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A post tensioned prestressed concrete beam is tensioned successively by 4 cables of equal area and equal stress. The percentage loss in each cable is found to be 6%, 4%, 2% and 0% respectively. What will be the total percentage loss in prestressing force?
- a)12%
- b)4%
- c)3%
- d)6%
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A post tensioned prestressed concrete beam is tensioned successively b...
Percentage Loss in Each Cable:
Given that the cables are tensioned successively, we can assume that the initial prestressing force in each cable is the same. Let's denote this initial prestressing force as P.
The percentage loss in each cable is given as 6%, 4%, 2%, and 0% respectively. This means that each cable experiences a loss of 6%, 4%, 2%, and 0% of the initial prestressing force, P.
Total Percentage Loss in Prestressing Force:
To find the total percentage loss in prestressing force, we need to consider the cumulative effect of the individual losses in each cable.
Let's calculate the loss in each cable:
- The first cable experiences a loss of 6% of the initial prestressing force, which is 0.06P.
- The second cable experiences a loss of 4% of the initial prestressing force, which is 0.04P.
- The third cable experiences a loss of 2% of the initial prestressing force, which is 0.02P.
- The fourth cable experiences no loss, as the percentage loss is 0%.
Now, let's calculate the total loss in prestressing force:
Total loss = Loss in Cable 1 + Loss in Cable 2 + Loss in Cable 3 + Loss in Cable 4
= 0.06P + 0.04P + 0.02P + 0
= 0.12P
The total loss in prestressing force is 0.12P.
Finding the Percentage Loss:
To find the percentage loss, we need to express the total loss as a percentage of the initial prestressing force.
Percentage loss = (Total loss / Initial prestressing force) x 100
= (0.12P / P) x 100
= 12%
Therefore, the total percentage loss in prestressing force is 12%. Hence, option D is the correct answer.
In conclusion, when tensioning a prestressed concrete beam successively with four cables of equal area and equal stress, with percentage losses of 6%, 4%, 2%, and 0% in each cable respectively, the total percentage loss in prestressing force is 12%.
Given that the cables are tensioned successively, we can assume that the initial prestressing force in each cable is the same. Let's denote this initial prestressing force as P.
The percentage loss in each cable is given as 6%, 4%, 2%, and 0% respectively. This means that each cable experiences a loss of 6%, 4%, 2%, and 0% of the initial prestressing force, P.
Total Percentage Loss in Prestressing Force:
To find the total percentage loss in prestressing force, we need to consider the cumulative effect of the individual losses in each cable.
Let's calculate the loss in each cable:
- The first cable experiences a loss of 6% of the initial prestressing force, which is 0.06P.
- The second cable experiences a loss of 4% of the initial prestressing force, which is 0.04P.
- The third cable experiences a loss of 2% of the initial prestressing force, which is 0.02P.
- The fourth cable experiences no loss, as the percentage loss is 0%.
Now, let's calculate the total loss in prestressing force:
Total loss = Loss in Cable 1 + Loss in Cable 2 + Loss in Cable 3 + Loss in Cable 4
= 0.06P + 0.04P + 0.02P + 0
= 0.12P
The total loss in prestressing force is 0.12P.
Finding the Percentage Loss:
To find the percentage loss, we need to express the total loss as a percentage of the initial prestressing force.
Percentage loss = (Total loss / Initial prestressing force) x 100
= (0.12P / P) x 100
= 12%
Therefore, the total percentage loss in prestressing force is 12%. Hence, option D is the correct answer.
In conclusion, when tensioning a prestressed concrete beam successively with four cables of equal area and equal stress, with percentage losses of 6%, 4%, 2%, and 0% in each cable respectively, the total percentage loss in prestressing force is 12%.
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Community Answer
A post tensioned prestressed concrete beam is tensioned successively b...
In post-tensioning, when cables are tensioned sequentially, the loss in each cable will be different.
Let the cable be numbered as 1,2,3,4 and they were tensioned in a sequence of 1,2,3,4.
Since cable is 4 tensioned, at last, there will be no loss in cable 4.
The loss in prestressing force in wire 1 is maximum and it happens when cables 2,3,4 are tensioned and that will be a total loss in pre-stressing force because after that no wire is tensioned.
The final pre-stressing force to be considered after accounting for the losses will be the one that has a minimum value.
The final pre-stressing force which has a minimum value given as:
Final pre-stressing force = Initial pre-stressing force – maximum loss due to elastic shortening
Therefore, the total percentage loss in prestressing force is the percentage of loss in the cable which was maximum loss i.e. first tensioned i.e. 6 %.
Let the cable be numbered as 1,2,3,4 and they were tensioned in a sequence of 1,2,3,4.
Since cable is 4 tensioned, at last, there will be no loss in cable 4.
The loss in prestressing force in wire 1 is maximum and it happens when cables 2,3,4 are tensioned and that will be a total loss in pre-stressing force because after that no wire is tensioned.
The final pre-stressing force to be considered after accounting for the losses will be the one that has a minimum value.
The final pre-stressing force which has a minimum value given as:
Final pre-stressing force = Initial pre-stressing force – maximum loss due to elastic shortening
Therefore, the total percentage loss in prestressing force is the percentage of loss in the cable which was maximum loss i.e. first tensioned i.e. 6 %.
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