Hostname: page-component-77c89778f8-vpsfw Total loading time: 0 Render date: 2024-07-18T17:14:34.509Z Has data issue: false hasContentIssue false

Formulæ and Methods of Calculation of the Strength of Plate and Shell Structures in Aeroplane Construction

Published online by Cambridge University Press:  28 July 2016

Extract

The object of the present report is to make a general survey of the simple formulas and methods of calculation for the determination of the strength of thin-walled structures (plate and shell structures) which are increasing in importance in aeroplane construction, and to facilitate the study of original papers by adding a detailed list of relevant literature. an essential characteristic of the sheet metal covered structures in question is, that the metal skin in addition to the stiffening elements participates in the transmission of force. structures in which the metal sheet serves merely as a covering but which is not loaded in accordance with its strength, do not come within the scope of the present considerations. non-stiffened and stiffened plates and shells, mostly of very small wall-thickness (about 0.5 to 1.2 mm.) may be regarded as structural elements in plate and shell structures (especially shell fuselages, “ monocoques ” and wings).

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society 1936

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

References

Dealing with the strength of isotropic rectangular plates under pressure stress

1. Bryan, G. H. On the stability of elastic systems. Proc. Camb. Philos. Soc. Bd.6 (1888), S.199/210. T.Google Scholar
2. Bryan, G. H. On the stability of a plane plate under thrusts in its own plane, with applications to the “buckling“ of the sides of a ship. Proc. Lond. Math. Soc. Bd.22 (1891), S.54/67. T.CrossRefGoogle Scholar
3. Bryan, G. H. On the buckling and wrinkling of plating when supported on parallel ribs or on a rectangular framework. Proc. Lond. Math. Soc. Bd.25 (1894), S.141/150. T.CrossRefGoogle Scholar
4. Reissner, H. Über die Knicksicherheit ebener Bleche, Zbl. Bauverw. Bd.29 (1909), S.93/96, 151. T.Google Scholar
5. Timoschenko, S. Einige Stabilitätsprobleme der Elastizitätstheorie. Z. Math. Physik. Bd.58 (1910), S.337/385. T.Google Scholar
6. Timoschenko, S. Sur la stabilité des systèmes élastiques. Extrait des Ann. Ponts Chauss. (1913), Paris 1913, Verlag A. Dumas. T.Google Scholar
7. Southwell, R. V. On the general theory of elastic stability. Philos. Trans. Ser. A. Bd.213 (1914), S.187/244. T.CrossRefGoogle Scholar
8. Rode, H. H. Beitrag zur Theorie der Knickerscheinungen. Eisenbau Bd. 7 (1916), S.121/136, 157/167, 210/218, 239/246, 295/299. T.Google Scholar
