验证例题53.pdf

1Example 53 Title Buckling analyses of a column Description Determine the buckling modes and the corresponding critical loads of a column subjected to a vertical load with various boundary conditions.Structural geometry and boundary conditions Verification Example 2Model Analysis Type Buckling analysis Unit System m,tonf Dimension Length 15 m Element Beam element and plate element(Thick type)Material Modulus of elasticity E=10000 tonf/m2 Section Property Beam element Solid rectangular 0.25 0.25 m Plate element Thickness 0.25m Boundary Condition Case 1:The top end is a roller and the bottom is a pin support.Case 2:The top end is free and the bottom is a fixed support.Case 3:Lateral displacement and rotational displacement of the top end are constrained and the bottom is a fixed support.Case 4:The top end is a roller and the bottom is a fixed support.Example 53 3Results Buckling Analysis Results Case 1:The top end is a roller and the bottom is a pin support.beam element model plate element model Case 2:The top end is free and the bottom is a fixed support.Beam element model Plate element model Verification Example 4 Case 3:Lateral and rotational displacement of the top end are constrained and the bottom is a fixed support Beam element model Plate element model Case 4:The top end is a roller and the bottom is a fixed support.Beam element Plate element Example 53 5Comparison of Results Unit:tonf Critical load for 1st buckling MIDAS/Gen Case Theoretical Beam element Plate element 1 0.5712 0.5708 0.5712 2 0.1428 0.1428 0.1428 3 2.2846 2.2796 2.2846 4 1.1684 1.1670 1.1684 Critical load :Load applied in the Load Case Eigenvalue Case 1:Pcr=22LEI Case 2:Pcr=224LEI Case 3:Pcr=224LEI Case 4:Pcr=22046.2LEI Reference Gere&Timoshenko“Mechanics of Materials”Chapter 11