Determine the critical buckling load of the member.
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- The 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.A 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.5. Determine the greatest load P the frame will support without causing the A-36 steel member BC to buckle. Due to the forked ends on the member, consider the supports at B and C to act as pins for x-x axis buckling and as fixed supports for y-y axis buckling. Given E = 200 Gpa. -1.2 m- -1.2 m- 0.9 m 75 mm 25 mm Figure 5
- Determine the critical axial buckling load for an 8 3/4 x 12 inches glue-laminated column braced at 10ft from the bottom in the y axis for a total height of 25ft. Assume pin connections at top and bottom. Fc= 1750 psi, E= 1.8x106 psi. (Western cross-section glu-lam data is in the text).A long, slender structural aluminum [E = 69 GPa] flanged shape is used as al = 9.2-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. Lateral support is provided to the column so that deflection in the x-z plane is restrained at mid-height B; however, the column is free to deflect in the x-y plane at B. Assume that b; = 102 mm, d = 122 mm, t; = 8 mm, and tw = 6 mm. Determine the maximum compressive load P the column can support if a factor of safety of 2.9 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 aluminum column. P bf C L d Lateral B bracing LAn aluminum alloy tube with an outside diameter of 3.1 in. and a wall thickness of 0.36 in. is used as a 16-ft-long column. Assume that E = 9300 ksi and that pinned connections are used at each end of the column. Determine the slenderness ratio L/r and the Euler buckling load Per for the column. Answers: L/r= Por= kips
- 3. A steel bolt and nut are tightened around an aluminum sleeve. Find the internal forces as the nut is rotated 1 turn (1 turn = 1.5 mm) given the cross sectional areas and the moduli of elasticity for the steel and the aluminum. AST = 150 mm? EST = 200 GPa EAL = 70 GPa AAL = 100 mm? L=150 mm AST Final 1.5 mm Position Al7 ft 5 ft The assembly shown above includes column AB, which has the following properties: Pinned (top and bottom) for buckling about x-axis Free at top and fixed at bottom for buckling about y-axis Circular cross-section with 8-inch diameter E = 10000 ksi Which of the following is closest to the critical buckling force of column AB? O Per = 269 kip O Per = 1080 kip O Per = 538 kip O Per = 135 kipProblem 6 3-7. A structural member in a nuclear reactor is made of a zirconium alloy. If an axial load of 4 kip is to be supported by the member, determine its required cross-sectional area. Use a factor of safety of 3 relative to yielding. What is the load on the member if it is 3 ft long and its elongation is 0.02 in.? E = 14(10) ksi, y Ez = 57.5 ksi. The material has elastic behavior.
- kips. Determine the Euler Buckling axial compressive load of W 12 x 72 section having a length of L=48 ft and fixed ends, Pe= Assume that the column is made of A441 steel with E = 29 x 103 ksi, and assume that the normal stress generated by P is still within the elastic range of the material. Reminder: use the minimum moment of inertial of the cross section. Please calculate your answer to 1 decimal place. Lft Fixed end Fixed endThe horizontal link BC is 1/4 in. Of thickness and width w = 1.25 in., It is made of steel with an ultimate tensile strength of 65 ksi. What is the factor of safety if the structure shown was designed to support a load P 10 kips?A 900 N axial load (y direction) is applied to the column having 2 m length. The column is made of steel and support details are given below. • Specify the buckling plane (does column buckle in x-y or y-z plane)? • Which dimension of the column should be increased to support the applied load? Determine the amount of improvement/increase? Esteel=200GPA (Hint : Be careful about the support conditions (effective lengths) for different planes) 15mm 15mm front view top view Jide view