1. The structurally - power fuselage schemes.

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1 Lecture 24(14). Strength analysis of fuselages Plan: 1. The structurally - power fuselage schemes. 2. Strength calculation of the fuselages cross-sections. 3. The semimonocoque fuselage cross-section calculation. Calculation from external forces that operating in a vertical plane. 4. Calculation from external forces operating in a horizontal plane 5. The fuselage calculation at simultaneous horizontal and vertical tail loading. 6. Loading from an overpressure 1. The structurally - power fuselage schemes. Now metal fuselages on a carrying capacity can be subdivided on two aspects: a semimonocoque and monocoque. In the semi-monocoque fuselages for the moment of a structural failure is accepted the moment of stability loss in compressed stringers under bending. With the purposes of creation of a fuselage with a minimum mass the skin enough thin ( = 1.5 mm) is applied and it works behind a stability limit from shear force and torque. In a monocoque fuselages skin is the basic load-bearing element that operates on bending and torsion and should work only in stability limits, because the loss of stability under bending and torsion will cause a structural failure as a whole. Fig. 1. The structurally - power fuselage schemes Fuselages can have some baseline designs, which are shown on fig. 1., a,b,c. The cross-sections are rather diverse: round, elliptical, rectangular etc. Recently for large transport airplanes (airbuses) multideck fuselages are applied. 1

2 2. Strength calculation of the fuselages cross-sections. Having the starting diagrams of external loads Q, Mb, Мt constructed on length of a fuselage, it is possible to pass at the calculation of normal and shear stresses. The analytical models of fuselage are identical to the wing analytical models and theirs calculation methods are similar to wing calculation methods. At normal stresses determination of longitudinal load-bearing elements from bending moment it is possible to use one of two approximate computational methods: the computational method through reduction factors with the usage of strain diagrams, or the computational method on a carrying capacity without reduction factors (semigraphical computational method). The shearing stresses from a shear force and torque are determined simply enough, because the majority of fuselage cross-sections is represented by closed sections except the airbus fuselages cross-sections. Airbus fuselage cross-sections are closed sections. For determination of shearing stresses from shear force and torque they should be considered as statically indeterminable systems. 3. The semimonocoque fuselage cross-section calculation. Calculation from external forces operating in a vertical plane. Let us have a symmetrical semimonocoque fuselage cross-section, which longitudinal power set consists of four spars, stringers and skin, and transversal power set from frames. The skin of a fuselage works simultaneously on normal and shearing stresses from bending and shear force. The normal stresses from a bending moment for a case, when the skin does not lose stability from shear stresses up to ultimate loads, can be computed by the known formula: Mbz N i уi (1) Fr where I r the reduced area's inertia moment, which is equal: 2 ( f str skintskin ) уi where: cr.skin skin - is the reduced factor of skin in compressed zone; skin 1 - for str tension zone, cr. skin - is the critical stress of skin, str is the stress in stringer; Fr ( f str skint skin )- is a reduced area of fuselage cross section; N is the axial force. 2

3 If the skin early loses stability from shear force and torque, then normal stresses from bending moment will be М y b str skin,i i 0 (2) Fstr After loss of stability skin gives part of load to stringers. Axial effort in a stringer at the result of stability loss of a skin N str = ( d - cr )h ctg (3) where d is shear stress in skin from calculation without account loss of stability, cr is the critical stress in skin. Stringer load per unit of length at the result of loss of stability htg q y d cr. (4) R In calculation of a moment of inertia in the formulas (1), (2) it is necessary to use a method of reduction factors. In case of asymmetrical loading of a horizontal tail the fuselage will work simultaneously on bending and torsion moments. Let's consider separately the calculation from shear force and torque. The shear effort per unit length or shear flow from shear force is in open contour: Q S y N u k q p (5) For the determination of shear flow q 0, which arises because of a circuit section, let us make an equation of moments about axis, through which the external force passes Qu: q q rds 0 (6) 2 0 p where - is area of all cross section on mean line of skin. For symmetrical cross-section the second member in an equation (6) will vanish, so q 0 = 0. (7) The shear stresses in symmetrical sections are the same as and for an open circuit, will be determined by the formula Q S I u c (8) Moment of inertia of a cross-section I r in the formulas (5) and (8) is selected pursuant to that approximation, at which the normal stresses from the bending moment were determined. It implies from an equilibrium condition between normal and shear stresses of any cut out element. The shear flow (SF) from a torque is determined simply enough: r sum 3

