1. Tasks of designing

Size: px

Start display at page:

Download "1. Tasks of designing"

Barrie White
6 years ago
Views:

1 1 Lecture #18(14) Designing calculation of cross section of a highly aspect ratio wing Plan: 1 Tass of designing Distribution of shear force between wing spars Computation of the elastic center 4 Distribution of bending moments between spars of a wing 5 Sequence of designing calculation 6 Selection of the spar position 7 Loading of a wing panel 1 Tass of designing The purposes of designing calculation are selection of materials, estimation of geometrical characteristics of cross section We believe that projections of shear force and bending moment in connected coordinate system are nown from calculation of loading At realization of this calculation we use the simplified analytical designing model The simplified designing analytical model covered is, that we consider: 1) A spar is flat beam which belts (caps) wor on a tension and compression; ) Lift capability of a sin on normal stress is jointed to longitudinal elements - to stringers and spar caps; ) A sin and walls of spars wor only on shear During calculation it is necessary: 1) Choose thicness of a sin and the stringer pitch in the tension and compressed panels; ) Calculate the area of stringers; pic up from the assortment a necessary profile; ) Calculate the area of spar caps; 4) Calculate thicness of spar webs; 5) Calculate distances between in-line wing ribs Distribution of shear force between spars of a wing From experience we now that wing deflection is comparatively bigger than angle of torsion So in the beginning we believe that shear force is enclosed in the elastic center In that case twisting of a contour does not occur also vertical deflections of spars are equal between themselves Let's calculate a deflection of first spar Y1 by the Mohr s formula: l M M Y1 dz, 0 E1I 1 where E 1 I 1 bending rigidity of a spar, М р, М - bending moments from external loading and unit force accordingly According to of Vereshagin s rule we have: p 1

2 1 1 Y1 Q1ll l EI 1 EC Q Fig 1 Deflection of spars Whence Q1l Y1 E1I Similarly for the second spar Q l Y EI As deflections are equal, we may record Ql 1 Ql E1I1 EI From here follows Q1 Q E1I1 EI Let's record an equation of equilibrium on axis Y Q1 Q Q,

3 where Q 1 and Q - the shear forces which are operational in the first and second spar accordingly Hence Q1 Q 1 1 E1I1 EI ; For the second spar Q Q E I If a structure has some spars, for j-th spar Q j Q i 1 EI i i i i i 1 That is shear force is distributed between spars of a wing proportionally to their bending rigidity E j I j Computation of the elastic center in the first iteration The elastic center is a point in cross section of a wing at application of the shear force to which twisting of a contour does not occur In that case the torque is equal to zero M EC 0 In case of a two-spar wing this equation may be write down lie Q X Q ( B X ) 1 EC S EC, X ec Fig The elastic center Whence follows We substitute value Q Q X EC B S Q

4 4 Q Q E1I1 EI We receive E I BS X EC = Ei I i For a multispar wing we have generally X EC Ei I i X i i1, Ei I i i1 Here Xi is distance from the first spar up to i-th a spar Thus, the elastic center in the simplified model coincides with the center of gravity of bending stiffness of spars 4 Distribution of bending moments between spars of a wing Vertical displacement spars are equal from the adopted simplified model, and as their the first and the second derivatives, then y 1 =y, y1 y, y1 y From a course of the mechanic of materials it is nown M y 1 M 1 y E1I1 ; EI, where M1 and M - the moments are perceived by 1 and spars From here follows M1 M E1I1 EI Let's record an equation of moment balance concerning axis Z M1 +M = M, where M is the external bending moment from previous calculations We solve this system of equations and it is received M M E1I1 EI, M M E 1 I 1 1 i 1 EI i i In case of a multispar wing for j-th spar bending moment is equal to: 4

5 M M E j I j j EI i i i 1, That is bending moment, as well as shear force, is distributed in the simplified model proportional bending stiffness of spars 5 Sequence of designing calculation 1 Calculation of sin thicness and of stringers pitch The sin executes two functions: а) Together with stringers and ribs provide an invariance of an airfoil section; b) Together with a longitudinal primary structure participates in perception of external loading From aerodynamic calculations and experiments it is nown, that resistance of a airfoil is increased not essentially if its relative sinuosity does not exceed y 000, where Y y max t 5 Fig The sinuosity of sin Examining a strip of a sin between stringers of unit width as the restrained beam loaded in regular intervals with constant spread load Р, we have 4 Рt Ymax 84D, where E D 1( 1 ) - is cylindrical rigidity, - is the Poisson s ratio From here we find out a relative deflection of a sin Y max pt p( 1 ) t ( 1 ) t E E This deflection should be less given 5

6 6 p( 1 ) t y E From here we find out ratio tot δ t p(1 μ ) EI It is necessary to emphasize that we have the inequality That is for its satisfaction it is possible to tae the big thicness of a sin at the chosen stringer pitch or a smaller the stringer pitch at the chosen sin that the sinuosity of a sin was given or less given Decreasing of a sinuosity reduces an aerodynamic drag of a wing Owing to non-uniformity of distribution of air pressure on the top and bottom sin of a wing it is received Pt Pb Fig 4 The distribution of air pressure G 1 G p t ; p S b w S w Calculations carry out conduct for the basic level flight condition Thus, we calculate ratio ( ) t t, ( ) t b (for the top and bottom sin) We select stringer pitch, we find out thicness of a sin, and we choose the nearest greater thicness from standard set of sin thicness From design restrain it is necessary, that min 08 mm On statistics stringer pitch is t sm 6 Selection of the spar position By selection we must tae into account some factors: 1) Necessity of accommodation of fuel in wing tans; ) Necessity of fastening of high-lift devices (slats, flaps); ) Aim is at greatest possible using of a building height According to statistic we have that: 6

7 7 Fig 5 The spar position 7 Loading of a wing panel At designing calculation the difficult contour of a wing is replaced by the rectangular cross section This section can be to include one or two stringer pitches in a wing leading edge if mechanization there is not located Fig 6 The wing cross section The mean height of wing cross section is equal to: H 1 H Hm 1, where H1 and H are an heights of front and rear spars on a theoretical contour; - the factor which is taing into account that the center of gravity of a spar does not lay on a theoretical contour, it is possible to accept μ 1 = 095, Hm - a mean height Then load perceived by panels is equal to: M Р ; H m Here M is bending moment in the wing cross section 7

UNIT- I Thin plate theory, Structural Instability:

UNIT- I Thin plate theory, Structural Instability: Analysis of thin rectangular plates subject to bending, twisting, distributed transverse load, combined bending and in-plane loading Thin plates having