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15 kips 20 kips applied loads assumed axial force axis beam structure bending bridge cantilever Celestial Software chord column concentrated load conjugate beam constant continuous beam contraflexure defined deformations determine diagonal direction disk displacement distributed load elastic curve engineering equilibrium equations Example factor FEMs Figure fixed-end frame ft 10 ft geometry girder global hinge horizontal IMAGES-2D impact factor influence line internal kip ft kipsT linear elastic live loads maximum member forces Menu method midspan moment-area nodal plane positive primary structure prismatic Prob radians reaction components redundant forces restraint roller rotation shear shown in Fig sidesway sign convention simple beam slope deflection solution solved span statically indeterminate stiffness matrix structural analysis superposition support reactions symmetric theorem tion truss member U.S. Customary Units uniform load unit load unknown vertical virtual zero