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The Problem of Structural Analysis
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antisymmetric applied load axial bending moment diagram calculated cantilever carry-over factors column compatibility equations deflected shape deformations degrees of freedom displacement method displacement system distribution factors elastic centre elastic structure elements equilibrium equations example external fixed-end moments flexibility and stiffness flexibility matrix force method force system forces and displacements frame structure free body Free body diagrams Hardy Cross Hence horizontal indeterminate initial-sway moments internal forces joint kinematic linear linearly elastic member forces moment-sway equation no-sway nodal displacements nodes obtained pin-jointed truss point-directions portal frame principle of virtual problem reaction redundant forces section stiffness shear force shown in fig sign convention simply supported slope slope-deflection equations solution solved statically determinate structure stiffness and carry-over stiffness factors strain energy structural analysis structure of fig superposition symmetric Table transverse uniform beam unit displacement vector vertical vertical deflection virtual displacements virtual forces written zero