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The moment distribution method is a structural analysis method for statically indeterminate beams and frames developed by Hardy Cross. It was published in 1930 in an ASCE journal. [ 1 ] The method only accounts for flexural effects and ignores axial and shear effects.
Moment redistribution refers to the behavior of statically indeterminate structures that are not completely elastic, but have some reserve plastic capacity. When one location first yields , further application of load to the structure causes the bending moment to redistribute differently from what a purely elastic analysis would suggest.
Shear and Bending moment diagram for a simply supported beam with a concentrated load at mid-span. Shear force and bending moment diagrams are analytical tools used in conjunction with structural analysis to help perform structural design by determining the value of shear forces and bending moments at a given point of a structural element such as a beam.
In engineering and architecture, the Müller-Breslau principle is a method to determine influence lines. [1] The principle states that the influence lines of an action (force or moment) assumes the scaled form of the deflection displacement. OR, This principle states that "ordinate of ILD for a reactive force is given by ordinate of elastic ...
The built-in beams shown in the figure below are statically indeterminate. To determine the stresses and deflections of such beams, the most direct method is to solve the Euler–Bernoulli beam equation with appropriate boundary conditions. But direct analytical solutions of the beam equation are possible only for the simplest cases.
Hardy Cross's description of his method follows: "Moment Distribution. The method of moment distribution is this: Imagine all joints in the structure held so that they cannot rotate and compute the moments at the ends of the members for this condition; at each joint distribute the unbalanced fixed-end moment among the connecting members in ...
The fixed end moments are reaction moments developed in a beam member under certain load conditions with both ends fixed. A beam with both ends fixed is statically indeterminate to the 3rd degree, and any structural analysis method applicable on statically indeterminate beams can be used to calculate the fixed end moments.
Simply supported beam with a single eccentric concentrated load. An illustration of the Macaulay method considers a simply supported beam with a single eccentric concentrated load as shown in the adjacent figure. The first step is to find . The reactions at the supports A and C are determined from the balance of forces and moments as