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Simplified Wing Stress Analysis of a Strut-Braced Monoplane

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Simplified Wing Stress Analysis of a Strut-Braced Monoplane Simplified Wing Stress Analysis Or A Strut-Braced Monoplane The following references have been used in TABLE 1 summarizing the data applied in this article: THE CORBEN C-l "BABY ACE" (Modified version by Paul H. Poberezny) No. 1—Stress Analysis of Commercial Aircraft Airfoil section Clark "Y" (1928), by A. Klemin; Gross weight, (Wg) ................ 828 pounds No. 2—Elementary Airplane Structural Analysis by Weight of wings, (Ww) ..... 123 pounds, (See Note 1) Graphic Methods, (1938) by J. P. Eames; Net weight, (Wg-Ww) ............ 705 pounds No. 3—Air Service Information Circular No. 520, Total wing span, (S) ............ 25 ft., 9 in. (309 in.) Stress Analysis of Lieut. Phillip's "Alouette" Length of lift strut bay ........ 95 in. (See Note 2) Biplane; Length of overhang ........... 59.5 in. (See Note 2) No. 4—Procedure Handbook for Aircraft Stress An- Chord of wing ................................ 54 in. alysis (1940), by Nye-Hamilton-Eames; Incidence ............................. 1V6 deg. No. 5—Aircraft Structures (1950), by D. J. Peery; Area, (incl. ailerons) ....................... 112.3 sq. ft. No. 6—Aircraft Design (1954), by K. D. Wood; Location of spars from the leading edge: No. 7—ANC-18, Design of Wood Aircraft Structures; Front spar, in inches—8.COO in.— No. 8—Civil Aeronautics Manuals, Volume II, (incl. in % of chord—14.8% Rear spar, in inches—38.375 in.— supplements to May 1, 1958). in % of chord—71.0% The easiest way to assimilate something new is by Center of pressure in % of chord, (See Note 3): reference to an example. Hence, the methods of analysis PHAA, (Positive high angle of attack condition) 24% used in this report will be exemplified by a wing an- PLAA, (Positive low angle of attack condition) 51% alysis of the Corben C-l "Baby Ace." Most EAA members NLAA, (Negative low angle of attack condition) 24% are familiar with this design. Another reason for select- ing this airplane is its general similarity to the design Load factors, (See Note 4): of a majority of homebuilts, namely, a strut-braced, single PHAA—4.5 bay, rectangular wing monoplane. The analysis of this PLAA—4.5 design can be used by substituting values applying to NLAA—2.0 one's own design and thus solve for stresses and design Ratio of chord to beam components, (See Note 5): components which will be adequate in strength. PHAA— —.30 This article should make it possible, when applied to PLAA— +.15 a similar design, to determine the maximum stresses to be NLAA— 0 expected under various conditions of loading and to com- pute sizes of members to withstand such loads. Of more Note 1—The required weights must be computed as close- importance, possibly, is the consideration of what it will ly as possible from comparison with similar air- NOT enable you to do: planes or from average figures. An average weight schedule for wings which have been con- A—It will NOT provide a method of analysis which will structed in wooden designs are: guarantee FAA approval from the analysis alone, Lightly loaded biplanes--.8 to 1.0 Ib. per sq. ft. without static or sand-bag proof loading, - - and Heavily-loaded biplanes—1.0 to 1.2 Ib. per sq. ft. B—It does NOT attempt refinements of procedure en- Semi-cantilever monoplanes—1.1 to 1.3 Ib. per abling construction of the highest efficiency to stem sq. ft. from its application. Full-cantilever monoplanes—1.2 to 1.5 Ib. per A simplified stress analysis considers only that por- sq. ft. tion which is absolutely essential in calculating the re- Metal wings for each type would average .1 to .3 quirements for a safe structure. Nothing else is possible Ib. per sq. ft. increase over the above figures. in a short article of this type. In this design, 1.1 Ibs. per sq. ft. will be used to compute wing weight. DESIGN DATA Note 2—95 inches is approximately the mean of the ac- It is usual in discussing methods of stress analysis tual lift strut bay dimensions for the front spar, to review basic mechanics and compare the analytical (actual—94.66 in.) and the rear spar, (actual— and graphical methods of solution. However, it was felt 95.25 in.), while 59.5 in. is close to the mean of that this report would be more concise and of more im- the actual overhang for the front spar, (actual— mediate use to the amateur constructor by commencing 59.84 in.) and the rear spar, (actual—59.25 in.). the