6.3 Evaluate the stiffness matrix for the elements shown in Figure P6-3. The coordinates are in units of inches. Assume plane stress conditions. Let E = 10 × 106 psi, v = 0.25, and thickness t = 1 in. Figure P6-3 3 (0, 1) (0, -1) 2 (2,0) (a) X (1.2. 1) (1.2, 0) (b) (2.4, 0) 2 3 (0, 1) 1 (0,0) (2,0)

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Consider the loaded shaft illustrated in Figure Q4 (i). The shaft is simply supported at A and D. The shoulder fillet radius is 0.3 cm at B and C. If the shaft is subjected to a force of F-800 N, determine the following: (a) The reaction forces at the two ends of the shaft A and D. (b) The bending moments at shoulder fillets B andC. (c) The nominal stresses at shoulder fillets B and C. (d) The stress concentration factor at shoulder fillet B. (e) The maximum stress in the shaft taking into account stress concentrations. 800 N T-0.3 can A d, - 3 cm d, = 5 cm d, - 3 cm 5 cm 8 cm 8 cm 12 cm Figure Q4 (i) The reference parameters are shown in Figure Q4 (ii) in the page that follows. For 0.002 srlds 0.3 and 1.01 s Dlds 6.0, the stress concentration factor for bar bending is given as: kn -4.4 = 0.632 + 0.377 -0.14 – 0.363(P/a)" + 0.503(P/a) 1- 2.39(P/a) + 3.368(2la)* -0.5 The nominal stress is: 32M %3D nd3

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