Question

A fixed beam of span 8 m and flexural rigidity $EI = 51,200$ kNm$^2$ is subjected to a concentrated load of 96 kN at mid span. The maximum deflection under the load is

• A. $1.25 \times 10^{-3}$ mm
• B. $2.5 \times 10^{-3}$ mm
• C. 5 mm
• D. 2.5 mm

Hint:

The maximum deflection for a fixed beam is much smaller than for a simply supported beam under the same load.
- Fixed Beam, Center Load: $\delta_{max} = \frac{PL^3}{192EI}$
- SS Beam, Center Load: $\delta_{max} = \frac{PL^3}{48EI}$
The fixed beam is $192/48 = 4$ times stiffer.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
Continuous beam rests on more than two supports. Is it determinate or indeterminate?

Step 2: Key Concept (Alternate):
Count unknowns vs equations. 3 equilibrium equations available. Each extra support adds reactions beyond 3.

Step 3: Detailed Explanation:
3 supports → 4 reactions (pin=2, two rollers=2). Unknowns(4) > equations(3) → 1° indeterminate. More supports = more redundant. Continuous beams always statically indeterminate.

Step 4: Final Answer:
Statically indeterminate structure.