I'm trying to refresh my mechanics by solving some fairly simple, self invented, beam problems. This goes fine, but I can't figure out how to solve the following one.. it sounds simple enough, though..(adsbygoogle = window.adsbygoogle || []).push({});

Imagine a (two dimensional) beam of size d with a vertical outside distributed constant downward force acting on it (for instance gravity).

It is supported by four points that can exert a vertical force on the beam, to keep it in balance. They are placed completely symmetrical: two of them at the outsides of the beam and two at a distance, for instance, d/10 away from the center of the beam. Their forces can be named Va,Vb,Vc,Vd or something. When i use the symmetric properties I can reduce the number of unknowns to two, but then I'm stuck. I can use Sum_verticals=0 and Sum_Moments=0, but they both give the same relation between the two unknowns that are left over.

Is there a fundamental reason why this cannot be solved this way? Does the outcome mean that there is in fact one degree of freedom left? This does not sound very physical, as I can imagine that the forces exerted by the points on the beam will always be the same in a true situation.

Could anyone help me on this one? I'm probably making some very stupid mistakes.

Thanks!

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# Simple (?) beam problem

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