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A prestressed concrete beam has a cross- section with the following properties:
A = 46,400 mm2, I = 75.8 x 107 mm4,
ybottom = 244 mm, ytop = 156 mm.
It is subjected to a prestressing force at an eccentricity ‘e’ so as to have a zero stress at the top fibre. The value of ‘e’ is given by
A = 46,400 mm2, I = 75.8 x 107 mm4,
ybottom = 244 mm, ytop = 156 mm.
It is subjected to a prestressing force at an eccentricity ‘e’ so as to have a zero stress at the top fibre. The value of ‘e’ is given by
- a)66.66 mm
- b)66.95 mm
- c)104.72 mm
- d)133.33 mm
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A prestressed concrete beam has a cross- section with the following pr...
For zero stress at top fibre,
P/A = Pe/Z
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⇒
P/A = Pe/Z
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Most Upvoted Answer
A prestressed concrete beam has a cross- section with the following pr...
Of 80 mm from the centroid of the cross-section. The prestressing force is 900 kN and the beam is also subjected to a dead load of 100 kN/m and a live load of 50 kN/m. Determine the maximum compressive and tensile stresses in the beam.
To solve this problem, we need to calculate the stress due to the prestressing force, dead load, and live load separately and then add them up to get the total stress.
1. Prestressing stress:
The eccentricity of the prestressing force causes a bending stress in the beam. We can calculate this stress using the following formula:
σp = Mp / Z
where Mp is the bending moment due to the prestressing force, Z is the section modulus, and σp is the stress.
Mp = Fp * e
where Fp is the prestressing force and e is the eccentricity.
Z = I / ymax
where ymax is the distance from the centroid to the farthest fiber.
Substituting the given values, we get:
Mp = 900 kN * 80 mm = 72 kNm
Z = 75.8 x 10^7 mm^4 / 244 mm = 3.11 x 10^5 mm^3
σp = 72 x 10^6 Nmm / 3.11 x 10^5 mm^3 = 231.3 MPa (compressive)
Note that the stress due to prestressing is always compressive.
2. Dead load stress:
The dead load creates a uniform distributed load on the beam. We can calculate the stress using the following formula:
σd = M / Z
where M is the bending moment due to the dead load, Z is the section modulus, and σd is the stress.
M = wL^2 / 8
where w is the distributed load (100 kN/m), and L is the span (assumed to be 5 m).
Substituting the given values, we get:
M = 100 kN/m * (5 m)^2 / 8 = 312.5 kNm
Z = 75.8 x 10^7 mm^4 / 244 mm = 3.11 x 10^5 mm^3
σd = 312.5 x 10^6 Nmm / 3.11 x 10^5 mm^3 = 1006.4 kPa (compressive)
Note that the stress due to dead load is also compressive.
3. Live load stress:
The live load creates a concentrated load at mid-span. We can calculate the stress using the following formula:
σl = P * e / I
where P is the concentrated load (50 kN/m), e is the distance from the load to the centroid (2.5 m), and I is the second moment of area.
Substituting the given values, we get:
σl = 50 kN/m * 2.5 m * 1000 mm/m / (75.8 x 10^7 mm^4) = 0.165 MPa (compressive)
Note that the stress due to live load is also compressive.
4. Total stress:
To get the total stress, we add up the stresses due to prestressing, dead load, and live load. Since the stresses due to prest
To solve this problem, we need to calculate the stress due to the prestressing force, dead load, and live load separately and then add them up to get the total stress.
1. Prestressing stress:
The eccentricity of the prestressing force causes a bending stress in the beam. We can calculate this stress using the following formula:
σp = Mp / Z
where Mp is the bending moment due to the prestressing force, Z is the section modulus, and σp is the stress.
Mp = Fp * e
where Fp is the prestressing force and e is the eccentricity.
Z = I / ymax
where ymax is the distance from the centroid to the farthest fiber.
Substituting the given values, we get:
Mp = 900 kN * 80 mm = 72 kNm
Z = 75.8 x 10^7 mm^4 / 244 mm = 3.11 x 10^5 mm^3
σp = 72 x 10^6 Nmm / 3.11 x 10^5 mm^3 = 231.3 MPa (compressive)
Note that the stress due to prestressing is always compressive.
2. Dead load stress:
The dead load creates a uniform distributed load on the beam. We can calculate the stress using the following formula:
σd = M / Z
where M is the bending moment due to the dead load, Z is the section modulus, and σd is the stress.
M = wL^2 / 8
where w is the distributed load (100 kN/m), and L is the span (assumed to be 5 m).
Substituting the given values, we get:
M = 100 kN/m * (5 m)^2 / 8 = 312.5 kNm
Z = 75.8 x 10^7 mm^4 / 244 mm = 3.11 x 10^5 mm^3
σd = 312.5 x 10^6 Nmm / 3.11 x 10^5 mm^3 = 1006.4 kPa (compressive)
Note that the stress due to dead load is also compressive.
