u₁ = 1.10-4 m and V₁ = 0m. V1

Consider the truss made of 2 bars with lengths 1 m, orientated in the structure shown in Figure 1. The two bars have the same cross-sectional areas A = 5·10-4 m² and modulus of elasticity E = 2·10¹¹ N/m². 10 kN is applied in the x-direction at node 1. A force of F1,x = 850 P 2 = 90° 2 AE L 1 1m 3 1m F1,x = 10KN Figure 1: Truss assembly formed of two bars. Nodes and bars are numbered, with bars numbered with underlines. X a) Using the numbering system of nodes and bars shown in Figure 1, state the 2 local stiffness matrices for each bar and combine these into a global stiffness system for all nodal displacements of the truss. Use the matrix system given in Eq. 1 below relating the local displacements of a single bar to the local forces applied to its nodes. fix fiy fjx fjy Here C = cos(0) and S = sin(0), where is the angle of orientation of the bar. CS -C² -CS C² CS S² -CS -S² -C² -CS C² -CS -S² CS CS S² R Wi Vi U j (1) What is the force required on node 1 for the displacement of the node 1 to be u₁ = 1.10-4 m and V₁ = 0m. V1

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter2: Axially Loaded Members

Section: Chapter Questions

Problem 2.7.8P: The statically indeterminate structure shown in the figure consists of a horizontal rigid bar AB...

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