Shear stress

tristanmagnum · Nov 9, 2013

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

alzabroo · Nov 9, 2013

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 · Nov 9, 2013

so then what would the equation be?

alzabroo · Nov 9, 2013

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 · Nov 9, 2013

so stress can be used to find the shear modulus?

Chestermiller · Nov 9, 2013

tristanmagnum said: ↑

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 · Nov 9, 2013

what is this equatiomn Δl=(1/G)(F/A)l

haruspex · Nov 9, 2013

Chestermiller said: ↑

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 · Nov 9, 2013

tristanmagnum said: ↑

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 · Nov 9, 2013

so is that what im looking for ?

PhanthomJay · Nov 9, 2013

tristanmagnum said: ↑

so is that what im looking for ?

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

tristanmagnum · Nov 9, 2013

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

PhanthomJay · Nov 9, 2013

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 · Nov 10, 2013

tristanmagnum said: ↑

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 = [itex]\frac{E}{2(1+\nu)}[/itex], where [itex]\nu[/itex] is the Poisson ratio.

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Shear stress

tristanmagnum

alzabroo

tristanmagnum

alzabroo

tristanmagnum

Chestermiller

Staff: Mentor

tristanmagnum

haruspex

PhanthomJay

tristanmagnum

PhanthomJay

tristanmagnum

PhanthomJay

Chestermiller

Staff: Mentor

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