Lecture 22(18). TRENGTH ANALY OF FUELAGE Plan: 1. tructurally - power fuselage schemes. 2. trength analyss of fuselages cross-sectons. 3. emmonocoque fuselage cross-secton calculaton. Calculaton from external forces that operatng n a vertcal plane. 4. Calculaton from external forces operatng n a horzontal plane 5. Fuselage strength analysss at smultaneous horzontal and vertcal tal loadng. 6. Loadng from overpressure 1. tructurally - power fuselage schemes. Now metal fuselages by analytcal models can be subdvdedd by two aspects: a sem- a monocoque and monocoque. n sem-monocoque fuselages for a moment of a structural falure s accepted moment of stablty loss n compressed strngers under bendng. Wth purposes of creaton of a fuselage wth a mnmum mass a skn enough thn ( = 1.5 2 mm) s appled and t works behnd a stablty lmt from shear force and torque. n monocoque fuselages a skn s a basc load-bearng lmts, because loss of stablty under element that operates at bendng and torson and should work only n stablty bendng and torson wll cause a structural falure as a whole. Fg. 1. tructurally - power fuselage schemes Fuselages can have some baselne desgns, whch are shown on fg. 1., a,b,c. Cross-sectons are rather dverse: round, ellptcal, rectangular etc. Recently for large transport arplanes (arbuses) multdeck fuselages are appled. 2. trength analyss of fuselages cross-sectons. By the dagrams of external loads, M b, М t were plotted by length of a fuselage, t s possble to pass at calculaton of normal and shear stresses. 1
Analytcal models of a fuselage are dentcal to wng analytcal models and ther calculaton methods are smlar to wng calculaton methods. At normal stresses determnaton of longtudnal load-bearng elements from bendng moment t s possble to use the analytcal model by reduced factors wth usage of stran stress dagrams. hearng stresses from a shear force and a torque are determned smply enough, because majorty of fuselage cross-sectons s represented by one closed sectons except an arbus fuselages cross-sectons. Arbus fuselage cross-sectons are double closed sectons. For determnaton of shearng stresses from shear force and torque they should be consdered as statcally ndetermnable systems. 3. emmonocoque fuselage cross-secton calculaton. Calculaton from external forces operatng n vertcal plane. Let us have a symmetrcal semmonocoque fuselage cross-secton, whch longtudnal power set conssts of four spars, strngers and skn, and transversal power set from frames. A skn of a fuselage works smultaneously by normal and shearng stresses from bendng and shear force. Normal stresses from bendng moment for a case, when the skn does not lose stablty from shear stresses up to ultmate loads, can be computed by the known formula: Mbz N у (1) r Fr where r the reduced area's nerta moment, whch s equal: 2 r ( f t ) у str, skn, skn, where: cr.skn skn - s the reduced factor of skn n compressed zone; skn 1 - for str tenson zone, cr. skn - s a crtcal stress of skn, str s a stress n strnger; F ( f t ) r - s a reduced area of fuselage cross secton; N s an axal str, skn, skn, force. f the skn early loses stablty from shear force and torque, then normal stresses from bendng moment wll be N Мb str skn, y (2) F r str After loss of stablty skn gves part of load to strngers. Axal effort n a strnger at the result of stablty loss of a skn 2
N str = ( d - cr ) sk t ctg (3) where d s a shear stress n a skn from calculaton wthout account loss of stablty, cr s a crtcal stress n a skn, α45 - s an angle of nclnaton for nstablty wave, t s a strnger ptch, sk - a thckness of a skn. A strnger load per unt of length at result of loss of stablty s equal: ttg q. (4) y d cr R where R s radus of a fuselage. n calculaton of moment of nerta n the formulas (1), (2) t s necessary to use the method of reduced factors. n case of asymmetrcal loadng of a horzontal tal a fuselage works smultaneously from bendng and torson moments. Let's consder separately a calculaton from a shear force and a torque. A shear effort per unt length or shear flow from a shear force s n an open contour: u k q p (5) r where k s a statc moment of nerta for a cutted off part of contour, whch from the prevous lectures s equal:,. For determnaton of a shear flow q 0, whch arses because of a crcut secton, let us make an equaton of moments about axs, whch passes by an external force u : q q rd 0 (6) 2 0 p where - s area of all the cross secton by mean thckness of a skn. For a symmetrcal cross-secton the second member n an equaton (6) wll vansh, so q 0 = 0. (7) hear stresses n symmetrcal sectons are the same as and for an open crcut, wll be determned by the formula u c (8) r t where t s a total thckness of a skn wth account of strnger areas, whch s equal to:, where t s strnger ptch, f s strnger area. Moment of nerta of a cross-secton r n formulas (5) and (8) s selected pursuant to that approxmaton, at whch normal stresses from the bendng moment were determned. t mples from equlbrum condton between normal and shear stresses of any cut out element. A shear flow (F) from torque s determned smply enough: 3
