The modern aeroplane can be looked upon more conveniently as a system of thin-walled tubes designed to take torsion and bending. In a way we must change our present point of view to look from the outside in, by way of the thin-walled tube, instead of from the inside outwards (as we have just done) from structure to skin. A thin-walled tube is an interesting phenomenon because it amounts to a piece of thin sheet, wrapped around into a tubular shape that may be cylindrical, conical or ogival. It is called thin-walled because of the relatively small ratio of wall thickness to tube diameter.
The modern metal aeroplane may be approximated to a family of thin-walled tubes for the purposes of some stress analyses. The fuselage is, in effect, two tapering tubes joined at their bases to a cylinder. The wings and tail surfaces are approximately flattened tubes, tapering from roots to tips. Ribs, spars, frames, longerons and stringers are methods of internal stiffening. In many respects the tubes are also torsion boxes, which are developments of the pure thin-walled tube, in that the strength of such members is vested in the ability of the skin to resist shear forces. The skin takes a moderate range of end-loading, but its great virtue lies in the way it is made to work in shear.
In Fig. 11.14 an aeroplane is shown as a family of thin-walled tubes. The weights of the fuselage ahead of and behind the wings are reacted at the centre-section shown, for simplicity, as a single frame, part of which is an arc CD. Clearly, the fuselage is in bending and shear, as shown in Fig. 11.14(b), where the split arrows show that the side AB of one panel, ABCD, is being displaced downwards relative to CD. Similarly, the side EF of the rear fuselage panel is being displaced downwards relative to side CD. If the fuselage is in torsion due, for example, to fin side-load or to a side-load from the nosewheel undercarriage, then torsion is transmitted as shear around each section. Depending upon the direction of normal bending loads (such as those shown), the shear caused by a system of bending loads is increased on one side of the fuselage, and decreased on the other by the additional torsion.
Fig. 11.14 The aeroplane as a family of thin-walled tubes. In addition to shear in the fuselage sidewalls, the top skin is in tension and the bottom in compression.
Now, panels ABCD and CDEF are in equilibrium in that they cannot change their positions relative to the aircraft datum. To be in equilibrium the torque of the shear along AB and CD (which tends to rotate the first panel in an anti-clockwise direction) must be opposed by an equal and opposite torque due to opposing shear along sides AD and BC as shown. The same argument applied to panel CDEF enables us to postulate the existence of counter-shear along sides DE and CF. Here then is the interesting property of the thin-walled tube/torsion-box: loads normal to the length are reacted by complementary shear stresses along the length.
Each panel, ABCD, CDEF, is formed by a boundary frame consisting of portions of fuselage frames or formers and longitudinal stringers, and skin. Ignoring the skin for a moment we see that each panel boundary is tending to distort in a similar way to the deficient frames in Fig. 11.10(b) and Fig. 11.11(c). The skin reacts against the distortion by providing tensile strength parallel with diagonals BD and DF. The tension fields are accompanied by compression parallel with diagonals AC and CE. The existence of tension fields and
wrinkling, as shown in Fig. 11.14(b) and (c), can often be seen in flight. Looking along the upper surface of the wing of an airliner which, for economy, has a light, thin skin one can often see diagonal wrinkling during turns. The wrinkles are caused by compression in the upper skin, aerodynamic pitching moments and by torques from the engine-mountings.
(lying along the fuselage length) is in tension, while that below is in compression. The total loading applied to the structure is, therefore, a combination of tension, compression and shear. Stressing cases are examined to see what combinations of maneuvers and atmospheric accelerations result in the highest resultant sums of tension, compression and shear. Of course, wings and tail surfaces behave, and are treated, in a similar way to the fuselage. The only difference is that some of the applied loads have different origins, but all come together to be met by the structure as a complete whole.
Cutouts
Cutouts, i.e. windows, doors, servicing panels, hatches, bomb-bays, etc., cause a recurring headache for the structural engineer. As soon as one makes a hole in a load-bearing skin a stronger surrounding structure must be introduced to provide adequate paths for the detour of the stresses. Perhaps the most noticeable feature of cutouts is the rounding of the corners: sharp corners cause excessively high stress concentrations.
Figure 11.15 shows the cylindrical form of an ideal pressure cabin.
Fig. 11.15 Shapes of cutouts in skin.
It may be shown that a cutout of elliptical form with the proportions 2: V2 is neutral in its effect upon the overall tensile stress concentration, in that the maximum principal tensile stress in the vicinity of the hole is no greater than the hoop stress. The principal tensile stress factor for each cutout, K, is given by:
K = maximum principal tensile stress / hoop stress, 2 pt (117)
Many airliner windows are variants of the ‘neutral-hole’. The variants lie between the pure neutral-hole form and the rectangular, ‘corners’ being introduced to improve the view. The stresses caused by pressurization must be added to those already mentioned. Pressurization is increased with height and hence the pressure differential varies from zero to some required value each time an aeroplane flies. As such it must be taken into account in the calculation of fatigue and airframe life. As airframes grow older the pressure differentials, and consequently operating heights, are usually reduced as a means of reducing the tensile stress levels. 11.4.2 Beams, booms and grids
We have seen how the skin and internal structure of an aeroplane is made to work in shear and tension, the final view is of the behavior of the structure as a family of beams, i.e. in compression as well as tension and shear. If the aerofoil surfaces can be approximated to thin-walled tubes, flattened about one axis, then such flattening works against the general value of the tube as a member able to resist bending.
