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- A hollow, circular, cast-iron pipe (Ec =12,000 ksi) supports a brass rod (Ec= 14,000 ksi} and weight W — 2 kips, as shown. The outside diameter of the pipe is dc= 6 in. (a) If the allowable compressive stress in the pipe is S00O psi and the allowable shortening of the pipe is 0.02 in., what is the minimum required wall thickness trmm? (Include the weights of the rod and steel cap in your calculations.) (b) What is the elongation of the brass rod Srdue to both load Wand its own weight? (c) What is the minimum required clearance h?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~ .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.
- The 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 copper alloy pipe with a yield stress aY= 290 MPa. is to carry an axial tensile load P = 1500 kN (see figure part a). Use a factor of safety of 1.8 against yielding. (a) If the thickness t of the pipe is one-eighth of its outer diameter, what is the minimum required outer diameter dmin? (b) Repeat part (a) if the tube has a hole of diameter dt 10 drilled through the entire tube, as shown in the figure part b.A two-story building has steel columns AB in the first floor and BC in the second floor, as shown in the figure. The roof load P:equals 400 KN, and the second-floor load P-, equals 720 kN. Each column has a length L = 3.75 m. The cross-sectional areas of the first- and second-floor columns are 11,000 mm" and 3900 mm", respectively. (a) Assuming that E = 206 GPa. determine the total shortenings aof the two columns due to the combined action of the loads Ptand P,. (b) How much additional load P0can be placed at t he top of t he column (point C) if t he total shortening: SACis not to exceed 4.0 mm?
- A punch for making a slotted hole in ID cards is shown in the figure part a. Assume that the hole produced by the punch can be described as a rectangle (12 mm X 3 mm) with two half circles (r = 1.5 mm) on the left and the right sides. If P = 10 N and the thickness of the ID card is 1 mm, what is the average shear stress in the card?Solve the preceding problem if the internal pressure is 3,85 MPa, the diameter is 20 m, the yield stress is 590 MPa, and the factor of safety is 3.0. (a) Determine the required thickness to the nearest millimeter. (b) If the tank wall thickness is 85 mm, what is the maximum permissible internal pressure?A solid steel bar of a diameter d1= 60 mm has a hole of a diameter d2= 32 mm drilled through it (see figure). A steel pin or a diameter d2passes through the hole and is attached to supports. Determine the maximum permissible tensile load P allow in the bar if the yield stress for shear in the pin is ty= 120 MPa, the yield stress for tension in the bar is ??y= 250 MPa, and a factor of safety of 2.0 with respect to yielding is required. Hint: Use the formulas of Case 15, Appendix E.
- 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?A hollow circular tube T of a length L = 15 in. is uniformly compressed by a force P acting through a rigid plate (see figure). The outside and inside diameters of the tube are 3.0 and 2.75 in., respectively. A concentric solid circular bar B of 1.5 in. diameter is mounted inside the lube. When no load is present, there is a clearance c = 0.0I0 in. between the bar B and the rigid plate. Both bar and tube are made of steel having an c[autoplastic stress-strain diagram with E = 29 X LO3 ksi and err= 36 ksi. (a) Determine the yield load Pt- and the corresponding shortening 3yof the lube. (b) Determine the plastic load Ppand the corresponding shortening Spof the tube. (c) Construct a load-displacement diagram showing the load Pas ordinate and the shortening 5 of the tube as abscissa. Hint: The load-displacement diagram is not a single straight line in the region 0 ^ P ^ PrA flat bar of width b and thickness t has a hole of diameter d drilled through it (see figure). The hole may have any diameter that will fit within the bar. What is the maximum permissible tensile load Pmaxif the allowable tensile stress in the material is st?