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A man is standing on a cantilever plank at the free end over a swimming tank. The cantilever plank is 2 m long, 300mm wide and 20mm thick. The unit weight of the plank is 10kN/m³. If the deflection of the plank is to be limited to 20mm, what should be the maximum weight of the man standing on the plank? Also calculate the maximum slope occurring at any section. E=80 x 10⁴ N/mm²?
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A man is standing on a cantilever plank at the free end over a swimmin...
Cantilever Plank Analysis
Given Data:
- Length of the plank (L) = 2 m
- Width of the plank (b) = 300 mm = 0.3 m
- Thickness of the plank (h) = 20 mm = 0.02 m
- Unit weight of the plank (γ) = 10 kN/m³
- Maximum deflection allowable (δ) = 20 mm = 0.02 m
Calculating the Maximum Weight
To calculate the maximum weight the plank can withstand without exceeding the maximum allowable deflection, we need to consider the deflection equation for a cantilever beam:
δ = (5 * w * L^4)/(384 * E * I)
Where:
- δ is the deflection
- w is the distributed load per unit length
- L is the length of the cantilever beam
- E is the modulus of elasticity
- I is the moment of inertia
Calculating the Moment of Inertia (I)
The moment of inertia of a rectangular section is given by the formula:
I = (b * h^3)/12
Substituting the given values:
I = (0.3 * 0.02^3)/12 = 1.2 x 10^-7 m^4
Calculating the Modulus of Elasticity (E)
The modulus of elasticity for the plank is given as E = 80 x 10⁴ N/mm². To convert it to N/m², we need to multiply it by 10^6.
E = 80 x 10⁴ N/mm² * 10^6 = 8 x 10^10 N/m²
Calculating the Distributed Load per Unit Length (w)
The distributed load per unit length can be calculated by dividing the weight of the man by the length of the plank:
w = (Weight of the man)/(Length of the plank)
Substituting the given values:
w = (Weight of the man)/(2 m)
Deriving the Maximum Weight
To find the maximum weight the man can have without exceeding the maximum allowable deflection, we rearrange the deflection equation:
w = (δ * 384 * E * I)/(5 * L^4)
Substituting the given values:
w = (0.02 * 384 * 8 x 10^10 * 1.2 x 10^-7)/(5 * 2^4) = 0.12 N/m
Finally, to determine the maximum weight, we multiply the distributed load per unit length by the length of the plank:
Maximum Weight = w * L = 0.12 N/m * 2 m = 0.24 N
Therefore, the maximum weight the man can have without exceeding the maximum allowable deflection is 0.24 N.
Calculating the Maximum Slope
The maximum slope occurring at any section of the cantilever plank can be calculated using the formula:
θ = (w * L^3)/(24 * E * I)
Substituting the given values:
θ = (0.12 N/m * 2^3)/(24 * 8 x 10^10 * 1.2 x 10^-7
Given Data:
- Length of the plank (L) = 2 m
- Width of the plank (b) = 300 mm = 0.3 m
- Thickness of the plank (h) = 20 mm = 0.02 m
- Unit weight of the plank (γ) = 10 kN/m³
- Maximum deflection allowable (δ) = 20 mm = 0.02 m
Calculating the Maximum Weight
To calculate the maximum weight the plank can withstand without exceeding the maximum allowable deflection, we need to consider the deflection equation for a cantilever beam:
δ = (5 * w * L^4)/(384 * E * I)
Where:
- δ is the deflection
- w is the distributed load per unit length
- L is the length of the cantilever beam
- E is the modulus of elasticity
- I is the moment of inertia
Calculating the Moment of Inertia (I)
The moment of inertia of a rectangular section is given by the formula:
I = (b * h^3)/12
Substituting the given values:
I = (0.3 * 0.02^3)/12 = 1.2 x 10^-7 m^4
Calculating the Modulus of Elasticity (E)
The modulus of elasticity for the plank is given as E = 80 x 10⁴ N/mm². To convert it to N/m², we need to multiply it by 10^6.
