HW02sol - UNIVERSITY OF CALIFORNIA, BERKELEY Spring...

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1 UNIVERSITY OF CALIFORNIA, BERKELEY Dept. of Civil and Environmental Engineering Spring Semester 200 9 CE 121 – Advanced Structural Analysis Homework Set #2 (due Feb. 6 , 200 9 ) 1. Problem ( 10 points) 10 10 10 5 12 15 1 2 3 4 5 a b c d 1 2 3 4 5 a b c d 2.5 The two span beam in the figure is to be analyzed for two loading conditions, as shown. 1. Number the global degrees of freedom (dof) in the most complete way without accounting for the axial dof's, which are obviously not relevant for this loading. 2. Set up the equilibrium equations in terms of the element forces Q and the applied forces at free dofs f P , i.e. ff = B PQ for the first loading case. 3. Remove trivial equations from the equilibrium equations in question (2) and renumber free dofs and basic forces accordingly. 4. Solve for the unknown basic element forces Q . Then use the equilibrium equations at the restrained dofs to determine the support reactions R and check global equilibrium. 5. Draw the shear and bending moment diagram. 6. Repeat questions #4 and #5 above for the second load case, and draw the shear and bending moment diagram for this load case as well. Determine support reactions and check global equilibrium. Determine the maximum bending moment. NOTE : no units are specified for either problem. It is assumed that all values are in consistent units, i.e. kip and ft for the U.S. system and kN and m for SI.
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CE 121 - Advanced Structural Analysis Homework 2 Filip C. Filippou The following structural model and loading are given. Nodes and elements are numbered as shown. a b cd 12 15 10 5 1 2 3 4 5 We number all unrestrained degrees of freedom (dofs) systematically, as shown in the following figure. For each node free body we need to write an equilibrium equation in the direction of the free dofs. The following figure shows the numbering of the complete set of unknown basic forces Q . 1 2 3 4 5 6 7 2 Q 3 Q 1 Q 4 Q 5 Q 6 Q 7 Q Page 2
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CE 121 - Advanced Structural Analysis Homework 2 Filip C. Filippou The following figure shows the node free bodies with all forces of interest for writing the equilibrium equations for the free dofs.
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This note was uploaded on 02/27/2011 for the course CE 121 taught by Professor Filippou during the Fall '09 term at Berkeley.

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HW02sol - UNIVERSITY OF CALIFORNIA, BERKELEY Spring...

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