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Formula of shear stress

  1. Jul 21, 2016 #1
    1. The problem statement, all variables and given/known data
    in the old thread , i was told that
    The formula for calculating the shear stress is a beam is ##τ = \frac{V ⋅ Q}{I ⋅ t}##

    τ - shear stress
    V - shear force
    Q - first moment of area above the location where the shear stress is calculated.
    I - second moment of area for the entire beam about the N.A.
    t - width of the beam where the shear stress is calculated
    But , how to change the ##τ = \frac{V ⋅ Q}{I ⋅ t}## into V and A only ?
    just like below ?

    2. Relevant equations


    3. The attempt at a solution
    The V represent shear force , it's not volume , am i right ?
     
  2. jcsd
  3. Jul 21, 2016 #2
    sorry , i left out something in post # 1 , so continue here :
    as we can see shear stress of various shape is in terms of V and A ,
    The V represent shear force , it's not volume , am i right ?

    How to change shear stress = (V)(Q)/ (It) into in terms of V and A ?
     

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  4. Jul 21, 2016 #3

    PhanthomJay

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    V is the conventional designation for shear (in force units). Clearly it doesn't stand for Volume here, right?
    V/A is average shear stress, whereas VQ/It is maximum shear stress which usually is at the neutral axis. You cannot generalize a relationship between them since it depends on the cross section shape. For example for the rectangle, max shear stress is 3/2 avg shear stress, and for the circle, max shear stress is 4/3 avg shear stress. Note that for certain shapes like I beams, the area of the web and not the entire shape is used to determine A when computing avg shear stress, because the shear stresses mostly are in the web.
     
  5. Jul 21, 2016 #4
    so , shear stress is VQ/It for beam , and for the other shape , it's function of V and A ..There's no way to derive he shear stress of other shape from VQ/It ?
     
  6. Jul 21, 2016 #5

    PhanthomJay

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    I think you misunderstood. repeat: For the rectangle, max shear stress VQ/It is 3/2(V/A), or 3/2 times the avg shear stress in the rectangle. For the circle, max shear stress VQ/It is 4/3 (V/A), or 4/3 times the average shear stress in the circle.
     
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