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The barrier shown between two water tanks of unit width (1 m) into the plane of the screen is modelled as a cantilever.
Taking the density of water as 1000 kg/m3, and the acceleration due to gravity as 10m/s2, the maximum absolute bending moment developed in the cantilever is ______ kN.m (round off to the nearest integer).
Correct answer is between '104,106'. Can you explain this answer?
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The barrier shown between two water tanks of unit width (1 m) into the...
Concept:
Net hydrostatic force exerted by fluid on flat surface, F = ρ × g × h̅ × A
Where, ρ = density of fluid, g = acceleration due to gravity, A = Area of the flat surface, h̅ = depth of centroid from free surface
This force is assumed to be acting at a point.
Centre of the pressure of rectangular lamina from free surface,
CP = 2/3h (h = height of rectangular lamina)
Calculation:
For left side of the barrier
Area = 4 m × 1 m = 4 m2, h¯= 4 / 2 = 2m,
Center of pressure from top surface of the water, CP1 = 2 × 4 / 3 = 8 / 3m
F1= ρ × g × h̅ × A = 1000 × 10 × 2 × 4 = 80 kN
For right side of the barrier
Area = 1 m × 1 m, h¯= 1 / 2 = 0.5m,
Center of pressure from top surface of the water CP2 = 2 × 1 / 3 = 2 / 3m
F2 = ρ × g × h̅ × A = 1000 × 10 × (1 × 1) × 0.5 = 5 kN
Distance of centre of pressure from bottom end:
CP1 = h/3 = 4/3
CP2 = h/3 = 1/3
These forces will act as point load on the barrier. If the barrier is treated as a cantilever and the fixed end of this cantilever beam is on the bottom side of the tank, then the loading conditions will look like the figure drawn below
F1 = 80 kN, F2 = 5 kN
From the above-simplified diagram:
A moment about the fixed end of barrier,
Net hydrostatic force exerted by fluid on flat surface, F = ρ × g × h̅ × A
Where, ρ = density of fluid, g = acceleration due to gravity, A = Area of the flat surface, h̅ = depth of centroid from free surface
This force is assumed to be acting at a point.
Centre of the pressure of rectangular lamina from free surface,
CP = 2/3h (h = height of rectangular lamina)
Calculation:
For left side of the barrier
Area = 4 m × 1 m = 4 m2, h¯= 4 / 2 = 2m,
Center of pressure from top surface of the water, CP1 = 2 × 4 / 3 = 8 / 3m
F1= ρ × g × h̅ × A = 1000 × 10 × 2 × 4 = 80 kN
For right side of the barrier
Area = 1 m × 1 m, h¯= 1 / 2 = 0.5m,
Center of pressure from top surface of the water CP2 = 2 × 1 / 3 = 2 / 3m
F2 = ρ × g × h̅ × A = 1000 × 10 × (1 × 1) × 0.5 = 5 kN
Distance of centre of pressure from bottom end:
CP1 = h/3 = 4/3
CP2 = h/3 = 1/3
These forces will act as point load on the barrier. If the barrier is treated as a cantilever and the fixed end of this cantilever beam is on the bottom side of the tank, then the loading conditions will look like the figure drawn below
F1 = 80 kN, F2 = 5 kN
From the above-simplified diagram:
A moment about the fixed end of barrier,
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The barrier shown between two water tanks of unit width (1 m) into the plane of the screen is modelled as a cantilever.Taking the density of water as 1000 kg/m3, and the acceleration due to gravity as 10m/s2, the maximum absolute bending moment developed in the cantilever is ______ kN.m(round off to the nearest integer).Correct answer is between '104,106'. Can you explain this answer?
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The barrier shown between two water tanks of unit width (1 m) into the plane of the screen is modelled as a cantilever.Taking the density of water as 1000 kg/m3, and the acceleration due to gravity as 10m/s2, the maximum absolute bending moment developed in the cantilever is ______ kN.m(round off to the nearest integer).Correct answer is between '104,106'. 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 The barrier shown between two water tanks of unit width (1 m) into the plane of the screen is modelled as a cantilever.Taking the density of water as 1000 kg/m3, and the acceleration due to gravity as 10m/s2, the maximum absolute bending moment developed in the cantilever is ______ kN.m(round off to the nearest integer).Correct answer is between '104,106'. 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 The barrier shown between two water tanks of unit width (1 m) into the plane of the screen is modelled as a cantilever.Taking the density of water as 1000 kg/m3, and the acceleration due to gravity as 10m/s2, the maximum absolute bending moment developed in the cantilever is ______ kN.m(round off to the nearest integer).Correct answer is between '104,106'. Can you explain this answer?.
The barrier shown between two water tanks of unit width (1 m) into the plane of the screen is modelled as a cantilever.Taking the density of water as 1000 kg/m3, and the acceleration due to gravity as 10m/s2, the maximum absolute bending moment developed in the cantilever is ______ kN.m(round off to the nearest integer).Correct answer is between '104,106'. 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 The barrier shown between two water tanks of unit width (1 m) into the plane of the screen is modelled as a cantilever.Taking the density of water as 1000 kg/m3, and the acceleration due to gravity as 10m/s2, the maximum absolute bending moment developed in the cantilever is ______ kN.m(round off to the nearest integer).Correct answer is between '104,106'. 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 The barrier shown between two water tanks of unit width (1 m) into the plane of the screen is modelled as a cantilever.Taking the density of water as 1000 kg/m3, and the acceleration due to gravity as 10m/s2, the maximum absolute bending moment developed in the cantilever is ______ kN.m(round off to the nearest integer).Correct answer is between '104,106'. Can you explain this answer?.
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