Abstract
A weight is placed on the top of a rectangular rigid ideal table with four legs, each leg is placed at each vertex of the rectangular table. It is assumed that the legs do not bend when the weight is added. The reactions are computed by assuming the table is supported on a beam, introducing two new beam parameters and minimizing a deflection function of the new parameters. A physical experiment is performed in the lab and the reactions on each leg are provided. The experimental results match the theoretical ones obtained by the proposed model. Geometrical interpretations of the results are given.
Highlights
Euler [1] set a problem in St
The problem consisted of placing a weight on the surface of a rectangular table supported on four legs and determining the four reaction forces of the legs
Reaction forces were measured by digital scales affixed to the corners of the plate
Summary
Euler [1] set a problem in St. Petersburg Academy of Sciences in 1773 in his dissertation De pressione ponderis in planum cui incumbit. Euler claimed that the solution to this problem “is much harder and doubtful and misleading” He said that the imperfections of the feet might force the body to rest on only three legs and the pressure on the fourth one may be null. This linear system of equations is called an indeterminate system
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