Static Equilibrium for a Plate with Support at Three Points

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A plate of negligible mass has a load force on top of a flat plate supported by three vertical columns, assumed to be welded to the plate. This Demonstration computes the compression or tension in each column in the free body diagram (FBD). Click the "equivalent center" button to find the location of the load force so that the three columns provide equal support.

Contributed by: Frederick Wu (July 2010)
Open content licensed under CC BY-NC-SA



As shown in the FBD, the forces holding the plate in equilibrium are described by a system of three independent equilibrium equations ( and ). Because there are also three unknowns for the supporting force, the problem can be solved.

Snapshot 1: the load force is inside the triangle; the three columns are load-bearing with compression

Snapshot 2: the load force is outside the triangle; two columns are load-bearing with compression, one column holds the plate by downward tension

Snapshot 3: the load force is on the equivalent center; the three columns are load-bearing with equivalent compressions

Engineers can select the position of the load force to determine the forces exerted by the three columns.


A. Pytel and J. Kiusalaas, Engineering Mechanics: Statics, 2nd ed., Beijing: Tsinghua & Thomson, 2001, pp. 209, 227–228.

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