Do we now express mm as the letter m with a superscript?

[richard9678]

Hi. I'm looking at a stress/strain graph. The vertical axis is marked Stress/MN m^-2. Is this saying that the figures on the axis have been calculated using KN for force, and cm² as area? Thanks.

 

[Doug Huffman]

No, it is saying that the vertical axis label is unity, to be multiplied by the figures.

 

[SteamKing]

Hi. I'm looking at a stress/strain graph. The vertical axis is marked Stress/MN m^-2. Is this saying that the figures on the axis have been calculated using KN for force, and cm² as area? Thanks.

MNm^-2 means stress is measured in mega Newtons per square meter.

And for anyone who doesn't realize it, m^-2 = 1/m²,which is not the same thing as a centimeter, which is 0.01 times a meter.

There are 10⁴ cm² (100 cm * 100 cm = 10,000 cm²) in 1 m².

 

[richard9678]

Stress, I know is very often given in Giga Pascals. I suppose then, where it says 1000 on the graph, that is indicating 1GPa? Still not sure what m^-2 is about.

 

[SteamKing]

1 pascal is defined as 1 Newton per square meter, or 1 Pa = 1 Nm^-2.

1 kPa = 1000 Pa = 10³ Pa = 1kNm^-2

1 MPa = 10⁶ Pa = 1 MNm^-2

1 GPa = 10⁹ Pa = 1GNm^-2

If you are having trouble interpreting a graph, why don't you post the graph and let us take a look?

 

[richard9678]

Where the axis reads 1000, that I believe should be taken as 1000 MN. That is a very great force. However, the graph is also indicating that the area associated with that force is 1m², or 1 square metre. When you take these things into account, you calculate the stress to be 1000MN / 1m², which is 1Gpa. Okay. but I still don't get why the graph says MN m^-2, rather than MN m². I understand the latter, but not the former.

 

[SteamKing]

Okay. but I still don't get why the graph says MN m^-2, rather than MN m². I understand the latter, but not the former.

The stress should be in units of MN/m² (the '/' is very important here).

If you don't understand how exponents work, here is a short lesson:

x * x = x²

1 / (x * x) = 1 / x² = x^-2

I know MNm^-2 looks odd, but this is how MN/m² is sometimes written.

 

[richard9678]

It's the notation I don't get. Area is measured in square meters. So, if I calculate the area of something that is 3m x 3m I'd give the answer as 9m². I would not give the answer as 9m^-2.

Lets say my tensile test set-up involves a steel bar with an area of 1 m². And I applied force in Mega Newtons. In such circumstances to get any meaningful strain results I would be applying force in the hundreds of MN. Indeed, I would easily be required to apply 1000MN to get an adequate indication of strain. Okay, so, stress, which is a ratio of force / area is being expressed in terms of force in MN and area in square meters, or 1m². So, to my mind, if I annotated the stress axis, to indicate the nature of the values on the stress axis, I'd write stress/ MNm².

I'd be indicating to the reader that where the axis indicates 1000 on the stress axis, that is to be read as 1000MN per metre squared.

Of course if area is 1m² this is the same as 1/m² which I think equals 1m^-2.

Is m² the same as m^-2 is the same as 1/^m2? If not, why not?

What am I missing?

 

[richard9678]

The stress should be in units of MN/m² (the '/' is very important here).

If you don't understand how exponents work, here is a short lesson:

x * x = x²

1 / (x * x) = 1 / x² = x^-2

I know MNm^-2 looks odd, but this is how MN/m² is sometimes written.

Okay, I'm beginning to see this I think. Stress is N/m². So the value of stress is a function of the reciprocal of m². Or 1/m². The minus figure in m^-2 is, I think just saying reciprocal of m².

 

[SteamKing]

It's the notation I don't get. Area is measured in square meters. So, if I calculate the area of something that is 3m x 3m I'd give the answer as 9m². I would not give the answer as 9m^-2.

Nor should you. Area is measured in square units.

Okay, so, stress, which a a ratio of force / area is being expressed in terms of force in MN and area in square meters, or 1m2. I'd be indicating to the reader that where the axis indicates 1000 on the stress axis, that is to be read as 1000MN per metre squared.

Of course if area is 1m² this is the same as 1/m² which I think equals 1m^-2.

Is m² the same as m^-2 is the same as 1/m²? If not, why not.

[Note: corrected this expression]

It is, which is why you must either write the units of stress as MN / m² or as MNm^-2. A unit of MNm² is not stress. It is 'mega Newtons times square meters'.

What am I missing?

This is where you are getting mixed up. Stress is the ratio of applied force to the area on which it acts. A ratio of two quantities implies the division of one quantity by the other, so the ratio of a to b can be expressed in several ways:

a : b

$a \div b$

or a / b, where the '/' stands for 'is divided by'

The units for calculating stress in the SI system are the force in N divided by the area in square meters.

These units are abbreviated N / m², which is read as 'Newtons per square meter'. Some people prefer to replace the division of force by area instead with multiplication of the force by the reciprocal of the area, which is the same as saying force × 1 / the area.

Because the reciprocal of X² is the same as 1 / X² is the same as X^-2, then

N / m² is the same as Nm^-2. Notice, the latter expression has no ' / ', and because the two units N and m^-2 are written next to each other this implies multiplication.

 

[Mark44]

Is m² the same as m^-2 is the same as 1/m²? If not, why not?

It is, which is why you must either write the units of stress as MN / m² or as MNm^-2. A unit of MNm² is not stress. It is 'mega Newtons times square meters'.

I think that SteamKing missed one of the things you said. m² IS NOT the same as m^-2. However, m^-2 IS the same as 1/m².