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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.
Shear and moment diagram for a simply supported beam with a concentrated load at mid-span. In solid mechanics, a bending moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend.
The bending moment diagram and the influence line for bending moment at the centre of the left-hand span, B, are shown. In engineering, an influence line graphs the variation of a function (such as the shear, moment etc. felt in a structural member) at a specific point on a beam or truss caused by a unit load placed at any point along the ...
Below is a shear, moment, and deflection diagram. A M/EI diagram is a moment diagram divided by the beam's Young's modulus and moment of inertia. To make use of this comparison we will now consider a beam having the same length as the real beam, but referred here as the "conjugate beam." The conjugate beam is "loaded" with the M/EI diagram ...
The bending moment and the shear force ... direction, a free body diagram of the beam gives us ... from the expressions for the bending moment and shear force, we ...
where is the area moment of inertia of the cross-section, is the cross-sectional area, is the shear modulus, is a shear correction factor, and () is an applied transverse load. For materials with Poisson's ratios ( ν {\displaystyle \nu } ) close to 0.3, the shear correction factor for a rectangular cross-section is approximately
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However, shear force stresses are negligible in comparison to bending moment stresses in all but the stockiest of beams as well as the fact that stress concentrations commonly occur at surfaces, meaning that the maximum stress in a beam is likely to be at the surface.