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What is the deflection at the surface of a flexible pavement due to a wheel load of 40 kN and a tyre pressure of 0.5 MPa? The value of E for pavement and subgrade is 20 MPa.
- a)15 mm
- b)11 mm
- c)9 mm
- d)6 mm
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
What is the deflection at the surface of a flexible pavement due to a ...
To calculate the deflection at the surface of a flexible pavement due to a wheel load, we can use the Boussinesq's equation. The equation relates the deflection at the surface to the applied load and the elastic properties of the pavement and subgrade.
The Boussinesq's equation is given by:
δ = (q/E) * (1 / (1 - σ^2)) * (1 / √(πr))
where:
δ = deflection at the surface
q = applied load per unit area
E = modulus of elasticity of the pavement and subgrade
σ = Poisson's ratio
r = radius of the contact area
Given data:
Applied load (q) = 40 kN
Tyre pressure = 0.5 MPa
Modulus of elasticity (E) = 20 MPa
Now, let's calculate the radius of the contact area (r).
The contact area can be approximated as a circular area given by:
A = (q / P)
where:
A = contact area
q = applied load
P = tyre pressure
Substituting the given values, we have:
A = (40 kN / 0.5 MPa) = 80 m²
The radius (r) can be calculated using the formula:
r = √(A / π)
Substituting the value of A, we get:
r = √(80 / π) = 5.65 m
Now, let's substitute the values of q, E, σ, and r into the Boussinesq's equation to calculate the deflection (δ).
δ = (q/E) * (1 / (1 - σ^2)) * (1 / √(πr))
Substituting the given values, we have:
δ = (40 kN / (20 MPa)) * (1 / (1 - 0.5^2)) * (1 / √(π * 5.65))
Simplifying the equation, we get:
δ = 6 mm
Therefore, the deflection at the surface of the flexible pavement due to the given wheel load and tyre pressure is 6 mm.
The Boussinesq's equation is given by:
δ = (q/E) * (1 / (1 - σ^2)) * (1 / √(πr))
where:
δ = deflection at the surface
q = applied load per unit area
E = modulus of elasticity of the pavement and subgrade
σ = Poisson's ratio
r = radius of the contact area
Given data:
Applied load (q) = 40 kN
Tyre pressure = 0.5 MPa
Modulus of elasticity (E) = 20 MPa
Now, let's calculate the radius of the contact area (r).
The contact area can be approximated as a circular area given by:
A = (q / P)
where:
A = contact area
q = applied load
P = tyre pressure
Substituting the given values, we have:
A = (40 kN / 0.5 MPa) = 80 m²
The radius (r) can be calculated using the formula:
r = √(A / π)
Substituting the value of A, we get:
r = √(80 / π) = 5.65 m
Now, let's substitute the values of q, E, σ, and r into the Boussinesq's equation to calculate the deflection (δ).
δ = (q/E) * (1 / (1 - σ^2)) * (1 / √(πr))
Substituting the given values, we have:
δ = (40 kN / (20 MPa)) * (1 / (1 - 0.5^2)) * (1 / √(π * 5.65))
Simplifying the equation, we get:
δ = 6 mm
Therefore, the deflection at the surface of the flexible pavement due to the given wheel load and tyre pressure is 6 mm.
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What is the deflection at the surface of a flexible pavement due to a ...
Burmister’s Method:
Assumptions
Assumptions
- Materials in each layers are isotropic, homogeneous and elastic.
- Pavement forms a stiffer layer having higher value of E than that of subgrade.
- Layers are in constant contact.
- Surface layer is infinite in horizontal direction but finite in vertical direction.
This method gives the following design deflection values for pavements with different layers
Where, p = contact pressure at road surface due to wheel load (kg/m2)
Es = modulus of elasticity of subgrade (kg/cm2), a = radius of contact area(cm) and
F2 = deflection factor which depends upon Es/EP and h/a, for single layer system F2 = 1.
Formula used:-
Design deflection for single-layered flexible pavement is given by,
Radius of contact area is given by,
Calculation:
Wheel Load, P = 40kN
Modulus of elasticity for subgrade and pavement, ES = EP = 20MPa
Tyre pressure, p = 0.50 MPa
Design deflection for flexible pavement
Where, p = contact pressure at road surface due to wheel load (kg/m2)
Es = modulus of elasticity of subgrade (kg/cm2), a = radius of contact area(cm) and
F2 = deflection factor which depends upon Es/EP and h/a, for single layer system F2 = 1.
Formula used:-
Design deflection for single-layered flexible pavement is given by,
Radius of contact area is given by,
Calculation:
Wheel Load, P = 40kN
Modulus of elasticity for subgrade and pavement, ES = EP = 20MPa
Tyre pressure, p = 0.50 MPa
Design deflection for flexible pavement
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What is the deflection at the surface of a flexible pavement due to a wheel load of 40 kN and a tyre pressure of 0.5 MPa? The value of E for pavement and subgrade is 20 MPa.a)15 mmb)11 mmc)9 mmd)6 mmCorrect answer is option 'D'. Can you explain this answer?
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What is the deflection at the surface of a flexible pavement due to a wheel load of 40 kN and a tyre pressure of 0.5 MPa? The value of E for pavement and subgrade is 20 MPa.a)15 mmb)11 mmc)9 mmd)6 mmCorrect answer is option 'D'. 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 What is the deflection at the surface of a flexible pavement due to a wheel load of 40 kN and a tyre pressure of 0.5 MPa? The value of E for pavement and subgrade is 20 MPa.a)15 mmb)11 mmc)9 mmd)6 mmCorrect answer is option 'D'. 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 What is the deflection at the surface of a flexible pavement due to a wheel load of 40 kN and a tyre pressure of 0.5 MPa? The value of E for pavement and subgrade is 20 MPa.a)15 mmb)11 mmc)9 mmd)6 mmCorrect answer is option 'D'. Can you explain this answer?.
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