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If the permissible stress in steel in tension is 140 N / mm2, then the depth of neutral axis for a single reinforced rectangular balanced section will be
- a)0.45d
- b)0.30d
- c)0.40d
- d)0.35d
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If the permissible stress in steel in tension is 140 N / mm2, then the...
A balanced section is one in which the area of tension steel is such that the failure of both concrete and steel occurs simultaneously.
For WSM method:
The critical depth of the neutral axis is given by –
From stress distribution diagram,
Where, Xc = kd (k = Neutral axis depth factor for balanced section)
Put the value of modular ratio,
Thus the neutral axis factor for the balanced section depends only on σst and is independent of σcbc.
Calculation:
σst = 140 N / mm2
Neutral axis depth factor for balanced section
Hence, the depth of neutral axis for a single reinforced rectangular balanced section is 0.40d.
For WSM method:
The critical depth of the neutral axis is given by –
From stress distribution diagram,
Where, Xc = kd (k = Neutral axis depth factor for balanced section)
Put the value of modular ratio,
Thus the neutral axis factor for the balanced section depends only on σst and is independent of σcbc.
Calculation:
σst = 140 N / mm2
Neutral axis depth factor for balanced section
Hence, the depth of neutral axis for a single reinforced rectangular balanced section is 0.40d.
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If the permissible stress in steel in tension is 140 N / mm2, then the...
Explanation:
In a reinforced concrete beam, the neutral axis is the line that separates the compression zone (concrete) from the tension zone (steel reinforcement). The depth of the neutral axis is denoted by 'x'.
The permissible stress in steel in tension is given as 140 N/mm².
For a single reinforced rectangular balanced section, the depth of the neutral axis can be determined using the following formula:
x = (σ_st / σ_c) * d
Where:
x = depth of the neutral axis
σ_st = permissible stress in steel in tension (140 N/mm²)
σ_c = permissible stress in concrete in compression (usually taken as 0.45√fck for M20 grade concrete, where fck is the characteristic compressive strength of concrete)
d = effective depth of the beam
Since the question does not provide the value of σ_c or the grade of concrete, we assume it to be M20 grade concrete.
Calculation:
Given: σ_st = 140 N/mm²
Assuming M20 grade concrete, we have σ_c = 0.45√fck = 0.45√20 = 0.45 * 4.47 = 2.01 N/mm²
Substituting the values in the formula, we get:
x = (140 / 2.01) * d
Simplifying,
x ≈ 69.65 * d
Therefore, the depth of the neutral axis (x) for a single reinforced rectangular balanced section is approximately 0.40d (where d is the effective depth of the beam).
Hence, the correct answer is option 'C' (0.40d).
In a reinforced concrete beam, the neutral axis is the line that separates the compression zone (concrete) from the tension zone (steel reinforcement). The depth of the neutral axis is denoted by 'x'.
The permissible stress in steel in tension is given as 140 N/mm².
For a single reinforced rectangular balanced section, the depth of the neutral axis can be determined using the following formula:
x = (σ_st / σ_c) * d
Where:
x = depth of the neutral axis
σ_st = permissible stress in steel in tension (140 N/mm²)
σ_c = permissible stress in concrete in compression (usually taken as 0.45√fck for M20 grade concrete, where fck is the characteristic compressive strength of concrete)
d = effective depth of the beam
Since the question does not provide the value of σ_c or the grade of concrete, we assume it to be M20 grade concrete.
Calculation:
Given: σ_st = 140 N/mm²
Assuming M20 grade concrete, we have σ_c = 0.45√fck = 0.45√20 = 0.45 * 4.47 = 2.01 N/mm²
Substituting the values in the formula, we get:
x = (140 / 2.01) * d
Simplifying,
x ≈ 69.65 * d
Therefore, the depth of the neutral axis (x) for a single reinforced rectangular balanced section is approximately 0.40d (where d is the effective depth of the beam).
Hence, the correct answer is option 'C' (0.40d).
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If the permissible stress in steel in tension is 140 N / mm2, then the depth of neutral axis for a single reinforced rectangular balanced section will bea)0.45db)0.30dc)0.40dd)0.35dCorrect answer is option 'C'. Can you explain this answer?
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