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:
The question asks for the statement of the Second Moment-Area Theorem.

Step 2: Detailed Explanation:
The Moment-Area Theorems are a method for finding the slope and deflection of beams. There are two theorems:

• First Moment-Area Theorem: The change in slope between any two points on the elastic curve of a beam is equal to the area of the $M/EI$ diagram between those two points.

• Second Moment-Area Theorem: The vertical deviation (or vertical intercept) of a point B on the elastic curve with respect to the tangent drawn at another point A is equal to the

moment of the area of the $M/EI$ diagram between points A and B, taken about point B.

The question describes "the vertical intercept at a point between the tangents drawn from two points". This is a direct statement of the Second Moment-Area Theorem. The area it refers to is the area of the bending moment diagram divided by $EI$ (the $M/EI$ diagram). The moment is taken about the point where the deviation is being measured.

Step 3: Final Answer:
The vertical intercept is equal to the moment of the area of the bending moment diagram between those two points about the point under consideration, divided by $EI$.