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Lab 09 - Questions

Lab 09 - Questions - UNIVERSITY OF CALIFORNIA BERKELEY...

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UNIVERSITY OF CALIFORNIA, BERKELEY Engineering 7 – Spring 2009 Department of Civil and Environmental Engineering Instructor: Professor Rector 1 Lab 09 [15 pts] Topics : Linear Equations Assigned : Monday, 4/13/2009, 8:00 am Due : Monday, 4/20/2009, 12:00 pm (noon) Type : Take-home 1. Solution of a Set of Linear Equations Exercise 1 – Truss Systems (5 pts) A truss is a structure whose components are connected by hinges. Hinges cannot support moments, and the loading can only be applied on the two ends of any truss component. The internal force in the truss component then is oriented only along the direction of the component, and is either tensile or compressive. F(z) S a S b HB VB VA HA A C a 5m 13.5m 24m b B θ a cos θ a = 0.6 cos θ b = 0.8 θ b In order to determine the internal force of each member of the truss, we can form a system of linear equations and solve the system. The equations are: – 0.6 Sa – HA = 0 – VA – 0.8 Sa = 0 0.8 Sb – HB = 0 0 – VB – 0.6 Sb = 0 0.6 Sa – 0.8 Sb = 0 0.6 Sb + 0.8 Sa = – F(z) (a) Express the above equations in matrix form, Ax = b, and include them in your report. (b)
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Lab 09 - Questions - UNIVERSITY OF CALIFORNIA BERKELEY...

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