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a2 cos a3 a2 sin a3 analysis applied approximate method assumed cantilever Castigliano's Castigliano's method changes in length Chapter complementary energy complementary-energy method components of deflection conditions of equilibrium conservation of energy conservative systems considered cos2 cosa2 degrees of freedom derived due to unit elt e2 energy methods equation of virtual equations of equilibrium example flexibility coefficients follows force F forces Tl Fv and FH geometrical Hooke's law law of conservation line of action linear elastic system linear systems load Fv load-deflection characteristics pin-jointed position of equilibrium potential energy potential-energy method principle of virtual reciprocal theorem redundant member redundant system respectively shown in fig simultaneous equations sin2 sina2 sinatcosa2 small displacement spring stable equilibrium statically statically-determinate system stationary stiffness coefficients strain energy strain-energy method structure Substitution from equations system of forces system shown tions variables vertical vertical deflection virtual displacements equal