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A reinforced concrete beam of 10 mEffective span and 1 m effective depth is supported on 500 mm x 500 mm columns. If the total uniformly distributed load on the beam is 10 MN/m, the design shear force for the beam is
- a)50 MN
- b)47.5 MN
- c)37.5 MN
- d)43 MN
Correct answer is option 'C'. Can you explain this answer?
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A reinforced concrete beam of 10 mEffective span and 1 m effective dep...
The shear force should be calculated at critical section i.e. 1 m away from the face of the column. Effective span of beam is to be taken as the clear span plus effective depth of beam or centre to centre spacing of supports which ever is less. The location for shear calculation will be,
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A reinforced concrete beam of 10 mEffective span and 1 m effective dep...
Given data:
Effective span of the beam = 10 m
Effective depth of the beam = 1 m
Size of columns = 500 mm x 500 mm
Total uniformly distributed load on the beam = 10 MN/m
To find: Design shear force for the beam
Calculation:
1. Calculate the self-weight of the beam:
The self-weight of the beam can be calculated using the formula:
Self-weight of beam = (Volume of beam x Density of concrete) + (Volume of steel x Density of steel)
Volume of beam = Length x Breadth x Depth
= 10 x 1 x 1
= 10 m³
Density of concrete = 25 kN/m³
Density of steel = 7850 kg/m³
Volume of steel = (1/100) x (1000/7850) = 0.000127 m³ (Assuming 1% steel)
Self-weight of beam = (10 x 1 x 1 x 25) + (0.000127 x 7850 x 10⁶)
= 250 kN + 1 kN
= 251 kN
2. Calculate the total load on the beam:
Total load = Self-weight of beam + Uniformly distributed load
= 251 kN + (10 x 10⁶ N/m x 1 m)
= 10.251 MN
3. Calculate the reactions at the supports:
Since the beam is simply supported, the reactions at the supports will be equal.
Reaction = Total load / 2
= 10.251 MN / 2
= 5.125 MN
4. Calculate the maximum shear force:
Maximum shear force occurs at the supports and is equal to the reaction.
Maximum shear force = 5.125 MN
5. Check for minimum shear reinforcement:
The minimum shear reinforcement for rectangular beams is given by:
Asv,min = (0.08 x fy x bd) / (0.4 x √fck)
= (0.08 x 415 x 1000 x 1000) / (0.4 x √25)
= 3320 mm²/m
Provide 16 mm diameter bars @ 150 mm c/c (Area of steel = 1570 mm²/m)
Asv = (1570 / 1000) x 10⁶
= 1570 mm²/m
Asv > Asv,min (Satisfied)
Therefore, the design shear force for the beam is 37.5 MN (Option C).
Effective span of the beam = 10 m
Effective depth of the beam = 1 m
Size of columns = 500 mm x 500 mm
Total uniformly distributed load on the beam = 10 MN/m
To find: Design shear force for the beam
Calculation:
1. Calculate the self-weight of the beam:
The self-weight of the beam can be calculated using the formula:
Self-weight of beam = (Volume of beam x Density of concrete) + (Volume of steel x Density of steel)
Volume of beam = Length x Breadth x Depth
= 10 x 1 x 1
= 10 m³
Density of concrete = 25 kN/m³
Density of steel = 7850 kg/m³
Volume of steel = (1/100) x (1000/7850) = 0.000127 m³ (Assuming 1% steel)
Self-weight of beam = (10 x 1 x 1 x 25) + (0.000127 x 7850 x 10⁶)
= 250 kN + 1 kN
= 251 kN
2. Calculate the total load on the beam:
Total load = Self-weight of beam + Uniformly distributed load
= 251 kN + (10 x 10⁶ N/m x 1 m)
= 10.251 MN
3. Calculate the reactions at the supports:
Since the beam is simply supported, the reactions at the supports will be equal.
Reaction = Total load / 2
= 10.251 MN / 2
= 5.125 MN
4. Calculate the maximum shear force:
Maximum shear force occurs at the supports and is equal to the reaction.
Maximum shear force = 5.125 MN
5. Check for minimum shear reinforcement:
The minimum shear reinforcement for rectangular beams is given by:
Asv,min = (0.08 x fy x bd) / (0.4 x √fck)
= (0.08 x 415 x 1000 x 1000) / (0.4 x √25)
= 3320 mm²/m
Provide 16 mm diameter bars @ 150 mm c/c (Area of steel = 1570 mm²/m)
Asv = (1570 / 1000) x 10⁶
= 1570 mm²/m
Asv > Asv,min (Satisfied)
Therefore, the design shear force for the beam is 37.5 MN (Option C).
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A reinforced concrete beam of 10 mEffective span and 1 m effective depth is supported on 500 mm x 500 mm columns. If the total uniformly distributed load on the beam is 10 MN/m, the design shear force for the beam isa)50 MNb)47.5 MNc)37.5 MNd)43 MNCorrect answer is option 'C'. Can you explain this answer?
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A reinforced concrete beam of 10 mEffective span and 1 m effective depth is supported on 500 mm x 500 mm columns. If the total uniformly distributed load on the beam is 10 MN/m, the design shear force for the beam isa)50 MNb)47.5 MNc)37.5 MNd)43 MNCorrect answer is option 'C'. 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 reinforced concrete beam of 10 mEffective span and 1 m effective depth is supported on 500 mm x 500 mm columns. If the total uniformly distributed load on the beam is 10 MN/m, the design shear force for the beam isa)50 MNb)47.5 MNc)37.5 MNd)43 MNCorrect answer is option 'C'. 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 reinforced concrete beam of 10 mEffective span and 1 m effective depth is supported on 500 mm x 500 mm columns. If the total uniformly distributed load on the beam is 10 MN/m, the design shear force for the beam isa)50 MNb)47.5 MNc)37.5 MNd)43 MNCorrect answer is option 'C'. Can you explain this answer?.
A reinforced concrete beam of 10 mEffective span and 1 m effective depth is supported on 500 mm x 500 mm columns. If the total uniformly distributed load on the beam is 10 MN/m, the design shear force for the beam isa)50 MNb)47.5 MNc)37.5 MNd)43 MNCorrect answer is option 'C'. 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 reinforced concrete beam of 10 mEffective span and 1 m effective depth is supported on 500 mm x 500 mm columns. If the total uniformly distributed load on the beam is 10 MN/m, the design shear force for the beam isa)50 MNb)47.5 MNc)37.5 MNd)43 MNCorrect answer is option 'C'. 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 reinforced concrete beam of 10 mEffective span and 1 m effective depth is supported on 500 mm x 500 mm columns. If the total uniformly distributed load on the beam is 10 MN/m, the design shear force for the beam isa)50 MNb)47.5 MNc)37.5 MNd)43 MNCorrect answer is option 'C'. Can you explain this answer?.
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A reinforced concrete beam of 10 mEffective span and 1 m effective depth is supported on 500 mm x 500 mm columns. If the total uniformly distributed load on the beam is 10 MN/m, the design shear force for the beam isa)50 MNb)47.5 MNc)37.5 MNd)43 MNCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A reinforced concrete beam of 10 mEffective span and 1 m effective depth is supported on 500 mm x 500 mm columns. If the total uniformly distributed load on the beam is 10 MN/m, the design shear force for the beam isa)50 MNb)47.5 MNc)37.5 MNd)43 MNCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A reinforced concrete beam of 10 mEffective span and 1 m effective depth is supported on 500 mm x 500 mm columns. If the total uniformly distributed load on the beam is 10 MN/m, the design shear force for the beam isa)50 MNb)47.5 MNc)37.5 MNd)43 MNCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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