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The maximum elastic deflection on a beam supported by two simple supports, loaded at a distance from the closest support, is given by: [1] = / where F {\displaystyle F} = force acting on the beam L {\displaystyle L} = length of the beam between the supports
Another way to remember this is if the moment is bending the beam into a "smile" then the moment is positive, with compression at the top of the beam and tension on the bottom. [1] Normal positive shear force convention (left) and normal bending moment convention (right). This convention was selected to simplify the analysis of beams.
The actual approach appears to have been developed by Clebsch in 1862. [2] Macaulay's method has been generalized for Euler-Bernoulli beams with axial compression, [3] to Timoshenko beams, [4] to elastic foundations, [5] and to problems in which the bending and shear stiffness changes discontinuously in a beam. [6]
The moment-area theorem is an engineering tool to derive the slope, rotation and deflection of beams and frames. This theorem was developed by Mohr and later stated namely by Charles Ezra Greene in 1873.
(0) real beam, (1) shear and moment, (2) conjugate beam, (3) slope and displacement The conjugate-beam methods is an engineering method to derive the slope and displacement of a beam. A conjugate beam is defined as an imaginary beam with the same dimensions (length) as that of the original beam but load at any point on the conjugate beam is ...
Euler–Bernoulli beam theory can also be extended to the analysis of curved beams, beam buckling, composite beams, and geometrically nonlinear beam deflection. Euler–Bernoulli beam theory does not account for the effects of transverse shear strain. As a result, it underpredicts deflections and overpredicts natural frequencies. For thin beams ...
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In engineering, beams are of several types: [2] Simply supported – a beam supported on the ends which are free to rotate and have no moment resistance. Fixed or encastré (encastrated) – a beam supported on both ends and restrained from rotation. Overhanging – a simple beam extending beyond its support on one end.