Consider The Beam And Loading Shown. Assume That The Flexural Rigidity Ei Of The Beam Is Constant.

In 1915, George A. Maney introduced the slope-deflection method as one of the classical methods of analysis of indeterminate beams and frames. The method accounts for flexural deformations, but ignores axial and shear deformations. Thus, the unknowns in the slope-deflection method of analysis are the rotations and the relative joint displacements. For the determination of the end moments of members at the joint, this method requires the solution of simultaneous equations consisting of rotations, joint displacements, stiffness, and lbrianowens.tvths of members.

You are watching: Consider the beam and loading shown. assume that the flexural rigidity ei of the beam is constant.

11.2 Sign Conventions

An end moment M is considered positive if it tends to rotate the member clockwise and negative if it tends to rotate the member counter-clockwise. The rotation θ of a joint is positive if its tangent turns in a clockwise direction. The rotation of the chord connecting the ends of a member (

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Solving equations 11.1 and 11.2 for βA and βB and substituting them into equations 11.5 and 11.6 suggests the following:

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