How many constraints are there in a fixed support in a planar system?

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

Detailed Explanation

A fixed (built-in) support holds the end of a member completely — it cannot move or turn. In a plane that means all three degrees of freedom are restrained.

Why “3” Is Correct

A planar fixed support gives a horizontal reaction R_x, a vertical reaction R_y and a fixing moment M. That is 3 constraints. A cantilever is fixed at one end, which is why it can be solved with this single support.

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. 2: Two constraints describe a hinge, which allows rotation.
C. 6: Six constraints apply to a fixed support in 3-D space, not in a plane.
D. None of these: The correct value, 3, is listed.

Key Point

Fixed support: 3 constraints in 2-D (Rx, Ry, M); 6 in 3-D.

Key Concepts for Students

A cantilever needs only one fixed support.
A propped cantilever has 4 reactions, so it is indeterminate to degree 1.
A beam fixed at both ends (vertical loads only) is indeterminate to degree 2.

Practice more: this is question 11 in Force Analysis MCQs – Part 1. Try the whole set and check every answer instantly.