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The total compressive force at the time of failure of a concrete beam section of width 'b' without considering the partial safety factor of the material is
- a)0.6 fck b xu
- b)0.54 fck b xu
- c)0.66 fck b xu
- d)0.8 fck b xu
Correct answer is option 'B'. Can you explain this answer?
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Answer:
Total Compressive Force at Failure of Concrete Beam Section
The total compressive force at the time of failure of a concrete beam section of width b without considering the partial safety factor of the material is given by:
0.54 fck b xu
where fck is the characteristic compressive strength of concrete, b is the width of the beam section, and xu is the depth of the neutral axis.
Explanation
The compressive force at failure of a concrete beam section is the maximum compressive stress that the section can withstand before it fails. The compressive stress is determined by dividing the compressive force by the cross-sectional area of the beam section.
The depth of the neutral axis is the depth at which the compressive stress is zero. It is an important parameter in the analysis of reinforced concrete beams. The neutral axis divides the beam section into two parts: the compression zone and the tension zone.
The compressive stress in the compression zone is given by the formula:
fc = 0.85 fck
where fc is the compressive stress in the compression zone and fck is the characteristic compressive strength of concrete.
The total compressive force at the time of failure of a concrete beam section is equal to the area of the compression zone times the compressive stress in the compression zone.
The area of the compression zone is given by:
Ac = b xu
where b is the width of the beam section and xu is the depth of the neutral axis.
Therefore, the total compressive force at the time of failure of a concrete beam section is given by:
F = fc Ac = 0.85 fck b xu
Without considering the partial safety factor of the material, the total compressive force at the time of failure of a concrete beam section is:
F = 0.54 fck b xu
Conclusion
In summary, the total compressive force at the time of failure of a concrete beam section of width b without considering the partial safety factor of the material is 0.54 fck b xu. This formula is derived from the compressive stress in the compression zone and the area of the compression zone, which are determined by the characteristic compressive strength of concrete and the depth of the neutral axis.
Total Compressive Force at Failure of Concrete Beam Section
The total compressive force at the time of failure of a concrete beam section of width b without considering the partial safety factor of the material is given by:
0.54 fck b xu
where fck is the characteristic compressive strength of concrete, b is the width of the beam section, and xu is the depth of the neutral axis.
Explanation
The compressive force at failure of a concrete beam section is the maximum compressive stress that the section can withstand before it fails. The compressive stress is determined by dividing the compressive force by the cross-sectional area of the beam section.
The depth of the neutral axis is the depth at which the compressive stress is zero. It is an important parameter in the analysis of reinforced concrete beams. The neutral axis divides the beam section into two parts: the compression zone and the tension zone.
The compressive stress in the compression zone is given by the formula:
fc = 0.85 fck
where fc is the compressive stress in the compression zone and fck is the characteristic compressive strength of concrete.
The total compressive force at the time of failure of a concrete beam section is equal to the area of the compression zone times the compressive stress in the compression zone.
The area of the compression zone is given by:
Ac = b xu
where b is the width of the beam section and xu is the depth of the neutral axis.
Therefore, the total compressive force at the time of failure of a concrete beam section is given by:
F = fc Ac = 0.85 fck b xu
Without considering the partial safety factor of the material, the total compressive force at the time of failure of a concrete beam section is:
F = 0.54 fck b xu
Conclusion
In summary, the total compressive force at the time of failure of a concrete beam section of width b without considering the partial safety factor of the material is 0.54 fck b xu. This formula is derived from the compressive stress in the compression zone and the area of the compression zone, which are determined by the characteristic compressive strength of concrete and the depth of the neutral axis.
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