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The cantilever method is an approximate method for calculating shear forces and moments developed in beams and columns of a frame or structure due to lateral loads. The applied lateral loads typically include wind loads and earthquake loads, which must be taken into consideration while designing buildings.
The starting point is the relation from Euler-Bernoulli beam theory = Where is the deflection and is the bending moment. This equation [7] is simpler than the fourth-order beam equation and can be integrated twice to find if the value of as a function of is known.
The stress due to shear force is maximum along the neutral axis of the beam (when the width of the beam, t, is constant along the cross section of the beam; otherwise an integral involving the first moment and the beam's width needs to be evaluated for the particular cross section), and the maximum tensile stress is at either the top or bottom ...
(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 ...
The property of remaining a constant length under load has been made use of in length metrology. When metal bars were developed as physical standards for length measures, they were calibrated as marks made on a length measured along the neutral plane. This avoided the minuscule changes in length, owing to the bar sagging under its own weight.
Like other structural elements, a cantilever can be formed as a beam, plate, truss, or slab. When subjected to a structural load at its far, unsupported end, the cantilever carries the load to the support where it applies a shear stress and a bending moment. [1] Cantilever construction allows overhanging structures without additional support.
Figure 1: (a) This simple supported beam is shown with a unit load placed a distance x from the left end. Its influence lines for four different functions: (b) the reaction at the left support (denoted A), (c) the reaction at the right support (denoted C), (d) one for shear at a point B along the beam, and (e) one for moment also at point B. Figure 2: The change in Bending Moment in a ...
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