ESDU 80035 1

[40818]

Hi,
I'm looking for help using ESDU 80035 (Buckling of outstanding flanges , direct stresses varying linearly or parabolically).

This EDSU allows you to determine a new buckling coefficient depending upon the stress state of the flange (i.e under varying degrees of bending stress). My problem, is that you are required to calculate the coefficient of rotational restraint acting along the edge of the flange (not the free edge or the loaded edges), to enable the calculation it is required to know/calculate the perameter "M", which is the "elastic retraint per unit length against rotation of edge) in units of (N.m/rad)/m or (lbf.in/rad)/in

There is no further information given about this "M" in the ESDU.

The ESDU gives reference to a NACA tech note (734 (Lundquist & Stowell), and review of this gives the similar parameter as being "the stiffness per unit length of elastic restrain medium or moment required to rotate a unit length of elastic medium through one fourth radian".

The ESDU essentially rewrites the NACA equations into a way of using a full radian.

I am struggling to calculate the perameter "M" in the ESDU to allow me to calculate the coefficient of rotational restraint acting along the edge. There is an example calculation in the ESDU (which isnt any help), but it simply gives a number for "M".

If anyone could shed some light on this as to how to calculate this, it would be greatly receieved.

Thanks.
Andy.

 

[JJ22mW]

I've ran into this situation before as well. Even in Niu, the equation for calculating rotational restraint along the unloaded edge (Eq. 11.2.5) requres a variable 'Sv' (which is the same as your 'M' variable) to be known. The book says that the value of Sv is very difficult to determine and usually is based on engineer's judgement.

For structure I'm going to test in development phase, I usually just use a rotational restraint on the unloaded edge that is pretty close to midway between hinged and clamped (depending on if it's extrusion, formed, wall thickness, etc) and I get pretty good correlation between test data and empirical curves.

But there's always the conservative route and just assuming it's hinged

 

[rb1957]

how psi do you gain (between SS and FF) ? ... like JJ22mW, i'd assume simply supported, and keep a little something in the back pocket.

 

[40818]

Unfortunately, conservatism is the thing i'm interested in removing. Trying to prove existing structure is adequate rather than designing.
Mike Niu's equation is identical to the NACA reports (with a little artistic licence), didn't realise it was in his book though.
There can be quite some difference in the level of critical stress between the zero fixity and fixed.

 

[rb1957]

is a test out of the question ?

i assume your case is with a varying stress on the standing flange which has (i'm guessing) either a bulb or a lip ? bruhn has some equations for the size of bulb/lip to make the flange fully effective ... if the flange is fully effecive for compression it'd be fully effective for (P+M), no?

 

[40818]

Testing is unfortunately not an option (though having been flying for 30 odd years you would this would suffice!!)
Yup with the stress distribution, however, no lip or bulb.

 

[JJ22mW]

Are you analyzing a Z, U, or T section beam? If so there's some empirical equations in the McCombs supplement that let you calculate allowable bending moments that are limited obviously by buckling of the outstanding flanges.

 

[rb1957]

C5.8a on pg 40 if you're looking ... good catch JJ22mW