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HW11sol

# HW11sol - CE 121 Advanced Structural Analysis Homework 11...

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CE 121 - Advanced Structural Analysis Homework 11 Filip C. Filippou Geometric properties: L a 10 := Material properties EI 60000 := L b 10 := L c 8 := L d 10 := basic force and deformation numbering in italics 10 10 8 a b c d 1 2 3 4 5 1 2 3 4 5 6 7 Identify number of free global dofs 1 2 3 a b c d Page 1-1

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CE 121 - Advanced Structural Analysis Homework 11 Filip C. Filippou We move each degree of freedom in turn a unit value, while holding all others fixed. dof 1 to determine the first column of the compatibility matrix A f 1 a b c d A f 1 ⟨⟩ 1 L a 1 L a 1 L b 0 0 1 L d 1 L d := dof 2 to determine the second column of the compatibility matrix A f a b c d 1 A f 2 0 1 1 1 0 0 0 := Page 1-2
CE 121 - Advanced Structural Analysis Homework 11 Filip C. Filippou dof 3 to determine the third column of the compatibility matrix A f a b c d 1 A f 3 ⟨⟩ 0 0 0 0 1 0 1 := Collection of all element stiffness matrices of structural model K s 4 EI L a 2 EI L a 0 0 0 0 0 2 EI L a 4 EI L a 0 0 0 0 0 0 0 3 EI L b 0 0 0 0 0 0 0 4 EI L c 2 EI L c 0 0 0 0 0 2 EI L c 4 EI L c 0 0 0 0 0 0 0 4 EI L d 2 EI L d 0 0 0 0 0 2 EI L d 4 EI L d := (2) Form the structure stiffness matrix : KA f T K s A f := K 1.62 1.8 3.6

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HW11sol - CE 121 Advanced Structural Analysis Homework 11...

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