actual analysis and referring to the type of solution Use of the approximate mean values will not by example. materially affect results of the final computa- Actual wing analysis should begin by listing pertinent tions, but will simplify the work. data applying to the design in question. This information is listed in TABLE 1 for the "Baby Ace." The source of Note 3—The current method most commonly used is to some of this information will be covered in appropriate compute the loading based on the elastic axis. notes following the table: • However, this is a refinement such as referred 12 NOVEMBER 1963 to in sub-paragraph B on the first page. The 4—Compute the normal chord loads. method used here, (center of pressure location) 5—Compute distribution of loads between spars. uses values obtained from airfoil wind tunnel 6—Compute moments, shears and reactions on each data from sources referred to in our report No. spar. 1, such as NACA Technical Report No. 824, etc. For the PHAA and NLAA conditions the C.P. is 7—Compute loads in lift struts. considered to b2 at the most forward location 8—Solve for drag truss loads. given in the wind tunnel data charts. For the 9—Summarize final total loads in all members. PLAA condition the C.P. is obtained by observ- ing its location at the point where the lift co- 1—Effective Span is the distance from wing tip to wing tip efficient, (C,) is 25% of its maximum value. For less any portion covered by the fuselage and an allow- some of the most commonly used sections, the ance for tip loss. The full span of the wing is not ef- values following are expressed in % of chord fective because the lift forces are greatly reduced at length from the leading edge: the tips due to air slipping off the tip portion. The decrease in effective semi-span, to allow for tip loss, C.P. Location C.P. Location is shown in Fig. 1 for the externally braced wing Airfoil for PHAA & NLAA for PLAA where the distance from the outer strut point to the Clark Y 51% tip is substantially the same as the wing chord. A Gottingen 398 30% 50% length equal to ¥4 of the overhang, (.25 L,) is sub- USA 27 29% 50% tracted from the actual semi-span to obtain the effec- USA 35B 30% 49% tive semi-span, or: USA 45 27% 38% Effective semi-span, (Se) = (95 + 59.5)—(.25x59.5)= 139.6 in. NACA M6 25% 40% 2—Normal Gross Beam Load equals gross weight of the NACA M12 25% 40% airplane divided by the effective span, or: Note 4—The load factor to be used is selected by the de- Gross beam load, (Wgb) = Wg/Se x 2 = 828/139.6 x 2 = signer. FAA specifies a minimum positive man- 2.97 Ib. per in. euvering load factor of 4.4 for utility aircraft or 3—Normal Net Beam Load equals the gross beam load 6.0 for acrobatic. The minimum negative man- minus the dead weight of the wings, dead weight of euvering load factor is .4 times the positive fac- wings, (Wwd) per inch run is computed by dividing tor for utility and .5 times the positive factor weight of wings, (Ww) by the actual, (not effective) for the aerobatic category. A positive load fac- span, (S), or: tor of 4.5 is selected for this design, as it is in- Wwd = Ww/S = 123/309 = .4 Ib. per in. run. tended to be non-aerobatic, thus giving a nega- Net beam load, (Wn) = Wgb—Wwd = 2.97 — .4 = tive load factor of 1.8 (4.5 x .4). However, to sim- 2.57 Ib. per in. run. plify computations and err on the safe side, we Check on work: 2(Wn x Se) + Ww = Wg shall use a value of 2.0. 2(2.57 x 139.6) + 123 = 840 Ibs. Note 5—Ratio of chord to beam components are posi- 840 Ibs. is 12 Ibs. more than 828 Ibs., but is satisfactory, tive ( + ), when chord loads are applied toward as it loads the wing more severely and is, therefore, the rear of the drag truss and negative (—), on the safe side. when applied in a forward direction. For the PLAA condition, CAM No. 8 in Appendix B, 4—Normal Chord Loads are computed by multiplying the paragraph .2121 states, "Although no aft acting net beam load by the chord/beam ratio: chordwise loading is specified, the structure Flight Net beam Chord/beam Chord load Load Design should be capable of sustaining aft chordwise Condition lood Rotio. per inch Factor Chord load loads." It has been the practice for many years PHAA 2.57 —.30 —0.77 4.5 —3.47 to apply the value given, ( + .15) for this condi- PLAA 2.57 + .15 0.39 4.5 1.76 tion in the case of most all wing sections. NLAA 2.57 0 — — __ Dive — — 2.28 1 2.28 SEQUENCE OF WING ANALYSIS For the Dive condition, net weight of the airplane, 1—Compute the effective span of the wing.
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