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# Plots Interpretation

Hello:

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.

Thank you

Jose

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### Replies to This Discussion

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

horizontal stress.

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

Hi Bob:

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.

Cheers!
Jose

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!

Looking at a stress element in a beam  loaded under vertical shear, there has to be a horizontal shear component to offset the vertical shear for static equalibrium to occur

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.

HI:

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.

Bob

HI:

I guess I'm thinking of a beam with depth and you are thinking of a flat panel

which would be a layer in a composite, so here is my reference so we are comparing apples

and apples.  I will try a calculation and post  it with the eqivalent in SnS and see how I do.