HW03sol with parts 4 and 5

# HW03sol with parts 4 and 5 - UNIVERSITY OF CALIFORNIA,...

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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 #3 (due Feb. 1 3 , 200 9 ) 1. Problem (5 points) 4 4 6 1 2 3 4 w = 10 w = 10 a b c d 1. Number the global degrees of freedom (dof) without including the trivial equations with a single unknown basic force whose value can therefore be determined by inspection. 2. Set up the equilibrium equations in terms of the element forces Q and the equivalent nodal forces due to the uniformly distributed element loading w = 10 units of force/unit of length. 3. Solve the equilibrium equations for the basic forces Q . 4. Determine the dependent element forces and draw the axial force, shear force, and bending moment diagrams. 5. Determine the support reactions and check global equilibrium. 6. Return to question #2 above and separate the equilibrium equations into two groups: those involving only end moments as basic forces and the axial force in the brace, and those that also include the axial forces in column and girder. Solve the first group of equations for the end moments and brace force, and then use node equilibrium to determine the axial forces in girder and column. Compare the answers with those of question (3) above and confirm that they are identical. 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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2 2. Problem (3 points) – Degree of static indeterminacy a b c d e 1 2 3 4 5 1 2 3 4 5 6 a bc d e f g For the structural models above determine the degree of redundancy or static inderminacy. To do in a systematic fashion answer the following questions: 1. Number all available equations of equilibrium that do not involve support reactions and the corresponding basic forces (include trivial equations). The difference between number of basic forces and available equilibrium equations is the degree of redundancy. 2. Remove trivial equations that involve a single basic force. Is the degree of redundancy still the same? 3. Number all available equilibrium equations that do not include the axial forces in the frame elements (a through d in the first model, a through e in the second) and the corresponding primary basic forces. Is the degree of redundancy still the same? NOTE : dimensions are not provided so that you do not get tempted to write the equations; you just need to identify them with numbers in a sketch of the structural model.

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3 3. Problem (7 points) The degree of static indeterminacy of the cable stayed structure in the figure on the left is NOS=2. The structure is subjected to a uniform load of 5 units in elements b and c, as shown.

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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 University of California, Berkeley.

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HW03sol with parts 4 and 5 - UNIVERSITY OF CALIFORNIA,...

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