A structure is considered Statically Indeterminate when
- AThe number of unknown reaction components exceeds the number of available equilibrium equations.Correct
- BThe structure is capable of moving as a rigid body under any load system.
- CThe equations of statics are sufficient to determine all internal forces and reactions.
- DThe degrees of freedom (DOF) represent the number of independent variables required to describe the displacement.
Solution
Concept
Static Indeterminacy
Formula
N/A
Step-by-step solution
1. Review the given question about static indeterminacy in structural analysis. 2. Recall that static indeterminacy occurs when unknown reaction components exceed the available static equilibrium equations. 3. Match with the choices and select Option (a).
Explanation
A structure is statically indeterminate when it has more unknown support reactions or internal forces than the basic equations of equilibrium (force and moment balance) can solve on their own. Because there are extra unknown forces, basic static equations alone are not enough, and additional equations accounting for material deformation are required to solve for all forces.
Shortcut
To remember statically indeterminate structures, use the rule "Unknowns > Equations" (U > E): - Statically Determinate: Unknowns = Equations (Can be solved using statics alone). - Statically Indeterminate: Unknowns > Equations (Too many unknown reactions to solve using basic equilibrium equations alone).
Common mistake
A common mistake is selecting option C by confusing statically indeterminate structures with statically determinate structures, where equilibrium equations alone are sufficient. Another frequent mistake is selecting option B by confusing indeterminacy with instability or rigid body motion, or selecting option D by confusing static indeterminacy with kinematic indeterminacy (degrees of freedom).
Correct answer: A) The number of unknown reaction components exceeds the number of available equilibrium equations.