Question

According to moment area method, the vertical intercept at a point between the tangents drawn from two points is equal to moment of the area of

• A. shear force diagram between those two points about the point under consideration divided by EI.
• B. bending moment diagram between those two points about the point under consideration divided by EI
• C. deflected curve between those two points about the point under consideration divided by EI
• D. axial thrust diagram between those two points about the point under consideration divided by EI

Hint:

Remember the two Moment-Area theorems in short form:
- Theorem 1 (Slope): $\Delta \theta$ = Area of $M/EI$ diagram.
- Theorem 2 (Deflection): Deflection = Moment of Area of $M/EI$ diagram.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
What does EI(d²y/dx²) represent in beam theory?

Step 2: Key Formula (Alternate):
From Euler-Bernoulli equation: curvature = M/EI. Also curvature = d²y/dx² (for small deflections). Equate: d²y/dx² = M/EI → M = EI(d²y/dx²).

Step 3: Detailed Explanation:
Taking derivatives: y=deflection, dy/dx=slope, EI(d²y/dx²)=bending moment, EI(d³y/dx³)=shear force, EI(d⁴y/dx⁴)=load intensity. The second derivative term directly gives the internal moment at that section.

Step 4: Final Answer:
EI(d²y/dx²) represents the bending moment at that section.