Buckling of suwnio Ex. 3: A horizontal beam AB is pin-supported at end A and carries a load Q at end B, as shown in the figure. The beam is supported at C by a pinned-end column. The column is a solid steel bar ( E = 200 GPa) of square cross section having length (L = 1.8 m ) and side dimensions ( b = 60 mm ). Based %3D %3D

Buckling of suwnio Ex. 3: A horizontal beam AB is pin-supported at end A and carries a load Q at end B, as shown in the figure. The beam is supported at C by a pinned-end column. The column is a solid steel bar ( E = 200 GPa) of square cross section having length (L = 1.8 m ) and side dimensions ( b = 60 mm ). Based %3D %3D

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter11: Columns

Section: Chapter Questions

Problem 11.3.6P: A horizontal beam AB is pin-supported at end A and carries a clockwise moment M at joint B, as shown...

See similar textbooks

Similar questions

Solve the preceding problem for a W 250 × 89 steel column having a length L = 10 m. Let E = 200 GPa.
A square wood column with side dimensions b (see figure) is constructed of a structural grade of spruce for which Ft. = 900 psi and E = 1,500,000 psi. An axial force P = 8.0kips acts on the column. If the dimension b = 3.5 in., what is the maximum allowable length Lmaxof the column? If the length L = 10 ft, what is the minimum required dimension bmin?
A cantileverbeam^Cßsupportstwo concentrated loads Ptand A, as shown in the figure. Calculate the deflections SBand 8Cat points B and C, respectively. Assume Px= 10 kN, P\ = 5 kN, L = 2.6 m, E = 200 GPa, and / = 20.1 x I0ft mm4.
A wood column with, a rectangular cross section (see figure) is constructed of 4 in. × 8 im construction grade, western hemlock: lumber (Fc = 1000 psi, E = 1,300,000 psi). The net cross-sectional dimensions of the column arc b = 3.5 in. and h = 7.25 in. (see Appendix G). Determine the allowable axial load Pallow. for each of the following lengths: L = 6 ft, 8ft, and 10 ft.
A simply supported slender column is subjected to axial load P = 175 kips applied at distance e = 0,5 in. from joint s A and B (see figure). The column has a circular cross section with an outer diameter of 10 in. and wall thickness of 0.5 in. Calculate the height of the column if the maximum deflection caused by the axial loads is 0,1 in. Assume that E = 29,000 ksi.
A horizontal beam AB has a sliding support at end A and carries a load Q at end B, as shown in the figure part a. The beam is supported at C and D by two identical pinned-end columns of length L. Each column has flexural rigidity EI. Find an expression for the critical load QCT. (In other words, at what load Qcrdoes the system collapse because of Eu 1er buckling of the columns?) Repeat part (a), but assume a pin support at A. Find an expression for the critical moment Mcr(i.e., find the moment M at B at which the system collapses because of Euler buckling of the columns).
A horizontal beam AB is pin-supported at end A and carries a clockwise moment M at joint B, as shown in the figure. The beam is also supported at C by a pinned-end column of length L: the column is restrained laterally at 0.6Z, from the base at D. Assume the column can only buckle in the plane of the frame. The column is a solid steel bar (E = 200 GPa) of square cross section having length L = 2.4 m and side dimensions h = 70 mm. Let dimensions d = LI2. Based upon the critical load of the column, determine the allowable moment M if the factor of safety with respect to buckling is n = 2.0.
A simple beam thai is IS ft long supports a uni¬form load of intensity a. The beam is constructed of two angle sections, each L (1 × 4 × 1/2, on either side of a 2 in. x 8 in. (actual dimensions! wood beam (see the cross section shown in the figure part a]. The modulus of elasticity of the s I eel is 10 limes that of the wood, (a) If the allowable stresses in the steel and wood are 12,000 psi and 900 psi. respectively, what is the allow atile load a t. A olc. Disregard the weight of the beam, and see Table F-5(a) of Appendix I ' for I lie dimensions and properties of the angles. (b) Repeal partial if a I in. 10 in. wood Hange tactual dimensions) is added i see figure pallhi b).
Beam ABC is loaded by a uniform load q and point load P at joint C. Using the method of superposition, calculate the deflection at joint C. Assume that L = 4 m, a =2ra, q = 15 kN/m, P = 7.5 kN, £ = 200 GPa, and / = 70.8 X 106 mm4.
The horizontal beam ABC shown in the figure is supported by columns BD and CE. The beam is prevented from moving horizontally by the pin support at end A. Each column is pinned at its upper end to the beam, but at the lower ends, support D is a sliding support and support E is pinned. Both co lu in us arc solid steel bars (E = 30 × 106 psi) of square cross section with width equal to 0.625 in. A load Q acts at distance a from column BD. If the distance a = 12 in., what is the critical value Qcr of the load? If the distance a can be varied between 0 and 40 in., what is the maximum possible value of Qcr? What is the corresponding value of the distance a?
A reinforced concrete T-beam (see figure) is acted on by a positive bending moment of M = 175 kip-ft. Steel reinforcement consists of four bars of 1.41-inch diameter. The modulus of elasticity for the concrete is Ec= 3000 ksi while that of the steel is £s = 29,000 ksi. Let b = 48 im, rf = 4 in., bw=15 in,, and d = 24 in, Find the maximum stresses in steel and concrete, If allowable stresses for concrete and steel are o"ac = 1400 psi and tr^ =18 ksi, respectively, what is the maximum permissible positive bending moment?
An overhanging beam ABC with flexural rigidity EI = 15 kip-in" is supported by a sliding support at A and by a spring of stiffness k at point fi(see figure). Span AB has a length L = 30 in. and carries a u ni form load. The overhang BC has a length b = 15 in. For what stiffness k of the spring will the uniform load produce no deflection at the free end C?