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A cantilever beam of span 6 m carries a uniformly distributed load of 15 kN/m. The c/s of the beam is square shaped having side 200 mm with one of its diagonal horizontal. The maximum shear stress anywhere on the beam is ___(in MPa, round up to 2 decimal places).
Correct answer is between '2.4,2.6'. Can you explain this answer?
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A cantilever beam of span 6 m carries a uniformly distributed load of ...
Calculation of Maximum Shear Stress in the Cantilever Beam
To determine the maximum shear stress in the cantilever beam, we need to consider the bending moment and shear force at the critical section of the beam.
Given data:
- Span (L) = 6 m
- Uniformly distributed load (w) = 15 kN/m
- Side of square cross-section (d) = 200 mm = 0.2 m
Calculating the reactions:
- The reaction at the fixed end (A) of the cantilever beam is equal to the total load acting on the beam.
- RA = Total load = w * L
Calculating the bending moment:
- The maximum bending moment occurs at the fixed end (A) of the beam.
- Mmax = RA * L
Calculating the shear force:
- The maximum shear force occurs at the support (A) of the cantilever beam.
- Vmax = RA
Calculating the maximum shear stress:
- The maximum shear stress in a beam with square cross-section is given by: τmax = V * d / (2 * I)
- Where I is the moment of inertia of the cross-section about the neutral axis.
- For a square cross-section with one diagonal horizontal, the moment of inertia is equal to (1/6) * d^4
- Substituting the values, we get: τmax = Vmax * d / (2 * (1/6) * d^4)
- Simplifying the equation gives: τmax = 3 * Vmax / d^3
Substitute the values and calculate:
- τmax = 3 * RA / d^3
Now, substitute the values of RA and d into the equation to calculate the maximum shear stress in the cantilever beam. Finally, round up the answer to 2 decimal places.
Therefore, the maximum shear stress in the cantilever beam is between 2.4 MPa and 2.6 MPa.
To determine the maximum shear stress in the cantilever beam, we need to consider the bending moment and shear force at the critical section of the beam.
Given data:
- Span (L) = 6 m
- Uniformly distributed load (w) = 15 kN/m
- Side of square cross-section (d) = 200 mm = 0.2 m
Calculating the reactions:
- The reaction at the fixed end (A) of the cantilever beam is equal to the total load acting on the beam.
- RA = Total load = w * L
Calculating the bending moment:
- The maximum bending moment occurs at the fixed end (A) of the beam.
- Mmax = RA * L
Calculating the shear force:
- The maximum shear force occurs at the support (A) of the cantilever beam.
- Vmax = RA
Calculating the maximum shear stress:
- The maximum shear stress in a beam with square cross-section is given by: τmax = V * d / (2 * I)
- Where I is the moment of inertia of the cross-section about the neutral axis.
- For a square cross-section with one diagonal horizontal, the moment of inertia is equal to (1/6) * d^4
- Substituting the values, we get: τmax = Vmax * d / (2 * (1/6) * d^4)
- Simplifying the equation gives: τmax = 3 * Vmax / d^3
Substitute the values and calculate:
- τmax = 3 * RA / d^3
Now, substitute the values of RA and d into the equation to calculate the maximum shear stress in the cantilever beam. Finally, round up the answer to 2 decimal places.
Therefore, the maximum shear stress in the cantilever beam is between 2.4 MPa and 2.6 MPa.
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Community Answer
A cantilever beam of span 6 m carries a uniformly distributed load of ...
Max Shear force would be at the fixed end
V = 15 x 6 = 90 kN
For square c/s with diagonal horizontal,
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A cantilever beam of span 6 m carries a uniformly distributed load of 15 kN/m. The c/s of the beam is square shaped having side 200 mm with one of its diagonal horizontal. The maximum shear stress anywhere on the beam is ___(in MPa, round up to 2 decimal places).Correct answer is between '2.4,2.6'. Can you explain this answer?
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A cantilever beam of span 6 m carries a uniformly distributed load of 15 kN/m. The c/s of the beam is square shaped having side 200 mm with one of its diagonal horizontal. The maximum shear stress anywhere on the beam is ___(in MPa, round up to 2 decimal places).Correct answer is between '2.4,2.6'. 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 cantilever beam of span 6 m carries a uniformly distributed load of 15 kN/m. The c/s of the beam is square shaped having side 200 mm with one of its diagonal horizontal. The maximum shear stress anywhere on the beam is ___(in MPa, round up to 2 decimal places).Correct answer is between '2.4,2.6'. 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 cantilever beam of span 6 m carries a uniformly distributed load of 15 kN/m. The c/s of the beam is square shaped having side 200 mm with one of its diagonal horizontal. The maximum shear stress anywhere on the beam is ___(in MPa, round up to 2 decimal places).Correct answer is between '2.4,2.6'. Can you explain this answer?.
A cantilever beam of span 6 m carries a uniformly distributed load of 15 kN/m. The c/s of the beam is square shaped having side 200 mm with one of its diagonal horizontal. The maximum shear stress anywhere on the beam is ___(in MPa, round up to 2 decimal places).Correct answer is between '2.4,2.6'. 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 cantilever beam of span 6 m carries a uniformly distributed load of 15 kN/m. The c/s of the beam is square shaped having side 200 mm with one of its diagonal horizontal. The maximum shear stress anywhere on the beam is ___(in MPa, round up to 2 decimal places).Correct answer is between '2.4,2.6'. 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 cantilever beam of span 6 m carries a uniformly distributed load of 15 kN/m. The c/s of the beam is square shaped having side 200 mm with one of its diagonal horizontal. The maximum shear stress anywhere on the beam is ___(in MPa, round up to 2 decimal places).Correct answer is between '2.4,2.6'. Can you explain this answer?.
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