Plane_Truss_Ch4

Plane_Truss_Ch4 - Plane Truss Finite Elements e v1e ye e 2...

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h e 2 1 θ e y x e F 1 e F 2 e x e y 1 e v e u 1 2 e u 2 e v h e 2 1 e y x e F 1 , F e 2 e x e y e v 1 e u 1 e u 2 e v 2 e x F 1 e u 1 e y F 1 e v 1 e y F 2 e v 2 e x F 2 e u , 2 E e A e h e 10 00 ¯ u e 1 ¯ v e 1 ¯ u e 2 ¯ v e 2 = ¯ F e 1 0 ¯ F e 2 0 [ ¯ K e ] { ¯ e } = { ¯ F e } ¯ x e = x cos θ + y sin θ ¯ y e = x sin θ + y cos θ ½ ¯ x e ¯ y e ¾ = cos θ sin θ sin θ cos θ ¸½ x y ¾ ¯ u e 1 ¯ v e 1 ¯ u e 2 ¯ v e 2 = cos θ e sin θ e sin θ e cos θ e c o s θ e sin θ e sin θ e cos θ e u e 1 v e 1 u e 2 v e 2 { ¯ e } =[ T e ] { e } Plane Truss Finite Elements Truss Finite Element Equations Transformation Equations
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[ ¯ K e ][ T e ] { e } =[ T e ] { F e } , [ T e ] 1 T e ] T [ T e ] T [ ¯ K e ][ T e ] { e } = { F e } or [ K e ] { e } = { F e } [ K e ]=[ T e ] T [ ¯ K e ][ T e ] , { F e } T e ] T { ¯ F e } [ K e ]= EA h cos 2 θ 1 2 sin 2 θ cos 2 θ 1 2 sin 2 θ 1 2 sin 2 θ sin 2 θ 1 2 sin 2 θ sin 2 θ cos 2 θ 1 2 sin 2 θ cos 2 θ 1 2 sin 2 θ 1 2 sin 2 θ sin 2 θ 1 2 sin 2 θ sin 2 θ { F e } = F e 1 F e 2 F e 3 F e 4 = ¯ P e 1 cos θ e ¯ P e 1 sin θ e ¯ P e 2 cos θ e ¯ P e 2 sin θ e + ¯ f e 1 cos θ e ¯ f e 1 sin θ e ¯ f e 2 cos θ e ¯ f e 2 sin θ e P = 100 kN y x A B C 2 P = 200 kN L L P = 100 kN y x 3 2 P = 200 kN 1 2 x F 1 y F 2 y F 1 x F 2 ( a )( b ) x y x y ) 2 , 1 ( 1 ) 4 , 3 ( 2 D 90 2 = θ D 45 3 = ) 6 , 5 ( 3 Example 1 Transformation Element Stiffness Matrix and Force Vector
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Example Element Global Geom. Mater. Orient.
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Plane_Truss_Ch4 - Plane Truss Finite Elements e v1e ye e 2...

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