Structures - Stress Concentrations - Stepped Thickness 2

[Lyster]

My question relates to the stepping down of material thickness on wing rib upper and lower flanges and I only wish I could draw a picture to make it clearer.
I'm wanting to step down some flanges to save weight however this obviously causes stress concentrations.
I've checked both the company manual and 'Stress Concentrations' by Peterson and they both deal with either notches or symmetrical reductions. None really deal with unsymmetrical reductions.
I'm currently handling the situation by considering the 'extra' stress being produced by the offset of the material centrelines so that the total stress = the minimum field stress + the extra bending stress produced by the centreline offset. In addition, if the load is compressive, I then investigate the plate buckling capability.
This also applies if there is a step produced by an offset of each surface rather than a step up / down in thickness,
i.e.
P<-- _____ P--> _____
\______ -->P OR \______ <--P

Does this seem reasonable or can anyone refer me to an adequate theory for the determination of the allowable step?

Thanks in advance.

 

[rb1957]

i think you may be being too conservative, considering the rib flange alone. The flange is supported by the rib web, which is typically thickened near the flange (and this'll reduce the bending streses significantly). you've also got the skin (working with the rib flange).

P/A should be good enough, and provide the biggest radius design will let you have (probably the cutter diameter, imagining this to be machine for a billet, else why (how?)change the thickness).

There shouldn't be too big a step along the flange ... the load in the rib cap is due (mostly) to shear, which implies gradual changes in load.

good luck

 

[WKTaylor]

Lyster...

Emphasizing RB1957's comments: The transition between thicknesses is critical.

A tapered-flange thickness is ideal, since the transition is "seamless" [non-existent]. Note: driven rivets or blind rivets/bolts should have no problem with a ~7 degrees taper; also swaged-lock-bolt collars will easily conform up-to ~7 degree taper; and there are self aligning collars and nuts for Hi-Loks and bolts for upto a 7-degree taper.

A shallow-stepped [single or multi step] flange with Fillet Radii 5X the step height will generate relatively low KTs [stress concentrations]... whereas a sharp [notch cross-section] step might be a guaranteed crack. Also the transition fillet MUST have a realtively fine machined-finish parallell to the step], better than 125-RA, and must NOT undercut at the radius [a slight step-up miss-match can always be hand-sanded to a "smooth transition!!! Refer to Peterson's Book for KT effects of radius...

NOTE: my ROT [Rule Of Thumb] from satisfactory experience is that each step should be =< 20% of the base thickness with a 5X fillet radius [or round-off to nearest standard size radius]. For steps larger than 20%, I increase the fillet radius proportionally. NOTE: I ONLY stretch this rule to 33% max step thickness... and increase the fillet radii proportionately.

Examples [note the greater-the-step, the larger the ROT fillet radius].

0.20 thick flange X 20% = 0.040" step X 5 = 0.20"R fillet [round to 0.19”R]

0.20 thick flange X 33% = 0.066" step X 5 X (33/20) = ~ X8 = 0.528"R fillet [round to 0.500”R or 0.532”R]

NOTE: these steps/radii are not as dramatic as they seem, when drawn to scale.

CAUTION: Steps can FORCE flanges to become WIDER due to practical fastening issues, IE: minimum 1.0D ED from a step or fillet tangency… and room for the fastener tail, nut or collar installation [including tools].

OBVIOUSLY, stepped flanges may be impossible [or very exotic] to integrate with staggered fastener patterns!

Regards, Wil Taylor