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Shear stress at centroid vs other point

  1. Nov 7, 2016 #1
    [ Mod Note: moving this to Physics H/W ]

    1. The problem statement, all variables and given/known data
    for this question , I'm having problem with the shear stress at point E and shear stress at centorid.
    normally , the shear stress at the centoid will be maximum .

    But , in my working , I found that the shear stress at the centroid is smaller than the shear stress at E. What's wrong with the working ?

    i get y coordinates of centorid = 66.7mm
    For Ixx , i get (5.00x10^-5)(m^4) , For V(shear force ) , I use (437.5x10^3)N

    For shear stress at centroid , i use formula of $$\tau = V(Q) / It $$

    so at centroid , Q = (66.67x10^-3)(160x10^-3)(66.67x10^-3 / 2 ) = 3.56x10^-4
    so $$\tau $$= (437.5x10^3)(3.56x10^-4) / (5.00x10^-5)(160x10^-3) = 1.9x 10^7 Pa

    at E , Q = Ay = (40x10^-3)(80x10^-3)(53.33x10^-3)**(2)** = 3.41x10^-4

    so , $$\tau $$= (437.5x10^3)(3.41x10^-4) / (5.00x10^-5)(80x10^-3) = 3.6x 10^7 Pa

    For Q at E i have labelled it with the orange part ,
    for Q at centroid , i have labelled it with the green part ....



    2. Relevant equations


    3. The attempt at a solution
     

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    Last edited by a moderator: Nov 7, 2016
  2. jcsd
  3. Nov 7, 2016 #2
    Aything wrong with the question given ?
    I'm getting the shear stress at centroid lower than the other point ( point E ) , is it possible ?

    Or the question gt error
    ?
     
    Last edited: Nov 7, 2016
  4. Nov 12, 2016 #3

    PhanthomJay

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    Yes it is possible because the thickness at the centroid is large. At point E there is a sharp decrease in shear stress due to the sharp increase in thickness at the webs interface.
     
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