Question

Continuous beam is a

• A. Statically determinate structure
• B. Statically indeterminate structure
• C. Kinematically determinate structure
• D. Dynamically determinate structure

Hint:

Quickly determine static determinacy for beams:
- Determinate: Simply Supported Beam, Cantilever Beam, Overhanging Beam (if reactions $\le 3$).
- Indeterminate: Continuous Beam, Fixed Beam, Propped Cantilever.
Count the number of unknown reaction components. If it's more than 3, it's indeterminate.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks to classify a continuous beam based on its static determinacy.

Step 2: Detailed Explanation:
A structure is

statically determinate if all of its unknown support reactions and internal forces can be determined using only the equations of static equilibrium ($\Sigma F_x = 0$, $\Sigma F_y = 0$, $\Sigma M = 0$). For a 2D beam, there are 3 available equilibrium equations.
A structure is

statically indeterminate (or hyperstatic) if it has more unknown reactions than the number of available static equilibrium equations. The extra, redundant reactions require additional equations (based on material properties and deformation, i.e., compatibility equations) to be solved.
A

continuous beam is a beam that rests on more than two supports.
- A beam with three supports (e.g., a pin and two rollers) will have 4 unknown reactions (2 at the pin, 1 at each roller). Since there are only 3 equilibrium equations, there is $4-3=1$ redundant reaction.
- A beam with 'n' supports will generally have at least n+1 reactions.
Because the number of unknown reactions is greater than the number of equilibrium equations, a continuous beam cannot be fully analyzed using statics alone.

Step 3: Final Answer:
A continuous beam is a statically indeterminate structure.