Concept explainers
Consider an ideal column as in Fig. 17–10d, having one end fixed and the other pinned. Show that the critical load on the column is
Want to see the full answer?
Check out a sample textbook solutionChapter 17 Solutions
Statics and Mechanics of Materials (5th Edition)
- Determine the allowable axial load Pallowfor a steel pipe column that is fixed at the base and free at the top (see figure) for each of the following lengths: L = 6 ft, 9 ft, 12 ft, and 15 ft. The column has an outside diameter d = 6.625 in. and wall thickness t = 0.280 in, (Assume E = 29,000 ksi and y= 36 ksi.)arrow_forwardA 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.arrow_forwardAn 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 GPaarrow_forward
- 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.arrow_forwardDetermine the allowable axial load Pallowfor a steel pipe column that is fixed at the base and free at the top (see figure) for each of the following lengths: L = 2,6 m, 2.8 m, 3.0 m, and 3.2 m. The column has an outside diameter d = 140 mm and wall thickness t = 7 mm, (Assumed = 200 GPa and ( y= 250 MPa.)arrow_forwardAn aluminum bar having a rectangular cross section (2.0 in. × 1.0 in.) and length L = 30 in. is compressed by axial loads that have a resultant P = 2800 lb acting at the midpoint of the long side of the cross section (sec figure). Assuming that the modulus of elasticity E is equal to 10 × 106 psi and that the ends of the bar are pinned, calculate the maximum deflection and the maximum bending moment Mmax.arrow_forward
- 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.arrow_forwardThe upper end of a WE × 21 wide-flange steel column (E = 30 × 103ksi) is supported laterally between two pipes (see figure). The pipes arc not attached to the column, and friction between the pipes and the column is unreliable. The base of the column provides a fixed support, and the column is 13 ft long. Determine the critical load for the column, considering Euler buckling in the plane of the web and also perpendicular to the plane of the web.arrow_forwardDetermine 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.arrow_forward
- An aluminum tube AB with a circular cross section has a sliding support at the base and is pinned at the top to a horizontal beam supporting a load Q = 200 kN (sec figure). Determine the required thickness t of the tube if its outside diameter d is 200 mm and the desired factor of safety with respect to Eu 1er buckling is n = 3.0. (Assume E = 72 GPa.)arrow_forwardA 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?arrow_forwardA cantilever aluminum column has a square tube cross section with an outer dimension of 150 mm. The column has a length L = 4 m and is designed to support an axial load of 45 kN. Find the minimum required thickness of the section if the factor of safety n = 2.5 with respect to buckling. Assume that the modulus of elasticity is 72 GPa and the proportional limit is 480 MPa.arrow_forward
- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning