验证例题44.pdf

1Example 44 Title Simply supported beam subjected to dynamic loads Description A steel beam is subjected to dynamic loads.Assume that the weight of the beam is negligible.Determine the time at which the maximum deflection occurs and the corresponding bending stresses.2 Structural geometry and analysis model Example 44 3Model Analysis Type 2-D time history analysis Unit System in,lbf Dimension Length L =240 in Mass M =25.9067 lbf sec2/in(in the Z direction)Analysis time t =0.1 sec Time step t =0.001 sec Element Beam element Material Modulus of elasticity E=30 106 psi Section Property Depth H =18.00 in Moment of inertia Iyy=800.6 in4 Boundary Condition Node 1;Constrain Dz.(Roller support)Node 3;Constrain Dy and Dz.(Hinge support)Analysis Case Time step force acts in the Z direction.The time step force data are as follows:Time(sec)Force(lbf)0.000 0 0.075 20000 0.100 20000 4Results Displacements Stresses Example 44 5Z-displacements at the node 2 Comparison of Results Unit:sec,in,psi Result Theoretical SAP2000 MIDAS/GenTime at which the maximum displacement occurs(t)0.092 0.093 0.093 Maximum displacement(z,max)0.331 0.336 0.336 Maximum bending stress(max)18.6 103 18.87 103 18.87 103 References Biggs,J.M.,“Introduction to Structural Dynamics”,McGraw-Hill Book Co.,New York,1964,p.50,Example E.6 Time History Loading Data