Skeletal Structures: Matrix Methods of Linear Structural Analysis Using Influence Coefficients |
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INTRODUCTION | 8 |
SOME ELEMENTARY MATRIX OPERATIONS | 16 |
ADJUSTMENT OF AN INVERSE OF A MATRIX | 28 |
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applied loads axial force ball-joint bending moment C.S. diagrams column matrix Complementary Solution complete structure Consider deformations degree of statical degrees of freedom denoted dv₁ end-displacements example a11 flexibility matrix Flexibility Method frame shown given ground node Hence kinematical indeterminacy lack of fit leading diagonal linear Lower triangular matrix LT)(Row m₂ matrix form matrix inversion matrix multiplication member g ments number of members number of nodes number of releases obtained P₂ particular solution pin-jointed plane frame portal frame principal diagonal released structure rigid rotation S₁ settlement of supports shear force shown in Fig simultaneous equations SKELETAL STRUCTURES space frame square matrix statical indeterminacy statically determinate statically indeterminate structure stiffness matrix Stiffness Method stress resultant diagrams structure co-ordinates symmetric symmetric matrix T-Ft t₁ temp Tons total stress resultants truss unit bi-actions v(temp v₁ yields or lack zero