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A concrete beam is prestressed by a cable carrying an initial prestress of 500 N/mm2. The percentage loss in prestressing due to shrinkage of concrete if the beam is pre-tensioned and post-tensioned. (Consider the age of concrete at transfer is 8 days, Es = 2 x 105 N/mm2)
- a)12%, 8%
- b)8%, 12%
- c)11%, 9%
- d)12%, 9%
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A concrete beam is prestressed by a cable carrying an initial prestres...
Shrinkage strain in concrete in pretension
ϵcs = 3 × 10-4
∴ loss in prestress, Δσ = ϵcs x Es
= 3 × 10-4 × 2 × 105
= 60 N/mm2
% loss in prestress = 60/500 × 100 = 12%
Shrinkage strain in post – tension,
Shrinkage strain in post – tension,
= 2 × 10-4
∴ loss in prestress = ϵc × Es
= 2 × 10-4 × 2 × 105
= 40 N/mm2
% loss in presstress in post tension = 
Most Upvoted Answer
A concrete beam is prestressed by a cable carrying an initial prestres...
Prestressing in Concrete Beam
Given:
- Initial prestress: 500 N/mm^2
- Age of concrete at transfer: 8 days
- Elastic modulus of steel (Es): 2 x 10^5 N/mm^2
To Find:
Percentage loss in prestressing due to shrinkage of concrete for pre-tensioned and post-tensioned beams
Solution:
1. Pre-tensioned Beam:
Pre-tensioning is a method in which the steel cable is tensioned before the concrete is poured. The loss of prestress due to shrinkage can be calculated using the following formula:
Loss of prestress = (σs / Es) x (εc - εs)
Where:
- σs = Initial prestress = 500 N/mm^2
- Es = Elastic modulus of steel = 2 x 10^5 N/mm^2
- εc = Strain in concrete due to shrinkage
- εs = Strain in steel cable
To calculate the strain in concrete due to shrinkage (εc), we can use the formula:
εc = α x (t - t0)
Where:
- α = Coefficient of thermal expansion of concrete
- t = Age of concrete at transfer = 8 days
- t0 = Age of concrete at pouring
As the values of α and t0 are not given in the question, we cannot determine the exact percentage loss in prestressing due to shrinkage for pre-tensioned beam.
2. Post-tensioned Beam:
Post-tensioning is a method in which the steel cable is tensioned after the concrete has hardened. The loss of prestress due to shrinkage can be calculated using the following formula:
Loss of prestress = (σs / Es) x (εc + εs)
To calculate the strain in concrete due to shrinkage (εc), we can use the same formula as mentioned above:
εc = α x (t - t0)
Now, let's assume that the coefficient of thermal expansion of concrete (α) is 10 x 10^-6 per °C and the age of concrete at pouring (t0) is 0 days.
Plugging in the values, we get:
εc = 10 x 10^-6 x (8 - 0) = 8 x 10^-5
To calculate the strain in steel cable (εs), we can use the formula:
εs = σs / Es
Plugging in the values, we get:
εs = 500 N/mm^2 / 2 x 10^5 N/mm^2 = 2.5 x 10^-3
Now, substituting the values of σs, Es, εc, and εs in the formula for loss of prestress, we get:
Loss of prestress = (500 N/mm^2 / 2 x 10^5 N/mm^2) x (8 x 10^-5 + 2.5 x 10^-3)
Loss of prestress = 0.004
To find the percentage loss in prestressing, we can use the formula:
Percentage loss = (Loss of prestress / Initial prestress) x 100
Plugging in the values, we get:
Percentage loss
Given:
- Initial prestress: 500 N/mm^2
- Age of concrete at transfer: 8 days
- Elastic modulus of steel (Es): 2 x 10^5 N/mm^2
To Find:
Percentage loss in prestressing due to shrinkage of concrete for pre-tensioned and post-tensioned beams
Solution:
1. Pre-tensioned Beam:
Pre-tensioning is a method in which the steel cable is tensioned before the concrete is poured. The loss of prestress due to shrinkage can be calculated using the following formula:
Loss of prestress = (σs / Es) x (εc - εs)
Where:
- σs = Initial prestress = 500 N/mm^2
- Es = Elastic modulus of steel = 2 x 10^5 N/mm^2
- εc = Strain in concrete due to shrinkage
- εs = Strain in steel cable
To calculate the strain in concrete due to shrinkage (εc), we can use the formula:
εc = α x (t - t0)
Where:
- α = Coefficient of thermal expansion of concrete
- t = Age of concrete at transfer = 8 days
- t0 = Age of concrete at pouring
As the values of α and t0 are not given in the question, we cannot determine the exact percentage loss in prestressing due to shrinkage for pre-tensioned beam.
