HW #6 SOL

SOLUTION to HOMEWORK 6, MECH101 Spring 2009- 1 -

SOLUTION to HOMEWORK 6, MECH101 Spring 2009Downwards16-47. The W610 ∞ 155 beam is made of A-36 steel and issubjected to the loading shown. Determine the displacementat its end A. E = 210 GPa.Solution- 2 -

SOLUTION to HOMEWORK 6, MECH101 Spring 2009Elastic Curve : The elastic curves for the uniform distributed load and concentrated load are drawnseparately as shown.Method of Superposition : Using the table in Appendix C, the required displacements are16-57. The beam is used to support the 20-kN loading. Determinethe reactions at the supports. Assume A is fixed and B is a roller.SolutionSupport Reactions: FBDMethod of Superposition: Using the table in Appendix C, therequired displacements are:The compatibility condition requires- 3 -

SOLUTION to HOMEWORK 6, MECH101 Spring 200916-58. The beam has a constant E1I1 and is supported by thefixed wall at B and the rod AC. If the rod has a cross-sectionalarea A2 and the material has a modulus of elasticity E2,determine the force in the rod.SolutionBy superposition:.SolutionSupport reactions:(1)Method of superposition: Using the table in Appendix C, therequired displacements are:The compatibility condition requires:Substituting By into equation (1), yields:- 4 -

SOLUTION to HOMEWORK 6, MECH101 Spring 200917-1. Determine the critical bucking load for the column. The material can beassumed rigid.SolutionRequire:17-5. The aircraft link is made from an A-36 steel rod.Determine the smallest diameter of the rod, to the nearest mm,that will support the load of 4 kN without buckling. The endsare pin connected. E = 210 GPa, σ Y = 250 MPa.Solutiond = 7.71mm. use d = 8mm, check:Therefore, Euler’s formula is valid..17-31. The A-36 steel bar AB has a square cross section. If it ispin-connected at its ends, determine the maximum allowableload P that can be applied to the frame. Use a factor of safetywith respect to buckling of 2. E = 210 GPa, σ Y = 250 MPa.SolutionBuckling load:,- 5 -

SOLUTION to HOMEWORK 6, MECH101 Spring 2009Check:17-33. Determine if the frame can support a load ofw = 6 kN/m if the factor of safety with respect to buckling ofmember AB is 3. Assume that AB is made of steel and ispinned at its ends for x–y axis buckling and fixed at its ends fory–y axis buckling E st = 200 GPa, σ Y = 360 MPa.SolutionCheck x-x axis buckling:Therefore, AB will buckle and the frame can NOT support the loading.- 6 -