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- An aluminum bar has length L = 6 ft and diameter d = 1.375 in. The stress-strain curse for the aluminum is shown in Fig. 1.34. The initial straight, line part of the curve has a slope (modulus of elasticity) of 10.6 × 106 psi. The bar is loaded by tensile forces P = 44.6 k and then unloaded. (a) That is the permanent set of the bar? (b) If the bar is reloaded. what is the proportional limit? hint: Use the concepts illustrated in Figs. l.39b and 1.40.A steel cable with a nominal diameter of 25 mm (see Table 2-1) is used in a construction yard to lift a bridge section weighing 38 kN. as shown in the figure. The cable has an effective modulus of elasticity E = 140 GPa. (a) If the cable is 14 m long, how much will it stretch when the load is picked up? (b) If the cable is rated for a maximum load of 70 kN, that is the factor of safety with respect to failure of the cable?-11 A rubber cube R of a side L = 3 in. and cross- sectional area A = 9 in2 is compressed inside a steel cube S by a force F = 5 lb that applies uniformly distributed pressure to the rubber. Assume E 0.3ksi and,, = 0.45. (a) Calculate the lateral pressure between the rubber and steel (disregard friction between the rubber and the steel, and assume that the steel block is rigid when compared to the rubber). (b) Calculate the change in volume of the rubber.
- Solve the preceding problem if the diameter is 480 mm, the pressure is 20 MPa, the yield stress in tension is 975 MPa, the yield stress in shear is 460 MPa, the factor of safety is 2,75, the modulus of elasticity is 210 GPa, Poissorfs ratio is 0.28, and the normal strain must not exceed 1190 x 10" . For part (b), assume that the tank thickness is 8 mm and the measured normal strain is 990 x 10~ .-19 The mechanical assembly shown in the figure consists of an aluminum tube, a rigid end plate, and two steel cables. The slack is removed from the cables by rotating the turnbuckles until the assembly is snug but with no initial stresses. Afterward, the turnbuckles are tightened by 1.5 turns. Calculate the forces in the tube and the cables and determine the shortening of the tube. As= 0.85 in2 for each cable, AA= 4.5 in2, L = 20 in., Es= 29,000 ksi, EA= 10,600 ksi, and p = 1/16 inThe rails of a railroad track are welded together at their ends (to form continuous rails and thus eliminate the clacking sound of the wheels) when the temperature is 60°F. What compressive stress ?? =6.5×10-6 /? is produced in the rails when they are heated by the sun to 120"F if the coefficient of thermal expansion a = the modulus of elasticity E = 30 × 106 psi?
- A capped cast-iron pipe is compressed by a brass rod, as shown. The mil is turned until it is just snug, then add an additional quarter turn to pre-compress the cast-iron pipe. The pitch of the threads of the bolt ap = 52 mils (a mil is one-thousandth of an inch). Use the numerical properties provided. (a) What stresses a and arwill be produced in the cast-iron pipe and brass rod. respectively, by the additional quarter turn of the nut? (b) Find the bearing stress ahbeneath the washer and the shear stress t(in the steel cap.Compare the angle of twist 1 for a thin-walled circular tube (see figure) calculated from the approximate theory for thin-walled bars with the angle of twist 2 calculated from the exact theory of torsion for circular bars, Express the ratio 12terms of the non-dimensional ratio ß = r/t. Calculate the ratio of angles of twist for ß = 5, 10, and 20. What conclusion about the accuracy of the approximate theory do you draw from these results?A woodpile, driven into the earth, supports a load P entirely by friction along its sides (see figure part a). The friction force/per unit length of the pile is assumed to be uniformly distributed over the surface of the pile. The pile has a length L, cross-sectional area A. and modulus of elasticity E. (a) Derive a formula for the shortening
- A bar of monel metal with a length L = 9 in. and a diameter d = 0225 in. is loaded axially by a tensile force P (see figure). If the bar elongates by 0.0)95 in., what is the decrease in diameterA cantilever beanie B is loaded by a uniform load q and a concentrated load P, as shown in the figure. Select the most economical steel C shape from Table F-3(a) in Appendix F; use q = 20 lb/ft and P = 300 lb (assume allowable normal stress is cra= IS ksi). Select the most economical steel S shape from Table F-2(a) in Appendix F; use q = 45 lb/ft and P = 2000 lb (assume allowable normal stress is tra= 20 ksi), Select the most economical steel W shape from Table F-1(a) in Appendix F; use q = 45 lb/ft and P = 2000 lb (assume allowable normal stress is (T = 20 ksi). However, assume that the design requires that the W shape must be used in weak axis bending, i.e., it must bend about the 2-2 (or v) axis of the cross section. Note: For parts (a), (b), and (c), revise your initial beam selection as needed to include the distributed weight of the beam in addition to uniform load q.Two sections of steel drill pipe, joined by bolted flange plates at Ä are being tested to assess the adequacy of both the pipes. In the test, the pipe structure is fixed at A, a concentrated torque of 500 kN - m is applied at x = 0.5 m, and uniformly distributed torque intensity t1= 250 kN m/m is applied on pipe BC. Both pipes have the same inner diameter = 200 mm. Pipe AB has thickness tAB=15 mm, while pipe BC has thickness TBC= 12 mm. Find the maximum shear stress and maximum twist of the pipe and their locations along the pipe. Assume G = 75 GPa.