Question

What is the deflection equation for a simply supported beam with a uniformly distributed load?

Answer 1

Answer:

$\Delta _{max}=\dfrac{5wL^4}{384EI}$

Explanation:

Given that

Load is uniformly distributed load and beam is simply supported.

Ra + Rb= wL

Ra = Rb =wL / 2

Lets x is measured from left side,then the deflection of beam at any distance x is given as

$\Delta _x=\dfrac{wx}{24EI}(L^3-2Lx^2+x^3)$

The maximum deflection of beam will at   x = L/2 (mid point )

$\Delta _{max}=\dfrac{w\times \dfrac{L}{2}}{24EI}(L^3-2L\times \left (\dfrac{L}{2}\right)^2+\left(\dfrac{L}{2}\right)^3)$

$\Delta _{max}=\dfrac{5wL^4}{384EI}$