Question

The expression $EI \frac{d^2y}{dx^2}$ at a section of a beam represents

• A. Rate of loading
• B. Deflection
• C. Shear force
• D. Bending moment

Hint:

Memorize the hierarchy of beam equations:
- $y(x)$ = Deflection
- $\frac{dy}{dx}$ = Slope
- $EI \frac{d^2y}{dx^2}$ = Bending Moment ($M$)
- $EI \frac{d^3y}{dx^3}$ = Shear Force ($V$)
- $EI \frac{d^4y}{dx^4}$ = - (Load Intensity, $w$)

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
Cantilever 2m, point load 48kN at free end, EI=20000 kNm². Find slope at free end.

Step 2: Key Formula (Alternate):
Slope at free end = PL²/(2EI). Direct standard formula for cantilever with tip load.

Step 3: Detailed Explanation:
θ = 48×(2)²/(2×20000) = 48×4/40000 = 192/40000 = 0.0048 rad = 4.8×10⁻³ rad.

Step 4: Final Answer:
Slope is 4.8×10⁻³ radians.