The cast-iron frame of a small press is shaped as shown below on the left. The cross section a-a of the frame is shown on the right. For a load P of 20 kip, determine (a) the axial load and bending moment at cross section a-a, and (b) the maximum tensile and compressive stresses on cross section a-a. 17 in 1 a- a E 8 in- 2 in 5 in 2 in 1 5 in

Question 1 A steel bar with length of 4.5 m is subjected to forces as shown in the figure: 1. Determine the stress in the square section 2. Determine the elongation of each sections Take the modules of elasticity for the bar is 200 GPa Circular section Square section Circular section Diameter =15 mm Area =20 mm*20mm Diameter =10 mm 50 kN 35 kN 30 kN 45 kN 1 m 2 m 1.5 m

2. The tapered cylindrical bar in Fig. 2 is subjected to opposing torques T on its free ends. For the tapered section only, the angle of twist 0 can be expressed as: 32 TI(d? + d,d2 + dž) Gd d? 37n (a) Derive an expression for the effective spring constant keff for the entire bar, treating each segment as a torsional spring in series. Fig. 2 (b) For the bar shown, let; I, = 12 = 12 in., 1= 24 in., d1= 0.25 in., d2= 1 in., T = 1000 lbf-in., and G = 13.5 x 103 kpsi. Calculate the angle twist 0 for the entire bar using the expression for kef determined in (a). Verify that this value is the sum the angles of twist for each individual %3D %3D segment.

a) Determine the tensile force T’ in the rope on the side connected to joint B: b) Determine the internal compressive normal force ƒBC in the tube BC: c) Determine the horizontal reaction force Rx and the vertical reaction force Ry in joint A: d) Determine the moment M of the center of bar AB: e) Determine the compressive stress σBC in the tube BC: f) Determine the critical load Pc for the tube BC: g) Which of the following statements about the tube BC is correct: A. The tube BC fails due to yielding B. The tube BC fails due to buckling C. The tube BC fails due to both yielding and buckling D. The tube BC is safe against both yielding and buckling h) Pin C has a diameter of 30 mm; calculate the shear stress τ of the pin C, when considering one cross-section for shear stress calculation: