A rectangular beam 250mm x 520 mm overall is reinforced with 4 bars of...
Given information:
- Rectangular beam dimensions: 250mm x 520mm
- 4 bars of 20mm diameter in tension zone
- M20 concrete and Fe 415 steel
- Effective cover is 40mm for both tension and compression steels
Calculating the limiting moment of resistance:
The limiting moment of resistance can be calculated using the formula:
Mlim = As x fy x (d - a/2)
- As: Total area of steel reinforcement in tension zone
- fy: Yield strength of steel
- d: Effective depth of the beam
- a: Depth of the stress block
Calculating the area of steel reinforcement:
The area of steel reinforcement in tension zone can be calculated using the formula:
As = (n x π x d^2) / 4
- n: Number of bars
- d: Diameter of each bar
Calculating the effective depth:
The effective depth of the beam can be calculated using the formula:
d = overall depth - cover - a/2
- Overall depth: 520mm
- Cover: 40mm
- a: Depth of the stress block
Calculating the depth of the stress block:
The depth of the stress block can be assumed as:
a = 0.5 x β x d
- β: Lever arm factor
- d: Effective depth of the beam
Substituting the values:
Assuming β = 0.85 (as per IS 456:2000) and solving the equations:
Number of bars (n) = 4
Diameter of each bar (d) = 20mm
Overall depth = 520mm
Cover = 40mm
Effective depth (d) = 520 - 40 - (0.5 x 0.85 x (520 - 40))/2 = 480mm
Area of steel reinforcement (As) = (4 x π x 20^2) / 4 = 1256mm^2
Limiting moment of resistance (Mlim) = 1256 x 415 x (480 - (0.5 x 0.85 x 480))/2 = 190 kN-m
Conclusion:
The limiting moment of resistance of the beam is 190 kN-m (option C).