Question

A simply supported beam AB of span 8 m carries a uniformly distributed load of 24 kN/m over the left half of span. The ratio of the reactions of left support to right support is

• A. 0.50
• B. 0.33
• C. 3
• D. 2

Hint:

For calculating reactions, always replace a UDL with its equivalent point load.
The magnitude of the point load is the area of the UDL rectangle ($w \times l$).
The location of the point load is at the centroid of the UDL.
Then apply the standard equilibrium equations $\Sigma M = 0$ and $\Sigma F_y = 0$.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
Simply supported beam 8m, UDL 24kN/m on left 4m. Find R_A/R_B.

Step 2: Key Formula (Alternate):
Replace UDL with equivalent point load at its centroid. Use moment equilibrium about one support to find other reaction.

Step 3: Detailed Explanation:
Total UDL=24×4=96kN at 2m from A. ΣM_B=0: R_A×8=96×6 → R_A=72kN. ΣF_y=0: R_B=96-72=24kN. Ratio R_A/R_B=72/24=3.

Step 4: Final Answer:
Ratio is 3.