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HYPERSTATIC OR STATICALLY INDETERMINATE STRUCTURES
THE ENERGY THEOREMS OF STRUCTURAL ANALYSIS
GENERAL THEOREMS FOR LINEAR ELASTIC STRUCTURES
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analysis applied loads arch axial forces axial load behaviour bending moment diagram Betti's Theorem calculations cantilever carry-over Castigliano's Theorem Chapter coefficients column complementary energy components compression continuous beam contraflexure convenient corresponding critical load cross-section deflected deflexion direction distortion distribution effect elastic centre Engineering equal equilibrium equations example external loads fixed end moments frame of FIGURE framework give given Hardy Cross Hence Hooke's Law horizontal hyperstatic structures influence line linear matrix method Mohr's Equation non-linear obtained pin-jointed pinned plastic hinge portal frame position potential energy primary structure principle of virtual problem redundant member rigidly jointed rotation Section shearing force shearing stress shown in FIGURE shows simply-supported beam slope-deflexion solution solved space frames span statically determinate stiffness strain energy stress strut sway equation symmetrical TABLE thrust truss unit load vector virtual displacements zero