验证例题40.pdf

1Example 40 Title 3-D,2-story unsymmetrical structure Description Assume that each floor acts as a rigid diaphragm.Calculate the natural frequencies.Perform a response spectrum analysis.Verification Example 2 Structural geometry and structural analysis model Example 40 3Model Analysis Type 3-D response spectrum analysis Unit System ft,kip Dimension Length 50 ft Width 25 ft Height 25 ft Floor mass Mx =My=3.88 kips sec2/ft Rotational mass moment of inertia Mzz =1011 kips sec2/ft Damping ratio =0.05(5%)Gravitational acceleration g =32.2 ft/sec2 Response spectrum data (Accelerations with respect to periods)Unit:ft/sec2 Period(sec)0.0 0.1 0.125 0.167 0.182 0.200 0.250 0.333 Acceleration 0.400 0.581 0.628 0.787 0.94391.0056 0.7980 0.8806Period(sec)0.431 0.500 0.667 1.000 1.273 2.000 10.00 100.0 Acceleration 0.9212 1.04660.64180.48220.25860.1602 0.0102 0.0 Element Beam element Material Modulus of elasticity E =432000 ksf Section Property Columns Area A =2.25 ft2 Moment of inertia Iyy =0.4219 ft4(=Izz)Beams Moment of inertia Iyy =0.6667 ft4 Verification Example 4Boundary Condition Nodes 1 6 ;Constrain all DOFs.Nodes 19 and 20;Constrain Dx,Dy and Rz of all nodes at each floor to these nodes.(Master nodes)Analysis Case Floor masses are assigned to the master nodes at each floor in the directions of X and Y-axes.Mass moment of inertia about Z-axis is assigned to each master nodes.The response spectrum data act in the direction 30 degrees counterclockwise from the X-axis.Number of natural frequencies to be computed=6 Results Eigenvalue Analysis Results Displacements Example 40 5 (a)1st vibration mode (b)2nd vibration mode (c)3rd vibration mode (d)4th vibration mode (e)5th vibration mode (f)6th vibration mode Vibration modes of the structure Verification Example 6Comparison of Results Unit:sec Natural period Vibration mode SAP2000 MIDAS/Gen 1st 0.4146 0.4146 2nd 0.3753 0.3753 3rd 0.2436 0.2436 4th 0.1148 0.1148 5th 0.1103 0.1103 6th 0.0729 0.0729 Unit:ft Displacement at the master node Node Displacement component SAP2000 MIDAS/Gen X displacement 0.0489 0.0489 Y displacement 0.0341 0.0340 19 Z rotational displacement 0.0003 0.0003 X displacement 0.1060 0.1059 Y displacement 0.0782 0.0782 20 Z-rotational displacement 0.0008 0.0008 Reference “SAP90,A Series of Computer Programs for the Finite Element Analysis of Structures,Structural Analysis Verification Manual”,Computer and Structures,Inc.,1992,Example 8.Example 40 7 Response Spectrum Data