Stress/strain+general bending equation

[ar202]

Stress/strain+general bending equation...

Homework Statement

A steel strip is to be bent around a drum of radius 1m. What is the maximum thickness of strip that can be bent in this way if the stress in the strip is not to exceed 100 MPa.

The steel has a modulus of elasticity of 210 GPa.

Am i correct in thinking i should be using the general bending equation here?

as well as the second moment of area for a cylinder?

pi x d^4/64

any help would be great, cheers.

Homework Equations

The Attempt at a Solution

I'm stuck on where to begin, a nod in the direction would be really helpful thanks.

 

[rock.freak667]

I think that would be correct to do.

 

[ar202]

1 x 10⁶ / 2.1 x 10¹¹ = 4.76 x 10^-4 ...?

 

[rock.freak667]

1 x 10⁶ / 2.1 x 10¹¹ = 4.76 x 10^-4 ...?

I am not sure what those numbers are supposed to mean.

$$\frac{M}{I} = \frac{\sigma _b}{y} = \frac{E}{R}$$

Which equality did you use?

 

[rdl]

As a scientist, your approach to this problem is correct. The general bending equation, also known as the flexural formula, is used to determine the maximum stress in a material due to bending. It takes into account the material properties, the geometry of the object, and the applied loads. In this case, the applied load is the bending caused by wrapping the steel strip around the drum.

The formula is as follows:

σ = (M*y)/I

Where:
σ = maximum stress
M = bending moment
y = distance from the neutral axis (in this case, the radius of the drum)
I = second moment of area (also known as the moment of inertia)

To determine the bending moment, you can use the simple formula:

M = F*d
Where:
F = force (in this case, the force required to bend the steel strip)
d = distance from the force to the point of bending (in this case, the radius of the drum)

To determine the second moment of area, you can use the formula for a cylinder that you mentioned:

I = π*d^4/64

Now, to solve for the maximum thickness of the steel strip, you need to rearrange the equation to solve for d:

d = ∛((64*σ*I)/π)

Then, you can plug in the given values for the stress, modulus of elasticity, and radius of the drum to solve for the maximum thickness of the steel strip. Keep in mind that the units need to be consistent, so you may need to convert from MPa to Pa and from GPa to m^4.

I hope this helps guide you in the right direction. Remember to always consider the relevant equations and units when approaching a problem in science.