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 , right ?

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)

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 ....

That's a poorly worded question and you have cut off the bottom of fig 1(b).

 

So what is the dimension across the soffit of the trough?

The part 2 has a length of 80mm , so total length of base = 40 +80 + 80 =160

bump