As a physics student, I never came across the following problem:(adsbygoogle = window.adsbygoogle || []).push({});

A uniform beam of mass M and length L rests on three identical supports: one at each end of the beam and one in the middle. What are the forces of reaction on each of the supports?

I now realise that that was the case because this system is statically intederminate in the sense that we have too few equations of equlibrium to solve for the three unknowns. But, surely the problem must have a unique solution. So, how would one solve this (in principle, very simple) problem?

1) One option is symmetry - since the supports are placed symmetrically, each would carry equal weight. That means that the reaction force is Mg/3 for each support.

2) Or, one can divide the beam into two equal parts by (imaginary) cutting it in the middle. Then the problem is solvable and gives Mg/2 for the middle support and Mg/4 for the each of the outer supports.

3) I'm guessing that the correct answer is something else, so please, enlighten me :)

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# Understanding statically indeterminate beams

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