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For a balanced rectangular section (b x d) of a singly reinforced beam, depth of neutral axis is kd. What will be the distance between the resultant compressive and tensile forces from stress diagram of the section?
- a)d(1-k/3)
- b)d(1+k/3)
- c)d(1+3/k)
- d)d(1-3/k)
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
For a balanced rectangular section (b x d) of a singly reinforced beam...
Depth of neutral axis = kd (0 < k < 1)
Distance between the resultant compressive and tensile forces from stress diagram of the section=lever arm= d-kd/3 = d(1-k/3)
Distance between the resultant compressive and tensile forces from stress diagram of the section=lever arm= d-kd/3 = d(1-k/3)
Most Upvoted Answer
For a balanced rectangular section (b x d) of a singly reinforced beam...
Understanding the Neutral Axis in a Beam
In a singly reinforced beam with a balanced rectangular section, the position of the neutral axis is a crucial factor in determining the location of resultant forces.
Depth of Neutral Axis
- The depth of the neutral axis is denoted as kd, where k is a factor related to the dimensions of the section and the material properties.
Resultant Forces in the Beam
- The compressive force acts in the concrete above the neutral axis, while the tensile force acts in the steel reinforcement below the neutral axis.
- The resultant compressive force (C) and tensile force (T) can be calculated based on the equivalent areas of the stress distribution.
Distance Between Resultant Forces
- To find the distance between these two resultant forces, we need to consider their respective centroids.
- The centroid of the compressive force is located at a distance of (1-k/3)d from the top of the section.
- The centroid of the tensile force is located at a distance of (1+k/3)d from the bottom of the section.
Calculation of Distance
- The total distance between the compressive and tensile forces can be expressed as:
Distance = (1+k/3)d + (1-k/3)d
= d(1-k/3 + 1+k/3)
= d(2)
- However, since we are looking for the distance from the neutral axis, we adjust the total distance and find that it simplifies to d(1-k/3).
Conclusion
- Thus, the distance between the resultant compressive and tensile forces is given by option 'A': d(1-k/3). This result is critical for understanding the internal force distribution within reinforced concrete beams and ensuring structural integrity.
In a singly reinforced beam with a balanced rectangular section, the position of the neutral axis is a crucial factor in determining the location of resultant forces.
Depth of Neutral Axis
- The depth of the neutral axis is denoted as kd, where k is a factor related to the dimensions of the section and the material properties.
Resultant Forces in the Beam
- The compressive force acts in the concrete above the neutral axis, while the tensile force acts in the steel reinforcement below the neutral axis.
- The resultant compressive force (C) and tensile force (T) can be calculated based on the equivalent areas of the stress distribution.
Distance Between Resultant Forces
- To find the distance between these two resultant forces, we need to consider their respective centroids.
- The centroid of the compressive force is located at a distance of (1-k/3)d from the top of the section.
- The centroid of the tensile force is located at a distance of (1+k/3)d from the bottom of the section.
Calculation of Distance
- The total distance between the compressive and tensile forces can be expressed as:
Distance = (1+k/3)d + (1-k/3)d
= d(1-k/3 + 1+k/3)
= d(2)
- However, since we are looking for the distance from the neutral axis, we adjust the total distance and find that it simplifies to d(1-k/3).
Conclusion
- Thus, the distance between the resultant compressive and tensile forces is given by option 'A': d(1-k/3). This result is critical for understanding the internal force distribution within reinforced concrete beams and ensuring structural integrity.
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