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Unformatted text preview: CEE 379 Midterm Exam Winter 2007 Name: Closed Book; 1 pages of notes. Part I: Short Answer (3 points each) 1. What special property or properties does the equilibrium matrix, [ B ] T , have in the case of a statically determinate system? The matrix is invertible (i.e., square and nonsingular). 2. Use the figure below to answer each of the following questions: 1 2 3 4 k d k a k b k c 5 k e 5 k (a) What are the dimensions of the kinematic matrix, [ B ], for this configuration (including both sup ported and unsupported joints)? Number of rows = 5 (number of members) Number of columns = 5 (number of joints) (b) Write down an expression for the overall system stiffness matrix entry K 34 (i.e., the value in the 3rd row, 4th column of the complete system stiffness matrix). K 34 = k c (c) Give an expression for { P f } for the loading shown, including the effect of a misfit in member b of 0.1 inches. Assume k b = 10 k/in. P = (0 . 1 in)(10 k / in) = 1 kip { P f } = 5 1 1 kip = 4 1 kip (d) Write down an expression for { Δ s } for this system assuming Joint 1 moves to the right by 0.02 inches. { Δ s } = braceleftbigg . 02 bracerightbigg in (e) Write down an equilibrium equation relating member forces f d , f e , and f c that you could use to check the results of a computergenerated solution....
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 Spring '08
 Taylor,A
 Equilibrium, Force, The Matrix Reloaded, La La, 000 ksi)., 0 k

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