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Torsion in Box Beams

Torsion in Box Beams 130 AIRCRAFT ENGINEERING May, 1942 A Suggested Simplifying Assumption—Making Analysis Easier To the Editor G = Shear Modulus. SIR , T = Torque a t Section. The method of illustrating the results has I n the January issue of AIRCRAFT ENGINEER­ been taken from R & M 1617. It indicates ING (Vol. XIV , No . 158) ther e is a n extremely clearly th e proportion of torqu e taken by direct interesting article by Payne on " Torsion in and shear stresses. The general form of these Box Beams". Unfortunately, as with most results is indicated in Figs . 2, 3 an d 4. rigid analyses, a considerable amount of work I t will be apparent tha t any variation s from is necessary before arriving a t th e final distribu­ true rcctangularity of th e bo x section can be tion of th e applied torque. The scope is also taken into account by appropriat e adjustment extremely limited. In order to overcome this a of Batho's torsion coefficient. simplifying assumption has been made, namely I n th e case of a tapere d box, th e direct stresses tha t the proportion of th e applied torque taken a t an y section are dependent on th e taper, since, as differential bending in th e to p an d bottom when such a box is under torsion, even when panels is small compared with that ta"ken as torsional shear and differential bending of the bot h ends are free from constraint, the spars spars, and ca n b e neglected. As a result th e are subject to torqu e produced bending. When analysis is simplified, the numerical computa­ th e taper is small, there is n o need t o tak e any tion is made easier and th e scope considerably account of thi s effect, but if a bo x of large taper widened. This assumption is perfectly justi­ ratio is unde r review a correction will have to be made to th e torsion coefficients by inserting in fiable since :— th e Batho formula a modified area and peri­ (a) Actual calculations in accordance with th e meter of cross section as given b y Southwell in rigid theory show that this proportion of " Proceedings of th e Royal Society", Vol. 163, tota l torque is small, with normal forms of No . 914. As a first approximation the effect cross sections an d tw o spar wings. of taper can be included by takin g the valu e of (b) In norma l construction, the to p panels are th e Batho's stiffness at th e section as equa l t o usually not rigidly built in, hence the bend­ th e mean stiffness over the length from the ing moments in th e panels will be smaller encastre end t o th e section. This gives:— tha n thos,e calculated by th e rigid theory. ■^Boctlon=-Sx Wit h this assumption the torque can be divided into two parts. (i) That portion which is carrie d as bending moment in th e spars. I t will thus be apparen t that the expressions (ii) That portion which is distribute d round given in equation s 1, 2 an d 3 ca n be used when th e walls of th e box in accordance with considering tapered forms'of construction, by adjusting th e stiffness a t eac h section in accord­ Batho's formula. ance with the abov e paragraph. There is no The analysis of R &• M—" Torsional Stiffness limitation on th e form of taper. of Two Spar Cantilever Wings "—can then be This method has given an approximate rapid applied to this case, replacing, in th e equations, analysis of wings of two-spa r construction of an y th e torsional coefficients of th e front and rear form. The results obtained by this method spars by th e torsional coefficients, according t o have been compared with Williams in " The Batho, of th e box. This yields in th e general Stresses in Certain Tubes of Rectangular Cross case for a concentrated torque applied inboard of the tip , th e following expressions for th e dis­ Section under Torque " (R &■ M 1761). Un­ tribution of th e bending moment in th e spar. fortunately, owing t o th e war , the actua l results have been lost, bu t the y showed extremely good Region between encastre' and poin t of appli­ agreement even in th e case of a high taper ratio. cation of torque The accuracy was of th e order of th e estimation of load distribution. No experimenta l results are available. I feel that this method could be applied to cases where there are discontinuities (e.g. cut ­ outs) in th e structure, but I have not ye t tried / = moment of inerti a of spar in which th e bending moment is required. t o do this . The work was done under the direc­ tion of Dr. H . Roxbee Cox. m = Ifjlr I regret the lack of references and actual If — moment of inerti a of front spar. results and incompleteness of th e report, bu t where Ir = moment of inertia of rear spar. M = Bending moment in spar these are unavoidable under the present cir­ E = Young's Modulus. d = Distance between centre lines of spars . cumstances. K = Batho's torsion coefficient, defined as I i = Distance of point of application, of th e torque required to produce unit I am, Sir, torque from an encastre' end . twist. In the ' case of a rectangular Yours faithfully, x = Distance of Section under consideration box of dimensions shown in Fig. 1, T. S. BRAYBROOKE, B.Sc, from encastrd end . this reduces t o A.C.G.I., D.I.C. St. Michael's North Road, Williton, Somerset. March 16 New R.A.F. Types long ducted fairing. This rearward radiator H E NA-73 (P.51) Mustang was produced XXI.—The North American Mustang results in th e engine being placed well forward in 1940 and is now going into service with of the wing—giving the aeroplane a very dis­ the R.A.F. It differs considerably from th e lack of buckling in th e skin, which is pu t tinctive long narrow nose. The undercarriage, earlier North American types, in that it is on in large panels. Slotted flaps are fitted. All which has two semi-cantilever legs, retracts long and slender instead of being short and fat . control surfaces are fabric covered. inboard. I n fact, the slender lines, coupled with th e The engine is th e liquid-cooled Allison V-1710. " squared " main and auxiliary surfaces, are The installation differs considerably from that Snan 37 ft. 0 in. (11.27 m.) reminiscent of German rather than U.S. design. on the Tomahawk, Kittyhawk and Lightning, Length ' 32 ft. 3 in. (9.75 m.) The structure is the typical strcssed-skin where the radiator s are placed well forward. Height 8 ft. 8 in. (2.65 m.) Wing area 235.75 sq. ft. (21.55 sq.m.) light alloy of to-day. Details have not been The radiator in th e Mustang is carried under Tare weight 5,9901b. (2,7 l h Kg. released, but th e covering is remarkable for th e fuselage, aft of th e cockpit, in a n unusually Gross weight. 7,708 lb. (3,498 bg.) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Aircraft Engineering and Aerospace Technology Emerald Publishing

