Bruhn C10.18 1

[fbt]

Taking a look at Bruhn C10.18 for the first time in years. In equation C10.18 (and accompanying Fig C10.20) there is reference to both plate width "c" and "h". For the life of me I can't figure out what the difference between "c" and "h" are, why distinguish between them? fsh and fsc have identical descriptions.

In reviewing NACA L-323 (I assume this is the source material for this section), "c" is referred to as the length between holes (c = B-d). But in Bruhn this length is called [capital] "C". With C' being the flat portion. In the end L-323 did not clear this up for me.

Anyone know if I'm missing something or making some egregious error by assuming that c=h and fsc = fsh? Or is lowercase-c the same as uppercase-C? Or is it something else?

Any guidance much appreciated.

 

[sdm919]

In reading L-323, they state that the formula is empirical. It appears that they took sort of an average between 2 shear buckling loads, fsh and fsc. fsh is the shear buckling load for a long rectangular plate with width "h" and length "long". fsc is the shear buckling load for a long rectangular plate with width "c" and length "long". q-allow is then sort of a weighted average between these 2 theoretical calculations.

fsh and fsc would therefore only be the same value if h = c.

Now look at the terms multiplying the fsh and fsc. They are functions of the hole size relative to the web height (D/h). For small holes (small D/h) the factor on fsh is close to one, so fsh dominates. For large holes (large D/h), fsc dominates. So it appears that to fit the test data, they simply came up with factors to multiply these 2 theoretical buckling loads make a good match.

Formula (3) in L-323 makes this a little more clear. Here the functions multiplying fsh and fsc are simply (D/h) and [1-(D/h)], that is to day, they are linear and have values ranging from 0 to 1, with the sum adding up to 1.

This approach may seem odd nowadays, but remember this was 1942, before computers, and there was a war going on and they needed quick answers. Estimate the bounds, then take some sort of average to match the tests...

 

[fbt]

sdm919, thanks for that perspective.

To get to the point of my question, say I am analyzing an aluminum, rectangular spar web with such flanged holes and want to use this method. What is c? Is it the height of the spar web? Or is it the length between the holes?

Thanks again.

 

[sdm919]

My interpretation is that "c" is the width of the space between the holes and "h" is the height of the web.

 

[WKTaylor]

FYI related ...
Bruhn 1973 'supplements' and 'eratta' are attached...

 

[rb1957]

I think we're dealing with the limitations of typewriters (mechanical and human).

I think "C" and "c" are the same thing.

Fsh is the shear buckling of a panel width "h" ... is this the full width of the beam, or the distance between the rivets (much ink has been split on this ... I favour the latter)
Fsc is the shear buckling of a panel width "c" ... which is the distance of plain web between the lightening hole flanges (= B-2D).

Bill Gran's Errata doesn't flag this section (C10.18) for clarification or correction. He does plot fig C10.20 so it is clearer.

 

[SWComposites]

I think "C" and "c" are the same thing.

I agree.