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12 tons 20 tons 30 tons ft beam ABC bending moment diagram Calculate cantilever Castigliano's Castigliano's second theorem centre cross-sectional area Deflected beam displacement of point Distribution factors Draw the bending equation Final bending Fixed end moments fixed in position fixed-ended beam force and bending free bending ft Span CD Hardy Cross hinged horizontal displacement horizontal reaction horizontal thrust influence line joint lb ft units left-hand abutment line for bending loaded as shown Loaded beam maximum deflection Maxwell's theorem modulus of elasticity moments of area Mydx parabolic arch pin-jointed point load position and direction redundant member secant Shear force diagram shown in Fig Sinking support Sketch the bending Span CD Mc statically determinate Strain energy due Take area moments take moments tangent tons Fig tons ft Span tons/ft tons/in2 Total strain energy two-hinged arch uniformly distributed load vertical deflection Vertical displacement