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A rectangular concrete beam of cross-section 150mm wide and 400mm deep is prestressed by a cable with cross-sectional area of 350 mm2. The effective span of the beam is 11m. The cable profile is parabolic with eccentricity of 75mm above the centroid of the cross-section at supports and 75mm below at midspan. If one end of the cable is tensioned, then percentage loss of prestress in the cable due to friction will be____?
Take wobble correction factor (k) and coefficient of friction (μ) between steel reinforcement and duct surface to be 0.15 per 100m and 0.55 respectively.
Correct answer is '7.5-7.8'. Can you explain this answer?
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A rectangular concrete beam of cross-section 150mm wide and 400mm deep...
Concept:
Loss of prestress due to friction is given by:
Loss = p0 (kx + μα)
Where,
p0 = initial prestress
k = wobble correction factor
x = distance from Jacking end
x = 
(when Jacking from both ends)
(when Jacking from both ends)x = L (when Jacking from one end)
μ = Coefficient of friction between steel reinforcement and duct surface
α = Net change in gradient between two points of considerations.
Equation of Cable:
h = e1 + e2
e1 = eccentricity at end
e2 = eccentricity at centre
For x = 0
Calculation:
e1 = 75 mm
e2 = 75 mm
h = e1 + e2 = 75 + 75 = 150 mm
= 0.10909radianWhen Cable is tensioned at one end, the maximum loss of prestress occur at other end
Hence, at x = L = 11m
Loss of prestress = p0 (kx + μα)
x = 11m
μ = 0.55
α = 0.10909 radian
Loss = p0 (0.0015 × 11 + 0.55 × 0.10909)
Loss = p0 (0.07649)
% loss = 7.65%
Most Upvoted Answer
A rectangular concrete beam of cross-section 150mm wide and 400mm deep...
To calculate the percentage loss of prestress in the cable due to friction, we need to determine the frictional force and the initial prestressing force.
First, let's calculate the initial prestressing force:
The cross-sectional area of the cable is given as 350 mm^2.
Assuming the cable material has a stress of 1600 MPa, the initial prestressing force can be calculated as:
Initial Prestressing Force = Stress x Area = 1600 MPa x 350 mm^2 = 560,000 N
Next, let's calculate the frictional force:
The eccentricity of the cable profile is given as 75 mm above the centroid of the cross-section at supports and 75 mm below at midspan.
Considering the effective span of the beam is 11 m, the maximum eccentricity is 75 mm + 75 mm = 150 mm.
The maximum frictional force can be calculated using the formula:
Frictional Force = u x Area x Eccentricity
The coefficient of friction (u) is not given in the question, so we cannot calculate the exact value. However, we can assume a typical value for steel on concrete contact, which is around 0.15.
Frictional Force = 0.15 x 350 mm^2 x 150 mm = 7875 N
Finally, let's calculate the percentage loss of prestress:
Percentage Loss of Prestress = (Frictional Force / Initial Prestressing Force) x 100
Percentage Loss of Prestress = (7875 N / 560,000 N) x 100 = 1.408 %
Therefore, the percentage loss of prestress in the cable due to friction is approximately 1.408%.
First, let's calculate the initial prestressing force:
The cross-sectional area of the cable is given as 350 mm^2.
Assuming the cable material has a stress of 1600 MPa, the initial prestressing force can be calculated as:
Initial Prestressing Force = Stress x Area = 1600 MPa x 350 mm^2 = 560,000 N
Next, let's calculate the frictional force:
The eccentricity of the cable profile is given as 75 mm above the centroid of the cross-section at supports and 75 mm below at midspan.
Considering the effective span of the beam is 11 m, the maximum eccentricity is 75 mm + 75 mm = 150 mm.
The maximum frictional force can be calculated using the formula:
Frictional Force = u x Area x Eccentricity
The coefficient of friction (u) is not given in the question, so we cannot calculate the exact value. However, we can assume a typical value for steel on concrete contact, which is around 0.15.
Frictional Force = 0.15 x 350 mm^2 x 150 mm = 7875 N
Finally, let's calculate the percentage loss of prestress:
Percentage Loss of Prestress = (Frictional Force / Initial Prestressing Force) x 100
Percentage Loss of Prestress = (7875 N / 560,000 N) x 100 = 1.408 %
Therefore, the percentage loss of prestress in the cable due to friction is approximately 1.408%.
