Indeterminate static beam loading

[Wesley]

Hello

I am creating a torsional testing rig for a Formula Sae car, the front of the car will be pivoted about the center on a beam with the loading off to one side. In the design I need to calculate the deflection of the beam in order to determine which material and what profile of metal will be most cost effective however my deflection equations appear to be statically indeterminate. Below is a free body diagram

My problem is when I arrive at the equation for deflection I have two integration constants but only one initial condition saying that the deflection is 0 at the pivot. Is there a way to solve this or is there a conservative approximate that will yield satisfactory results?

image url: http://imgur.com/n45Wyhw

 

[SteamKing]

You could also make the slope at the pivot = 0. It's not entirely clear how this rig tests the torsional rigidity of your car, though.

 

[Wesley]

So the back of the car will be held rigidly by 2 supports clamped down and the front will be held by this beam on supports that raise off of it to the hubs or the frame (universal design). In the middle of the beam where I have the pivot will be a piece of angle iron and on the far left weight will be applied to add a torsional force to the frame.

When doing the analysis I was unsure if I could say the slope is zero at the pivot I thought that was only for a cantiliver end. I know I can say the bending momment is zero however that doesn't help me.

 

[SteamKing]

A beam on one support is not indeterminate. It is kinematically unstable.

 

[Wesley]

knowing that this beam is kinematically unstable is there any way to find the constants?