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ECIV 520 Advanced Structural Analysis – FALL 2008
FINAL EXAM
Due Date: Monday December 8, 2006 2:00 pm. NAME:__________________________________________________________ With my signature I declare that I have not, and will not, discuss, collaborate in any way, or exchange any kind of information and ideas with anyone regarding the attached take- home final examination. The attached exam is my own work. I understand that if I will be found in violation of the terms and conditions of the take- home examination my Final Grade will be an F and my actions will be reported.
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Problem #1 (40 pnts) A hinged-fixed beam has a uniform cross section and is loaded as shown in the figure. A spring at the mid-span provides additional stiffness in the vertical direction. The deformations have been computed as 80 720 120 3 4 3 QL QL u QL b b a
Use matrix analysis procedures to compute the force in the spring and the moment at the midspan bc. Ignore axial deformations of the beams. k=12/L 3 L (^) L q(x) = Q EI= EI= a b c P=QL 30 0 X Y
Problem #3 (40 pnts) The axial member shown in figure 3a is hanging under its own weight, w lb/ft. The axial member will be modeled by a single axial element , and we plan to use the principle of virtual work to derive the exact element stiffness matrix. In order to establish the set of shape functions an appropriate distribution of the axial displacements, u(x), needs to be assumed. a) DERIVE an appropriate expression for the displacement field, u(x). b) How many degrees of freedom do you have to define on the element so that the u(x) of part (a) yields admissible displacements? Write the appropriate conditions for admissibility c) Derive the stiffness matrix using the principle of virtual work. Start from the equation for the Principle of Virtual Work and show all intermediate steps d) In addition to the weight of the member, a force P is applied as shown in Figure 3b. Will the distribution of the displacements, u(x), of part (a) yield the exact stiffness matrix? Justify your answer x Figure 3a x P Figure 3b
