Fuselage structure under pressure 1

[Chris31]

Quick question for anyone that has any insight. Fuselage stringer is modelled as a beam and the skin as a plate. The beams have offsets. When I run a pressure case only, the skin goes into tension and the beam goes into compression. Anyone have any ideas as to how this can happen? GPF balance shows a net tension, which is expected as the pressure bulkhead expands and the skin bulges out due to pressure. I'm trying to explain why the beams see compression. When I look at displacements, end a of the beam/skin (fwd grid) expands in the hoop direction, but end b (aft grid) contracts - im guessing because the pressure bulkhead is moving aft as this beam element is just fwd of the bulkhead. However, the net displacement between grids shows tension (moving away from each other), so how can the beam be in compression?


Thanks in advance

 

[rb1957]

?? ... it started out as though you were describing a typical piece of fuselage barrel, then you added in the bulkhead.

in a typical piece of fuselage barrel, under pressure the barrel expands in the radial direction. i suggest you make a simple test model to verify this; it is a little tricky to set up the proper constraints, but that is a constructive lesson (and very satisfying when it works !).

add in the bulkhead and all the simple answers fly out the window. the bulkhead constrains the fuselage skin in the radial direction, sucking up load. this alone will put the stringer into bending. i'm willing to bet that you haven't released any bending freedoms, so the stringers are effectively welded to the bulkhead, and this adds to the bending of the stringers.

 

[Dan320]

I'm probably way off the mark here, but could it have something to do with the way the connection btw stringer and skin is modeled?

 

[Chris31]

rb1957,

Thanks for the post - The bending freedoms are not released as I am getting high plane1 and 2 bending moments (E+03). I understand what you are saying about stringer bending but will this put the beam into compression?

Dan320,

Thanks to you as well. As far as the connections, the beams pick up the same GRID IDs as the surrounding skin elements

 

[btrueblood]

Um. If you model an open tube, with pressure on the i.d., but no end caps, the tube expands radially (well tangentially, really). There is a corresponding contraction in the axial direction (that old Poisson's ratio). If you tie an axial member to the tube, it resists the axial contraction, going into compression and/or bending with compression.

 

[rb1957]

it Could do ...

i'll assume you've got end caps on your fuselage. the skin is in bi-axial tension. the skin/stringer combination is in bending. the stringer, offset from the skin, could be in compression ... don't particularly believe it, but it Could happen.

try the test models ... it'll illuminate a lot of things !

 

[Chris31]

Thank you for the response btrueblook -

The fuselage isn't an open tube though, the pressure bulkheads act as plugs - therefore poisson's effect doesn't hold does it? Aft of the pressure bulkhead should exhibit no loads (or minimal) due to pure pressure cases. If you tape a paper empenage to one end of a balloon and a paper nose to the other end,then blow up the balloon, the nose and empenage just translate (go along for the ride). So under pressure only, I cannot come up with an explanation as to why I am getting beam elements (stringers) in compression around the pressure bulkhead region and aft.

Let me put some numbers with it. I'm getting axial tension in the skin on the order of say 2000 lbs (running load times skin bay width/2) and beam axial loads on the order of 1500 lbs compression for a net tension (as expected).

 

[btrueblood]

I'd hope you don't design fuselages with open ends...they may fly, but it'd be kinda breezy inside. Which is why I said you could model it, not that you could build it. I pointed it out mainly to hint that somehow your aft bulkhead is not transmitting its axial load into the fuselage, the way it should...

I dunno why you are seeing compression on the axial stringers, either, for a fully closed fuselage (capped tube). Bending, yes, especially near the bulkheads/ends, like rb notes. Are there any holes (windows, hatches) in the fuselage, could those be creating local contractions as the fuselage is loaded? Is the aft bulkhead tied to the stringers, or only to the skin?

 

[Chris31]

could it be that the skin is seeing tension at the skin ML and the NA (where beam forces are reported due to offsets)is in compression due to the high bending moments? ie, the imaginary nodes at the NA move close together due to curvature effects of bending?

 

[rb1957]

"Aft of the pressure bulkhead should exhibit no loads (or minimal) due to pure pressure cases." ... re-think that one ! (hint, what happens if it's not there ?) and your balloon analogy is off target.

and your last post is what i meant (in my previous post)

 

[Chris31]

rb1957,

Please explain - how is the analogy off target. The pressure vessel is "sealed" so if you don't have the empenage there is no difference. The only difference is that the tail won't translate aft as the bulkhead expands aft. aft of the pressure vessel is unpressurized, so there is no hoop expansion - where would the loads come from?

 

[btrueblood]

"could it be that the skin is seeing tension at the skin ML and the NA (where beam forces are reported due to offsets)is in compression due to the high bending moments?"

Without being able to see the connection details, I'd say it's certainly possible. Rotation of the fuselage skin and bulkhead near the corner can be pretty severe, possibly it is enough to put some compression into the stringers...are they external to the pressure-containing skin, or the major load path of the skin?

