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A prestress concrete rectangular beam of size 300 mm × 900 mm is pre-stressed with an initial prestressing force of 700 kN at an eccentricity of 300 mm. Stress at the top beam section due to prestress alone in, N/mm2 is:
- a)2.59 (compression)
- b)3.59 (compression)
- c)2.59 (tension)
- d)3.59 (tension)
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A prestress concrete rectangular beam of size 300 mm × 900 mm is...
⇒ 2.593 – 5.185
⇒ -2.592 N/mm2
Most Upvoted Answer
A prestress concrete rectangular beam of size 300 mm × 900 mm is...
X 500 mm is subjected to a service load of 100 kN. The concrete has a compressive strength of 30 MPa and the steel has a yield strength of 500 MPa. Calculate the required prestressing force to ensure that the concrete remains in compression under the service load.
To calculate the required prestressing force, we need to determine the maximum bending moment and the corresponding stress in the concrete.
The maximum bending moment (M) can be calculated using the formula:
M = (w * l^2) / 8
where w is the service load per unit length and l is the span length.
Given that the width of the beam (b) is 300 mm and the depth (d) is 500 mm, we can calculate the section modulus (S) using the formula:
S = (b * d^2) / 6
The stress in the concrete (σc) can be calculated using the formula:
σc = M / S
Finally, the required prestressing force (Fp) can be calculated using the formula:
Fp = σc * Ac
where Ac is the cross-sectional area of the concrete.
Given:
Width of the beam (b) = 300 mm
Depth of the beam (d) = 500 mm
Service load (w) = 100 kN
Span length (l) = ?
Compressive strength of concrete (fc) = 30 MPa
Yield strength of steel (fy) = 500 MPa
First, let's calculate the span length (l) using the formula:
w = (Total load) / (length)
100 kN/m = (100 kN) / (l)
l = (100 kN) / (100 kN/m)
l = 1 m
Now, let's calculate the section modulus (S) using the formula:
S = (b * d^2) / 6
S = (300 mm * (500 mm)^2) / 6
S = 25,000,000 mm^3
Next, let's calculate the maximum bending moment (M) using the formula:
M = (w * l^2) / 8
M = (100 kN/m * (1 m)^2) / 8
M = 12.5 kNm
Now, let's calculate the stress in the concrete (σc) using the formula:
σc = M / S
σc = 12.5 kNm / 25,000,000 mm^3
σc = 0.0005 MPa
Finally, let's calculate the required prestressing force (Fp) using the formula:
Fp = σc * Ac
Fp = 0.0005 MPa * (300 mm * 500 mm)
Fp = 75 kN
Therefore, the required prestressing force to ensure that the concrete remains in compression under the service load is 75 kN.
To calculate the required prestressing force, we need to determine the maximum bending moment and the corresponding stress in the concrete.
The maximum bending moment (M) can be calculated using the formula:
M = (w * l^2) / 8
where w is the service load per unit length and l is the span length.
Given that the width of the beam (b) is 300 mm and the depth (d) is 500 mm, we can calculate the section modulus (S) using the formula:
S = (b * d^2) / 6
The stress in the concrete (σc) can be calculated using the formula:
σc = M / S
Finally, the required prestressing force (Fp) can be calculated using the formula:
Fp = σc * Ac
where Ac is the cross-sectional area of the concrete.
Given:
Width of the beam (b) = 300 mm
Depth of the beam (d) = 500 mm
Service load (w) = 100 kN
Span length (l) = ?
Compressive strength of concrete (fc) = 30 MPa
Yield strength of steel (fy) = 500 MPa
First, let's calculate the span length (l) using the formula:
w = (Total load) / (length)
100 kN/m = (100 kN) / (l)
l = (100 kN) / (100 kN/m)
l = 1 m
Now, let's calculate the section modulus (S) using the formula:
S = (b * d^2) / 6
S = (300 mm * (500 mm)^2) / 6
S = 25,000,000 mm^3
Next, let's calculate the maximum bending moment (M) using the formula:
M = (w * l^2) / 8
M = (100 kN/m * (1 m)^2) / 8
M = 12.5 kNm
Now, let's calculate the stress in the concrete (σc) using the formula:
σc = M / S
σc = 12.5 kNm / 25,000,000 mm^3
σc = 0.0005 MPa
Finally, let's calculate the required prestressing force (Fp) using the formula:
Fp = σc * Ac
Fp = 0.0005 MPa * (300 mm * 500 mm)
Fp = 75 kN
Therefore, the required prestressing force to ensure that the concrete remains in compression under the service load is 75 kN.
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A prestress concrete rectangular beam of size 300 mm × 900 mm is pre-stressed with an initial prestressing force of 700 kN at an eccentricity of 300 mm. Stress at the top beam section due to prestress alone in, N/mm2is:a)2.59 (compression)b)3.59 (compression)c)2.59 (tension)d)3.59 (tension)Correct answer is option 'C'. Can you explain this answer?
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A prestress concrete rectangular beam of size 300 mm × 900 mm is pre-stressed with an initial prestressing force of 700 kN at an eccentricity of 300 mm. Stress at the top beam section due to prestress alone in, N/mm2is:a)2.59 (compression)b)3.59 (compression)c)2.59 (tension)d)3.59 (tension)Correct 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 prestress concrete rectangular beam of size 300 mm × 900 mm is pre-stressed with an initial prestressing force of 700 kN at an eccentricity of 300 mm. Stress at the top beam section due to prestress alone in, N/mm2is:a)2.59 (compression)b)3.59 (compression)c)2.59 (tension)d)3.59 (tension)Correct 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 prestress concrete rectangular beam of size 300 mm × 900 mm is pre-stressed with an initial prestressing force of 700 kN at an eccentricity of 300 mm. Stress at the top beam section due to prestress alone in, N/mm2is:a)2.59 (compression)b)3.59 (compression)c)2.59 (tension)d)3.59 (tension)Correct answer is option 'C'. Can you explain this answer?.
A prestress concrete rectangular beam of size 300 mm × 900 mm is pre-stressed with an initial prestressing force of 700 kN at an eccentricity of 300 mm. Stress at the top beam section due to prestress alone in, N/mm2is:a)2.59 (compression)b)3.59 (compression)c)2.59 (tension)d)3.59 (tension)Correct 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 prestress concrete rectangular beam of size 300 mm × 900 mm is pre-stressed with an initial prestressing force of 700 kN at an eccentricity of 300 mm. Stress at the top beam section due to prestress alone in, N/mm2is:a)2.59 (compression)b)3.59 (compression)c)2.59 (tension)d)3.59 (tension)Correct 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 prestress concrete rectangular beam of size 300 mm × 900 mm is pre-stressed with an initial prestressing force of 700 kN at an eccentricity of 300 mm. Stress at the top beam section due to prestress alone in, N/mm2is:a)2.59 (compression)b)3.59 (compression)c)2.59 (tension)d)3.59 (tension)Correct answer is option 'C'. Can you explain this answer?.
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