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- - A specimen used in a coupon test has norm al stress ??. = 15 MPa (see figure). Using Mohr’s circle, find the state of stress on the element oriented at angle ? = 20° and show the full stress state on a sketch of a properly oriented element.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?A fire extinguisher tank is designed for an internal pressure of 825 psi. The tank has an outer diameter of 4.5 in. and thickness of O.OS in. Calculate the longitudinal stress, the circumferential stress, and the maximum shear stresses (out-of-plane and in-plane) at the outer surface of the tank.
- A prismatic bar with a length L = 3 ft and cross-sectional area A = 8 in2 is compressed by an axial centroidal load P = 10 kips. Determine the complete state of stress acting on an inclined section pq that is cut through the bar at an angle W = 35", and show the stresses on a properly oriented stress element.At a point on the web of a girder on an overhead bridge crane in a manufacturing facility, the stresses arc known to be x = —4300 psi, a = 1700 psi, and r = 3100 psi (the sign convention for these stresses is shown in Fig, 7-1). A stress clement located at the same point in the structure (but oriented at a counterclockwise angle 0, with respect to the _y axis) is subjected to the stresses shown in the figure {b, r», and 2100 psi). Assuming that the angle 8Xis between zero and 90°, calculate the normal stress trA, the shear stress ta, and the angle BvAn aluminum tube is required to transmit an axial tensile force P = 33 k (sec figure part a). The thickness of the wall of the tube is 0.25 in. (a) What is the minimum required outer diameter d minif the allowable tensile stress is 12.000 psi? (b) Repeat part (a) if the tube has a hole of a diameter J/10 at mid-length (see figure parts b and C).
- A copper rod of length L = 18.0 in. is to be twisted by torques T (see figure) until the angle of rotation between the ends of the rod is 3.0°. (a) If the allowable shear strain in the copper is 0.0006 rad, what is the maximum permissible diameter of the rod? (b) If the rod diameter is 0.5 in., what is the minimum permissible length of the rod?A circular copper bar with diameter d = 3 in. is subjected to torques T = 30 kip-in. at its ends. Find i lie maximum shear, ion si le. and compressive stresses in the tube and their corresponding strains. Assume that G = 6000 ksi.(a) Solve part (a) of the preceding problem if the pressure is 8.5 psi, the diameter is 10 in., the wall thickness is 0,05 in., the modulus of elasticity is 200 psi, and Poisson's ratio is 0.48. (b) If the strain must be limited to 1.01, find the maximum acceptable inflation pressure
- A solid circular bar of steel (G = 78 GPa) transmits a torque T = 360 N - m. The allowable stresses in tension, compression, and shear arc 90 MPa, 70 MPa, and 40 MPa, respectively. Also, the allowable tensile strain is 220 x 10-6, Determine the minimum required diameter d of the bar, If the bar diameter d = 40 mm, what is Tmax?The stresses on an element are sx= 1000 Psi. sy= 500 psi, and txy= 350 psi. Find the stresses acting on an element oriented at an angle 0 = 250. Show these stresses on the rotated element.An element of aluminum is subjected to tri-axial stresses. Calculate the strains in the element in x, y, and z directions lithe stresses axayand az are -2000 psi, 3500 psi, and 2700 psi, respectively. Assume E = 10,000 ksi and v = 0.33. Also, find the unit volume change of the element.