E = 80 x 10⁴ N/mm² * 10^6 = 8 x 10^10 N/m²
Calculating the Distributed Load per Unit Length (w)
The distributed load per unit length can be calculated by dividing the weight of the man by the length of the plank:
w = (Weight of the man)/(Length of the plank)
Substituting the given values:
w = (Weight of the man)/(2 m)
Deriving the Maximum Weight
To find the maximum weight the man can have without exceeding the maximum allowable deflection, we rearrange the deflection equation:
w = (δ * 384 * E * I)/(5 * L^4)
Substituting the given values:
w = (0.02 * 384 * 8 x 10^10 * 1.2 x 10^-7)/(5 * 2^4) = 0.12 N/m
Finally, to determine the maximum weight, we multiply the distributed load per unit length by the length of the plank:
Maximum Weight = w * L = 0.12 N/m * 2 m = 0.24 N
Therefore, the maximum weight the man can have without exceeding the maximum allowable deflection is 0.24 N.
Calculating the Maximum Slope
The maximum slope occurring at any section of the cantilever plank can be calculated using the formula:
θ = (w * L^3)/(24 * E * I)
Substituting the given values:
θ = (0.12 N/m * 2^3)/(24 * 8 x 10^10 * 1.2 x 10^-7
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A man is standing on a cantilever plank at the free end over a swimming tank. The cantilever plank is 2 m long, 300mm wide and 20mm thick. The unit weight of the plank is 10kN/m³. If the deflection of the plank is to be limited to 20mm, what should be the maximum weight of the man standing on the plank? Also calculate the maximum slope occurring at any section. E=80 x 10⁴ N/mm²?
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A man is standing on a cantilever plank at the free end over a swimming tank. The cantilever plank is 2 m long, 300mm wide and 20mm thick. The unit weight of the plank is 10kN/m³. If the deflection of the plank is to be limited to 20mm, what should be the maximum weight of the man standing on the plank? Also calculate the maximum slope occurring at any section. E=80 x 10⁴ N/mm²? 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 man is standing on a cantilever plank at the free end over a swimming tank. The cantilever plank is 2 m long, 300mm wide and 20mm thick. The unit weight of the plank is 10kN/m³. If the deflection of the plank is to be limited to 20mm, what should be the maximum weight of the man standing on the plank? Also calculate the maximum slope occurring at any section. E=80 x 10⁴ N/mm²? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man is standing on a cantilever plank at the free end over a swimming tank. The cantilever plank is 2 m long, 300mm wide and 20mm thick. The unit weight of the plank is 10kN/m³. If the deflection of the plank is to be limited to 20mm, what should be the maximum weight of the man standing on the plank? Also calculate the maximum slope occurring at any section. E=80 x 10⁴ N/mm²?.
A man is standing on a cantilever plank at the free end over a swimming tank. The cantilever plank is 2 m long, 300mm wide and 20mm thick. The unit weight of the plank is 10kN/m³. If the deflection of the plank is to be limited to 20mm, what should be the maximum weight of the man standing on the plank? Also calculate the maximum slope occurring at any section. E=80 x 10⁴ N/mm²? 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 man is standing on a cantilever plank at the free end over a swimming tank. The cantilever plank is 2 m long, 300mm wide and 20mm thick. The unit weight of the plank is 10kN/m³. If the deflection of the plank is to be limited to 20mm, what should be the maximum weight of the man standing on the plank? Also calculate the maximum slope occurring at any section. E=80 x 10⁴ N/mm²? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man is standing on a cantilever plank at the free end over a swimming tank. The cantilever plank is 2 m long, 300mm wide and 20mm thick. The unit weight of the plank is 10kN/m³. If the deflection of the plank is to be limited to 20mm, what should be the maximum weight of the man standing on the plank? Also calculate the maximum slope occurring at any section. E=80 x 10⁴ N/mm²?.
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