Torsion in Box Beams

Aircraft Engineering and Aerospace Technology , Volume 14 (5): 1 – May 1, 1942

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Emerald Publishing
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Copyright © Emerald Group Publishing Limited
ISSN
0002-2667
DOI
10.1108/eb030902
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Abstract

130 AIRCRAFT ENGINEERING May, 1942 A Suggested Simplifying Assumption—Making Analysis Easier To the Editor G = Shear Modulus. SIR , T = Torque a t Section. The method of illustrating the results has I n the January issue of AIRCRAFT ENGINEER­ been taken from R & M 1617. It indicates ING (Vol. XIV , No . 158) ther e is a n extremely clearly th e proportion of torqu e taken by direct interesting article by Payne on " Torsion in and shear stresses. The general form of these Box Beams". Unfortunately, as with most results is indicated in Figs . 2, 3 an d 4. rigid analyses, a considerable amount of work I t will be apparent tha t any variation s from is necessary before arriving a t th e final distribu­ true rcctangularity of th e bo x section can be tion of th e applied torque. The scope is also taken into account by appropriat e adjustment extremely limited. In order to overcome this a of Batho's torsion coefficient. simplifying assumption has been made, namely I n th e case of a tapere d box, th e direct stresses tha t the proportion of th e applied torque taken a t an y section are dependent on th e taper, since, as differential bending in th e to p an d bottom when such a box is under torsion, even when panels is small compared with that ta"ken as torsional shear and differential bending of the bot h ends are free from constraint, the spars spars, and ca n b e neglected. As a result th e are subject to torqu e produced bending. When analysis is simplified, the numerical computa­ th e taper is small, there is n o need t o tak e any tion is made easier and th e scope considerably account of thi s effect, but if a bo x of large taper widened. This assumption is perfectly justi­ ratio is unde r review a correction will have to be made to th e torsion coefficients by inserting in fiable since :— th e Batho formula a modified area and peri­ (a) Actual calculations in accordance with th e meter of cross section as given b y Southwell in rigid theory show that this proportion of " Proceedings of th e Royal Society", Vol. 163, tota l torque is small, with normal forms of No . 914. As a first approximation the effect cross sections an d tw o spar wings. of taper can be included by takin g the valu e of (b) In norma l construction, the to p panels are th e Batho's stiffness at th e section as equa l t o usually not rigidly built in, hence the bend­ th e mean stiffness over the length from the ing moments in th e panels will be smaller encastre end t o th e section. This gives:— tha n thos,e calculated by th e rigid theory. ■^Boctlon=-Sx Wit h this assumption the torque can be divided into two parts. (i) That portion which is carrie d as bending moment in th e spars. I t will thus be apparen t that the expressions (ii) That portion which is distribute d round given in equation s 1, 2 an d 3 ca n be used when th e walls of th e box in accordance with considering tapered forms'of construction, by adjusting th e stiffness a t eac h section in accord­ Batho's formula. ance with the abov e paragraph. There is no The analysis of R &• M—" Torsional Stiffness limitation on th e form of taper. of Two Spar Cantilever Wings "—can then be This