验证例题52.pdf

1Example 52 Title P-Delta effect analysis of a portal frame.Description Shown below is a 2-D,one story,one bay,portal frame supported at the base subjected to a symmetric load and an eccentric load separately.Compare the displacements,shear forces and bending moments between the results based on a P-Delta effect analysis and a conventional frame analysis.Structural geometry and analysis model 2Model Analysis Type 2-D P-Delta analysis Unit System in,lbf Dimension Height H=100.0 in Width B=100.0 in Relative displacement tolerance 0.001 Element Beam element Material Modulus of elasticity E=29 106 psi Section Property Area A =1.0 in2 Moment of inertia Iyy=1/12 in4 Boundary Condition Nodes 1,3,5 and 7;Constrain all DOFs.Analysis Case Case 1;A symmetric load,1000 lbf is applied to the mid-point of the element in the-Z direction.Case 2;An eccentric load,1000 lbf is applied to the first quarter point of the element in the-Z direction.Maximum number of iteration for the P-Delta effect analysis=5 Example 52 3Results Displacements(P-Delta effect analysis EX52-1)Member Forces(P-Delta effect analysis-EX52-1)4 Displacements(Conventional analysis EX52-2)Member Forces(Conventional analysis-EX52-2)Example 52 5 Bending moment diagram of the structure(P-Delta effect analysis)Bending moment diagram of the structure(Conventional analysis)6Comparison of Results Symmetric Load Case Unit:rad,lbf-in,lbf P-Delta effect analysis Conventional analysis Result Theoretical SAP2000MIDAS/Gen TheoreticalSAP2000 MIDAS/Gen Rotational displacement(2)0.091920.09178 0.091790.08620 0.08620 0.08621Moment(M12)4606.64589.14588.94166.7 4166.7 4166.5Moment(M21)8254.08260.48260.38333.3 8333.3 8333.2Shear force(F)128.6128.5128.5125.0 125.0 125.0 Eccentric Load Case Unit:rad,lbf-in,lbf P-Delta effect analysis Conventional analysis Result TheoreticalSAP2000MIDAS/Gen TheoreticalSAP2000 MIDAS/Gen Lateral displacement()1.893 1.8941.8931.385 1.385 1.385Rotational displacement(6)0.1013 0.10140.10140.0924 0.0924 0.0924Rotational displacement(8)0.0367 0.03670.03670.0369 0.0369 0.0370Moment(M21)2544.9 2550.92551.22455.4 2455.4 2455.6Moment(M21)6088.6 6183.66183.46919.6 6919.6 6919.2Moment(M21)4456.9 4503.54502.83794.6 3794.6 3794.1Moment(M21)6153.0 6124.96125.05580.4 5580.4 5580.7Shear force(F)101.4 101.6101.693.75 93.75 93.75 Example 52 7References Livesley,R.K.,and Chandler,D.B.,“Stability Functions for Structural Frameworks”,Manchester University Press,UK,1956.“SAP90,A Series of Computer Programs for the Finite Element Analysis of Structures,Structural Analysis Verification Manual”,Computer and Structures,Inc.,1992,Example 27.