Troubleshooting Shear Stress Equation for Physics Test

[tristanmagnum]

Homework Statement

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

Homework Equations

she gave me F=Δx/l *A

The Attempt at a Solution

 

[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)).

 

[tristanmagnum]

so then what would the equation be?

 

[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.

 

[tristanmagnum]

so stress can be used to find the shear modulus?

 

[Chestermiller]

so then what would the equation be?

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.

 

[tristanmagnum]

what is this equatiomn Δl=(1/G)(F/A)l

 

[haruspex]

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.

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

 

[PhanthomJay]

what is this equatiomn Δl=(1/G)(F/A)l

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

 

[tristanmagnum]

so is that what I am looking for ?

 

[PhanthomJay]

so is that what I am looking for ?

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

 

[tristanmagnum]

so what's the shear stress equation because that's the only equation i can find in my book?

 

[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.

 

[Chestermiller]

what is this equatiomn Δl=(1/G)(F/A)l

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.