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A uniform cantilever beam is 4m long and carries a concentrated load of 40 Kn at a point 3m from the support. Determine the vertical downward deflection from the free end of the cantilever if the flexural rigidity is 40MNm^2
Ans 12mm?
Ans 12mm?
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A uniform cantilever beam is 4m long and carries a concentrated load o...
Given data:
- Length of the cantilever beam (L) = 4m
- Concentrated load (W) = 40 kN
- Distance of the load from the support (x) = 3m
- Flexural rigidity (EI) = 40 MNm^2
Assumptions:
- The beam is uniform and has a constant cross-section throughout its length.
- The beam is subjected to vertical loading only.
- The deflection of the beam is small compared to its length.
Formula:
The deflection of a cantilever beam under a concentrated load can be calculated using the formula:
δ = (W * x^2) / (6 * EI) * (3L - x) (1)
where:
δ = Deflection of the beam at the free end
W = Concentrated load
x = Distance of the load from the support
L = Length of the cantilever beam
EI = Flexural rigidity
Calculation:
Substituting the given values into equation (1), we can calculate the deflection:
δ = (40 * 3^2) / (6 * 40 * 10^6) * (3 * 4 - 3)
= (360 / (6 * 40 * 10^6)) * 9
= (9 / (6 * 10^6)) * 9
= 81 / (6 * 10^6)
= 0.0000135 m
Converting the deflection from meters to millimeters:
δ = 0.0000135 * 1000
= 0.0135 mm
Therefore, the vertical downward deflection from the free end of the cantilever beam is 0.0135 mm or 13.5 micrometers.
Conclusion:
The vertical downward deflection from the free end of the cantilever beam is 0.0135 mm (or 13.5 μm) when subjected to a concentrated load of 40 kN at a point 3 m from the support.
- Length of the cantilever beam (L) = 4m
- Concentrated load (W) = 40 kN
- Distance of the load from the support (x) = 3m
- Flexural rigidity (EI) = 40 MNm^2
Assumptions:
- The beam is uniform and has a constant cross-section throughout its length.
- The beam is subjected to vertical loading only.
- The deflection of the beam is small compared to its length.
Formula:
The deflection of a cantilever beam under a concentrated load can be calculated using the formula:
δ = (W * x^2) / (6 * EI) * (3L - x) (1)
where:
δ = Deflection of the beam at the free end
W = Concentrated load
x = Distance of the load from the support
L = Length of the cantilever beam
EI = Flexural rigidity
Calculation:
Substituting the given values into equation (1), we can calculate the deflection:
δ = (40 * 3^2) / (6 * 40 * 10^6) * (3 * 4 - 3)
= (360 / (6 * 40 * 10^6)) * 9
= (9 / (6 * 10^6)) * 9
= 81 / (6 * 10^6)
= 0.0000135 m
Converting the deflection from meters to millimeters:
δ = 0.0000135 * 1000
= 0.0135 mm
Therefore, the vertical downward deflection from the free end of the cantilever beam is 0.0135 mm or 13.5 micrometers.
Conclusion:
The vertical downward deflection from the free end of the cantilever beam is 0.0135 mm (or 13.5 μm) when subjected to a concentrated load of 40 kN at a point 3 m from the support.
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A uniform cantilever beam is 4m long and carries a concentrated load of 40 Kn at a point 3m from the support. Determine the vertical downward deflection from the free end of the cantilever if the flexural rigidity is 40MNm^2Ans 12mm?
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A uniform cantilever beam is 4m long and carries a concentrated load of 40 Kn at a point 3m from the support. Determine the vertical downward deflection from the free end of the cantilever if the flexural rigidity is 40MNm^2Ans 12mm? 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 uniform cantilever beam is 4m long and carries a concentrated load of 40 Kn at a point 3m from the support. Determine the vertical downward deflection from the free end of the cantilever if the flexural rigidity is 40MNm^2Ans 12mm? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uniform cantilever beam is 4m long and carries a concentrated load of 40 Kn at a point 3m from the support. Determine the vertical downward deflection from the free end of the cantilever if the flexural rigidity is 40MNm^2Ans 12mm?.
A uniform cantilever beam is 4m long and carries a concentrated load of 40 Kn at a point 3m from the support. Determine the vertical downward deflection from the free end of the cantilever if the flexural rigidity is 40MNm^2Ans 12mm? 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 uniform cantilever beam is 4m long and carries a concentrated load of 40 Kn at a point 3m from the support. Determine the vertical downward deflection from the free end of the cantilever if the flexural rigidity is 40MNm^2Ans 12mm? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uniform cantilever beam is 4m long and carries a concentrated load of 40 Kn at a point 3m from the support. Determine the vertical downward deflection from the free end of the cantilever if the flexural rigidity is 40MNm^2Ans 12mm?.
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