Loads on box structures

In Section 5.3 we said that aircraft structures were basically boxes. If we discuss what happens to boxes when they are subjected to the types of load which they receive when they are part of an aircraft, that is, the loads we discussed in Chapter 4, we shall build up an understanding of why air-craft are built in the way that they are.

The diagram Fig. 5.17 is similar to Fig. 4.11 and shows a representative piece of aircraft. We can call it a wing as we did in Fig. 4.11 (V is lift, H is drag and T is pitching moment), or we can call it a fuselage with the end ABCD built into the robust frames which carry the wings (V is then the tailplane load, H is the load on the fin and T the torque due to load H having been transferred down from its true position above the level of PQ).

To help us order our thoughts we are going to treat each of the three loads (V, H and T) separately; that is, we will discuss what happens when V is applied, when H and T are each applied, and then add together the separate effects. This method of dealing with complicated load systems is called the Principle of Superposition and can be applied to almost any piece of structure. In general, when a structure is loaded it bends or it stretches or in some way it deflects. The load and deflection, which are there for everyone to see, go hand in hand with stress and strain, which are the engineer’s concern and interest. The Principle of Superposition says that if two (or more) separate loads are applied to an elastic struc-ture, each load will produce a deflection and if the loads are applied together then the deflections will be added together. (If the deflections are in opposite directions, of course, one will be subtracted from the other.) When the loads and deflections can be added then the stress and the strain produced by the loads and deflections can also be added (or Fig. 5.17 Loads on a box structure.

subtracted if they are in opposite directions). This principle, which is used constantly by stressmen, can go awry if any part of the structure exceeds its elastic limit, nor does it work if the deflection produced by one load upsets the ability of the structure to carry another load (see Section 9.2), but generally it is a useful tool which allows complex problems to be broken down into a series of simple problems.

So, looking back to Fig. 5.17 and considering load V on its own, the first obvious thing to notice is that if V was applied at a point on line RS, as shown in the drawing, the thin sheet would collapse. To prevent this hap-pening we put in a flat member PQRS. If the structure is a wing the member would be a rib, and if the structure is a fuselage the member would be a frame; for ease in this example we will call the structure a wing.

With V pushing upwards, and thinking of the whole box as a beam, face PABQ is in compression and SDCR is in tension. However, we know (Section 5.6.1 above) that the loads tend to concentrate towards the web parts of sheet-metal beams, so for efficiency we should have more metal in the corners, i.e. along lines QB, etc. Since in practice we have to make joints in the corners, the need of extra metal there is not inconvenient.

(The joints do more than simply hold the bits together; they ‘carry’ the loads from one component to another either by lines of rivets or by bonded, i.e. glued, attachment.)

So far then, our structure has developed into that shown in Fig 5.18. We have elected to make this example a wing, which is an advantage because if we say that plane ABCD is on the centre line of the aircraft there is a

Fig. 5.18 Partially designed box structure.

because the loads are symmetrical the points A, B, C and D are as rigidly held in position as they would be if they were built into a wall, and we can think of them as being so.

Remembering what was said in Fig. 4.2 about transferring loads, con-sider the effect of transferring load V to position YY which is a distance x from QR. (Actually we should only be transferring half of V because the other half would be carried by the other side of the box.)

At YY we still have load V and we also have a moment Vx. Wherever YY is between QR and BC the load V is always the same, but the moment Vx changes from zero at QR to a maximum at BC. So if V, which is the shear, is constant, the web QBCR can be the same thickness from QR to BC, but if the moment Vx, which is called the bending moment, increases then the material along the corners QB and BC must be more highly loaded to resist the extra moment. For efficiency we want to keep a con-stant high stress in the material in the corners, so the area of material has to be lower where the load is lower, and the angles shown in Fig. 5.18(a) should taper as shown in Fig. 5.18(b). Summarising the situation so far we have:

•

shear in webs ADSP and BCRQ

•

compression in corners PA and QB increasing towards A and B

•

tension in corners SD and RC increasing towards D and C

If we now consider load H on its own we follow exactly the same stages of thought and conclude that we have:

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shear in webs PABQ and SDCR

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compression in corners PA and SD increasing towards A and D

•

tension in corners QB and RC increasing towards B and C

Dealing with the torque T introduces some ideas which have not previ-ously appeared in these notes. Earlier we discussed torsion in tubes of cir-cular section and in Section 5.6.2 we introduced the concept of stiffeners.

