How many constraints are there in a free-rotation support used in a planar system?

Asked in SSC JE 27/01/2018 (Evening)

Detailed Explanation

A body in a plane has three possible movements (degrees of freedom): sliding in x, sliding in y, and rotating. Each movement a support prevents is one constraint, and gives one reaction.

Why “2” Is Correct

A free-rotation support is a hinge or pin. It holds the point fixed in position — no horizontal and no vertical movement — but lets the member rotate freely. So it has 2 constraints, with reactions R_x and R_y.

Common supports in a planar (2-D) structure and the reactions they provide. A link (or roller) gives 1 reaction along its line; a hinge (pin, free-rotation support) gives 2 — horizontal and vertical; a fixed support gives 3 — two forces and a moment.

Why the Other Options Are Wrong

A. 1: One constraint is a roller or link.
C. 3: Three constraints is a fixed support, which also stops rotation.
D. 4: A planar support can have at most 3 constraints.

Key Point

Hinge (free rotation) = 2 constraints: Rx and Ry, no moment.

Key Concepts for Students

Moment at a frictionless hinge is zero.
Three-hinged arches use an internal hinge to make the arch determinate.
In 3-D, a ball-and-socket joint gives 3 force constraints.

Practice more: this is question 5 in Force Analysis MCQs – Part 1. Try the whole set and check every answer instantly.