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# Mass On Multiple Spring Supports

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Mechanics Corner

A Journal of Applied Mechanics and Mathematics by DrD, #48

Mass On Multiple Spring Supports

Introduction

One of the classic problems of elementary mechanics is to determine the load on each leg of a four-legged table. The table top is assumed to be a uniform rectangle, the legs are of equal length, the center of mass is the centroid of the table top, and the floor is level. What is the load in each of the legs?

With 381 views, no one has seen anything worth commenting on. Wow!! So all of you already knew this? Or perhaps you thought this was not a significant problem?

DrD

Hello,

in some cases you may circumvent the problem of solving a statically indeterminate system, if symmetry exists. In the ideal case of a table you have quarter symmetry, what makes it easy, to determine the leg forces. However, you have to be able to identify existing symmetry. In other cases solving the problem may be simplified by the existence of some guiding equipment.

Regards

Alban

Dear Alban,

Absolute symmetry is truly rare. Consider the case of a table on four legs of equal length. By your argument, all four legs each carry 1/4 of the total weight. Everything is perfect, the floor is level, the table is flat, the legs are all equally long. But now enter a tiny bit of reality (ever so slightly!). One of the legs is short by 0.0001 mm. To the eye, it appears that perfect symmetry still exists, but in actual fact, one of the four legs no even longer touches the floor. Do you still think that each leg in contact with the floor carries only 1/4 of the weight? What holds up the remaining quarter of the weight?

DrD

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