8. Select the lightest W shape that will act as a column 12 m long with fixed ends and support an axial load of 700 kN with a factor of safety of 2. Assume that the proportional limit is 200 MPa and E= 200 GPa.
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- An idealized column consists of rigid bar ABCD with a roller support at B and a roller and spring support at D. The spring constant at D. is ß = 750 N/m. Find the critical load Pcrof the column.A fixed-end column with circular cross section is acted on by compressive axial load P. The IS-ft-long-column has an outer diameter of 5 in., a thickness of 0.5 in., and is made of aluminum with a modulus of elasticity of 10,000 ksi. Find the buckling load of the column.An idealized column is composed of rigid bars ABC and CD joined by an elastic connection with rotational stiffness ßRIat C. There is a roller support at B and an elastic support at D with translationa1 spring stiffness ß and rotational stiffness ßR2. Find the critical buckling loads for each of the two buckling modes of the column. Assume that L = 3 m, ß = 9 kN/m, and ßR]= ßR1= ßL2. Sketch the buckled mode shapes.
- A sign for an automobile service station is supported by two aluminum poles of hollow circular cross section, as shown in the figure. The poles are being designed to resist a wind pressure of 75 lb/ft" against the full area of the sign. The dimensions of the poles and sign are hx= 20 ft, /r =5 ft, and h = 10 ft. To prevent buckling of the walls of the poles, the thickness e is specified as one-tenth the outside diameter d. (a) Determine the minimum required diameter of the poles based upon an allowable bending stress of 7500 psi in the aluminum. (b) Determine the minimum required diameter based upon an allowable shear stress of 300 psi.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 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 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.A 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?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 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 horizontal rigid bar ABC is pinned at end A and supported by two cables at points B and C. A vertical load P = 10 kN acts at end C of the bar. The two cables are made of steel with a modulus elasticity E = 200 GPa and have the same cross-sectional area. Calculate the minimum cross-sectional area of each cable if the yield stress of the cable is 400 MPa and the factor of safely is 2.0. Consider load P only; ignore the weight of bar ABC and the cables.An idealized column is made up of rigid segments ABC and CD that are joined by an elastic connection at C with rotational stiffness ßR= 100 kip-in./rad. The column has a roller support at B and a sliding support at D. Calculate the critical load Pcrof the column.