Question

A simply supported beam is changed to a beam with fixed ends. The order of static indeterminacy will

• A. increase by 3
• B. increase by 2
• C. decrease by 1
• D. decrease by 3

Hint:

Each fixed support contributes 2 extra unknowns over a simple support.

Answer 1

The Correct Option is B

A simply supported beam is statically determinate because it has the minimal number of supports required for equilibrium. Typically, a simply supported beam has one pinned support and one roller support, providing two reaction forces.

When the beam supports are changed to fixed ends, each fixed support provides three reaction components: two forces (vertical and horizontal) and a moment. Therefore, with fixed ends on both sides, there are a total of six reactions.

Static indeterminacy is calculated by the formula:

Static Indeterminacy = Total Reactions - Equilibrium Equations

For 2D beams, there are three equilibrium equations: ∑Fx = 0, ∑Fy = 0, and ∑M = 0.

For a simply supported beam: Static Indeterminacy = 2 (reactions) - 3 (equilibrium equations) = -1 (Determinate)

For a beam with fixed ends: Static Indeterminacy = 6 (reactions) - 3 (equilibrium equations) = 3 (Indeterminate)

Therefore, the order of static indeterminacy increases by 3 - (-1) = 2.

The correct answer is that the order of static indeterminacy will increase by 2.