The max deflection formula is an equation used to calculate the maximum deflection or displacement of a beam or structure under a load. It takes into account the material properties, geometry of the beam, and the applied load.
The max deflection formula was derived by French mathematician and physicist, Joseph Louis Lagrange, in the 18th century. It was later refined and expanded upon by other scientists and engineers.
The max deflection formula is based on the assumptions of linear-elastic behavior of the material, small deflections, and a constant cross-sectional area throughout the length of the beam.
The max deflection formula was derived using principles of calculus and mechanics, specifically the Euler-Bernoulli beam theory. This theory states that a beam will deform under a load due to bending moments and shear forces, and the resulting deflection can be calculated using the max deflection formula.
The accuracy of the max deflection formula depends on the assumptions made and the complexity of the beam's geometry. In some cases, it may not accurately predict the actual deflection, but it is a useful tool for estimating and designing structures.