Calculation of Maximum Bending Moment

To find the maximum bending moment in the simply supported beam, we first determine the total uniformly distributed load (UDL) per meter length.

1. Identify Given Parameters and Convert to Meters

• Span of the beam ($L$): $4\text{ m}$
• Beam width ($B$): $250\text{ mm} = 0.25\text{ m}$
• Beam depth ($D$): $600\text{ mm} = 0.6\text{ m}$
• Wall height ($H_w$): $2\text{ m}$
• Wall thickness ($t_w$): $250\text{ mm} = 0.25\text{ m}$
• Density of RCC ($\rho_{\text{rcc}}$): $25\text{ kN/m}^3$
• Density of brick masonry ($\rho_{\text{brick}}$): $18\text{ kN/m}^3$

2. Calculate the Load per Unit Length ($w$)

The total UDL ($w$) is the sum of the self-weight of the RCC beam and the weight of the brick wall.

A. Self-weight of the RCC beam ($w_{\text{beam}}$):

$$w_{\text{beam}} = (\text{Width} \times \text{Depth}) \times \text{Density} = (0.25\text{ m} \times 0.6\text{ m}) \times 25\text{ kN/m}^3$$ $$w_{\text{beam}} = 0.15\text{ m}^2 \times 25\text{ kN/m}^3 = 3.75\text{ kN/m}$$

B. Weight of the brick wall ($w_{\text{wall}}$):

$$w_{\text{wall}} = (\text{Thickness} \times \text{Height}) \times \text{Density} = (0.25\text{ m} \times 2\text{ m}) \times 18\text{ kN/m}^3$$ $$w_{\text{wall}} = 0.5\text{ m}^2 \times 18\text{ kN/m}^3 = 9.00\text{ kN/m}$$

C. Total UDL ($w$):

$$w = w_{\text{beam}} + w_{\text{wall}} = 3.75 + 9.00 = 12.75\text{ kN/m}$$

3. Calculate Maximum Bending Moment ($M_{\text{max}}$)

For a simply supported beam with a UDL over its entire span, the maximum bending moment occurs at the mid-span:

$$M_{\text{max}} = \frac{wL^2}{8}$$ $$M_{\text{max}} = \frac{12.75\text{ kN/m} \times (4\text{ m})^2}{8}$$ $$M_{\text{max}} = \frac{12.75 \times 16}{8} = 12.75 \times 2$$ $$M_{\text{max}} = 25.50\text{ kN-m}$$

Conclusion

The maximum bending moment in the beam is 25.50 kN-m.