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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.
A cantilever is a rigid structural element that extends horizontally and is unsupported at one end. Typically it extends from a flat vertical surface such as a wall, to which it must be firmly attached. Like other structural elements, a cantilever can be formed as a beam, plate, truss, or slab.
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 ...
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
Strength depends upon material properties. The strength of a material depends on its capacity to withstand axial stress, shear stress, bending, and torsion.The strength of a material is measured in force per unit area (newtons per square millimetre or N/mm², or the equivalent megapascals or MPa in the SI system and often pounds per square inch psi in the United States Customary Units system).
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.
A cantilever Timoshenko beam under a point load at the free end For a cantilever beam , one boundary is clamped while the other is free. Let us use a right handed coordinate system where the x {\displaystyle x} direction is positive towards right and the z {\displaystyle z} direction is positive upward.
Span is a significant factor in finding the strength and size of a beam as it determines the maximum bending moment and deflection. The maximum bending moment M m a x {\displaystyle M_{max}} and deflection δ m a x {\displaystyle \delta _{max}} in the pictured beam is found using: [ 2 ]