A simply supported beam of length 8 m carries a central point load of 20 kN. Find: Reactions at supports Maximum bending moment

 A simply supported beam of length 8 m carries a central point load of 20 kN. Find:

1. Reactions at supports

2. Maximum bending moment

Solution:

Step 1: Determine reactions

• For a central point load $P$ on a simply supported beam of length $L$:

$$R_A = R_B = \frac{P}{2}$$ $$R_A = R_B = \frac{20}{2} = 10 \text{ kN}$$

Step 2: Maximum bending moment

• Maximum moment occurs at midspan (under the load):

$$M_{\text{max}} = \frac{P L}{4}$$ $$M_{\text{max}} = \frac{20 \times 8}{4} = 40 \text{ kNm}$$

✅ Answer:

• Reactions: RA = RB = 10 kN

• Max bending moment: 40 kNm