How many of the following cases are improperly constrained? 1. Parallel forces 2. Concurrent forces 3. Perpendicular forces 4. Only moment

Asked in SSC JE 24/01/2018 (Morning)

Detailed Explanation

A body is improperly constrained when it has enough reactions in number, but they are arranged so that some movement is still possible.

Why “2” Is Correct

Parallel reactions cannot resist a force at right angles to them — the body slides. Improperly constrained.
Concurrent reactions cannot resist a moment about their common point — the body rotates. Improperly constrained.
Perpendicular reactions (in two directions, not all through one point) can resist forces in both directions and, with a third, rotation as well — this is a normal proper arrangement.
‘Only moment’ is not one of the two classic improper arrangements.

So 2 cases (parallel and concurrent) are improperly constrained.

Force systems in a plane. Concurrent: lines of action meet at one point — such forces cannot produce a moment about that point. Parallel: lines of action are parallel — such forces cannot resist anything at right angles to them. Non-concurrent, non-parallel: the general case. A set of reactions that is all concurrent or all parallel cannot hold a body in every direction, so the body is improperly constrained.

Why the Other Options Are Wrong

A. 1: Both parallel and concurrent arrangements are improper, not just one.
C. 3: Perpendicular reactions are a proper arrangement.
D. 4: Only parallel and concurrent arrangements are the classic improper cases.

Key Point

Improper constraint: reactions all parallel or all concurrent.

Key Concepts for Students

Improperly constrained bodies are geometrically unstable.
Properly constrained determinate body: 3 reactions, not parallel, not concurrent.
A beam on three rollers is improperly constrained (all reactions parallel).

Practice more: this is question 7 in Force Analysis MCQs – Part 1. Try the whole set and check every answer instantly.