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Chapter 10 Statically Indeterminate Beams

1 Chapter 10 Statically Indeterminate Beams Introduction in this Chapter we will analyze the beam in which the number of reactions exceed the number of independent equations of equilibrium integration of the differential equation, method of superposition compatibility equation (consistence of deformation) Types of Statically Indeterminate Beams the number of reactions in excess of the number of equilibrium equations is called the degree of static indeterminacy 2 the excess reactions are called static redundants the structure that remains when the redundants are released is called released structure or the primary structure Analysis by the Differential Equations of the Deflection Curve EIv" = M EIv'"

2. establish the force-displacement relations 3. consistence of deformation (compatibility equation) consider a propped cantilever beam (i) select RB as the redundant, then qL2 RA = qL - RB MA = CC - RBL 2 force-displacement relation qL4 BR L 3 ( B)1 = CC ( B)2 = CC 8EI 3EI compatibility equation B = ( B)1 - ( B)1 = 0 qL4 R BL 3 CC = CC 8EI 3EI

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