Question

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

Answer 1

`\Delta _(max)=(5wL^4)/(384EI)`

Step-by-step 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=(wx)/(24EI)(L^3-2Lx^2+x^3)`

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

`\Delta _(max)=(w* (L)/(2))/(24EI)(L^3-2L* \left ((L)/(2)\right)^2+\left((L)/(2)\right)^3)`

`\Delta _(max)=(5wL^4)/(384EI)`