2. Post-tensioned Beam:
Post-tensioning is a method in which the steel cable is tensioned after the concrete has hardened. The loss of prestress due to shrinkage can be calculated using the following formula:
Loss of prestress = (σs / Es) x (εc + εs)
To calculate the strain in concrete due to shrinkage (εc), we can use the same formula as mentioned above:
εc = α x (t - t0)
Now, let's assume that the coefficient of thermal expansion of concrete (α) is 10 x 10^-6 per °C and the age of concrete at pouring (t0) is 0 days.
Plugging in the values, we get:
εc = 10 x 10^-6 x (8 - 0) = 8 x 10^-5
To calculate the strain in steel cable (εs), we can use the formula:
εs = σs / Es
Plugging in the values, we get:
εs = 500 N/mm^2 / 2 x 10^5 N/mm^2 = 2.5 x 10^-3
Now, substituting the values of σs, Es, εc, and εs in the formula for loss of prestress, we get:
Loss of prestress = (500 N/mm^2 / 2 x 10^5 N/mm^2) x (8 x 10^-5 + 2.5 x 10^-3)
Loss of prestress = 0.004
To find the percentage loss in prestressing, we can use the formula:
Percentage loss = (Loss of prestress / Initial prestress) x 100
Plugging in the values, we get:
Percentage loss
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A concrete beam is prestressed by a cable carrying an initial prestress of 500 N/mm2. The percentage loss in prestressing due to shrinkage of concrete if the beam is pre-tensioned and post-tensioned. (Consider the age of concrete at transfer is 8 days, Es= 2 x 105N/mm2)a)12%, 8%b)8%, 12%c)11%, 9%d)12%, 9%Correct answer is option 'A'. Can you explain this answer?
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A concrete beam is prestressed by a cable carrying an initial prestress of 500 N/mm2. The percentage loss in prestressing due to shrinkage of concrete if the beam is pre-tensioned and post-tensioned. (Consider the age of concrete at transfer is 8 days, Es= 2 x 105N/mm2)a)12%, 8%b)8%, 12%c)11%, 9%d)12%, 9%Correct answer is option 'A'. 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 A concrete beam is prestressed by a cable carrying an initial prestress of 500 N/mm2. The percentage loss in prestressing due to shrinkage of concrete if the beam is pre-tensioned and post-tensioned. (Consider the age of concrete at transfer is 8 days, Es= 2 x 105N/mm2)a)12%, 8%b)8%, 12%c)11%, 9%d)12%, 9%Correct answer is option 'A'. 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 A concrete beam is prestressed by a cable carrying an initial prestress of 500 N/mm2. The percentage loss in prestressing due to shrinkage of concrete if the beam is pre-tensioned and post-tensioned. (Consider the age of concrete at transfer is 8 days, Es= 2 x 105N/mm2)a)12%, 8%b)8%, 12%c)11%, 9%d)12%, 9%Correct answer is option 'A'. Can you explain this answer?.
A concrete beam is prestressed by a cable carrying an initial prestress of 500 N/mm2. The percentage loss in prestressing due to shrinkage of concrete if the beam is pre-tensioned and post-tensioned. (Consider the age of concrete at transfer is 8 days, Es= 2 x 105N/mm2)a)12%, 8%b)8%, 12%c)11%, 9%d)12%, 9%Correct answer is option 'A'. 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 A concrete beam is prestressed by a cable carrying an initial prestress of 500 N/mm2. The percentage loss in prestressing due to shrinkage of concrete if the beam is pre-tensioned and post-tensioned. (Consider the age of concrete at transfer is 8 days, Es= 2 x 105N/mm2)a)12%, 8%b)8%, 12%c)11%, 9%d)12%, 9%Correct answer is option 'A'. 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 A concrete beam is prestressed by a cable carrying an initial prestress of 500 N/mm2. The percentage loss in prestressing due to shrinkage of concrete if the beam is pre-tensioned and post-tensioned. (Consider the age of concrete at transfer is 8 days, Es= 2 x 105N/mm2)a)12%, 8%b)8%, 12%c)11%, 9%d)12%, 9%Correct answer is option 'A'. Can you explain this answer?.
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