Calculate the ultimate moment of resistance of R.C. beam 250 mm × 500 mm. Reinforcement of 1256 mm2 is placed at a distance of 30 mm from the bottom face. Use M20 concrete and Fe250 steel.
To calculate the ultimate moment of resistance for a reinforced concrete (R.C.) beam, we follow these steps:
Determine the effective depth ():
- Overall depth of the beam () = 500 mm
- Cover to the reinforcement = 30 mm (from the bottom face)
- Effective depth () = = 500 mm - 30 mm = 470 mm
Calculate the design strengths of the materials:
- For M20 concrete:
- Design strength of concrete,
- For Fe250 steel:
- Design strength of steel,
- For M20 concrete:
Calculate the effective area of steel reinforcement ():
- Given
Calculate the depth of the neutral axis (): To simplify, we assume that the beam is under-reinforced. For under-reinforced sections, the neutral axis depth can be approximated using:
where:
- = width of the beam = 250 mm
Since the calculated exceeds the effective depth (), this indicates that the beam is in a condition of over-reinforcement. For an over-reinforced section, the neutral axis is taken at the maximum depth of .
Hence, (as assumed, this value of is used).
Calculate the lever arm (): The lever arm is approximately given by:
Calculate the ultimate moment of resistance ():
Thus, the ultimate moment of resistance for the given R.C. beam is approximately .
To calculate the ultimate moment of resistance for a reinforced concrete (R.C.) beam, we follow these steps:
Determine the effective depth ():
- Overall depth of the beam () = 500 mm
- Cover to the reinforcement = 30 mm (from the bottom face)
- Effective depth () = = 500 mm - 30 mm = 470 mm
Calculate the design strengths of the materials:
- For M20 concrete:
- Design strength of concrete,
- For Fe250 steel:
- Design strength of steel,
- For M20 concrete:
Calculate the effective area of steel reinforcement ():
- Given
Calculate the depth of the neutral axis (): To simplify, we assume that the beam is under-reinforced. For under-reinforced sections, the neutral axis depth can be approximated using:
where:
- = width of the beam = 250 mm
Since the calculated exceeds the effective depth (), this indicates that the beam is in a condition of over-reinforcement. For an over-reinforced section, the neutral axis is taken at the maximum depth of .
Hence, (as assumed, this value of is used).
Calculate the lever arm (): The lever arm is approximately given by:
Calculate the ultimate moment of resistance ():
Thus, the ultimate moment of resistance for the given R.C. beam is approximately .
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