# Direction of max shear strain

## Homework Statement

Hi Everyone,

I am going to be doing an experiment soon using strain gauges on a beam and I will have to, among other things, calculate the direction of the maximum shear strain with respect to the axis of the beam. I am trying to find the correct equation to use.

## The Attempt at a Solution

I have found this equation in a text book of mine: tan2θ = - (εxx - εyy) / 2εxy. I looks to me like the right one but the text is a bit ambiguous. I know this isn't a very specific question but is this the equation I would need to calculate what I said above? I just want to know roughly what I'm doing before I go to the lab.

Thanks

SteamKing
Staff Emeritus
Homework Helper

## Homework Statement

Hi Everyone,

I am going to be doing an experiment soon using strain gauges on a beam and I will have to, among other things, calculate the direction of the maximum shear strain with respect to the axis of the beam. I am trying to find the correct equation to use.

## The Attempt at a Solution

I have found this equation in a text book of mine: tan2θ = - (εxx - εyy) / 2εxy. I looks to me like the right one but the text is a bit ambiguous. I know this isn't a very specific question but is this the equation I would need to calculate what I said above? I just want to know roughly what I'm doing before I go to the lab.

Thanks
The Greek letter ε typically denotes axial strain. The Greek letter γ typically denotes shear strain.

The shear in your beam is going to depend on the loading and the support conditions.

It's a good idea to understand an experiment before you perform it. Unfortunately, PF is not set up to teach you what you should know.

Chestermiller
Mentor

## Homework Statement

Hi Everyone,

I am going to be doing an experiment soon using strain gauges on a beam and I will have to, among other things, calculate the direction of the maximum shear strain with respect to the axis of the beam. I am trying to find the correct equation to use.
I assume that you are attaching strain gauges to either the top or the bottom of the beam. Do you know what the principal directions of strain are when a beam is bent?

Chet

I assume that you are attaching strain gauges to either the top or the bottom of the beam. Do you know what the principal directions of strain are when a beam is bent?

Chet
They will be attached to the top of the beam. I'm not sure about the principle directions but there will be a small force pushing the beam directly downwards if that helps.

Chestermiller
Mentor
They will be attached to the top of the beam. I'm not sure about the principle directions but there will be a small force pushing the beam directly downwards if that helps.
Go back and check your textbook. The principal directions of strain in beam bending are along the beam and across the beam. What does that tell you about the direction of maximum shear strain?

Chet

Go back and check your textbook. The principal directions of strain in beam bending are along the beam and across the beam. What does that tell you about the direction of maximum shear strain?

Chet

As far as I can tell that means that the directions are just at 45o (or 90o on a mohr's cirlce). If that is the case, what is the equation I posted used for?

Thanks!

Chestermiller
Mentor
As far as I can tell that means that the directions are just at 45o (or 90o on a mohr's cirlce). If that is the case, what is the equation I posted used for?

Thanks!
If the components of the stress tensor are expressed with respect to a Cartesian x-y coordinate system, this equation give the angle of the maximum shear stress.

Chet