 

[Dan320]

If your skin-stringer assy is not fixed at the ends but allowed to translate fwd-aft, they will move closer to each other when the fuselage is pressurised (Poisson's Ratio). That will compress the stringers.

 

[rb1957]

"Please explain - how is the analogy off target. The pressure vessel is "sealed" so if you don't have the empenage there is no difference. The only difference is that the tail won't translate aft as the bulkhead expands aft. aft of the pressure vessel is unpressurized, so there is no hoop expansion - where would the loads come from?"

maybe i missed your point ? maybe you were trying to say that the empennage doesn't get loaded by cabin pressure ("cause of the bulkhead).

i'll assume you haven't tried the test models yet.

generally the frames (and particularly the floor beam) have a significant effect on the internal loads of the fuselage. would they skew the load distribution between the skin and the stringers to put the stringers in compression ? ... some how i doubt that.

are you using plate elements for the skin, or shell (membrane) ?

are you modelling the frames with beam elements, or "caps and webs" ?

i suspect you are using membrane elements for the skin, and beams for the stringers and the frames. to try and understnad the internal workings of your model i'd reduce the complexity. the model should work with end-load elements for the stringer (remove their bending stiffness, it isn't critical to the overall strength of the fuselage). the model i'd prefer to see would have beam elements for the stringer AND "caps and webs" for the frames (i'd go so far as not to model the outer cap of the frame, since this is discontinuous) but then that's just me.

 

[RPstress]

Some hand checks are in order.

Does the combined total axial load in the skin and stringers add up to the axial force (pressure times fuse area) on the bulkhead?

What is the total axial load in the skin?

Plus some trial and error. Remove all the stringer offsets and see what the model does. Does it behave how hand calcs say it should?

If the overall model is too complicated, then try a simplified noddy model to see what's going on.

 

[Chris31]

Thank you all - I've created a simple model to determine what is going on. I created 2 beam elements surrounded by 4 quad (plate) elements. the left side of the beam and skin is fixed and I apply a shear to the right end in order to cause bending of skin/stringer combination. Interesting - with offsets, the stringers (beams) go into compression. Without offsets, the beams see no axial loading because the skin and stringer elements are loaded at the ML (the same point, ie no moment arm). This area will be analyzed by hand calcs due to complex anomalies.

 

[RPstress]

A quick note: generally offsets cause screwups when differential stiffness matrixes are used, e.g. for non-linear or buckling runs. If you're non-linear, even with small deflections, offsets will probably cause significantly (sometimes wildly) inaccurate results.

Always do hand checks if you can.

A noddy model such as the one you've just described is a good idea, but with linear static it really should behave! (Confess I didn't quite understand your description of your little model.)

Pressing ahead by ringing off part of the model that's not behaving is a bit dangerous; unexplained behaviour implies something is *wrong*, and it may affect parts of the model that are not obviously giving strange answers.

 

[rb1957]

i, too, would be a little careful in my interpretation of your simple model (which i think is 4 quads with 2 beams elements on one of the common sides). look at the free body ... the beams have moment restraint, and the only way to balance this is a couple between the skin and the (offset) stringer ... no offset, no moment ?

but in a fuselage the stringer has another way to react these end moments, being a couple into the frames.

it should be interesting to see the difference between ...
a simple shell fuselage (no stringers, no frames)
a fuselage with stringers (rods or beams)
a fuselage with stringers and frames ...
you'll see how quickly the real world messes with our hoop stress equation !

 

[ieaz123]

my two cents worth..

For an internal pressure applied load the skin hoop load = pr and the skin (and stringer) longitudinal load = pr/2 assuming a cylindrical cross section. The hoop load is nominally carried by the skin only and longitudinal load is shared by the skin and stringer.

Because the skin hoop load is higher than the skin longitudinal load the skin will contract in the longitudinal direction due to poissons (actually just reduce the pr/2 elongation). This contraction is resisted by the stringers introducing a compression component to the stringer load. For a typical skin stiffeneing ratio this effect is not enough to get a net compression load in the stringer but it might be possible if the stringers were widly spaced. However that's not what I think is going on with your model.

As your simple model shows, when you offset a beam (or rod) from a shell element it allows a couple to develop between the shell and rod. If you have an applied (or induced) bending moment, you can develop compression in the rod element even if it appears to be loaded in tension.

You mentioned the odd stringer loads at the pressure bulkhead. Because the skin is pressurized forward of the bulkhead but not aft of the bulkhead, the skin has a tendancy to rotate at the bulkhead. This rotation would be resisted by a couple between the skin elements and the stringer elements if the stringers are offset from the skin. Although this effect is real, your modeling technique may be creating too much skin/stringer bending stiffness across the bulkhead resulting in artificially high loads.

As an aside, typical modeling practice for an internal loads model (at least in my experience) is to model the stringers with rod elements coincident with the skin membrane elements which should eliminate the problem you're having.

 

[Chris31]

Thank you ieaz123 - I believe you are exactly right. The fuselage sees area ruling at this location as well, which all contribute to very high bending moments. Thank you for your explanation.