Shear Stress in Beams: Proof & Explanation

[filterwin9]

Homework Statement

where

V = total shear force at the location in question;
Q = statistical moment of area;
t = thickness in the material perpendicular to the shear;
I = Moment of Inertia of the entire cross sectional area.
based on this formula , the shear stress is max at the neutral axis of beam ... Why it is so ? Can someone prove me ?

Homework Equations

The Attempt at a Solution

 

[filterwin9]

for Q=Ay , i gt A= (b)(0.5h - y) , y = y , so Q = (b)(0.5h - y)(y) , eventually , i gt
τ = (V)(Q)/ (I)(b)
= (V)(b)(0.5h - y)(y) / Ib
= (V)(0.5h - y)(y) / I
which is different with the author 's working , am i wrong ?
http://fp.optics.arizona.edu/optomech/references/OPTI_222/OPTI_222_W10.pdf
refer to page 2

 

[PhanthomJay]

The author's working is correct. You are not calculating Q correctly. Q is the area below the section of interest time the distance from the centroid of that area to the neutral axis. Use y1, not y, when calculating the area and the distance of the centroid of that area to the neutral axis.

 

[filterwin9]

The author's working is correct. You are not calculating Q correctly. Q is the area below the section of interest time the distance from the centroid of that area to the neutral axis. Use y1, not y, when calculating the area and the distance of the centroid of that area to the neutral axis.

solved