The present tube is just as capable of resisting or ‘carrying’ torsion as a circular tube. We already have jointing members in the corners QB, etc., although the corner, even if it was only folded, could provide an anti-buck-ling stabiliser of the type which we needed to add to the circular tube.

However, the large faces PABQ and SDCR will need to be divided into smaller areas to avoid large buckles or to delay the onset of buckling, since small areas of thin sheet begin to buckle later and at a higher load than large areas of the same thickness sheet. (This is an extension of the argu-ments in Section 5.6.1, but is fairly obvious since for the same sheet the smaller the area the greater the influence of the thickness. A 1-mm thick sheet 10 ft square would buckle more easily than a 1-mm thick sheet only 6 in. square.)

Redrawing the wing again gives a structure as shown in Fig. 5.19(a), which is now recognisable as part of an aircraft, even though in practice it would be shaped as shown in Fig. 5.19(b). This diagram is in advance of

the discussion because we have not finished with the torque load. An important aspect of applying torque to boxes of this shape is that they distort under load in such a way as to warp ribs such as PQRS out of plane (Fig. 5.20). A rib ABCD would not warp because the other half of the wing, the other side of ABCD, produces a symmetry of loading. If there was no compensating structure, or if for some reason the load on the other half wing was different (as during a rolling manoeuvre), then rib ABCD would tend to warp as well.

There are at least two important considerations here. First, if the rib is strong for some reason not connected with the particular case we are con-sidering (for instance the undercarriage may be bolted to it) then it may object to being warped. In fighting against the warping loads it may produce other stresses back in the torsion box. Second, because it warps and is no longer a plane, flat, easy to analyse piece of structure, it may upset the principle of superposition.

Having introduced some of the side effects of torsion we can now say that the shear loads in the skin are not very different from those in the circular thin-walled tube. In fact they vary according to the area of cross-section of the whole tube or box, i.e. the bigger the box the lower the shear load, but the length of box makes no difference to the shear load. (Note, however, that it will make a difference to the deflection and the warping.) The shear due to torsion acts all around the box but the shear due to V and the shear due to H each only act on two faces. Looking back to Fig.

5.17 we can see that the shear due to T increases the shear in PQBA, which Fig. 5.19 Completed box structure.

was due to H, but reduces the shear in SRCD, and there is a similar effect in the shears due to V. We can now add together all the effects of V, H and T for the case we have considered and the results are shown in Table 5.1. The shear due to load T we will call + (read ‘positive’) for this example.

Tension in a member we will call + and compression will be - (read ‘nega-tive’). Without putting physical dimensions into the example we cannot say whether the members (also called edge members or booms) QB and SD are in tension or compression. This depends on the relative sizes of the loads due to V and H.

Before proceeding further we must sound some warnings. The example above is not ‘stressing’ which is more mathematical and much more searching. Nor is it really representative because a wing would not, for instance, have all its lift (load V) concentrated at a single point. However, as an example it introduces some of the concepts associated with box structures in torsion and bending and gives a hint of the way a stressman might begin to approach the problems of analysis. His later stages would involve detailed examination of the skins and members to see if each of Fig. 5.20 Warping of rib or former in a thin-walled box subjected to torsion.

Table 5.1

Type of end load, i.e. tension (+) or compression (-)

due to V due to H due to T Type of load in total

Member PA - - 0 Large compressive load

QB - + 0 Smaller load

RC + + 0 Large tensile load

SD + - 0 Smaller load

Type of shear load

Skin PQBA 0 + + High-shear load

QRCB + 0 + High-shear load

SRCD 0 - + Lower-shear load

SPAD - 0 + Lower-shear load

these could carry the loads imposed on it; examination of the loads in the rivets or other fasteners in the joints; reallocation of loads if he has been obliged to strengthen one part and alter the strain on another. After all this, remember, he has only examined the structure under one loading case with all other cases still to come.

In document Understanding Aircraft Structures (Page 84-89)