Wing spars are a development of the simple beam designed to take bending and shear loads. The type of beam we are most concerned with in aircraft work is the cantilever variety, which is supported at one end only. However, other types of beams, usually having encastre or ‘built-in’ fixing at both ends, are met with in component design. Examples are bomb-bay structures and floor-beams running across a number of frames.
The weight of material making up a spar depends upon the length and cross-sectional area. For greatest efficiency spars must have the greatest area of cross-section furthest away from the neutral axis: the moment of inertia of the cross-section about the neutral axis must be a maximum. In Fig. 11.16(a) a spar is loaded with a shear load, W, which is reacted at a distance x further away along the spar.
Fig. 11.16 Wing spars.
The moment of the shear force is W x and this is reacted by end-loads in the top and bottom booms. If the moment is 100,000 lb in and the depth of the spar, z, is 20 in then the tension in the top boom is around 100,000/20, i.e. 5,000 lb, and the compression in the bottom boom is also 5,000 lb. If the same bending moment must be met by a spar of half the depth, then the end-loads in tension and compression are 10,000 lb, respectively. In fact we have erred on the dangerous side by using the spar depth overall, the depth we should have used is the distance between the centroids of the booms, a smaller distance. Even then the calculation is approximate, serving to make the point that the deeper a spar the smaller are the end-loads in the booms and, therefore, the lighter is the required structure. The minimum amount of material needed in a cross-section depends also, of course, upon the required levels of shear and bearing strength needed.
From the foregoing we deduce that the thicker a wing in absolute measure the lighter it will be. A delta wing is lighter than a straight or swept wing with sections having the same thickness distribution or, weight for weight, a delta wing can be designed with a finer section. This means that there is a ‘trade-off’ as it is called between structural and aerodynamic design. One may have a thin very low drag delta wing with more surface area than straight or swept versions, and relatively simple high-lift devices, or one may have smaller straight or swept wings with more complicated high-lift devices. The choice is not as simple as it might seem, however, for it depends upon stability, control and a number of other factors. The uncertainty accounts for the large number of straight, swept and delta planforms one sees around the world on aircraft designed for similar
(usually interceptor) roles.
The relatively simple structure shown in Fig. 11.13 cannot be used in more advanced layouts. The arrangement of spars and supporting ribs which serve to maintain profiles and to transmit diffuse aerodynamic loads into concentrations of members give way to more complex arrangements of many spars and many ribs, all of which behave rather like a flexible network of intersecting beams. An arrangement of this kind is shown in Fig. 11.17, for a M = 2.2 SST designed in 1960 by the College of Aeronautics. The spars and ribs form a structural grid, which is again reproduced in the fin. The box-like cells formed within the wing structure contain fuel.
Fig. 11.17 Advanced structure of an integrated M = 2.2 supersonic transport (College of Aeronautics, Cranfield, 1960).
The analysis of stress and strain in advanced aircraft structures has forced the development of very elegant and complicated mathematical techniques. The structural engineer must relate the effects of weights, aerodynamic inputs, elastic responses and stress distributions through-out the structure as one whole, for a wide variety of different shapes. Fortunately, the grid-like construction allows accurate analyses to be made and translated into mathematical statements that can be handled by computers.
11.5 Fabrication
Early aeroplanes were made of spruce, fabric and piano-wire, and this form of construction is still to be found in some light aeroplanes. Later the welded steel tube framework, fabric covered, became the standard for light-aircraft engineering, with plywood-sandwiched balsa wood as a good material for light monocoque structures.
Airframes made from strip and sheet metal are riveted, welded, or stuck together with special glues. Sheet metal is provided in a number of standard thicknesses, called gauges, and one uses the next thickness of gauge above the required thickness of material as determined by stress analysis. In the pursuit of efficiency and low weight in large aircraft one must turn to more expensive methods of manufacture. Using gauged sheet, that is manufactured in stock sizes within certain tolerances, it would be possible for an aircraft with a wing area of 2,000 ft2 to show an increase in weight of 3,000 lb if the skin was on the high side of the tolerance. American aircraft repaired in the UK, using British standard gauge materials, may be heavier than their American counterparts, because the Americans have a more finely graded range of gauges from which to choose.
Modern manufacturing techniques involve machine milling of skins and stabilizing members as
complete units from solid billets of material. Machining is expensive, but for large, costly aircraft the expense is worth the dividends. Chemicals are used to etch and dissolve away unwanted metal, and the use of chemicals and machining in this way enables structures to be made with fewer joints. Weaknesses usually originate in the joints and their elimination enables the behavior and life of the structure to be predicted with far greater accuracy.