验证例题07.pdf

1Example 7 Title Beam with elastic supports and an internal hinge Description Determine the displacements of a structure subjected to two concentrated loads.Structural geometry and analysis model 2Model Analysis Type 2-D static analysis (X-Z plane)Unit System ft,kip Dimension Length 54 ft Height 12 ft Element Beam element Material Modulus of elasticity E =4.32 106 ksf Section Property Elements and -Area A =0.125 ft2 Moment of inertia Iyy =0.263 ft4 Element -Area A =0.175 ft2 Moment of inertia Iyy =0.193 ft4 Boundary Condition Node 2 ;Constrain all DOFs.Nodes 1 and 4 ;Spring constant(Z direction),K=1200 kips/ft Release Ry of the node 3 of the element in the element local coordinates.Load Cases A concentrated load,P1=5 kips is applied to the mid-point of the element in the X direction.A concentrated load,P2=15 kips is applied to the mid-point of the element in the-Z direction.Example 60 3Results Displacements Comparison of Results Unit:ft,rad X-displacement,X(10-3)Z-displacement,Z(10-3)Y-rotational,Y(10-3)Node TheoreticalSAP2000 MIDAS/Gen TheoreticalSAP2000MIDAS/Gen Theoretical SAP2000 MIDAS/Gen 1 1.079 1.079 1.079 1.787 1.787 1.787-0.099-0.099-0.0993 1.079 1.079 1.079-0.180-0.180-0.1800.444 0.444 0.444 4 1.079 1.079 1.079-4.820-4.820-4.820-0.362-0.361-0.361 Reference Beaufait F.W.,et al.,“Computer Methods of Structural Analysis”,Prentice-Hall,Inc.,New Jersey,1970,pp.197210.