Forces in Structures

If a beam or rod is uniform its mass is evenly distributed so that it is the same as if all the mass was concentrated at a single point at the centre of the beam. The weight is the force acting vertically downwards from this point.

The resultant force and resultant moment both have to be zero for the structure to be stable.

The resultant force and resultant moment at any point in a stable structure are both zero. Either of these principles can be used to find the values of forces F1 and F2 in the ropes that support the beam shown in the diagram below.

• Both F1 and F2 could be found by resolving the vertical components of all the forces (which must balance) and the horizontal components of all the forces (which must also balance).
• Since F1 does not have a moment about A, taking moments about this point gives a relationship between F2 and the forces we know.
• Similarly, taking moments about B gives a relationship between F1 and the known forces.

Resolving horizontal and vertical components will always give the same answers as taking moments.

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