Slope Defletion Equations

Method of Slope-Deflection Equations belongs to displacement method of analysis for solving indeterminate structures.

When a structure is loaded, specified points on it called nodes will undergo unknown displacements which are known as degrees of freedom. The number of these unknowns is referred to as the degree of kinematic indeterminacy of structure.

The Displacement method requires;

•  the unknown displacements (slope and deflection) to be written in terms of the loads by using the load-displacement relations.

• these equations are solved for the displacement.

• after getting the displacements, the unknown loads are determined from the compatibility equations using the load displacement relations.

In general the Slope-deflection equations for a beam AC (both A and C fixed-ends) can be written as follows;  You are advised to visit solved Problem 7-4 which explains the step-wise and complete application of slope-deflection equations for solving indeterminate structures.

Most of the structures being used in construction are indeterminate in nature. Some of the common methods to solve for indeterminate structures are; method of consistent deformation (compatibility condition), moment distribution method, slope-deflection equations, flexibility method, Energy theorems, stiffness method etc.

You can also use our Moment Distribution Calculator for solving indeterminate beams

Use our Fixed Beam Calculator to determine fixed-end moments for different loading cases.

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