Shear Stress in an I Beam
Shear Stress in an I Beam
(OP)
I am checking a beam for shear and am trying to decipher the code requirements for shear. .4FyA is the allowable stress, but the issue is with calculating the stress in the beam to compare to allowable.
For an I beam, I ignore the stress in the flanges and focus on the web. Taking the area of the web as DTw, I get the shear area. Divide the shear force by web area and the shear stress is found. Easy enough.
The mechanics of solids method for a rectangular cross section states that maximum shear stress is 1.5 V/A. My method computes average shear stress.
My question is which one is it appropriate to design an I beam using? The mechanics of solids method is more conservative, but usually shear isn't an issue.
For an I beam, I ignore the stress in the flanges and focus on the web. Taking the area of the web as DTw, I get the shear area. Divide the shear force by web area and the shear stress is found. Easy enough.
The mechanics of solids method for a rectangular cross section states that maximum shear stress is 1.5 V/A. My method computes average shear stress.
My question is which one is it appropriate to design an I beam using? The mechanics of solids method is more conservative, but usually shear isn't an issue.






RE: Shear Stress in an I Beam
Check your connection too, if a significant amount of web is removed or modified it's worth checking a net area.
Generally though unless it's short highly loaded beams, shear never governs in steel design.
RE: Shear Stress in an I Beam
RE: Shear Stress in an I Beam
As for addressing your specific, original question:
1) AISC allows you to use the average stress I believe.
2) I personally go with peak stresses (3/2 V_ave).
Using the average stress would seem to imply post-yield stress distribution. A "plastic shear capacity" of sorts. As long as your member doesn't have a constant shear diagram, I can see how that might be rationalized. However, the mechanics of that seem pretty complicated to me. Too complicated to justify any material savings that might accrue.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Shear Stress in an I Beam
Thus, because we suppose full shear plastification, stress are indeed 'uniform' over the whole shear area...
RE: Shear Stress in an I Beam
RE: Shear Stress in an I Beam
I don't think about this often, so pardon my ignorance. Why wouldn't pure shear yield be sqrt(2)/2 of pure tension yield?
"It is imperative Cunth doesn't get his hands on those codes."
RE: Shear Stress in an I Beam
Never mind - I retract that question.
"It is imperative Cunth doesn't get his hands on those codes."
RE: Shear Stress in an I Beam
Fro a rectangular section (such as dimensional lumber or a plate), the maximum shear stress will be 1.5*(shear force)/(Area). This is a simplification of the same formula of (Shear Force * Q)/(I * Web Thickness).
RE: Shear Stress in an I Beam
BA
RE: Shear Stress in an I Beam
max shear stress in a rectangle is 1.5*(P/A), a result from VQ/It.
in an I beam the web shear stress (VQ/It) is much more constant, 'cause the flanges allow the ends of the webs to develop shear flow; so the average shear stress (P/A) is adequate for design. I'd expect that the "true" answer is that the web shear varies from 0.95 to 1.05*average.
another day in paradise, or is paradise one day closer ?
RE: Shear Stress in an I Beam
RE: Shear Stress in an I Beam
another day in paradise, or is paradise one day closer ?
RE: Shear Stress in an I Beam
"It is imperative Cunth doesn't get his hands on those codes."
RE: Shear Stress in an I Beam
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Shear Stress in an I Beam
In a previous thread here, it came to light that even the area of uncoped flanges can be included in the evaluation of the shear rupture capacity. Neat.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Shear Stress in an I Beam
If I recall correctly, the AISC does discuss analysis at copes (in particular long copes). I do not have access to the code at the moment, but it was somewhere in the connections portion of the latest code. Perhaps others in this tread can elaborate if they have ready access to a copy of the code.