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A simply supported prismatic concrete beam of rectangular cross-section, having a span of 8 m, is prestressed with an effective prestressing force of 600 kN. The eccentricity of the prestressing tendon is zero at supports and varies linearly to a value of e at the mid-span. In order to balance an external concentrated load of 12 kN applied at the mid-span, the required value of e (in mm, round off to the nearest integer) of the tendon, is _______.
Correct answer is '40'. Can you explain this answer?
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A simply supported prismatic concrete beam of rectangular cross-sectio...
P = 600 kN
Simply supported span = L = 8 m
To support a point load applied at mid span (W) = 12 kN
Balancing load = Point load
2P sin θ = W
= 40 mm
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A simply supported prismatic concrete beam of rectangular cross-sectio...
Calculation of Required Eccentricity
Given:
- Span of the beam = 8 m
- Effective prestressing force = 600 kN
- External concentrated load at mid-span = 12 kN
To find:
- Required value of e (in mm) of the tendon to balance the load
Assumptions:
- Beam is prismatic and has rectangular cross-section
- Eccentricity of the prestressing tendon varies linearly from zero at supports to e at mid-span
- Material properties of the beam are constant
Solution:
1. Calculate the flexural capacity of the beam without prestressing:
Mu = wl2/8 = 12x82/8 = 96 kNm
2. Calculate the required prestressing force to balance the external load:
Pb = 12x8/2 = 48 kN
3. Calculate the required eccentricity of the prestressing tendon at mid-span:
e = (Pbl)/fp
where fp is the stress in the prestressing tendon at mid-span due to the effective prestressing force:
fp = Pe/Ap
where Pe is the effective prestressing force and Ap is the area of the prestressing tendon.
Assuming a rectangular tendon with a width of 50 mm and a depth of 100 mm, the area of the tendon is:
Ap = bd = 50x100 = 5000 mm2
Therefore:
fp = 600x103/5000 = 120 MPa
Substituting values in the equation for e:
e = (48x8)/(120x106) = 0.004 mm
This value is too small and indicates that the prestressing force is insufficient to balance the external load.
4. Increase the eccentricity of the prestressing tendon at mid-span until the required prestressing force is achieved:
Pe = Pb/sinθ
where θ is the angle of the prestressing tendon at mid-span with respect to the horizontal.
Assuming a rectangular beam with a width of 200 mm and a depth of 400 mm, the moment of inertia of the cross-section is:
I = bd3/12 = 200x4003/12 = 21.33x106 mm4
The stress in the concrete due to the prestressing force is:
fc
Given:
- Span of the beam = 8 m
- Effective prestressing force = 600 kN
- External concentrated load at mid-span = 12 kN
To find:
- Required value of e (in mm) of the tendon to balance the load
Assumptions:
- Beam is prismatic and has rectangular cross-section
- Eccentricity of the prestressing tendon varies linearly from zero at supports to e at mid-span
- Material properties of the beam are constant
Solution:
1. Calculate the flexural capacity of the beam without prestressing:
Mu = wl2/8 = 12x82/8 = 96 kNm
2. Calculate the required prestressing force to balance the external load:
Pb = 12x8/2 = 48 kN
3. Calculate the required eccentricity of the prestressing tendon at mid-span:
e = (Pbl)/fp
where fp is the stress in the prestressing tendon at mid-span due to the effective prestressing force:
fp = Pe/Ap
where Pe is the effective prestressing force and Ap is the area of the prestressing tendon.
Assuming a rectangular tendon with a width of 50 mm and a depth of 100 mm, the area of the tendon is:
Ap = bd = 50x100 = 5000 mm2
Therefore:
fp = 600x103/5000 = 120 MPa
Substituting values in the equation for e:
e = (48x8)/(120x106) = 0.004 mm
This value is too small and indicates that the prestressing force is insufficient to balance the external load.
4. Increase the eccentricity of the prestressing tendon at mid-span until the required prestressing force is achieved:
Pe = Pb/sinθ
where θ is the angle of the prestressing tendon at mid-span with respect to the horizontal.
Assuming a rectangular beam with a width of 200 mm and a depth of 400 mm, the moment of inertia of the cross-section is:
I = bd3/12 = 200x4003/12 = 21.33x106 mm4
The stress in the concrete due to the prestressing force is:
fc
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A simply supported prismatic concrete beam of rectangular cross-section, having a span of 8 m, is prestressed with an effective prestressing force of 600 kN. The eccentricity of the prestressing tendon is zero at supports and varies linearly to a value of e at the mid-span. In order to balance an external concentrated load of 12 kN applied at the mid-span, the required value of e (in mm, round off to the nearest integer) of the tendon, is _______.Correct answer is '40'. Can you explain this answer?
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A simply supported prismatic concrete beam of rectangular cross-section, having a span of 8 m, is prestressed with an effective prestressing force of 600 kN. The eccentricity of the prestressing tendon is zero at supports and varies linearly to a value of e at the mid-span. In order to balance an external concentrated load of 12 kN applied at the mid-span, the required value of e (in mm, round off to the nearest integer) of the tendon, is _______.Correct answer is '40'. 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 prismatic concrete beam of rectangular cross-section, having a span of 8 m, is prestressed with an effective prestressing force of 600 kN. The eccentricity of the prestressing tendon is zero at supports and varies linearly to a value of e at the mid-span. In order to balance an external concentrated load of 12 kN applied at the mid-span, the required value of e (in mm, round off to the nearest integer) of the tendon, is _______.Correct answer is '40'. 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 prismatic concrete beam of rectangular cross-section, having a span of 8 m, is prestressed with an effective prestressing force of 600 kN. The eccentricity of the prestressing tendon is zero at supports and varies linearly to a value of e at the mid-span. In order to balance an external concentrated load of 12 kN applied at the mid-span, the required value of e (in mm, round off to the nearest integer) of the tendon, is _______.Correct answer is '40'. Can you explain this answer?.
A simply supported prismatic concrete beam of rectangular cross-section, having a span of 8 m, is prestressed with an effective prestressing force of 600 kN. The eccentricity of the prestressing tendon is zero at supports and varies linearly to a value of e at the mid-span. In order to balance an external concentrated load of 12 kN applied at the mid-span, the required value of e (in mm, round off to the nearest integer) of the tendon, is _______.Correct answer is '40'. 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 prismatic concrete beam of rectangular cross-section, having a span of 8 m, is prestressed with an effective prestressing force of 600 kN. The eccentricity of the prestressing tendon is zero at supports and varies linearly to a value of e at the mid-span. In order to balance an external concentrated load of 12 kN applied at the mid-span, the required value of e (in mm, round off to the nearest integer) of the tendon, is _______.Correct answer is '40'. 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 prismatic concrete beam of rectangular cross-section, having a span of 8 m, is prestressed with an effective prestressing force of 600 kN. The eccentricity of the prestressing tendon is zero at supports and varies linearly to a value of e at the mid-span. In order to balance an external concentrated load of 12 kN applied at the mid-span, the required value of e (in mm, round off to the nearest integer) of the tendon, is _______.Correct answer is '40'. Can you explain this answer?.
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