Signs of Tensile and Compressive Stresses

[a1234]

TL;DR

Signs (directions) of forces on FBDs are not matching up with the conventions used for tensile and compressive stresses

I have recently learned that, by convention, axial tensile stresses are positive and axial compressive stresses are negative. I am having some trouble incorporating this information into my FBDs that are used to find the axial forces leading to these stresses.

For instance, from the attached FBD, I ended up finding Fab to be -500 N, which indicates that the force is actually compressive (directed toward point A) and not tensile as drawn in the FBD. However, if I had originally drawn Fab to be in compression, then wouldn't I find Fab = +500 N?

If I had drawn the latter kind of FBD and used Fab = +500 N to find the axial stress in Fab, I would end up with a positive value for the stress, which I know is wrong because the stress is compressive. In this case, how can I make the stress a negative value?

Could someone please help me figure out what I am missing here?

Thanks!

 

[PhanthomJay]

Summary: Signs (directions) of forces on FBDs are not matching up with the conventions used for tensile and compressive stresses

I have recently learned that, by convention, axial tensile stresses are positive and axial compressive stresses are negative. I am having some trouble incorporating this information into my FBDs that are used to find the axial forces leading to these stresses.

For instance, from the attached FBD, I ended up finding Fab to be -500 N, which indicates that the force is actually compressive (directed toward point A) and not tensile as drawn in the FBD. However, if I had originally drawn Fab to be in compression, then wouldn't I find Fab = +500 N?

If I had drawn the latter kind of FBD and used Fab = +500 N to find the axial stress in Fab, I would end up with a positive value for the stress, which I know is wrong because the stress is compressive. In this case, how can I make the stress a negative value?

Could someone please help me figure out what I am missing here?

Thanks!

The plus and minus signs have multiple meanings in Physics and Engineering. Similar perhaps to your example, if you assume that a force acts down and you get a negative solution for that force, it means that you assumed the wrong direction for the force, and that it actually acts up. If you got a positive solution for that force, it means you assumed the correct direction for that force, even though it may be a compressive force.

Forget about actual signage for tension and compressive axial forces in a free body diagram...I mean how do you assign a positive or negative values to a force acting at a 45 degree angle?

The rule is this: if the force points inward toward the joint or member, it is a compressive force. If it points outward away from the joint or member, it is a tensile force. For the compression case , you call it a negative force, for the tension case, you call it a positive force, by convention. So don’t give it a sign until the end. If you assumed the direction of all forces correctly up front, you are going to get all positive numbers. Only after you determine if it is a pushing force or pulling force can you then give it a sign. Or don’t give it a sign, just say for sample that ‘the force is 10 N compressive’.

 

[a1234]

Thanks for the explanation. This makes a lot of sense.

Somehow, I assumed that the signs were supposed to "carry over" to the stresses in compression and tension, and I didn't think of them as having separate meanings.

 

[PhanthomJay]

You are welcome. Yeah, the minus sign is always a killer...