HW05sol - University of California Berkeley Spring Semester...

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University of California, Berkeley Dept. of Civil and Environmental Engineering Spring Semester 2009 1 CE 121 — Advanced Structural Analysis Homework Set #5 (due Feb. 28, 2009) 1. Problem (5 points) All frame elements in the structural model have negligible axial deformations. All elements are heated up so that a uniform thermal curvature field of 8 × 10 −4 rad per unit of length results (recall how a positive curvature is defined in the element coordinate system that points from lower to higher numbered node). 1. Determine the displacements at the free DOFs ° ± . 2. Draw the deformed shape of the structure.
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CE 121 - Advanced Structural Analysis Homework Filip C. Filippou Problem 10 10 8 a b c d 1 2 3 4 5 Geometric information L a 10 := L b 10 := L c 8 := L d 10 := We start the solution of this problem with the largest number of free dof's that account for the fact that all elements in the structural model are inextensible. In such case there are four free global dof's, as shown in the following figure. The numbering for the rows of the structural compatibility matrix A f is also shown. 10 10 8 1 2 3 4 dof 4 dof 1 dof 2 dof 3 Page
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CE 121 - Advanced Structural Analysis Homework 5 Filip C. Filippou For setting up the structural compatibility matrix we move each free dof by a unit value and record the angle between the node "whiskers" and the chord connecting the nodes. We write these angles only at the numbered locations in the following figure, because we intend to set up continuity relations at these locations. We show the effect only for the translation dof #1. 10 10 8 dof 1 1 2 3 4 A f 1 L a 1 L b 0 1 L d 1 0 0 0 0 1 0 0 0 0 1 0 := We state now that the element deformations are continuous at the four locations represented by the rows of the compatibility matrix. This allows us to write four compatibility relations. Since there are four compatibility relations involving four free global dofs, the structure is statically determinate. Let us write these compatibility relations out, so we appreciate a bit better how easy they are (the compatibility matrix has a lot of zeros in this problem), and what they say geometrically. V
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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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HW05sol - University of California Berkeley Spring Semester...

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