2-15 - 108 Finite Element Analysis and Design 15. For a...

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108 Finite Element Analysis and Design 15. For a two dimensional truss shown in the figure, determine displacements of the nodes and normal stresses developed in the members. Use E = 30×10 6 N/cm 2 and the diameter of the circular cross section is 0.25 cm. Solution: Connectivity table Elem Node1 Node2 E (N/cm 2 ) A (cm 2 ) L (cm) 1 1 2 30×10 6 .05 9 90° 2 4 2 30×10 6 .05 15 143.13° 3 3 4 30×10 6 .05 9 -90° 4 2 3 30×10 6 .05 12 Individual Element Stiffness Matrix after applying transformation 22 cos cos sin cos cos sin cos sin sin cos sin sin [] cos cos sin cos cos sin cos sin sin cos sin sin EA L     k Element 1: 1 1 3 2 2 0 0 0 0 0 166.7 0 166.7 [ ] 10 0 0 0 0 0 166.7 0 166.7 u v u v k Element 2: 4 4 3 2 2 64 48 64 48 48 36 48 36 [ ] 10 64 48 64 48 48 36 48 36 u v u v k Element 3: 3 3 3 4 4 0 0 0 0 0 166.7 0 166.7 [ ] 10 0 0 0 0 0 166.7 0 166.7 u v u v k 50 N 9 cm 12 cm N 1 N 3 N 4 N 2
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