What distinguishes statically determinate from indeterminate structures?

What distinguishes statically determinate from indeterminate structures?

• A. Statically determinate structures' reactions can be found using equilibrium equations alone; indeterminate require compatibility or material properties.
• B. Indeterminate structures' reactions can be found using equilibrium equations alone; determinate require compatibility.
• C. Both types require compatibility equations in all cases.
• D. Only indeterminate structures have reactions that cannot be found with equilibrium equations.

Answer: (A)

The key idea is whether equilibrium equations alone are enough to find the reactions. In two-dimensional structures, there are three independent equilibrium equations (sum of horizontal forces, sum of vertical forces, and sum of moments). If the unknown reactions total three, you can solve them directly from those equations, so the structure is statically determinate. When there are more unknown reactions than those equations provide, the system is statically indeterminate and you must bring in additional relations that connect deformations to forces—these are compatibility conditions tied to how the structure deforms, along with material properties through constitutive relationships. That’s why determinate structures rely solely on equilibrium, while indeterminate ones require compatibility (and material properties) to close the problem.

The key idea is whether equilibrium equations alone are enough to find the reactions. In two-dimensional structures, there are three independent equilibrium equations (sum of horizontal forces, sum of vertical forces, and sum of moments). If the unknown reactions total three, you can solve them directly from those equations, so the structure is statically determinate. When there are more unknown reactions than those equations provide, the system is statically indeterminate and you must bring in additional relations that connect deformations to forces—these are compatibility conditions tied to how the structure deforms, along with material properties through constitutive relationships. That’s why determinate structures rely solely on equilibrium, while indeterminate ones require compatibility (and material properties) to close the problem.