method has given an approximate rapid applied to this case, replacing, in th e equations, analysis of wings of two-spa r construction of an y th e torsional coefficients of th e front and rear form. The results obtained by this method spars by th e torsional coefficients, according t o have been compared with Williams in " The Batho, of th e box. This yields in th e general Stresses in Certain Tubes of Rectangular Cross case for a concentrated torque applied inboard of the tip , th e following expressions for th e dis­ Section under Torque " (R &■ M 1761). Un­ tribution of th e bending moment in th e spar. fortunately, owing t o th e war , the actua l results have been lost, bu t the y showed extremely good Region between encastre' and poin t of appli­ agreement even in th e case of a high taper ratio. cation of torque The accuracy was of th e order of th e estimation of load distribution. No experimenta l results are available. I feel that this method could be applied to cases where there are discontinuities (e.g. cut ­ outs) in th e structure, but I have not ye t tried / = moment of inerti a of spar in which th e bending moment is required. t o do this . The work was done under the direc­ tion of Dr. H . Roxbee Cox. m = Ifjlr I regret the lack of references and actual If — moment of inerti a of front spar. results and incompleteness of th e report, bu t where Ir = moment of inertia of rear spar. M = Bending moment in spar these are unavoidable under the present cir­ E = Young's Modulus. d = Distance between centre lines of spars . cumstances. K = Batho's torsion coefficient, defined as I i = Distance of point of application, of th e torque required to produce unit I am, Sir, torque from an encastre' end . twist. In the ' case of a rectangular Yours faithfully, x = Distance of Section under consideration box of dimensions shown in Fig. 1, T. S. BRAYBROOKE, B.Sc, from encastrd end . this reduces t o A.C.G.I., D.I.C. St. Michael's North Road, Williton, Somerset. March 16 New R.A.F. Types long ducted fairing. This rearward radiator H E NA-73 (P.51) Mustang was produced XXI.—The North American Mustang results in th e engine being placed well forward in 1940 and is now going into service with of the wing—giving the aeroplane a very dis­ the R.A.F. It differs considerably from th e lack of buckling in th e skin, which is pu t tinctive long narrow nose. The undercarriage, earlier North American types, in that it is on in large panels. Slotted flaps are fitted. All which has two semi-cantilever legs, retracts long and slender instead of being short and fat . control surfaces are fabric covered. inboard. I n fact, the slender lines, coupled with th e The engine is th e liquid-cooled Allison V-1710. " squared " main and auxiliary surfaces, are The installation differs considerably from that Snan 37 ft. 0 in. (11.27 m.) reminiscent of German rather than U.S. design. on the Tomahawk, Kittyhawk and Lightning, Length ' 32 ft. 3 in. (9.75 m.) The structure is the typical strcssed-skin where the radiator s are placed well forward. Height 8 ft. 8 in. (2.65 m.) Wing area 235.75 sq. ft. (21.55 sq.m.) light alloy of to-day. Details have not been The radiator in th e Mustang is carried under Tare weight 5,9901b. (2,7 l h Kg. released, but th e covering is remarkable for th e fuselage, aft of th e cockpit, in a n unusually Gross weight. 7,708 lb. (3,498 bg.)

Journal

Aircraft Engineering and Aerospace TechnologyEmerald Publishing

Published: May 1, 1942

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