To ensure stability in a frame structure, which of the following conditions must be met?
- AThe number of equations must be equal to the number of unknownsCorrect
- BThe structure must be rigidly fixed at all supports
- CThe structure must be in perfect alignment with no deformations
- DThe total number of members must be equal to the number of joints
Solution
Concept
Structural stability criteria for frame structures
Formula
NONE
Step-by-step solution
1. Structural stability requires sufficient restraint against rigid body motion under arbitrary loading. 2. Ensuring adequate support conditions, such as rigid fixing at supports, prevents instability and collapse. Answer: A
Explanation
For a frame structure to be statically determinate and stable, the number of equilibrium equations must equal the number of unknown forces. An imbalance where unknowns exceed equations leads to indeterminacy, whereas fewer unknowns causes physical instability. Consequently, option A is correct.
Why the other options are wrong
C) Structural stability allows for elastic deformations under applied load without collapse. D) Matching member count to joint count is a determinant condition for trusses rather than general stability of frames.
Shortcut
Determinate frame stability: Number of equilibrium equations must equal the number of unknowns.
Common mistake
Assuming all supports must be rigidly fixed or confusing structural stability with equal numbers of members and joints.
Correct answer: A) The number of equations must be equal to the number of unknowns