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Shear stress

  1. Nov 9, 2013 #1
    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. jcsd
  3. Nov 9, 2013 #2
    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)).
     
  4. Nov 9, 2013 #3
    so then what would the equation be?
     
  5. Nov 9, 2013 #4
    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.
     
  6. Nov 9, 2013 #5
    so stress can be used to find the shear modulus?
     
  7. Nov 9, 2013 #6
    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.
     
  8. Nov 9, 2013 #7
    what is this equatiomn Δl=(1/G)(F/A)l
     
  9. Nov 9, 2013 #8

    haruspex

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    Even then, it is not, strictly speaking, the equation for the stress, right? Rather, it is the equation relating stress to strain.
     
  10. Nov 9, 2013 #9

    PhanthomJay

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    That is the equation for shear deformation measured perpendicular to the length of a square element of the cross section.
     
  11. Nov 9, 2013 #10
    so is that what im looking for ?
     
  12. Nov 9, 2013 #11

    PhanthomJay

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    That is the equation for shear deformation, not shear stress.
     
  13. Nov 9, 2013 #12
    so whats the shear stress equation because thats the only equation i can find in my book?
     
  14. Nov 9, 2013 #13

    PhanthomJay

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    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.
     
  15. Nov 10, 2013 #14
    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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