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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...
Given:
- Length of the cantilever plank (L) = 2 m
- Width of the cantilever plank (b) = 300 mm = 0.3 m
- Thickness of the cantilever plank (h) = 20 mm = 0.02 m
- Unit weight of the cantilever plank (γ) = 10 kN/m³
- Maximum allowable deflection (δ) = 20 mm = 0.02 m
- Modulus of elasticity (E) = 80 × 10^4 N/mm²
Formula:
The maximum deflection (δ) of a cantilever beam with a point load at the free end can be calculated using the formula:
δ = (W x L³) / (3 x E x I)
Where:
- δ is the maximum deflection
- W is the load at the free end
- L is the length of the cantilever beam
- E is the modulus of elasticity
- I is the moment of inertia of the cantilever beam
The moment of inertia (I) of a rectangular beam can be calculated using the formula:
I = (b x h³) / 12
Where:
- I is the moment of inertia
- b is the width of the beam
- h is the depth of the beam
Calculation:
Step 1: Calculate the moment of inertia (I) of the cantilever plank.
I = (0.3 x 0.02³) / 12 = 1.2 x 10^-6 m^4
Step 2: Substitute the values into the deflection formula and solve for the load (W).
0.02 = (W x 2³) / (3 x 80 x 10^4 x 1.2 x 10^-6)
0.02 = (W x 8) / (3 x 80 x 1.2)
0.02 = (W x 8) / 288
W = (0.02 x 288) / 8
W = 0.72 kN
Therefore, the maximum weight of the man standing on the plank should be 0.72 kN.
Step 3: Calculate the maximum slope occurring at any section.
The maximum slope (θ) of a cantilever beam can be calculated using the formula:
θ = (W x L²) / (2 x E x I)
Substituting the values:
θ = (0.72 x 2²) / (2 x 80 x 10^4 x 1.2 x 10^-6)
θ = 2.88 / 0.192
θ = 15 degrees (approximately)
Therefore, the maximum slope occurring at any section is 15 degrees.
Summary:
The maximum weight of the man standing on the cantilever plank should be 0.72 kN, and the maximum slope occurring at any section is 15 degrees. These values ensure that the deflection of the plank is limited to 20 mm, as per the given requirements.
- Length of the cantilever plank (L) = 2 m
- Width of the cantilever plank (b) = 300 mm = 0.3 m
- Thickness of the cantilever plank (h) = 20 mm = 0.02 m
- Unit weight of the cantilever plank (γ) = 10 kN/m³
- Maximum allowable deflection (δ) = 20 mm = 0.02 m
- Modulus of elasticity (E) = 80 × 10^4 N/mm²
Formula:
The maximum deflection (δ) of a cantilever beam with a point load at the free end can be calculated using the formula:
δ = (W x L³) / (3 x E x I)
Where:
- δ is the maximum deflection
- W is the load at the free end
- L is the length of the cantilever beam
- E is the modulus of elasticity
- I is the moment of inertia of the cantilever beam
The moment of inertia (I) of a rectangular beam can be calculated using the formula:
I = (b x h³) / 12
Where:
- I is the moment of inertia
- b is the width of the beam
- h is the depth of the beam
Calculation:
Step 1: Calculate the moment of inertia (I) of the cantilever plank.
I = (0.3 x 0.02³) / 12 = 1.2 x 10^-6 m^4
Step 2: Substitute the values into the deflection formula and solve for the load (W).
0.02 = (W x 2³) / (3 x 80 x 10^4 x 1.2 x 10^-6)
0.02 = (W x 8) / (3 x 80 x 1.2)
0.02 = (W x 8) / 288
W = (0.02 x 288) / 8
W = 0.72 kN
Therefore, the maximum weight of the man standing on the plank should be 0.72 kN.
Step 3: Calculate the maximum slope occurring at any section.
The maximum slope (θ) of a cantilever beam can be calculated using the formula:
θ = (W x L²) / (2 x E x I)
Substituting the values:
θ = (0.72 x 2²) / (2 x 80 x 10^4 x 1.2 x 10^-6)
θ = 2.88 / 0.192
θ = 15 degrees (approximately)
Therefore, the maximum slope occurring at any section is 15 degrees.
Summary:
The maximum weight of the man standing on the cantilever plank should be 0.72 kN, and the maximum slope occurring at any section is 15 degrees. These values ensure that the deflection of the plank is limited to 20 mm, as per the given requirements.
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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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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 detailed solution 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.? has been provided alongside types of 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.? theory, EduRev gives you an
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