HW3Solutions - (1(a General local stiffness matrix ex 2 ex...

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(1) (a) General local stiffness matrix: = 2 2 2 2 2 2 2 2 y y x y y x y x x y x x y y x y y x y x x y x x e e e e e e e e e e e e e e e e e e e e e e e e L AE k Bar 1: j e e ˆ ˆ ˆ 21 ) 1 ( = = 0 ) 1 ( = x e 1 ) 1 ( = y e = 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 4 ) 1 ( L AE k Bar 2: i e e ˆ ˆ ˆ 31 ) 2 ( = = 1 ) 2 ( = x e 0 ) 2 ( = y e = 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 3 ) 2 ( L AE k Bar 3: j i e e ˆ 5 4 ˆ 5 3 ˆ ˆ 32 ) 3 ( + = = 5 3 ) 3 ( = x e 5 4 ) 3 ( = y e = 16 12 16 12 12 9 12 9 16 12 16 12 12 9 12 9 125 ) 3 ( L AE k (b) Bar 1: [1,2,3,4] [3,4,1,2] Bar 2: [1,2,3,4] [5,6,1,2] Bar 3: [1,2,3,4] [5,6,3,4]
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(c) (i) Joint 1: Joint 2: Joint 3:
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(ii and iii) Bar 1: + = = = 2 4 2 4 2 1 4 3 ) 1 ( 4 ) 1 ( 3 ) 1 ( 2 ) 1 ( 1 ) 1 ( 4 ) 1 ( 3 ) 1 ( 2 ) 1 ( 1 ) 1 ( 4 ) 1 ( 3 ) 1 ( 2 ) 1 ( 1 0 0 4 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 4 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 4 U U U U L AE U U U U L AE p p p p u u u u L AE p p p p Bar 2: + = = = 0 0 3 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 3 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 3 1 5 1 5 2 1 6 5 ) 2 ( 4 ) 2 ( 3 ) 2 ( 2 ) 2 ( 1 ) 2 ( 4 ) 2 ( 3 ) 2 ( 2 ) 2 ( 1 ) 2 ( 4 ) 2 ( 3 ) 2 ( 2 ) 2 ( 1 U U U U L AE U U U U L AE p p p p u u u u L AE p p p p Bar 3: + + + + + + = = 4
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This note was uploaded on 04/14/2011 for the course ASE 321K taught by Professor Dr.markmear during the Spring '06 term at University of Texas.

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HW3Solutions - (1(a General local stiffness matrix ex 2 ex...

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