I want to calculate how much a solid bar will flex when force is applied to it. The set up looks like this:
The rod (in green) rests on two stationary points, and the force is applied in the center between the two points. The rod has a rectangular cross section.
What I want to know is the length that the middle of the rod will be moved in the direction of the force. The force can be assumed to be small enough not to deform the rod.
What properties of the material in the rod do I need to know to calculate this?
And how do I do the actual calculation?
Best Answer
It is all explained here if you search simply supported beams.
You will find the equation $$w = \frac{F \ell^3}{48 E I}$$
Here $\ell$ is the distance between the supports, $F$ is the force applied, $E$ is the elastic modulus of the material and $I$ is area moment of the section. Rectangular sections have $I=\frac{1}{12} b h^3$ where $b$ is width and $h$ is height. The caveat here is the use of consistent units. You cannot mix metric with inches with feet.