How Do You Calculate Shear Stress in Beam Sections?

[mohamadh95]

1)When we are asked to calculate the shear stress at AB should we consider the width as T or as 2T?

2)And when applying t=vq/it what sections should we take and is the value we found located on the bottom of the area?(I'm not talking about this beam but any beam in general)

3)And finally given V how can we found the location of the maximum stress?Thank you. The first question is the most important for me.

 

[PhanthomJay]

1)When we are asked to calculate the shear stress at AB should we consider the width as T or as 2T?

I guess we need your thoughts on this first as to what you think should be the value to use, T or 2T. Does the 2nd leg serve any purpose in strengthening the section in bending and shear?

2)And when applying t=vq/it what sections should we take and is the value we found located on the bottom of the area?(I'm not talking about this beam but any beam in general)

the area to be used in determining Q depends on the location in the cross section where you want to determine the shear stress. So in determining Q, you could use the area above or below that location to find the shear stress at that location.

3)And finally given V how can we found the location of the maximum stress?

Q is max at the _____?____ of the cross section, but might there be a case, in general, where the shear stress is max elsewhere?

Thank you. The first question is the most important for me.

Back to the first question, is it T or 2T? Supposing you just wanted an average shear stress in the vertical legs instead of the max shear stress, would you ust the area of one leg or both in your V/A calc?

 

[mohamadh95]

Thank you for your reply.
I think you misunderstood a part in my second question. Let's say we took an area and applied the formula and we got the value of the stress. Let's say the value equals 10MPa, and if we want to draw the stress distribution of this area, where will be the 10MPa located?The bottom of the section?The top?The center?
As for the question 3, generally talking the maximum stress is at the neutral axis, but if we're asked to determine the maximum stress given a certain V should we just go for the calculation on the N.A?
Thank you, I hope you reply again.

 

[PhanthomJay]

Thank you for your reply.
I think you misunderstood a part in my second question. Let's say we took an area and applied the formula and we got the value of the stress. Let's say the value equals 10MPa, and if we want to draw the stress distribution of this area, where will be the 10MPa located?The bottom of the section?The top?The center?

I am assuming firstly that your shear force load V acts perpendicular to the line AB. If you want to find the shear stress in the beam at location AB, using VQ/Ib, Q is determined by finding the area of the cross section above (or below) the line AB and multiplying that area by the distance from the centroid of that area to the centroid (Neutral Axis) of the entire cross section. Let's say the numerical result is 10 MPa. That is the shear stress in each leg at that point...the shear stress is assumed constant from left to right across the cross section along AB where the material is (sort of an average shear stress at that location along AB). If you want to find the the shear stress at say the bottom of the beam, using the same method, you would find Q = 0 and therefore no shear stress at the bottom. The shear stress would vary parabolically, in vertical direction, max at NA and 0 at bottom. I don't know if that answers your question.

As for the question 3, generally talking the maximum stress is at the neutral axis, but if we're asked to determine the maximum stress given a certain V should we just go for the calculation on the N.A?

generally, yes, but remember, Q is max at the NA, but the shear stress is VQ/Ib, so you could have a case where the thicknesses "b" are not constant and you'd have to check locations where Q might be less, but the thickness ''b'' might be less also. (I am referring to plate thicknesses as 'b' and not 't', to avoid confusion with your original question about using T versus 2T).

 

[mohamadh95]

Yes it does, thank you very much.