2-26 - CHAP 2 Uniaxial Bar and Truss Elements 131 26. Use...

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CHAP 2 Uniaxial Bar and Truss Elements 131 26. Use FEA to determine the nodal displacements in the plane truss shown in Figure (a). The temperature of Element 2 is 100 o C above the reference temperature, i.e., T (2) =100 o C . Compute the force in each element. Show that the force equilibrium is satisfied at Node 3. Assume L = 1 m, AE = 10 7 N, = 5×10 -6 / o C. Solution: Connectivity table: Elem i - j EA [N] L [m] T [°C] [1/°C] 1 1, 2 10 7 1 0 5 x 10 -6 90° 2 2, 3 10 7 1 100 5 x 10 -6 3 3, 4 10 7 1 0 5 x 10 -6 -90° 4 1, 3 10 7 1.414 0 5 x 10 -6 45° Element stiffness matrices: Element 1 Element 2 1 1 (1) 7 2 2 0 0 0 0 0 1 0 1 [ ] 10 0 0 0 0 0 1 0 1 u v u v    k 2 2 (2) 7 3 3 1 0 1 0 0 0 0 0 [ ] 10 1 0 1 0 0 0 0 0 u v u v k Element 3 Element 4 3 3 (3) 7 4 4 0 0 0 0 0 1 0 1 [ ] 10 0 0 0 0 0 1 0 1 u v u v k 1 1 (4) 7 3 3 .354 .354 .354 .354 .354 .354 .354 .354 [ ] 10 .354 .354 .354 .354 .354 .354 .354 .354 u v u v  k The structural stiffness matrix can be obtained after assembling element stiffness matrices, as 10,000 N 4 L , T 2 1 2 3 4 2 L L 1 3 4 T 2 1 3 5 4 T 2 1 3 5 (a) (b) (c)
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132 Finite Element Analysis and Design 1 1 2 2 7 3 3 4 4 .354 .354 0 0 .354 .354 0 0 .354 1.354 0 1 .354 .354 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 [ ] 10 .354 .354 1 0 1.354 .354 0 0 .354 .354 0 0 .354 1.354 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
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2-26 - CHAP 2 Uniaxial Bar and Truss Elements 131 26. Use...

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