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Limit of Validity of Structural Idealisation

Limit of Validity of Structural Idealisation

Hello all,

I recently completed a modification that introduced a round penetration to the shear web of a folded sheet metal fuselage floor keel beam. The keel beam is 0.050" thick 2024, of channel cross section, about 8" deep and has 0.75" wide return flanges. The upper and lower flanges ('caps') are fastened to 0.032" thick skins.

During his review of my (hand) analysis, my Chief Engineer decided I was being too conservative assuming the existence of shear and some tension/compression in the web and that I could legitimately argue a shear web/boom idealisation whereby all axial stress introduced by bending is taken by the caps and the web only sees shear. I do understand this line of thinking, have used it and know it to be a common approach.

Does anyone here have any comments as to whether this structural idealisation has a limit of validity, per se? When does one's gut inform you that a more typical beam stress distribution is occuring and there is actually might be some tension in the beam web above the centroid when in bending? Or does it take more detailed FE models to get a better understanding of how the web is working if you can characterise the input loads correctly?

Any comments welcome.
Cheers, Greg

RE: Limit of Validity of Structural Idealisation

if you use the full web in your section properties then you need to combine shear and bending stresses in the web.

If you use only "effective" web ... something like 30t or h/6 then I think you've got bending reaction in the caps and shear reaction in the webs.

Now the problem remains if the shear stresses are high that the web shear buckles and now shear is carried as diagonal tension.

another day in paradise, or is paradise one day closer ?

RE: Limit of Validity of Structural Idealisation

What is the size of the hole? Seem to recall that if a hole is in the center 1/3 ish of the web, and the web is stable to DUL, then the effect of the axial stresses at the web cutout can be neglected; besides the peak stress due to axial and shear loads on the web with a circular cutout are at different locations. With larger holes the analysis gets more complex.

What is the issue with being conservative?

RE: Limit of Validity of Structural Idealisation

Most of the references I have come across (Bruhn, Niu, some OEM design manuals) for a cutout in a beam web deals with the assumption that web carries only shear. If I am correct, the collapse load of the web is presented in terms of 'Allowable shear flow' and the usual practice (in hand-calc) is to assume that web carries only shear and determine the shear flow due to applied loads and establish MS. I haven't done a calc/case study beyond DLL but like RB1957 mentioned, beyond DLL, if the web has buckled, the effects of Diagonal Tension needs to be factored in.

One of the recent projects I did, involved initial sizing of a Wing spar, I had to resort to FEA to establish MS for the web with cutouts. My project was limited to just limit loads and the web was considered effective.

My question is, how did you show good via your hand calc for web with cutout which contains both shear as well as internal axial tension/compression stresses? Curious to find out.

- Burner

RE: Limit of Validity of Structural Idealisation

rb1957 and SW - thank you. I was hoping for some sort of rule of thumb like the h/6 or 1/3-ish web height provided. The penetration was 2" in diameter.

SW and Burner - the penetration was afforded a ring doubler so my calculations assumed the doubler was partially effective for tensile stresses (determined using a typical ETB stress distribution) and fully effective in shear. I also studied the collapsing behaviour of the web in shear along the lines of what's presented by EDSU.

My Chief Engineer's point was my conservatism introduced a doubler that could have been smaller and may have been attached with too many rivets - even though we're only modding three aircraft his point was aimed toward production line efficiency.

RE: Limit of Validity of Structural Idealisation

As long as you're talking rule of thumbs, here's another one. If the h/t > 100, it is a "thin-webbed" beam and the bending load goes into the upper and lower caps as a couple and the web takes only a shear load. If the h/t < 100, it is a "thick web" beam and the bending moment (and Mc/I stress) is taken across the entire cross-section. For your example, h/r = 8/.050 = 160, so it's thin webbed, and your Chief's suggestion of taking the bending as a couple (pun intended) of point loads in the caps is correct.

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