To determine the peak stress on the outer surface of a 50% fibre composite vaulting pole that has a diameter of about 50 mm and is being bent to a radius of curvature, R, of about 0.5 m, we can use the following formula:
σ = (M/Z) * y
where,σ = stress
M = bending moment
Z = section modulus
y = distance from the neutral axis
To find M, we can use the following formula:
M = (Em/Ef) * (ρc/ρf) * (π/4) * d^3 * (1/R)where,
Em = modulus of elasticity of matrixEf = modulus of elasticity of fibre
ρc = density of the matrixρf = density of the fibreπ = 3.14d = diameter of the pole
R = radius of curvatureNow, substituting the given values:
M = (3/90) * (0.5/1.5) * (π/4) * (0.05)^3 * (1/0.5)M
= 0.000216 Nm
To find Z, we can use the following formula:
Z = (π/32) * d^4 * (ρf/ρc) * (Ef/Em) * (1 + (3h/d)^2)
where,h = height of the pole
Now, substituting the given values:
Z = (π/32) * (0.05)^4 * (0.5/1.5) * (90/3) * (1 + (3(0.5)/0.05)^2)Z
= 0.0001586 m^3To find y, we can use the following formula:
y = (d/2) * (ρf/ρc)where,ρc = density of the matrix
ρf = density of the fibre
Now, substituting the given values:y = (0.05/2) * (0.5/1.5)y = 0.00833 m
Substituting the values of M, Z, and y in the formula for stress, we get:σ = (M/Z) * yσ = (0.000216/0.0001586) * 0.00833σ = 11.77 MPa
Therefore, the peak stress on the outer surface of a 50% fibre composite vaulting pole with a diameter of about 50 mm and being bent to a radius of curvature, R, of about 0.5 m is 11.77 MPa.
Composite materials are known for their remarkable strength and durability, making them ideal for use in a variety of applications. One of these applications is in the production of vaulting poles used in pole vaulting, a track and field event that involves athletes using a long, flexible pole to clear a bar that is suspended above the ground. The poles used in this event are typically made of a composite material that consists of a matrix material, such as epoxy resin, and a reinforcing material, such as carbon fibre or fibreglass. These materials are chosen for their high strength-to-weight ratio, which allows the poles to be both strong and flexible. The strength of the pole is determined by its modulus of elasticity, which is a measure of its ability to resist deformation under load. The modulus of elasticity of the matrix material, Em, and the reinforcing material, Ef, are key factors in determining the strength of the pole. The density of these materials is also important, as it affects the weight of the pole. The peak stress on the outer surface of a pole is an important factor to consider when designing the pole, as it determines the maximum load that the pole can handle before it fails. In order to determine the peak stress on the outer surface of a 50% fibre composite vaulting pole with a diameter of about 50 mm and being bent to a radius of curvature, R, of about 0.5 m, we can use the formula σ = (M/Z) * y, where M is the bending moment, Z is the section modulus, and y is the distance from the neutral axis. By using the appropriate values for Em, Ef, density, diameter, and radius of curvature, we can calculate the peak stress on the outer surface of the pole.
In conclusion, the peak stress on the outer surface of a 50% fibre composite vaulting pole with a diameter of about 50 mm and being bent to a radius of curvature, R, of about 0.5 m, is 11.77 MPa. The strength of the pole is determined by its modulus of elasticity, which is a measure of its ability to resist deformation under load. The modulus of elasticity of the matrix material, Em, and the reinforcing material, Ef, are key factors in determining the strength of the pole. The density of these materials is also important, as it affects the weight of the pole. The peak stress on the outer surface of a pole is an important factor to consider when designing the pole, as it determines the maximum load that the pole can handle before it fails. Overall, composite vaulting poles are an excellent example of how composite materials can be used to create strong and durable structures that are ideal for a wide range of applications.
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