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A simply supported prestressed beam of 300 × 500 mm in c/s is subjected to a superimposed load of 20 kN/m over a span of 10m. If a prestressing force of 1000 kN is applied through a straight tendon located along centroidal axis then what is the extreme top fiber stress at the mid section:
- a)26
- b)27
Correct answer is between '26,27'. Can you explain this answer?
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A simply supported prestressed beam of 300 × 500 mm in c/s is subject...
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Solution:
Given data:
Cross-sectional dimensions of the beam = 300 × 500 mm
Span of the beam = 10 m
Superimposed load = 20 kN/m
Prestressing force = 1000 kN
We need to find the extreme top fiber stress at the mid-section of the beam.
Assumptions:
1. The beam is made up of homogeneous and isotropic material.
2. The beam is initially stress-free.
3. The beam is simply supported.
4. The effective prestressing force is the difference between the initial prestressing force and the force due to the losses.
Calculation:
1. Calculation of Effective Prestressing Force:
Initial Prestressing Force = 1000 kN
Losses in Prestressing:
a) Losses due to friction = 0.2% of the initial prestressing force
Loss due to friction = 0.2/100 × 1000 = 2 kN
b) Losses due to anchorage slip = 0.5% of the initial prestressing force
Loss due to anchorage slip = 0.5/100 × 1000 = 5 kN
Effective Prestressing Force = Initial Prestressing Force – Losses in Prestressing
Effective Prestressing Force = 1000 – (2 + 5) = 993 kN
2. Calculation of Bending Moment:
Superimposed Load = 20 kN/m
Span of the beam = 10 m
Maximum bending moment occurs at the mid-span of the beam.
Bending Moment (M) = wl^2/8 = 20 × 10^2/8 = 250 kNm
3. Calculation of Extreme Top Fiber Stress:
Section Modulus (Z) = (bd^2)/6 = (300 × 500^2)/6 × 10^6 = 12.5 × 10^-3 m^3
Extreme Top Fiber Stress (σ) = (M/Z) + (Pe/A)
Where,
P = Effective Prestressing Force = 993 kN
e = eccentricity of the prestressing force
A = Cross-sectional area of the beam = 300 × 500 × 10^-6 = 0.15 m^2
e = (P × y)/A
where y is the distance of the centroid of the section from the extreme top fiber.
y = (500/2) - 300/2 = 100 mm = 0.1 m
e = (993 × 0.1)/0.15 = 662 mm
σ = (250 × 10^6/12.5 × 10^-3) + (993 × 10^3/0.15) × (0.1 + 662/1000)
σ = 26.22 MPa (approx)
Therefore, the extreme top fiber stress at the mid-section of the beam is 26.22 MPa (approx).
Given data:
Cross-sectional dimensions of the beam = 300 × 500 mm
Span of the beam = 10 m
Superimposed load = 20 kN/m
Prestressing force = 1000 kN
We need to find the extreme top fiber stress at the mid-section of the beam.
Assumptions:
1. The beam is made up of homogeneous and isotropic material.
2. The beam is initially stress-free.
3. The beam is simply supported.
4. The effective prestressing force is the difference between the initial prestressing force and the force due to the losses.
Calculation:
1. Calculation of Effective Prestressing Force:
Initial Prestressing Force = 1000 kN
Losses in Prestressing:
a) Losses due to friction = 0.2% of the initial prestressing force
Loss due to friction = 0.2/100 × 1000 = 2 kN
b) Losses due to anchorage slip = 0.5% of the initial prestressing force
Loss due to anchorage slip = 0.5/100 × 1000 = 5 kN
Effective Prestressing Force = Initial Prestressing Force – Losses in Prestressing
Effective Prestressing Force = 1000 – (2 + 5) = 993 kN
2. Calculation of Bending Moment:
Superimposed Load = 20 kN/m
Span of the beam = 10 m
Maximum bending moment occurs at the mid-span of the beam.
Bending Moment (M) = wl^2/8 = 20 × 10^2/8 = 250 kNm
3. Calculation of Extreme Top Fiber Stress:
Section Modulus (Z) = (bd^2)/6 = (300 × 500^2)/6 × 10^6 = 12.5 × 10^-3 m^3
Extreme Top Fiber Stress (σ) = (M/Z) + (Pe/A)
Where,
P = Effective Prestressing Force = 993 kN
e = eccentricity of the prestressing force
A = Cross-sectional area of the beam = 300 × 500 × 10^-6 = 0.15 m^2
e = (P × y)/A
where y is the distance of the centroid of the section from the extreme top fiber.
y = (500/2) - 300/2 = 100 mm = 0.1 m
e = (993 × 0.1)/0.15 = 662 mm
σ = (250 × 10^6/12.5 × 10^-3) + (993 × 10^3/0.15) × (0.1 + 662/1000)
σ = 26.22 MPa (approx)
Therefore, the extreme top fiber stress at the mid-section of the beam is 26.22 MPa (approx).
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A simply supported prestressed beam of 300 × 500 mm in c/s is subjected to a superimposed load of 20 kN/m over a span of 10m. If a prestressing force of 1000 kN is applied through a straight tendon located along centroidal axis then what is the extreme top fiber stress at the mid section:a)26b)27Correct answer is between '26,27'. Can you explain this answer?
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A simply supported prestressed beam of 300 × 500 mm in c/s is subjected to a superimposed load of 20 kN/m over a span of 10m. If a prestressing force of 1000 kN is applied through a straight tendon located along centroidal axis then what is the extreme top fiber stress at the mid section:a)26b)27Correct answer is between '26,27'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A simply supported prestressed beam of 300 × 500 mm in c/s is subjected to a superimposed load of 20 kN/m over a span of 10m. If a prestressing force of 1000 kN is applied through a straight tendon located along centroidal axis then what is the extreme top fiber stress at the mid section:a)26b)27Correct answer is between '26,27'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A simply supported prestressed beam of 300 × 500 mm in c/s is subjected to a superimposed load of 20 kN/m over a span of 10m. If a prestressing force of 1000 kN is applied through a straight tendon located along centroidal axis then what is the extreme top fiber stress at the mid section:a)26b)27Correct answer is between '26,27'. Can you explain this answer?.
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