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- A rigid bar of length L is supported by a linear elastic rotational spring with rotational stiffness ßRat A. Determine the critical load Pcr for the structure.Solve the preceding problem for an aluminum column with b = 6,0 in., t = 0.5 in., P = 10 kips, and E = 10.6 × 106 ksi. The defied ion at the top is limited to 2.0 in.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 pipe column with pinned ends supports an axial load P = 21 kips. The pipe has outside and inside diameters of 3.5 in. and 2.9 in., respectively. What is the maximum permissible length Lmaxof the column if E = 29,000 ksi and y = 36 ksi?Determine the maximum permissible length Lmaxfor a steel pipe column that is fixed at the base and free at the top and must support an axial load P = 500 kN (see figure). The column has an outside diameter d = 200 mm, wall thickness; = 10 mm, E = 200 GPa, and y = 250 MPa.A steel bar has a square cross section of width b = 2.0 in. (sec figure). The bar has pinned supports at the ends and is 3.0 ft long. The axial forces acting at the end of the bar have a resultant P = 20 kips located at distance e = 0,75 in, from the center of the cross section. Also, the modulus of elasticity of the steel is 29,000 ksi. Determine the maximum compressive stress max, in the bar. If the allowable stress in the steel is 18,000 psi, what is the maximum permissible length Lmaxof the bar?
- 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.-11 Determine the maximum permissible length Lmaxfor a steel pipe column that is fixed at the base and free at the top and must support an axial load P = 40 kips (see figure). The column has an outside diameter d = 4.0 in., wall thickness t = 0.226 in., E = 29,000 ksi, and y = 42 ksi.An aluminum box column with a square cross section is fixed at the base and free at the top (sec figure). The outside dimension b of each side is 100 mm and the thickness t of the wall is 8 mm. The resultant of the compressive loads acting on the top of the column is a force P = 50 kN acting at the outer edge of the column at the midpoint of one side. What is the longest permissible length Lmaxof the column if the deflection at the top is not to exceed 30 mm? (Assume E = 73 GPa