2. A solid round steel rod with E = 207 GPa, Sy =350 MPa is 1 m long with fixed-pinned end supports. Find the rod diameter if the axial load applied is 15 kN and the safety factor is 4.
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- 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.A pinned-end strut of aluminum (E = 10,400 ksi) with a length L = 6 ft is constructed of circular tubing with an outside diameter d = 1 in. (sec figure). The strut must resist an axial load F = 4 kips with a factor of safety n = 2.0 with respect to the critical load. Determine the required thickness t of the tube.A 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?
- 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?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 steel column ( E = 30 X 103 ksi) that is fixed at the base and free at the top is constructed of a W8 x 35 wide-flange member (sec figure). The column is 9.0 ft long. The force P acting at the top of the column has an eccentricity e = 1.25 in. If P = 40 kips, what is the maximum compressive stress in the column? If the yield stress is 36 ksi and the required factor of safety with respect to yielding is 2.1, what is the allowable load Pallow?
- An aluminum pipe column (E = 10,400 ksi) with a length L = 10.0 ft has inside and outside diameters d1= 5.0 in. and d2= 6.0 in., respectively (sec figure). The column is supported only at the ends and may buckle in any direction. Calculate the critical load Pcrfor the following end conditions: (a) pinned-pinned, (b) fixed-free, (c) fixed-pinned, and (d) fixed-fixed.A circular steel rod AB? (diameter d, = 1.0 in., length L1= 3.0 Ft) has a bronze sleeve (outer diameter d2= 1-25 in., length L2= 1.0 ft) shrunk onto it so that the two parts are securely bonded (see figure). Calculate the total elongation 6 of the steel bar ¦due to a temperature rise AT = 500°F. (Material properties are as follows: For steel, Es= 30 ×106 psi and as= 6.5 × lO6/?; for bronze, Eb= 15 × 106psi and ab= 11 × l0-6/?.)Three round, copper alloy bars having the same length L but different shapes are shown, in the figure. The first bar has a diameter d over its entire length, the second has a diameter d over one-fifth of its length, and the third has a diameter d over one-fifteenth of its length. Elsewhere, the second and third bars have a diameter Id. All three bars are subjected to the same axial load P. Use the following numerical data: P = 1400 kN, L = 5m,d= 80 mm, E= 110 GPa. and v = 0.33. (a) Find the change in length of each bar. (b) Find the change in volume of each bar.
- A rigid bar of weight W = 750 lb hangs from three equally spaced wires: two of steel and one of aluminum (see figure). The diameter of the wires is 1/8 in. Before they were loaded, all three wires had the same length. What temperature increase T in all three wires will result in the entire load being carried by the steel wires? (Assume Es= 30 × 106 psi, as= 6.5 × 10-6 /'F, and aa= 12 × 10-6F.)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 rigid L-shaped frame is supported by a steel pipe column AB (sec figure) and is subjected to a horizontal load F = 140 kips. If the pipe has an outside diameter d = 4 in. and a factor of safety of 2.5 is required with respect to Euler buckling, what is the minimum acceptable thickness f of the pipe? Assume that E = 30,000 ksi for AB.