What Equation Calculates Maximum Shear Strain Direction?

In summary: 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.The equation is tan2θ = -(εxx-εyy)/2εxy.
  • #1
GBA13
73
0

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.

Homework Equations

The Attempt at a Solution


I have found this equation in a textbook 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
 
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  • #2
GBA13 said:

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.

Homework Equations

The Attempt at a Solution


I have found this equation in a textbook 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.
 
  • #3
GBA13 said:

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
 
  • #4
Chestermiller said:
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.
 
  • #5
GBA13 said:
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
 
  • #6
Chestermiller said:
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!
 
  • #7
GBA13 said:
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
 

Related to What Equation Calculates Maximum Shear Strain Direction?

1. What is the direction of maximum shear strain?

The direction of maximum shear strain is the direction in which the material is being deformed the most. It is perpendicular to the principal stress direction and is at a 45-degree angle to the normal stress direction.

2. How is the direction of maximum shear strain determined?

The direction of maximum shear strain is determined using the Mohr's circle method, which plots the normal and shear stresses in a graphical format. The point where the circle intersects the horizontal axis represents the direction of maximum shear strain.

3. What is the significance of the direction of maximum shear strain?

The direction of maximum shear strain is important in understanding the behavior and strength of materials. It helps in determining the direction in which a material is most likely to fail or deform, and is crucial in designing structures to withstand external forces.

4. Can the direction of maximum shear strain change?

Yes, the direction of maximum shear strain can change depending on the applied stress. As the magnitude and direction of the applied stress changes, the direction of maximum shear strain will also change accordingly.

5. How is the direction of maximum shear strain related to the maximum shear stress?

The direction of maximum shear strain is perpendicular to the principal stress direction, while the maximum shear stress occurs at a 45-degree angle to the principal stress direction. This means that the direction of maximum shear strain and the direction of maximum shear stress are mutually perpendicular.

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