In one line
A force system is classified by whether the forces lie in one plane and whether their lines of action meet at a point or are parallel.
Explained simply
Think of several people pulling ropes tied to a heavy box. If all ropes are on the floor (one plane) and tied to the same hook, the pulls meet at one point. If they push the box from different spots in the same direction, the pulls are parallel. If some ropes go up to the ceiling, the forces leave the floor plane.
Technically, a force system is a set of forces acting on a body. It is described by (1) the plane of the forces and (2) how their lines of action are arranged.
How it works
- Coplanar: all lines of action lie in one plane. Non-coplanar (space): they do not.
- Collinear: all forces act along one single line (e.g. tug of war).
- Concurrent: lines of action pass through one common point (e.g. forces at a joint of a truss, or a lamp hung by two strings).
- Parallel: lines of action are parallel. Like parallel forces act in the same sense; unlike parallel forces act in opposite senses (e.g. loads on a beam and the support reactions).
- General (non-concurrent, non-parallel): forces neither meet at one point nor are parallel (e.g. forces on a ladder).
- Combining the two ideas gives seven main types: coplanar collinear, coplanar concurrent, coplanar parallel, coplanar general, and the same groups in space (non-coplanar concurrent, parallel, general).
Key formula
| System | Resultant found by |
|---|---|
| Coplanar concurrent | \( \Sigma F_x, \Sigma F_y \) only (no moment) |
| Coplanar parallel | \( \Sigma F \) and \( \Sigma M \) for its position |
| Coplanar general | \( \Sigma F_x, \Sigma F_y, \Sigma M \) |
| Space concurrent | \( \Sigma F_x, \Sigma F_y, \Sigma F_z \) |
Quick example
A ceiling fan hanging from a hook: its weight and the rod tension are collinear. A street light held by two cables meeting at the lamp: coplanar concurrent. A bridge deck with vehicle loads and pier reactions: coplanar parallel. A tripod camera stand: the three leg forces meet at the top but are in different planes, so non-coplanar concurrent.
Common mistakes
- Calling forces 'concurrent' just because they act on the same body; their lines of action must actually meet at one point.
- Forgetting that collinear forces are a special case of both concurrent and parallel systems.
- Treating a space (3D) system as coplanar and ignoring the z-components.
How MU asks it
Usually a 3 to 4-mark short part in Q.1: 'Classify force systems with neat sketches'. For full marks draw one small sketch per type, label lines of action, and give one real example of each. It also helps to state which equations are needed to find the resultant of each type, as in the table above.