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If the permissible compressive and tensile stresses in a single reinforced beam are 50 kg/cm2 and 1400 kg/cm2 respectively and the modular ratio is 18, the percentage of the steel required for an economic section, is
- a)0.496%
- b)0.596%
- c)0.696%
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If the permissible compressive and tensile stresses in a single reinfo...
Taking Moment of area of tension and compression zone for a singly reinforced beam:
Where,
Xc = critical depth or economic depth of neutral axis
m = modular ratio
Ast = area of steel required for balanced section
m = 18
c = 50 kg/cm2
t = 1400 kg/cm2
Most Upvoted Answer
If the permissible compressive and tensile stresses in a single reinfo...
Given data:
Permissible compressive stress (fc) = 50 kg/cm2
Permissible tensile stress (ft) = 1400 kg/cm2
Modular ratio (m) = 18
To find: Percentage of steel required for an economic section
Formula used:
We know that the stress in steel (fs) and concrete (fc) is related as follows:
fs/fc = m/(m+1)
Where,
fs = stress in steel
fc = stress in concrete
m = modular ratio
Percentage of steel required (As%) can be calculated as:
As% = (100A/(bd)) x 1.2
Where,
A = area of steel
b = width of the beam
d = effective depth of the beam
Calculation:
From the given data, we have:
fs/fc = m/(m+1)
fs/50 = 18/19
fs = 50 x (18/19)
fs = 47.37 kg/cm2
Now, let's assume a value for the depth of the beam (d). Let's take d = 40 cm.
From the given data, we know that the permissible compressive stress (fc) is 50 kg/cm2. Therefore, the maximum compressive force that the concrete can bear is:
fc x bd = 50 x b x 40 = 2000b kg
Now, let's assume a value for the width of the beam (b). Let's take b = 20 cm.
The maximum compressive force that the concrete can bear is 2000b = 2000 x 20 = 40000 kg.
Now, let's calculate the maximum tensile force that the steel can bear. From the given data, we have:
fs = 47.37 kg/cm2
Therefore, the maximum tensile force that the steel can bear is:
fs x As = 47.37 x As
Now, for an economic section, the maximum compression force should be equal to the maximum tension force. Therefore, we have:
fs x As = fc x bd
Substituting the values, we get:
47.37 x As = 50 x 20 x 40
As = 0.696 cm2
Now, let's calculate the percentage of steel required for an economic section. We have:
As% = (100A/(bd)) x 1.2
As% = (100 x 0.696/(20 x 40)) x 1.2
As% = 0.696%
Therefore, the percentage of steel required for an economic section is 0.696%. Hence, the correct option is (c).
Permissible compressive stress (fc) = 50 kg/cm2
Permissible tensile stress (ft) = 1400 kg/cm2
Modular ratio (m) = 18
To find: Percentage of steel required for an economic section
Formula used:
We know that the stress in steel (fs) and concrete (fc) is related as follows:
fs/fc = m/(m+1)
Where,
fs = stress in steel
fc = stress in concrete
m = modular ratio
Percentage of steel required (As%) can be calculated as:
As% = (100A/(bd)) x 1.2
Where,
A = area of steel
b = width of the beam
d = effective depth of the beam
Calculation:
From the given data, we have:
fs/fc = m/(m+1)
fs/50 = 18/19
fs = 50 x (18/19)
fs = 47.37 kg/cm2
Now, let's assume a value for the depth of the beam (d). Let's take d = 40 cm.
From the given data, we know that the permissible compressive stress (fc) is 50 kg/cm2. Therefore, the maximum compressive force that the concrete can bear is:
fc x bd = 50 x b x 40 = 2000b kg
Now, let's assume a value for the width of the beam (b). Let's take b = 20 cm.
The maximum compressive force that the concrete can bear is 2000b = 2000 x 20 = 40000 kg.
Now, let's calculate the maximum tensile force that the steel can bear. From the given data, we have:
fs = 47.37 kg/cm2
Therefore, the maximum tensile force that the steel can bear is:
fs x As = 47.37 x As
Now, for an economic section, the maximum compression force should be equal to the maximum tension force. Therefore, we have:
fs x As = fc x bd
Substituting the values, we get:
47.37 x As = 50 x 20 x 40
As = 0.696 cm2
Now, let's calculate the percentage of steel required for an economic section. We have:
As% = (100A/(bd)) x 1.2
As% = (100 x 0.696/(20 x 40)) x 1.2
As% = 0.696%
Therefore, the percentage of steel required for an economic section is 0.696%. Hence, the correct option is (c).
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If the permissible compressive and tensile stresses in a single reinforced beam are 50 kg/cm2 and 1400 kg/cm2respectively and the modular ratio is 18, the percentage of the steel required for an economic section, isa)0.496%b)0.596%c)0.696%d)None of theseCorrect answer is option 'C'. Can you explain this answer?
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If the permissible compressive and tensile stresses in a single reinforced beam are 50 kg/cm2 and 1400 kg/cm2respectively and the modular ratio is 18, the percentage of the steel required for an economic section, isa)0.496%b)0.596%c)0.696%d)None of theseCorrect answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about If the permissible compressive and tensile stresses in a single reinforced beam are 50 kg/cm2 and 1400 kg/cm2respectively and the modular ratio is 18, the percentage of the steel required for an economic section, isa)0.496%b)0.596%c)0.696%d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the permissible compressive and tensile stresses in a single reinforced beam are 50 kg/cm2 and 1400 kg/cm2respectively and the modular ratio is 18, the percentage of the steel required for an economic section, isa)0.496%b)0.596%c)0.696%d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
If the permissible compressive and tensile stresses in a single reinforced beam are 50 kg/cm2 and 1400 kg/cm2respectively and the modular ratio is 18, the percentage of the steel required for an economic section, isa)0.496%b)0.596%c)0.696%d)None of theseCorrect answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about If the permissible compressive and tensile stresses in a single reinforced beam are 50 kg/cm2 and 1400 kg/cm2respectively and the modular ratio is 18, the percentage of the steel required for an economic section, isa)0.496%b)0.596%c)0.696%d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the permissible compressive and tensile stresses in a single reinforced beam are 50 kg/cm2 and 1400 kg/cm2respectively and the modular ratio is 18, the percentage of the steel required for an economic section, isa)0.496%b)0.596%c)0.696%d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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