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Equilibrium and Determinate Structures
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array assembled assumed axes backing store basic stiffness beam bending coefficients Cols column Consider coordinates corresponding derived determine direct stiffness method displacement method displacement vector elastic elongation end moments equations of equilibrium equivalent loads Example finite element fixing end forces flexibility matrix hinge integration internal forces joint displacements kinematic matrix kinematic relations load vector LU LU LU LU UJ member deformations member end forces member forces nodal nodes numerical integration obtain oooo ooooooooo plane frame plane stress plastic hinge problem procedure reactive forces redundants rg rg right hand side rotation shape functions shearing shown in Fig solution solving space frame statical statically determinate stiffness matrix stiffness relations strains stresses structural analysis SUBROUTINE transformation UI UI UI UJ LU UJ UJ UJ values variables virtual virtual displacement zero