Calculate Min Drum Diameter for Copper Strip 4mm Thick, max Stress 332MN/m2

[wock]

Homework Statement

3. Calculate the minimum diameter of drum on which copper strip 4mm thick may be wound if the maximum bending stress is not to exceed 332MN/m2.
Assume E = 95 GN/m2


σ /(yxE)=r

Homework Equations

The Attempt at a Solution

would this work if so i make it 1.7m aprox

 

[FredGarvin]

I believe you need to invert that answer. The form I am used to seeing is

$$\frac{1}{\rho}=\frac{\sigma_{max}}{E*c}$$

Where rho is the radius of curvature.

 

[piercas]

I would first verify that the units used are correct. The maximum bending stress is given in MN/m2, which should be converted to N/m2 for consistency. The equation used is also not clear, as it is missing some variables and it is not clear what is being solved for.

Assuming that the equation is meant to be σ = M(r/E), where M is the bending moment and r is the radius of the drum, and solving for r, the minimum drum diameter can be calculated as follows:

1. Convert maximum bending stress to N/m2: 332 MN/m2 = 332,000,000 N/m2
2. Calculate the bending moment using the thickness of the copper strip and its modulus of elasticity: M = (4mm x 95 GN/m2) / 2 = 190 MN/m
3. Substitute values into the equation: 332,000,000 = 190 MN/m (r/95 GN/m2)
4. Solve for r: r = (332,000,000 x 95 GN/m2) / 190 MN/m = 166m

Therefore, the minimum drum diameter for the given conditions would be approximately 166 meters. It is important to note that this is only an estimate, as the actual minimum diameter may vary depending on other factors such as the material properties of the drum and the method of winding. It is also important to consider safety factors and potential failure modes when designing a drum for winding copper strips.