Using Castigliano's method, determine the support reactions for the beam shown be- low. B W

b) A cylindrical rod AB is made of aluminum is connected at B to a brass qylindrical rod BCD as shown in Figure 8. The shear modulus, G of aluminum rod AB is given by 27 GPa and the brass rod BCD of 39 GPa. The torsional reactions, TA and Ts are located at the ends of A and B, respectively. Given the portion CD of the brass rod is hollow and has an inner diameter of 40 mm, examine the angle of twist at A. 60 mm Tg = 1600 N - m 36 mm TA = 800 N m 250 mm 375 mm A 400 mm Figure 8

The beams described in the problems for Section 9.9 have constant flexural rigidity El. A simple beam AB of length L is loaded at the lefthand end by a couple of moment M, (see figure). Determine the angle of rotation 6, at support A. (Obtain the solution by determining the strain energy of the beam and then using Castigliano's theorem.) Mo B L PROB. 9.9-1 Step-by-step solution Step 1 of 5 A Length of the simple beam AB = L Couple of moment at A,= M, Angle of rotation at A= 0,

*14-88. The state of strain at the point on the leaf of the caster assembly has components of = -400(1o). y = 860(10, and Yay = 375(10*). Use the strain transformation equations to determine the equivalent in-plane strains on an element ariented at an angle of e = 30 counterclockwise from the ariginal position. Sketch the deformed element due to these strains within the x-y plane.