验证例题46.pdf

1Example 46 Title Dynamic modal response for 2-D rigid frame Description Perform a time history analysis of a structure under lateral dynamic loads.Calculate the natural frequencies,the maximum displacement and the corresponding time.Verification Example 2 Structural geometry and analysis model Example 46 3Model Analysis Type 2-D time history analysis Unit System in,lbf Dimension Length L =360 in Level height H1(1st)=180 in H2(2nd)=120 in Mass M1(1st)=136 lbf sec2/in(in the Y direction)M2(2nd)=66 lbf sec2/in(in the Y direction)Analysis time t =0.2 sec Time step t =0.001 sec Element Beam Element Material Modulus of elasticity E=30 106 psi Section Property Columns (1st floor)Moment of inertia Iyy=248.6 in4 Columns (2nd floor)Moment of inertia Iyy=106.3 in4 Beams Moment of inertia Iyy=1.0 1015 in4(Rigid)Boundary Condition Nodes 1 and 2;Constrain all DOFs.Nodes 3 6;Constrain Dz and Rx.(Only Dy allowed)Nodes 7 and 8;Constrain Dy of all nodes at each floor to these nodes.(Master nodes)Verification Example 4Analysis Case Impulse loads are applied in the Y direction.1st floor ;P1(t)=10000(1-t/td)lbf(td=0.1)2nd floor ;P2(t)=20000(1-t/td)lbf(td=0.1)Number of natural frequencies to be computed=2 Results Eigenvalue Analysis Results Displacements Example 46 5Displacements Y-displacements at the node 3 Y-displacements at the node 5 Verification Example 6Comparison of Results Natural Frequencies Unit:Hz Result Ref.1 SAP2000 MIDAS/Gen 1st mode11.8 11.8 11.8 Natural frequency 2nd mode32.9 32.9 32.9 Maximum Displacements Unit:sec,in Time at which the maximum displacement occurrs(t)Maximum displacement(Y,max)Node SAP2000 MIDAS/Gen SAP2000 MIDAS/Gen 3 0.171 0.171 0.673 0.673 5 0.123 0.123 0.674 0.674 References Paz,Mario,“Structural Dynamics;Theory and Computation”,3rd Edition,Van Nostrand Reinhold,New York,1991,Example 11-1.“SAP90,A Series of Computer Programs for the Finite Element Analysis of Structures,Structural Analysis Verification Manual”,Computer and Structures,Inc.,1992.Example 46 7Time History Loading Data (a)Time history loads applied at the 1st floor (b)Time history loads applied at the 2nd floor