The maximum elastic deflection on a beam supported by two simple supports, loaded at a distance ${\displaystyle a}$ from the closest support, is given by:

${\displaystyle \delta _{max}={\frac {Fa(L^{2}-a^{2})^{3/2}}{9{\sqrt {3}}LEI}}}$

where

${\displaystyle F}$ = force acting on the beam

${\displaystyle L}$ = length of the beam between the supports

${\displaystyle E}$ = modulus of elasticity

${\displaystyle I}$ = area moment of inertia of cross-section

${\displaystyle a}$ = distance from the load to the closest support

This maximum deflection occurs at a distance ${\displaystyle x_{1}}$ from the closest support and is given by:

${\displaystyle x_{1}={\sqrt {\frac {L^{2}-a^{2}}{3}}}}$