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A rectangular concrete beam of cross-section 150mm wide and 400mm deep is prestressed by a cable with cross-sectional area of 350 mm2. The effective span of the beam is 11m. The cable profile is parabolic with eccentricity of 75mm above the centroid of the cross-section at supports and 75mm below at midspan. If one end of the cable is tensioned, then percentage loss of prestress in the cable due to friction will be____?Take wobble correction factor (k) and coefficient of friction (μ) between steel reinforcement and duct surface to be 0.15 per 100m and 0.55 respectively.Correct answer is '7.5-7.8'. Can you explain this answer?
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A rectangular concrete beam of cross-section 150mm wide and 400mm deep is prestressed by a cable with cross-sectional area of 350 mm2. The effective span of the beam is 11m. The cable profile is parabolic with eccentricity of 75mm above the centroid of the cross-section at supports and 75mm below at midspan. If one end of the cable is tensioned, then percentage loss of prestress in the cable due to friction will be____?Take wobble correction factor (k) and coefficient of friction (μ) between steel reinforcement and duct surface to be 0.15 per 100m and 0.55 respectively.Correct answer is '7.5-7.8'. 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 rectangular concrete beam of cross-section 150mm wide and 400mm deep is prestressed by a cable with cross-sectional area of 350 mm2. The effective span of the beam is 11m. The cable profile is parabolic with eccentricity of 75mm above the centroid of the cross-section at supports and 75mm below at midspan. If one end of the cable is tensioned, then percentage loss of prestress in the cable due to friction will be____?Take wobble correction factor (k) and coefficient of friction (μ) between steel reinforcement and duct surface to be 0.15 per 100m and 0.55 respectively.Correct answer is '7.5-7.8'. 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 rectangular concrete beam of cross-section 150mm wide and 400mm deep is prestressed by a cable with cross-sectional area of 350 mm2. The effective span of the beam is 11m. The cable profile is parabolic with eccentricity of 75mm above the centroid of the cross-section at supports and 75mm below at midspan. If one end of the cable is tensioned, then percentage loss of prestress in the cable due to friction will be____?Take wobble correction factor (k) and coefficient of friction (μ) between steel reinforcement and duct surface to be 0.15 per 100m and 0.55 respectively.Correct answer is '7.5-7.8'. Can you explain this answer?.
A rectangular concrete beam of cross-section 150mm wide and 400mm deep is prestressed by a cable with cross-sectional area of 350 mm2. The effective span of the beam is 11m. The cable profile is parabolic with eccentricity of 75mm above the centroid of the cross-section at supports and 75mm below at midspan. If one end of the cable is tensioned, then percentage loss of prestress in the cable due to friction will be____?Take wobble correction factor (k) and coefficient of friction (μ) between steel reinforcement and duct surface to be 0.15 per 100m and 0.55 respectively.Correct answer is '7.5-7.8'. 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 rectangular concrete beam of cross-section 150mm wide and 400mm deep is prestressed by a cable with cross-sectional area of 350 mm2. The effective span of the beam is 11m. The cable profile is parabolic with eccentricity of 75mm above the centroid of the cross-section at supports and 75mm below at midspan. If one end of the cable is tensioned, then percentage loss of prestress in the cable due to friction will be____?Take wobble correction factor (k) and coefficient of friction (μ) between steel reinforcement and duct surface to be 0.15 per 100m and 0.55 respectively.Correct answer is '7.5-7.8'. 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 rectangular concrete beam of cross-section 150mm wide and 400mm deep is prestressed by a cable with cross-sectional area of 350 mm2. The effective span of the beam is 11m. The cable profile is parabolic with eccentricity of 75mm above the centroid of the cross-section at supports and 75mm below at midspan. If one end of the cable is tensioned, then percentage loss of prestress in the cable due to friction will be____?Take wobble correction factor (k) and coefficient of friction (μ) between steel reinforcement and duct surface to be 0.15 per 100m and 0.55 respectively.Correct answer is '7.5-7.8'. Can you explain this answer?.
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ample number of questions to practice A rectangular concrete beam of cross-section 150mm wide and 400mm deep is prestressed by a cable with cross-sectional area of 350 mm2. The effective span of the beam is 11m. The cable profile is parabolic with eccentricity of 75mm above the centroid of the cross-section at supports and 75mm below at midspan. If one end of the cable is tensioned, then percentage loss of prestress in the cable due to friction will be____?Take wobble correction factor (k) and coefficient of friction (μ) between steel reinforcement and duct surface to be 0.15 per 100m and 0.55 respectively.Correct answer is '7.5-7.8'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
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