An aluminum wire has a diameter of d in. Determine the minimum diameter D of the coil in which the wire can be wound without exceeding a bending stress of 30,000psi
To determine the minimum diameter D of the coil in which the aluminum wire can be wound without exceeding a bending stress of 30,000 psi, we need to use the bending stress formula.
The bending stress formula is given by:
σ = (M * c) / (I * y)
Where:
σ is the bending stress
M is the bending moment
c is the distance from the neutral axis to the point of interest
I is the moment of inertia of the cross-sectional area of the wire
y is the distance from the neutral axis to the outermost fiber of the cross-sectional area of the wire
In this case, we need to find the minimum diameter D, which would correspond to the maximum distance from the neutral axis to the outermost fiber. This distance is equal to half the diameter of the wire, D/2.
We also know that the bending stress, σ, should not exceed 30,000 psi.
Given that the diameter of the wire is d, we can calculate the moment of inertia, I, for a circular cross-section using the formula:
I = (π * d^4) / 64
To find the bending moment, M, we need to consider the properties of the coil and the wire. However, since we only have the diameter of the wire, we can't calculate the bending moment accurately without additional information.
Therefore, to determine the minimum diameter D of the coil, we need more information about the coil such as its dimensions, the number of turns, or any other relevant factors related to the bending moment.