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 = 210¹¹ N/m². A force of F1,x = 10 kN is applied in the x-direction at node 1. fix fiy 90° fjs L ا fjv 2 1m 1 1m Figure 1: Truss assembly formed of two bars. Nodes and bars are numbered, with bars numbered with underlines. 3 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. AE CS → Fax = 10KN Ľ 14₂ 2₂ CS -C² -CS S² -CS -S² -C² -CS C² CS Uj -CS -S²2 CS S² Here C = cos(0) and S = sin(0), where is the angle of orientation of the bar. (1) b) Apply the boundary conditions and specified forces to your global stiffness system of equations and solve for the displacements. c) 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.

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 = 210¹¹ N/m². A force of F1,x = 10 kN is applied in the x-direction at node 1. fix fiy 90° fjs L ا fjv 2 1m 1 1m Figure 1: Truss assembly formed of two bars. Nodes and bars are numbered, with bars numbered with underlines. 3 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. AE CS → Fax = 10KN Ľ 14₂ 2₂ CS -C² -CS S² -CS -S² -C² -CS C² CS Uj -CS -S²2 CS S² Here C = cos(0) and S = sin(0), where is the angle of orientation of the bar. (1) b) Apply the boundary conditions and specified forces to your global stiffness system of equations and solve for the displacements. c) 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.

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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