Requires ΣF=0 and ΣM=0 in all directions.
For a rigid body in 2D: ΣFx=0, ΣFy=0, ΣM=0 (three equations); in 3D six equations. Choose a moment point that eliminates unknowns. Two-force and three-force members simplify analysis.
A simply supported beam with a central load P has reactions P/2 at each end.
Rigid bodies need both force and moment balance, so forgetting the moment equation gives unsafe designs that look fine on paper.
Requires ΣF=0 and ΣM=0 in all directions.
Rigid bodies need both force and moment balance, so forgetting the moment equation gives unsafe designs that look fine on paper.
Three: horizontal force, vertical force and moment about a point. They are enough to solve three unknown reactions for a determinate body.
The body may be statically indeterminate. Then you need compatibility of deformations, not just equilibrium.
Typical applications include checking a crane boom for both support force and tipping, verifying a platform bracket against rotation and translation and solving a beam with two supports and a point load.
Study "Couples" first (topic 8 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
Count unknowns versus equations. Static determinacy. Check moments about different points.
A simply supported beam with a central load P has reactions P/2 at each end.
The next topic is "Supports and reactions", which builds directly on this one.
It is classed as Beginner in Engineering Mechanics (topic 9 of 106). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.
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