SMTL301 Buckling Problem 1. Determine the maximum magnitude of the concentrated load W that can be applied to the the pinned truss structure without causing the compressive members to buckle. The members of the truss are made of steel tubes having 60 mm outside diameter and 5 mm thickness. The modulus of elasticity of steel is 210 GPa. Use a factor of safety 2 against buckling. Answer: 31.56 kN B 3m D W 3m C A 2.5 m 2m Problem 2. A long slender structural aluminium (E = 70 GPa) flanged shape is used as a 7-m long column. The column is supported in the x-direction at base A and pinned at ends A and C against translation in the y and z directions. A lateral support is provided to the column so that deflection in x − z plane is restrained at mid-height B; however, the column is free to deflect in x − y plane at B. Determine the maximum compressive load P the column can support if a factor of safety is 2.5 is required. In your analysis, consider the possibility that buckling could occur about either the strong axis (i.e., the z-axis) or the weak axis (i.e., the y-axis) of the aluminium column. Answer: 31.56 kN x 100 3.5 m C [mm] z B 3.5 m 152 z 9 5 A y DUT: Mech. Eng. 1 SMTL301 Buckling Problem 3. Columns AB and CD have pinned ends, are made of an aluminium alloy (E = 72.0 GPa), and have equal rectangular cross sections of 20 mm by 30 mm. Determine the magnitude of P that will first cause one of the columns to buckle. Assume elastic conditions. Answer: 9.47 kN. F A B G [mm] 600 500 P C 1000 1000 500 D Problem 4. Determine the maximum intensity w of the uniform distributed load that can be applied on the beam without causing the compressive members of the supporting truss to buckle. The members of the truss are made of steel tubes having 60 mm outside diameter and 5 mm thickness. The modulus of elasticity of steel is 210 GP a. Use a factor of safety 2 against buckling. Answer: 2.52 kN. w A D C 2m DUT: Mech. Eng. 3.6m 2 1.5m B SMTL301 Buckling Problem 5. A pin-jointed steel truss (E = 200GP a) is constructed of rectangular steel tubes of 40mm × 20mm and thickness 3mm. Using a safety factor Sf = 2 determine the maximum load Pallow that can be applied without buckling of any bar. Answer: 6.67 kN. P C 2m 11 00 00 11 00 11 00 11 00 11 00 11 00 11 00 11 40mm 3mm 20mm B A D 1m 1m Problem 6. The plane truss shown in the figure supports a load W . Each member is a slender circular pipe (E = 180 GPa) with an outside diameter of 60 mm and wall thickness of 4 mm. The truss is restrained against displacement perpendicular to the plane of the truss. Determine the allowable value of load Wallow which can be safely applied without buckling of any member. A safety factor of 1.5 is to be used. Assume that all joints are pinned. Answer: 14.72 kN. W D 2m E B C A 3m DUT: Mech. Eng. 2m 3 3m SMTL301 Buckling Problem 7. The figure below shows two (E = 200GP a) bars of a diameter d = 10mm on which a force F = 6kN is applied. Bars AP and BP have lengths LAP = 400mm and LBP = 600mm. The joint P can only move vertically. Determine the factor of safety for the assembly if the buckling to be avoided in the structure. Answer: 1. B 60◦ P 30◦ A F=6kN Problem 8. A pin-jointed truss (E = 200 GPa) is constructed of circular tubes of 50 mm external diameter and thickness 4 mm. Determine the maximum load Wallow that can be applied without buckling of any member. Use a safety factor of 2.5. Answer: 8.78 kN. 4m 4m D 30◦ 4m E W 60◦ F C 4m A B G DUT: Mech. Eng. 4