Unit Conversion in Bending Stress Calculations

[cjm181]

Homework Statement

This is the problem I am working through. I am up to (b). I am struggling with the units.

https://www.flickr.com/photos/93763273@N05/8815418518/lightbox/

My question is, why is the final answer in N/m^2? and why does the workbooks list stress in the units of N/m^-2

the beam is 100mm wide and 200mm deep

Homework Equations

m/I=σ/y

σ=(my)/I

I = (bd^3)/12

The Attempt at a Solution

I have drawn out the bending moment diagram, and calculated a max bending moment to be m = 8.333kN. This is the same as other people attempting this question are getting. So I am happy with that.
y = 100mm or 0.1m

I = (0.1x0.2^3)/12 = 6.66667x10^-5m^4

so, σ=(my)/I

σ=(8333 x 0.1) / 6.66667x10^-5
σ=12499499.94 N/m^2 or 12.5x10^6N/m^2
or
σ= 12.5 MN/m^2 or 12.5 N/mm^2

Thanks,
Craig

 

[SteamKing]

Homework Statement

This is the problem I am working through. I am up to (b). I am struggling with the units.

https://www.flickr.com/photos/93763273@N05/8815418518/lightbox/

My question is, why is the final answer in N/m^2? and why does the workbooks list stress in the units of N/m^-2

Are you sure the workbook isn't using units of Nm^-2 for stress? {No slash}

 

[cjm181]

Argh, yeah they are, so my answer shouldn't have a slash either? the units are MNm^-2

So ignoring the slash in my question, can you explain the units to me and what is the -2?

Kr
Craig

 

[SteamKing]

Argh, yeah they are, so my answer shouldn't have a slash either? the units are MNm^-2

So ignoring the slash in my question, can you explain the units to me and what is the -2?

Kr
Craig

Remember the Laws of Exponents? How 1/x² = x^-2 ?

 

[cjm181]

umm you have confused me a little more now, Stress is force per unit area, so should the answer as I have written it be MN/m²?

Argh, think I have it!
a/b² is the same as ab^-2

so my answer is 12.5MN/m² or 12.5MN m^-2

 

[cjm181]

haha was typing out my reply at the same time! thanks SteamKing for pointing me in the right direction!

 

[SteamKing]

umm you have confused me a little more now, Stress is force per unit area, so should the answer as I have written it be MN/m²?

Argh, think I have it!
a/b² is the same as ab^-2

so my answer is 12.5MN/m² or 12.5MN m^-2

Or 12.5 MPa

 

[cjm181]

Just on this subject, if in σ=(my)/I we got (Newtons x Metres)/Metres⁴, then why do we end up with Newton/Metres²??

 

[cjm181]

think I got it now, we actually have ((N x m) x m) / m⁴

so using
aⁿ/a^m=a^n-m

so it comes down to Nm²/m⁴ = N (m²/m⁴) = N/m²