A bar is subjected to fluctuating tensile load from 20KN to 100KN. The material has yield strength of 240 MPa and endurance limit in reversed bending is 160MPA. According to the soderberg principle, find the area of cross section of the bar for a factor of safety of 2
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- A high-strength steel bar used in a large crane has a diameter d = 2.00 in. (sec figure). The steel has a modulus of elasticity E = 29 × 10 psi and Poisson’s ratio is v = 0.29. Because of clearance requirements, the diameter of the bar is limited to 2.001 in. when it is compressed by axial forces. What is the largest compressive load Pmaxthat is permitted?A prismatic bar of length L = 1.8 m and cross-sectional area A = 480 mm" is loaded by forces P{= 30 kN and A = 60 kN (see figure) The bar is constructed of magnesium alloy having a stress-strain curve described by the Ram berg-Osgood equation: 45.000 618 UW id which u has units of mega pascals (MPa). (a) Calculate the displacement 8t- of the end of the bar when the load P:acts alone. (b) Calculate the displacement when the load P, acts alone. (c) Calculate the displacement when both loads act simultaneously.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.A round bar of 10 mm diameter is made of aluminum alloy 7075-T6 (see figure). When the bar is stretched by axial forces P, its diameter decreases by 0.0 16 mm. Find the magnitude of the load P. Obtain the material properties from Appendix 1.Rigid bar ACB is supported by an elastic circular strut DC having an outer diameter of 15 in. and inner diameter of 14.4 in. The strut is made of steel with a modulus elasticity of E = 29,000 ksi. Point load P = 5 kips is applied at B. Calculate the change in length of the circular strut DC. What is the vertical displacement of the rigid bar at point B?
- Solve the preceding problem for an aluminum plate with h = 10 in.. i = 0.75 in., E = 10,600 ksi, v = 0.33. P = 96 kips. Pt,. = 24 kips. and V =18 kips. For part (b) of Problem 7.5-12, assume that the required strain energy stored is 640 in.-lb. In part (c). the change in volume cannot exceed 0.05%.(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 pressureA 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 steel pad supporting heavy machinery rests on Four short, hollow, cast iron piers (see figure). The ultimate strength of the cast iron in compression in 50 ksi. The outer diameter of the piers is d = 4.5 in, and the wall thickness is t = 0.40 in. Using a factor of safety of 3.5 with respect to the ultimate strength, determine the total load P that can be supported by the pad.A symmetrical framework consisting of three pin-connected bars is loaded by a force P (see figure). The angle between the inclined bars and the horizontal is a = 52°. The axial strain in the middle bar is measured as 0.036. Determine the tensile stress in the outer bars if they are constructed of a copper alloy having the following stress-strain relationship:A steel wire- and an aluminum allay wire have equal lengths, and support equal loads P (see figure). The moduli of elasticity for the steel and aluminum alloy are Ea= 30,000 ksi and Ea= 11,000 ksi, respectively. (a) IF the wires have the same diameters, what is the ratio of the elongation of the aluminum alloy wire to the elongation of the steel wire? (b) If the wires stretch the same amount, what is the ratio of the diameter of the aluminum alloy wire to the diameter of the steel wire? (c) If the wires have the same diameters and same load P, what is the ratio of the initial length of the aluminum alloy wire to that of the steel wire if the aluminum alloy wire stretches 1.5 limes that of the steel wire? (d) If the wires have the same diameters, same initial length, and same load P. what is the material of the upper wire if it elongates 1.7 times that of the steel wire?