用戶手冊04_驗證手冊驗證例題46_h

1、Example 46TitleDynamic modal response for 2-D rigid frameDescriptionPerform a time history analysis of a structure under lateral dynamic loads.Calculate the natural frequencies, the maximum displacement and the corresponding time.1Verification ExampleStructural geometry and analysis model2Example 46

2、ModelAnalysis Type2-D time history analysisUnit Systemin, lbfDimensionLengthLevel heightL= 360 inH1 (1st ) = 180 in H2 (2nd ) = 120 inM1 (1st ) = 136 lbf sec2/in (in the Y direction)M2 (2nd ) = 66 lbf sec2/in (in the Y direction)MassAnalysis timeTime steptDt= 0.2 sec= 0.001 secElementBeam ElementMat

3、erialModulus of elasticityE = 30 106 psiSection Property Columns (1st floor) Columns (2nd floor) BeamsMoment of inertiaMoment of inertia Moment of inertiaIyy = 248.6 in4 Iyy = 106.3 in4Iyy= 1.0 1015 in4 (Rigid)Boundary ConditionNodes 1 and 2Nodes 3 6Nodes 7 and 8; Constrain all DOFs.; Constrain Dz a

4、nd Rx. (Only Dy allowed); Constrain Dy of all nodes at each floor to these nodes. (Master nodes)3Verification ExampleAnalysis CaseImpulse 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 frequen

5、cies to be computed = 2ResultsEigenvalue Analysis ResultsDisplacements4Example 46DisplacementsY-displacements at the node 3Y-displacements at the node 55Verification ExampleComparison of ResultsNatural FrequenciesUnit : HzResultRef. 1SAP2000MIDAS/GenNatural frequency1st mode2nd mode11.832.911.832.91

6、1.832.9Maximum DisplacementsUnit : sec, inTime at which the maximum displacement occurrs (t)Maximum displacement (dY,max)NodeSAP2000MIDAS/GenSAP2000MIDAS/Gen350.1710.1230.1710.1230.6730.6740.6730.674ReferencesPaz, Mario, “Structural Dynamics ; Theory and Computation”, 3rd Edition, Van NostrandReinhold, 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., 1992.6Example 46Time History L