Question

Consider the beam ACDEB given in the figure. Which of the following statements is/are correct: 

• A. Bending moment is zero between the points A and C.
• B. There is a sudden jump in shear force at the point D.
• C. There is a sudden jump in bending moment at the point E.
• D. Bending moment is zero somewhere between the points D and E.

Hint:

In the analysis of beams, remember that at points of internal hinges or support, the bending moment is zero. Additionally, the bending moment may change sign or magnitude abruptly at points with external loads or reactions.

Answer 1

The Correct Option is A, D

Let \( V_A \) and \( V_D \) be the vertical reactions at points A and D, respectively.

Step 1: Equilibrium Equations

Using the moment equilibrium condition about point B:

\[ \sum M_B = 0 \]

We get:

\[ - V_D(4) + 4(2) + 2(6) = 0 \]

Solving for \( V_D \):

\[ V_D = 5 \, \text{kN} \]

Now, using the equilibrium of vertical forces:

\[ V_A + V_D = 5 \]

Substituting \( V_D = 5 \) kN:

\[ V_A = 0, \quad M_A = 0. \]

Step 2: Shear Force Diagram (SFD)

- At point A, the shear force is positive (+).
- At point B, the shear force is negative (−).
- The shear force remains constant in spans BC and CD.

Step 3: Bending Moment Diagram (BMD)

- The bending moment at point A is zero.
- The bending moment is also zero in the spans AB and between C and D.
- The bending moment increases from C to D, then decreases towards point E.

Thus, the correct answers are (A) and (D).