Calculating Reactions in 4-Reaction Beam

[bumfluff]

If you have a beam with 4 reaction forces, how do you calculate the load taken by each reaction? It occurs to me that you cannot simply take moments about one point so what is the method you can use to find the reactions? I made one example where the beam was symmetrical so I tried equating it to a beam supported at two points but it seems to me that the way I did this would not work for a beam where there is no symmetry.

 

[Meir Achuz]

A beam with four (even with three) forces is said to be "statically indeterminate" because there are 4 unknowns and only two equations. In order to get an answer you have to make some assumption about the elastic properties of either the beam or the strings supporting it.

 

[bumfluff]

Would you be able to elaborate on the the assumptions of elastic properties that you would have to make?

 

[Meir Achuz]

As an example: If the bar is suspended from four identical springs, such that F=kx, where x is the extension in length of the spring, you can get an equation for the forces in terms of the distance the beam drops, and the angle it makes with the horizontal. This could be solved for the four forces. It is not easy.