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shear stress at boundary of beam

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In my book , it's stated that the at the boundary , the shear stress in beam = 0 .

 

However , wheni tried the circled equation , i didnt get shear stress = 0 .

 

What;s wrong with it ? Is the concept of at the boundary , the shear stress in beam = 0 . correct ?

 

http://imgur.com/a/k9geD

 

 

http://imgur.com/a/KKCGR

post-123336-0-23609200-1478308091_thumb.png

post-123336-0-50426200-1478308102_thumb.png

Edited by johnson9883

 

 

However , wheni tried the circled equation , i didnt get shear stress = 0 .

 

Could it be your arithmetic?

 

At the boundary,

 

[math]y = \frac{h}{2}[/math]
So substituting
[math]Q = \frac{1}{2}\left( {\frac{{{h^2}}}{4} - {y^2}} \right)b = \frac{1}{2}\left( {\frac{{{h^2}}}{4} - {{\left( {\frac{h}{2}} \right)}^2}} \right)b = 0[/math]

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