The truss shown in the figure below is made of three A-36 steel members (E=200 GPa), each having a cross-sectional area of 400 mm² . Determine the load P required to displace the roller at C downward 0.2 mm. 1.6m -
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- 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.)The figure shows an idealized structure consisting of rigid bars ABC And DEF joined by a linearly elastic spring ß between C and D. The structure is also supported by translational elastic support ß at B and rotational elastic support ßRat E. Determine the critical load Pcrfor the structure.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 = 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.)
- 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.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.)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?
- The figure shows an idealized structure consisting of two rigid bars joined by an elastic connection with rotational stiffness ßR. Determine the critical load PCTfor the structure.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.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.
- 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.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 column, pinned at top and bottom, is made up of two C 6 x 13 steel shapes (see figure) that act together. Find the buckling load (kips) if the gap is zero. Find required separation distance d(inches) so that the buckling load is the same in y and z directions. Assume that E = 30,000 ksi and L = 18 ft. Note that distance d is measured between the centroids of the two C shapes.