验证例题41.pdf

1Example 41 Title 3-D,2-story frame structure Description Given is a 3-D,2-story frame structure with rigid diaphragm floors.Calculate the natural periods of the structure.Determine the displacements at each floor.The structure is symmetrical in both directions in plan.The center of gravity at each floor is eccentric from the geometric center.Structural geometry and analysis model 2Model Analysis Type 3-D response spectrum analysis Unit System ft,kip Dimension Length 70 ft Width 50 ft Height 26 ft Floor mass Mx=My=6.21118 kips sec2/ft Damping ratio =0.04(4%)Gravitational acceleration g =32.2 ft/sec2 Response spectrum data(Accelerations with respect to periods)Unit:ft/sec2 Period(sec)0.0 100.0 X acceleration 0.4 0.4 Element Beam element Material Modulus of elasticity Ecolumn =3.5 105 ksf Ebeam =5.0 105 ksf Section Property Columns Area A=4.00 ft2 Moment of inertia Iyy=1.25 ft4(=Izz)Beams Moment of inertia Iyy=2.61 ft4(Strong axis)Example 41 3Boundary Condition Nodes 1 9 ;Constrain all DOFs.Nodes 28,29 ;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.The response spectrum data are applied in the X direction.Number of natural frequencies to be computed=4 Method of Mode Combination SRSS (Square Root of the Sum of the Squares)Results Eigenvalue analysis results Displacement results 4 (a)1st vibration mode (b)2nd vibration mode Vibration modes of the structure Displacements for the structure Example 41 5Comparison of Results Natural Periods Unit:sec Mode of vibration Ref.1 SAP2000 MIDAS/Gen 1st 0.2271 0.2271 0.2271 2nd 0.2156 0.2156 0.2156 3rd 0.0733 0.0733 0.0733 4th 0.0720 0.0720 0.0720 Global X-displacement at the Master Node 29 Unit:ft Node Ref.1 SAP2000 MIDAS/Gen 29 0.0201 0.0201 0.0201 References Peterson,F.E.,“EASE2,Elastic Analysis for Structural Engineering,Example Problem Manual”,Engineering Analysis Corporation,Berkeley,California,1981.“SAP90,A Series of Computer Programs for the Finite Element Analysis of Structures,Structural Analysis Verification Manual”,Computer and Structures,Inc.,1992,Example 3.