âComputational Civil Engineering - "Intersections" International Journal

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“Computational Civil Engineering 2005”, International Symposium 205Z is the vector of nodes displacements by the elastic degrees of freedom direction(unknown);D is the vector of nodes displacements in foundations (known);RSGeometric and mechanicStructure dataActionsapplied onstructureelementsActionsapplied onstructuresnodesElement stiffnessmatrixassamblation procedureVector of supportsdisplacementsStructure stiffnessmatrixVector ofcombinated nodesactionsTransformation procedureTranformed stiffnessstructure matrixSolving the ecuations systemusing the Cholesky methodForces on theelement endsDeplacements onthe nodes ofstructureFigure 2. Program algorithm
206 M. Petrina, Roxana BalcKDis the reduced stiffness matrix of the frameKRis a symmetric rectangular matrix. Its elements are representing the reactionsin the structure supports when displacements equal with 1 are introduced on theirdirections.KDRcontains the reactions in the eliminated degrees of freedom, as the effect ofintroducing the displacements equal with 1 on the directions of the structuresupports.KRDcontains the reactions in the structure supports, as the effect of introducingthe displacements equal with 1 on the directions of the elastic degrees of freedom.An important application of the effects superposition principle results inconsidering the exterior load as a sum of two systems of forces each one actingindependently. The final state of efforts and deformations is obtained by summingthe effects. The first loading system consists by the actions directly applied on thestructure beams and it will provide an equivalent set of forces that are acting on theblocked joints of the structure (the reactions from the ends of the loaded beamstaken with the opposite sign).The second system of forces consists of the actions directly applied on thestructure’s joints. Summing the effect of both systems of actions, the vectorof combined actions on the structure joints is obtained.3.3.ExamplesS.L. Chan and P.P.T. Chui have been proposed a program for non-linear analysesof frame structures. In this sections two frames have been analysed with program“CADRE’ and resuls are compared with those obtained by S.L. Chan and P.P.T.Chui computation program.A portal of width 16m, height 6m, was analyzed (with the presented program) withdifferent values of connection stiffness (Fig. 3.). A vertical concentrated force of100kN at beam mid-span loaded the frame and a lateral point load of 10kN isapplied in node.10kN8m100kN8mIb = 21500 cm^4Ab = 76 cm^2Ic = 9460 cm^4Ac = 110 cm^26mKbKbKcKcFigure 3.Structure analysed and idealized structural model
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COMPUTATIONAL CIVIL ENGINEERING2005
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“Computational Civil Engineering.
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A viscoelastic-plastic prediction o
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6 F. Paulet-Crainiceanu, C. Ionescu
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