# Shear stress

1. Nov 9, 2013

### tristanmagnum

1. The problem statement, all variables and given/known data

i am study for a physics test and i think my physics teacher gave me the wrong equation for shear stress

2. Relevant equations
she gave me F=Δx/l *A

3. The attempt at a solution

2. Nov 9, 2013

### alzabroo

That is definitely not right. The units on either side of the equation do not match up. Force(F) has units of Newtons(kg*m/(s^2)) while the right side comes out to units of (1/(m^2)).

3. Nov 9, 2013

### tristanmagnum

so then what would the equation be?

4. Nov 9, 2013

### alzabroo

The equation for any stress (shear, tensile, or compressive) is: stress = Force/(Area of application). Determining stress at specific points in an object is a lot more complicated, but hopefully that's not required immediately after an intro to the concept. The most important thing to remember though I suppose is that the units on either side of any equation have to match up.

5. Nov 9, 2013

### tristanmagnum

so stress can be used to find the shear modulus?

6. Nov 9, 2013

### Staff: Mentor

The equation you gave is for tensile stress, not shear stress, and, you left out Young's modulus on the right hand side of the equation.

7. Nov 9, 2013

### tristanmagnum

what is this equatiomn Δl=(1/G)(F/A)l

8. Nov 9, 2013

### haruspex

Even then, it is not, strictly speaking, the equation for the stress, right? Rather, it is the equation relating stress to strain.

9. Nov 9, 2013

### PhanthomJay

That is the equation for shear deformation measured perpendicular to the length of a square element of the cross section.

10. Nov 9, 2013

### tristanmagnum

so is that what im looking for ?

11. Nov 9, 2013

### PhanthomJay

That is the equation for shear deformation, not shear stress.

12. Nov 9, 2013

### tristanmagnum

so whats the shear stress equation because thats the only equation i can find in my book?

13. Nov 9, 2013

### PhanthomJay

For pure shear stress or average shear stress caused by a force F acting parallel to the plane of the cross section, it is F/A, as previously stated.

14. Nov 10, 2013

### Staff: Mentor

I've never seen an equation like this with the shear modulus G in it, and I have lots of experience with deformational mechanics. This is the equation for a tensile deformation, provided the G is replaced by the Young's modulus E (or some people use Y). For a shear deformation between two parallel plates separated by a distance Δy, the equation to use is (F/A)=GΔx/Δy, where F is the tangential force on the upper plate (a plane of constant y), Δx is the displacement in the x direction of the upper plate relative to the lower plate, A is the area of the plates, and G is the shear modulus = $\frac{E}{2(1+\nu)}$, where $\nu$ is the Poisson ratio.