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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.
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
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.
For live loads (any load that moves during the life of the structure, such as furniture and people), it becomes much harder to predict where the loads will be or how concentrated or distributed they will be throughout the life of the structure. Influence lines graph the response of a beam or truss as a unit load travels across it.
The two cases with distributed loads can be derived from the case with concentrated load by integration. For example, when a uniformly distributed load of intensity is acting on a beam, then an infinitely small part distance apart from the left end of this beam can be seen as being under a concentrated load of magnitude .
Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) [1] is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams. It covers the case corresponding to small deflections of a beam that
Concentrated load of magnitude = acts at a distance = from the support A. Uniform load of intensity q = 1 k N / m {\displaystyle q=1\ kN/m} acts on BC. Member CD is loaded at its midspan with a concentrated load of magnitude P = 10 k N {\displaystyle P=10\ kN} .
If there are only concentrated loads on the structure, the problem will be easy to draw M/EI diagram which will results a series of triangular shapes. If there are mixed with distributed loads and concentrated, the moment diagram (M/EI) will results parabolic curves, cubic, etc.
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