9. Schnadel, G. Über die Knickung von Platten. lb. Schiffbautechn. Ges. Bd.30 (1929), S.170/194. T.CrossRefGoogle Scholar
10. Schnadel, G. Knickung von Schiffsplatten, Werft Reed. Hafen Bd.ll (1930), S.461/465, 493/497. T.Google Scholar
11. Schnadel, G. Die Überschreitung der Knickgrenze bei dunnen Platten. Verhandl. 3. int. Kongr. techn. Mechanik Bd.3, S.73/81, Stockholm 1930. T.Google Scholar
12. Schleicher., F. Die Knickspannungen von eingespannten rechteckigen Platten, Mitt. Forsch.-Anst. GutehofmungshÜtte Bd.l (1931), S.186/193. T.Google Scholar
13. von Kármán, T., Sechler, E. E. und Donnell, L. H.. The strength of thin plates in compression. Trans Amer. Soc. mech. Engr. Bd.54 (1932), Heft 1. S.53/57. T.CrossRefGoogle Scholar
14. Yamana, M. On the elastic stability of aeroplane structures. J. Fac. Engng. Tokyo Univ. Bd.20 (1933), Heft 8, S.163/224. TV.Google Scholar
15. Taylor, G. J. The buckling load for a rectangular plate with four clamped edges. Z. angew. Math. Mech. Bd.13 (1933), Heft 2, S.147/152. T.CrossRefGoogle Scholar
16. Cox, H. L. The buckling of thin plates in compression. Aeron. Res. Comm. Rep. and Mem. 1554, London 1933. T.Google Scholar
17. Schuman, L. und Back, G.. Strength of rectangular flat plates under edge compression. N.A.C.A. Techn. Report 356, Washington 1930. V.Google Scholar
18. A. E. H. Love. Lehrbuch der Elastizität, Übersetzt von A. Timpe, Leipzig und Berlin 1907, Verlag B. G. Teubner. Z.Google Scholar
19. Bleich, F. Theorie und Berechnung der eisernen Brukken, Berlin 1924, Verlag J. Springer. Z.CrossRefGoogle Scholar
20. Nádai, A. Die elastischen Platten, Berlin 1925, Verlag J. Springer. Z.CrossRefGoogle Scholar
21. Geckeler, J. W. Elastostatik, Handbuch der Physik Bd.6, Berlin 1928, Verlag J. Springer. Z.CrossRefGoogle Scholar
22. Timoschenko, S. Stabilitatsprobleme der Elastizität, Handbuch der physikalischen and technischen Mechanik Bd.4, 1. Halfte, 2. Teil, Leipzig 1931, Verl. J. A. Barth. Z.Google Scholar
23. Timoschenko, S. Strength of materials 2 Bde., London 1931, Verlag Macmillan and Co. Z.Google Scholar
24. Timoschenko, S. Stability and strength of thin-walled constructions. Verhandl. 3. int. Kongr. techn. Mech. Bd.3, S.3/15, Stockholm 1930. Z.Google Scholar
25. Kármán., T. v. Analysis of some typical thin-walled structures. Aeron. Engng. Bd.5 (1933), Heft. 4, S.155/158. Z.Google Scholar
26. Cox, H. L. Summary of the present state of knowledge regarding sheet metal construction. Aeron. Res. Comm. Rep. and Mem. 1553, London 1933. Z.Google Scholar
27. Pollard, H. J. Some developments in aircraft construction. J. Roy. Aeron. Soc. Bd. 38 (1934), S.651/686. Z.CrossRefGoogle Scholar