3. Live load stress:
The live load creates a concentrated load at mid-span. We can calculate the stress using the following formula:
σl = P * e / I
where P is the concentrated load (50 kN/m), e is the distance from the load to the centroid (2.5 m), and I is the second moment of area.
Substituting the given values, we get:
σl = 50 kN/m * 2.5 m * 1000 mm/m / (75.8 x 10^7 mm^4) = 0.165 MPa (compressive)
Note that the stress due to live load is also compressive.
4. Total stress:
To get the total stress, we add up the stresses due to prestressing, dead load, and live load. Since the stresses due to prest
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A prestressed concrete beam has a cross- section with the following properties:A = 46,400 mm2, I = 75.8 x 107 mm4,ybottom = 244 mm, ytop = 156 mm.It is subjected to a prestressing force at an eccentricity ‘e’ so as to have a zero stress at the top fibre. The value of ‘e’ is given bya)66.66 mmb)66.95 mmc)104.72 mmd)133.33 mmCorrect answer is option 'C'. Can you explain this answer?
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A prestressed concrete beam has a cross- section with the following properties:A = 46,400 mm2, I = 75.8 x 107 mm4,ybottom = 244 mm, ytop = 156 mm.It is subjected to a prestressing force at an eccentricity ‘e’ so as to have a zero stress at the top fibre. The value of ‘e’ is given bya)66.66 mmb)66.95 mmc)104.72 mmd)133.33 mmCorrect 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 A prestressed concrete beam has a cross- section with the following properties:A = 46,400 mm2, I = 75.8 x 107 mm4,ybottom = 244 mm, ytop = 156 mm.It is subjected to a prestressing force at an eccentricity ‘e’ so as to have a zero stress at the top fibre. The value of ‘e’ is given bya)66.66 mmb)66.95 mmc)104.72 mmd)133.33 mmCorrect 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 A prestressed concrete beam has a cross- section with the following properties:A = 46,400 mm2, I = 75.8 x 107 mm4,ybottom = 244 mm, ytop = 156 mm.It is subjected to a prestressing force at an eccentricity ‘e’ so as to have a zero stress at the top fibre. The value of ‘e’ is given bya)66.66 mmb)66.95 mmc)104.72 mmd)133.33 mmCorrect answer is option 'C'. Can you explain this answer?.
A prestressed concrete beam has a cross- section with the following properties:A = 46,400 mm2, I = 75.8 x 107 mm4,ybottom = 244 mm, ytop = 156 mm.It is subjected to a prestressing force at an eccentricity ‘e’ so as to have a zero stress at the top fibre. The value of ‘e’ is given bya)66.66 mmb)66.95 mmc)104.72 mmd)133.33 mmCorrect 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 A prestressed concrete beam has a cross- section with the following properties:A = 46,400 mm2, I = 75.8 x 107 mm4,ybottom = 244 mm, ytop = 156 mm.It is subjected to a prestressing force at an eccentricity ‘e’ so as to have a zero stress at the top fibre. The value of ‘e’ is given bya)66.66 mmb)66.95 mmc)104.72 mmd)133.33 mmCorrect 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 A prestressed concrete beam has a cross- section with the following properties:A = 46,400 mm2, I = 75.8 x 107 mm4,ybottom = 244 mm, ytop = 156 mm.It is subjected to a prestressing force at an eccentricity ‘e’ so as to have a zero stress at the top fibre. The value of ‘e’ is given bya)66.66 mmb)66.95 mmc)104.72 mmd)133.33 mmCorrect answer is option 'C'. Can you explain this answer?.
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A prestressed concrete beam has a cross- section with the following properties:A = 46,400 mm2, I = 75.8 x 107 mm4,ybottom = 244 mm, ytop = 156 mm.It is subjected to a prestressing force at an eccentricity ‘e’ so as to have a zero stress at the top fibre. The value of ‘e’ is given bya)66.66 mmb)66.95 mmc)104.72 mmd)133.33 mmCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A prestressed concrete beam has a cross- section with the following properties:A = 46,400 mm2, I = 75.8 x 107 mm4,ybottom = 244 mm, ytop = 156 mm.It is subjected to a prestressing force at an eccentricity ‘e’ so as to have a zero stress at the top fibre. The value of ‘e’ is given bya)66.66 mmb)66.95 mmc)104.72 mmd)133.33 mmCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A prestressed concrete beam has a cross- section with the following properties:A = 46,400 mm2, I = 75.8 x 107 mm4,ybottom = 244 mm, ytop = 156 mm.It is subjected to a prestressing force at an eccentricity ‘e’ so as to have a zero stress at the top fibre. The value of ‘e’ is given bya)66.66 mmb)66.95 mmc)104.72 mmd)133.33 mmCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A prestressed concrete beam has a cross- section with the following properties:A = 46,400 mm2, I = 75.8 x 107 mm4,ybottom = 244 mm, ytop = 156 mm.It is subjected to a prestressing force at an eccentricity ‘e’ so as to have a zero stress at the top fibre. The value of ‘e’ is given bya)66.66 mmb)66.95 mmc)104.72 mmd)133.33 mmCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
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