Simulate Early, Simulate Often... In Rhino
I´m trying to interpretate SnS plots and compare them to analythical values for a clamped beam under distributed load.
Special concern about Shear stress XZ as I work with composites and for them out-of plane shear strength is 10+ times lower than tensile or compresion. Most of the times we must check this.
I used a standard 304 steel for the comparison. Plate is 80x220x12.4 mm clamped 40 mm. Load is distributed on last 40 mm, value 100.000 N as vector load (0,0,-100.000)
My analythical delivers:
deflection: 0.118 mm SNS result is -1.24
Maximum bending stress: 88.7 MPa
Out of plane Shear stress at clamping section: 36.6 MPa
I would like your help to interpretate the SnS results.
Are you asking about the meaning of the horizontal shear stress that exists in a
beam? This is important in composite beams because each layer of the beam is fastened
together and the strength of the fastening mechanisim has to be sufficient to withstand the
The horizontal shear stress is usually caculated using the general shea formula
T = VQ/IT
where V = vertical shearing force
I = moment of inertia
t = thickness
Q = Statical moment
Thanks for your reply. Yes I agree with you. Just replace the T at the denominator for beam width.
If the beam is in the X direction and the thickness in Z, then this shear is Sxz, "out-of plane shear", usually called.
At a particular point of a particular beam section, shear in the horizontal plane is the same as the one in vertical plane (for equilibrium).
In isoptropic materials, it reaches its maximum at the centreline of thickness, following a parabolic law from top to centreline.
In anisotropic materials, its value depends on the relative stiffness (EI) of the layers on top in respect to global beam stiffness and can be elsewhere.
This value is often difficult to obtain even with FEA, so it would be of great help if SnS can deliver it, even as an isotropic. Also provides an idea of the importance of "shear deflection".
My concerns are relatively to the plots obtained by SnS compared to analytical (Sx, deflection and Sxz) for this 40x220x12.4 mm AISI 304 clamped cantilever beam. Maybe I´m wrong with my analytical or the boundary conditions input, but discrepancy is huge...maybe you can help me.
I correct my analytical max Sxz at the clamping section to 55 MPa.
Sorry, that was a typo
T = VQ/It
it was a bad hair day.
Mike probably has lots to say about shear stress
because its his specialty.
My believe is that it is not t= thickness but b=beam width.
It would be brilliant if Mike could give us his thoughts!
If the stress element is three dimensional then there
would be horizontal shear in two horizontal directions
providing for static equalibriaum.
Yes, like in a panel suported at four sides. Then we have Sxz and Syz.
I have experienced similar problem discrepancies between my computer analysis and
hand calculations which I used to check my results on various projects. Previously, I found the problem
was the way I was contraining or holding the parts between the two models were different.
(Simply suported versus fixed or clamped). I havent used SnS to look at shear stress in this way
but I could give it a go and get back to you.