References

Dealing with the strength of isotropic rectangular plates under shear.

1. Timoschenko, S. Über die Stabilitat von versteiften Platten, Eisenbau Bd.12 (1921), Heft 5 und 6, S. 147/163. T.Google Scholar
2. Southwell, R. V. and Skan, S. W.. On the stability under shearing forces of a flat elastic strip. Proc. Roy. Soc. Land. Ser. A Bd.105 (1924). S.582/607.Google Scholar
3. Southwell, R. V. Notei on the stability under shearing forces of a flat elastic strip, and an analogy with the problem of the stability of laminar fluid motion. Verhandl. I. int. Kongr. techn. Mechanik. S.266/275, Delft 1925. T.Google Scholar
4. Bergmann, S. und Reissner, H.. Neuere Probleme aus der Flugseugstatik. Über die Knickung von rechteckigen Platten bei Schubbeanspruchung. Z. Flugtechn. Motorluftsch. Bd.23 (1932), Heft 1, S.6/12. T.Google Scholar
5. Seydel, E. Über das Ausbeulen von rechteckigen, isotropen oder orthogonal-anisotropen Platten bei Schubbeanspruchung, Ing.-Arch. Bd.4 (1933), Heft 2, S.169/191. T.CrossRefGoogle Scholar
6. Bollenrath, F. Ausbeulerscheinungen an ebenen, auf Schub beanspruchten Platten. Luftf.-Forschg. Bd.6 (1929), Heft I. -S.l/17. V.Google Scholar
7. Gough, H. J. and Cox, H. L.. Some tests on the stability of thin strip material under shearing forces in the plane of the strip. Proc. Roy. Soc. Lond. Ser. A Bd.137 (1932). S.145/157. V.Google Scholar
8. Seydel, E. Ausbeul.-Schublast rechteckiger Platten (Zahlenbeispiele und Versuchsergebnisse). Z. Flugtechn. Motorluftsch. Bd.24 (1933), Heft 3, S.78/83. V.Google Scholar
9. Nadai, A. Die elastischen Platten. Berlin, 1925, Verlag J. Springer. Z.CrossRefGoogle Scholar
10. Geckeler, J. W. Elastostatik. Handbuch der Physik Bd.6, Berlin 1928, Verlag J. Springer. Z.CrossRefGoogle Scholar
11. Timoschenko, S.. Stability and strength of thin-walled constructions. Verhandl. 3. int. Kongr. tech. Mechanik Bd.3, S.3/15. Stockholm 1930. Z.Google Scholar
12. Timoschenko, S.. Stabilitatsprobleme der Elastizitat. Handbuch der physikalischen und technischen Mechanik Bd.4, I. Halfte, 2. Teil, Leipzig 1931. Verlag J. A. Barth. Z.Google Scholar
13. Timoschenko, S. Strength of materials. 2 Bde., London 1931, Verlag Macmillan and Co. Z.Google Scholar
14. Cox, H. L. Summary of the present state of knowledge regarding sheet metal construction. Aeron. Res. Comm. Rep. and Mem. 1553, London 1923. Z.Google Scholar

References

Dealing with the strength of isotropic plates under compound loading.

1. Wagner, H., Über Konstruktions- und Berechnungs-fragen des Blechbaues. Jb. wiss. Ges. Luftf. (1928), S.113/125. TV.Google Scholar
2. Stein, O. Die Stabilitat der Blechtragerstehbleche im zweiachsigen Spannungszustand, Stahlbau Bd.7 (1934). Heft 8, S.57/60. T.Google Scholar

References

Dealing with the strength of orthotropic rectangular plates under pressure.

1. W. R. Dean. The elastic stability of a corrugated plate. Proc. Roy. Soc. Lond. Ser. A Bd.lll (1926). S.144/167. T.CrossRefGoogle Scholar
2. H. Wagner. Sheet-metal airplane construction. Aeron. Engng. Bd.3 (1931), Heft 4, S.151/161. T.CrossRefGoogle Scholar
3. M. Yamana. On the elastic stability of aeroplane structures. J. Fac. Engng. Tokyo Univ. Bd.20 (1933), Heft 8, S.163/224. TV.Google Scholar
4. J. S. Newell. The strength of aluminium alloy sheets. Airway Age, Bd.ll (1930). S.1420/1424, 1467, 1548/1551, 1574. V.Google Scholar
5. H. L. Cox. Summary of the present state of knowledge regarding sheet metal construction. Aeron. Res. Comm. Rep. and Mem. 1553, London 1933. Z.Google Scholar

References

Relative to the stiffness of orthotropic rectangular plates under shear.

