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Aviation History
1928
1928 - 0235.PDF
MABCH 29, 1928 23 THE AIRCRAFT ENGINEER SUPPLEMENT TO FLIGHT — are too low, the theoretical value of t/R for tubes showing a much greater discrepancy with experiment than does the value of h/B for flat plates. For the most carefully prepared and conducted tests on the most carefully made tubes the writer would expect to find increases of at least 50 per cent, in the value of f/R over the theoretical values for the same stresses. Unfortunately, similar mathematically established formulas have not been established for complete corrugated sections, but with the following notes and the above equations as a guide the trained technician should not experience great difficulty in inventing his own formulae for finding at what stresses the sections he designs will become elastically unstable, providing he has the opportunity of observing the behaviour of actual spars under load and has also the data to enable him to compare the results of a fair number of tests. Without of a section receives from an adjoining section, the numerical value of which is dependent almost entirely on experience. It is obvious, then, why it is inadvisable to attempt to publish formulae at the present time for general use on built-up structure members. Such formulae as have been deduced may be established mathematically at some time in the future ; then that will be the occasion for publication. Failing mathematical support, it is probable that formula* for par- ticular types of spar only will be available, the limitations of each type being strictly defined. Empirical formula? containing terms whose values in particular cases are dependent purely on the designer's experience are scarcely suitable for publication, since the probability of misapplication by the inexperienced is too great. It should, finally, be noted that, whatever expression is derived for determining the stress at which instability sets in, it must be capable of application to a complete section or -13-25 W 28 FIG. 2 FIG. 3 THICKNESS OF MATERIAL IN EACH CASE OIS DEVELOPED WIDTH 2 014 RADIUS Of GYRATION • 0786 1123 ABOUT AXIS THROC.G.& PARALLEL TO FLATS 1774 the opportunity of actual observation any formulae he may •deduce would probably have little value. In this summary of the factors that must have their place in the desired formulae, obviously one of the most important will be K, the radius of gj-ration of the section. Component curves (arcs of circles are usually taken) of the cross-section must have a radius to thickness ratio proportional to the stress that is to be developed. The desired general large radius of gyration must not be obtained by the use of extended flats. The amount that can be allowed depends on the boundary conditions, but the ratio of flat width to thickness may rarely be permitted to exceed 20. Equation (4) above shows that the breadth of the section must be included, and aho the thickness, as shown in equations (4) and (5). A term or terms involving the size and number of corrugations and their relative position must also be included, and a very important factor relates to the degree of fixation one portion 212c to any portion of a section, however small, because the instability may concern a section as a whole, as, for instance, a complete spar flange or a portion of such a flange ; in the latter case, for example, a portion of a flange might consist of an arc having an excessive R/t ratio at an early load, a dent or short-pitched wave might form along this part, which would subsequently develop and spread, causing the premature collapse of an otherwise perfectly stable section. Elasticians will doubtless solve these problems in time in spite of their complexity, but, as in the caae of the flat plate and tube formulae, it is quite certain that the results of the mathematical investigations will need considerable modification on being brought into line with practice ; hence is emphasised the need for large numbers of carefully conducted, recorded, and co-ordinated experiments. Consideration of a selected few of the large number which E 2
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