Estimate: 1- The normal stress in the bar. 2- The change in the length, if its original length before the load is applied is 100 cm.
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- A wine of length L = 4 ft and diameter d = 0.125 in. is stretched by tensile forces P = 600 lb. The wire is made of a copper alloy having a stress-strain relationship that may be described mathematically by =18,0001+30000.03(=ksi) in which is nondimensional and has units of kips per square inch (ksi). (a) Construct a stress-strain diagram for the material. (bj Determine the elongation, of the wire due to the Forces P. (c) IF the forces are removed, what is the permanent set of the bar? (d) If the forces are applied again, what is the proportional limit?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.-11 A solid steel bar (G = 11.8 X 106 psi ) of diameter d = 2,0 in. is subjected to torques T = 8.0 kip-in. acting in the directions shown in the figure. Determine the maximum shear, tensile, and compressive stresses in the bar and show these stresses on sketches of properly oriented stress elements. Determine the corresponding maximum strains (shear, tensile, and compressive) in the bar and show these strains on sketches of the deformed elements.
- 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~ .Solve the preceding problem if the cube is granite (E = 80 GPa, v = 0.25) with dimensions E = 89 mm and compressive strains E = 690 X l0-6 and = = 255 X 10-6. For part (c) of Problem 7.6-5. find the maximum value of cr when the change in volume must be limited to 0.11%. For part. find the required value of when the strain energy must be 33 J.
- A pressurized cylindrical tank with flat ends is loaded by torques T and tensile forces P (sec figure), The tank has a radius of r = 125 mm and wall thickness t = 6.5 mm. The internal pressure p = 7.25 MPa and the torque T = 850 N m. (a) What is the maximum permissible value of the forces P if the allowable tensile stress in the wall of the cylinder is 160 MPa? (b) If forces P = 400 kN, what is the maximum acceptable internal pressure in the tank?A solid circular steel cylinder S is encased in a hollow circular aluminum tube A. The cylinder and tube are compressed between the rigid plates of a testing machine which applies forces P. Calculate the allowable value of the compressive force if the yield stresses of sleel and aluminum are srs = 50 Ksi and ??A= 60 ksi, respectively. Assume that As= 12 in2. AA= 6 in2. L = 20 in., Es= 29,000 tsi and EA=10,600 ksiTruss members supporting a roof are connected to a 26-mm-thick gusset plate by a 22-mm diameter pin, as shown in the figure and photo. The two end plates on the truss members are each 14 mm thick. (a) If the load P = 80 kN, what is the largest bearing stress acting on the pin? (b) If the ultimate shear stress for the pin is 190 MPa, what force Pult is required to cause the pin to fail in shear? Disregard friction between the plates.
- Solve the preceding problem for the following data: diameter LO m, thickness 48 mm, pressure 22 MPa, modulus 210 GPa. and Poisson's ratio 0.29During a tension lest of a mild-steel specimen (see figure), the extensometer shows an elongation of 0.00120 in. with a gage length of 2 in. Assume that the steel is stressed below the proportional limit and that the modulus of elasticity E = 30 × 10 psi. (a) What is the maximum normal stress (j^, in the specimen? (b) What is the maximum shear stress tmax? (c) Draw a stress element oriented at an angle of 45° to the axis of the bar, and show all stresses acting on the faces of this element.A cylindrical pressure vessel having a radius r = 14 in. and wall thickness t = 0,5 in, is subjected to internal pressure p = 375 psi, In addition, a torque T = 90 kip-ft acts at each end of the cylinder (see figure), (a) Determine the maximum tensile stress ctniXand the maximum in-plane shear stress Tmjv in the wall of the cylinder. (b) If the allowable in-plane shear stress is 4.5 ksi, what is the maximum allowable torque T\ (c) If 7 = 150 kip-ft and allowable in-plane shear and allowable normal stresses are 4.5 ksi and 11.5 ksi, respectively, what is the minimum required wall thickness