4 q M 2 t (9) Shear force Qu in the formula (8) is substituted with allowance for fuselage conicity: 2M z Qu Q0 tg (10) H x where Q 0 - shear force (taken from diagrams); Мz the bending moment (taken from diagrams); Hx height of the side panel between spars in cross section; - an angle of spars inclination in relation to an ОХ axis; - thickness of a skin. 4. Calculation from external forces operating in a horizontal plane Let's consider a cross-section of a tail part of a fuselage, on which the load is affixed from a vertical tail. A normal stress from bending moment is equal to: Mby i zi z0 (11) y The shear flow from shear force is: Q 0 S uz c q p. (12) y For the determination of shear flow (SF) q 0, accepting a section of a circuit in a point 1, let's write an equation of moments about OX axis: 2q00 q prds Y f H f 0 From here we have: Y f H f q prds q0 (13) 20 So the total shear flow (SF) in any point of cross section is: q t = q q Q 0 5. The fuselage analysis at simultaneous horizontal and vertical tail loading. The fuselage calculation at simultaneous application of the forces on horizontal and vertical tail is reduced to its calculation on oblique bending. This loading condition of a tail unit for a fuselage can be calculated. Normal and the shear flow are determined by the following formulas: 4

5 sum М I bz rz q by y y z z sum M i 0 i 0 y QuyScz Quz S y q0, (14) I I where q 0 is the shear flow (SF), which arises at the result of closure of a cross-section circuit from external loading effect of a vertical tail. rz 6. Loading from an overpressure The hermetic fuselages can have volume from cubic meters on single-seat airplanes up to several hundreds cubic meters on transport airplanes, where they occupy a majority of a fuselage. The hermetic cabin is loaded by an overpressure, and if it's represented by a fuselage bay, then besides by shear force, bending moment and torsion in cross-section as a part of a fuselage. A ultimate value of an overpressure р =рf where р producing pressure in a cabin; f - a safety factor. The safety factor oscillates in rather broad limits. For transport airplanes it can reach 2.5, and on sites of a cabin, where there are strain concentrators by the way of excisions under windows and doors, it is accepted sometimes equal 3. ry. Fig. 2. Forms of hermetic cabin. In case of a large overpressure in a cabin it is required, that in a skin, which is the basic load-bearing element of a cabin, the stress concentration should be reduced to minimum. This request implies from a condition of reliability of a construction operation 5

6 during given service life. The most rational shape for a bay loaded by overpressure is sphere or circular cylindrical shell with the spherical bottoms. The skin of a cabin of such type appears uniformly loaded mainly by tensile strains. The shapes of substantial pressurized cabins tend to approximate to optimal. However more often cabins enter in free volumes retracted for them on conditions of arrangement and an airplane center-of-gravity position. Therefore their shapes have, as a rule, more composite contours essentially distinguished from optimal. In a fig. 2 as examples two schemes of pressurized cabins close under the shapes to optimal (a) and with composite contour (b) are shown. In the last scheme the end walls of a cabin for saving volumes of a fuselage are executed flat, side walls curvilinear, with the shape of air passages of drives and external contours of a fuselage cross-section. The walls of such cabin, alongside with tension and shearing, expose to bending. Therefore longitudinal and transverse members of rigidity reinforce them, which are usually necessary because of cabin loading as a part of a fuselage. Cabin of a circular section is shown on fig. 2, a. In the cylindrical part of a cabin the skin gets pulling stresses both in transversal, and in longitudinal sections from an overpressure operation. These stresses are determined from an equilibrium condition by the formulas from mechanic of materials: p u R X 2, (15) p u R r, (16) where R, the radius of an envelope and the thickness of a skin. The stresses x should be summarized with the any stresses from loads in a cabin In especially unfavorable conditions the skin is at the cabin's upper dome, as in this site from common a fuselage bending also arise mainly pulling stresses. The radial stresses r are twice more than stresses x, therefore, as a rule, they determine hardness of a cabin skin. Usually it is required, that for a construction from duralumin these stresses should do not exceed MPa. On transport airplanes the admissible level of radial stresses can be even lower. In the spherical bottom the stresses are determined by the formula (15). On a linking site of a cylindrical part of a cabin with the bottom radial efforts q f arise. These efforts tend to distort a cabin. To prevent flattening and to reduce a skin curving, in cross-section by the junction the power frame is set. 6

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