# Shear stress at centroid vs other point

#### fonseh

[ Mod Note: moving this to Physics H/W ]

1. Homework Statement
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. Homework Equations

3. The Attempt at a Solution

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#### fonseh

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:

#### PhanthomJay

Homework Helper
Gold Member
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.

"Shear stress at centroid vs other point"

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