q M 2 t (9) hear force u n the formula (8) s substtuted wth allowance for fuselage concty: 2M z u 0 tg (10) H x where 0 - shear force (taken from dagrams); М z bendng moment (taken from dagrams); H x heght of a sde panel between spars n cross secton; - angle of spars nclnaton n relaton to ОХ axs. 4. Calculaton from external forces operatng n horzontal plane Let's consder a cross-secton of a tal part of a fuselage, on whch a load s affxed from a vertcal tal. A normal stress from bendng moment s equal to: M by z (11) ry A shear flow from shear force s equal to: 0 uz c q p. (12) ry For determnaton of a shear flow (F) q 0, acceptng a cross secton of a crcut n a pont 1, let's wrte an equaton of moments about OX axs: 2q00 q prd Y f H f 0 From here we have: Y f H f q prd q0 (13) 20 o the total shear flow q t (F) n any pont of cross secton s: q t = q q0. 5. Fuselage strength analyss at smultaneous horzontal and vertcal tal loadng. A fuselage strength analyss at smultaneous applcaton of forces on horzontal and vertcal tal s reduced to ts calculaton from oblque bendng. Ths loadng condton of a tal unt for a fuselage can be calculated. Normal stress and shear flow are determned by the followng formulas: 4
М е q rz bz y M ry by z uy cz uz y q, (14) t 0 rz ry where q 0 s a shear flow (F), whch arses at the result of closure of a cross-secton crcut from external loadng effect of a vertcal tal. 6. Loadng from overpressure Hermetc fuselages can have volume from 1.5 2 cubc meters n sngle-seat arplanes up to several hundred cubc meters n transport arplanes, where they occupy majorty of a fuselage. The hermetc cabn s loaded by overpressure, and f t s represented by a fuselage bay, then besdes by shears force, bendng moment and torson n a cross-secton as a part of a fuselage. An ultmate value of an overpressure s equal to: р =рf where р producng pressure n a cabn; f - a safety factor. The safety factor oscllates n rather broad lmts. For transport arplanes t can reach 2.5, and on stes of a cabn, where there are stran concentrators n cut out under wndows and doors, t s accepted sometmes equal 3. Fg. 2. Forms of hermetc cabn. n case of large overpressure n a cabn t s requred, that n a skn, whch s a basc load-bearng element of a cabn, stress concentraton should be reduced to mnmum. Ths request mples from a condton of relablty of a constructon operaton durng gven servce lfe. A most ratonal shape for a bay loaded by overpressure s sphere or crcular 5
cylndrcal shell wth sphercal bottoms. The skn of a cabn of such type appears unformly loaded manly by tensle strans. hapes of substantal pressurzed cabns tend to approxmate to optmal. However more often cabns enter n free volumes retracted for them from condtons of arrangement and an arplane center-of-gravty poston. Therefore ther shapes have, as a rule, more composte contours essentally dstngushed from optmal. n the fg. 2 as examples two schemes of pressurzed cabns close to shapes to optmal (a) and wth composte contour (b) are shown. n a last scheme end walls of a cabn for savng volumes of a fuselage are executed flat, sde walls curvlnear, wth a shape of ar passages of drves and external contours of a fuselage cross-secton. Walls of such cabn, alongsde wth tenson and shearng, expose to bendng. Therefore longtudnal and transverse members of rgdty renforce them, whch are usually necessary because of cabn loadng as a part of a fuselage. Cabn of a crcular secton s shown on fg. 2, a. n a cylndrcal part of a cabn a skn gets pullng stresses both n transversal, and n longtudnal sectons from overpressure operaton. These stresses are determned from an equlbrum condton by the formulas from mechanc of materals: p R u X 2 sk, (15) pur r sk, (16) where R, sk s a radus of a fuselage and a thckness of a skn. The stresses x should be summarzed wth any stresses from loads n a cabn n especally unfavorable condtons the skn s at the cabn's upper dome, as n ths ste from common a fuselage bendng also arse manly pullng stresses. The radal stresses r are twce more than stresses x, therefore, as a rule, they determne hardness of a cabn skn. Usually t s requred, that for a constructon from duralumn these stresses should do not exceed 80 100 MPa. For transport arplanes an admssble level of radal stresses can be even lower. n a sphercal bottom stresses are determned by the formula (15). On a lnkng ste of a cylndrcal part of a cabn wth a bottom radal efforts q f arse. These efforts tend to dstort a cabn. To prevent flattenng and to reduce a skn curvng, n cross-secton by the juncton a power frame s set. D:\Документы\Users\kr\A18nt\T8FusL22(18)Afus 6