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Old Nov 4th 2016, 09:03 AM   #1
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shear stress in hollow beam

I m going to find the shear stress at section n-n .
So , shear stress in beam has formula of τ = V(Ay) / It

I gt the I ( second moment of inertia correctly ( same as the given ans ) , but I'm having problem of finding the shear stress at A .



For V ( shear force ) , it is 40kN constant from 0m to 0.4 m ( in my SFD diagram)
For Ay , i have (100x10^-3)(12x10^-3) (94-50)(10^-3) = 5.28x10^-5 (mm^4)

Is my Area ( green coloured part ) correct ?

so τ= (40x10^3) ( 5.28x10^-5 ) / (5553152 x 12x10^-3) = 3.81x10^-6 , but the given ans is 15.85x10^6

Does the section n-n mean when we cut off the beam at n-n , the side view of n-n look like in the diagram ?
Attached Thumbnails
shear stress in hollow beam-img_20161104_123716.jpg   shear stress in hollow beam-img_20161104_120244.jpg  

Last edited by ling233; Nov 4th 2016 at 09:07 AM.
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Old Nov 7th 2016, 08:39 AM   #2
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It looks like you mis-entered the values of VQ/It into your calculator - using your values you should have gotten 3.17x10^-5. The reason the answer is half that is because the thickness of the beam at point 'a' is two times 12 mm. The shear load is carried by both the left and right half of the hollow beam, so you add the two thicknesses together.
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