1. Bergmann, S. und Reissner, H.. Neuere Probleme aus der Flugzeugstatik. Cber die Knickung von Wellblechstreifen bei Schubbeanspruchung. Z. Flugtechn. Motorluftsch. Bd.20 (1929), Heft 18, S.475/481. T.Google Scholar
2. Schubbeanspruchung, C. Z. Flugtechn. Motorluftsch. Bd.21 (1930), Heft 3, S.61/65. T.CrossRefGoogle Scholar
3. Bergmann, S. und Reissner, H.. Neuere Probleme aus der Flugzeugstatik. Cber die Knickung von Wellblechstreifen bei Schubbeanspruchung. Z. Flugtechn. Motorluftsch. Bd.21 (1930), Heft 12, S.306/310. T.Google Scholar
4. Seydel, E. Beitrag zur Frage des Ausbeulens von versteiften Platten bei Schubbeanspruchung. 195: DVL-Berecht. Luftf.-Forschg. Bd.8 (1930), Heft. 3, S.71/90, und DVL.-Jb. (1930), S.235/254. T.Google Scholar
5. Wagner, H. Sheet-metal airplane construction. Aeron. Engng. Bd.3 (1931), Heft 4, S.151/161. T.CrossRefGoogle Scholar
6. Seydel, E. Über das Ausbeulen von rechteckigen, isotropen oder orthogonal-anisotropen Platten bei Schubbeanspruchung. Ing.-Arch. Bd.4 (1933). Heft 2. S.169/191. T.Google Scholar
7. Seydel, E. Schubknickversuche mit Wellblechtafeln, 230. DVL-Bericht, DVL-Jb. (1931). S.233/245. V.Google Scholar
8. Seydel, E. Ausbeul-Schublast rechteckiger Platten (Zahlenbeispiele und Versuchsergebnisse), Z. Flugtechn. Motorluftsch. Bd.24 (1933), Heft 3, S.78/83. . V.Google Scholar
9. L. Cox, H. Summary of the present state of knowledge regarding sheet metal construction. Aeron. Res. Comm. Rep. and Mem. 1553, London 1933. Z.Google Scholar

References

Dealing with the strength of rectangular plates with the stiffeners under pressure.

1. Timoschenko, S. Über die Stäbilitat von versteiften Platten. Eisenbau Bd.12 (1921), Heft 5 und 6, S. 147/163. T.Google Scholar
2. Kármán, T. v. Sechler, E. E. und Donnell., L. H. The strength of thin plates in compression. Trans Amer. Soc. mech. Engr. Bd.54 (1932), Heft 1. S.53/57. T.CrossRefGoogle Scholar
3. Lundquist, E. E. Comparison of three methods for calculating the compressive strength of flat and slightly curved sheet and stiffener combinations. N.A.C.A. Techn. Note 455, Washington 1933. T.Google Scholar
4. Schuman, L. und Back., G. Strength of rectangular flat plates under edge compression. N.A.C.A. Tech. Report 356, Washington 1930. V.Google Scholar
5. Newell, J. S. The strength of aluminium alloy sheets. Airway Age, Bd.ll (1930), S.1420/1424, 1467, 1548/1551, 1574. V.Google Scholar
6. Newell, J. S. Data on the strength of aircraft materials. Aviat. Engng. Bd.6 (1932). Heft 3, S.ll/14. V.Google Scholar
7. Timoschenko, S. Stability and strength of thin-walled constructions. Verhandl. 3. int. Kongr. techn. Mechanik. Bd.3, S.3/15. Stockholm 1930. Z.Google Scholar
8. Timoschenko, S. Stabilitatsprobleme der Elastizität. Handbuch der physikalischen und technischen Mechanik Bd.4, 1. Hälfte, 2. Teil. Leipzig 1931, Verlag J. A. Barth. Z.Google Scholar
9. Kármán, T. v. Analysis of some typical thin-walled structures. Aeron. Engng. Bd.5 (1933). Heft 4, S.155/158. Z.Google Scholar
10. Sechler, E. E. Strength of thin metal structures beyond the stability limit. Aeron. Engng. Bd.5 (1933), Heft 4, S.151/153. Z.CrossRefGoogle Scholar

References

Relative to the strength of rectangular plates with stiffeners under stress.

1. Wagner, H. Cber Konstruktions- und Berechnungs-fragen des Blechbaues. Jb. wiss. Ges. Luftf. (1928). S.113/125. TV.Google Scholar
2. Wagner, H. Ebene Blechwndträger mit sehr dünnem Stegblech. Z. Flugtechn. Motorluftsch. Bd.20 (1929), Heft 8 bis 12, S.200/207, 227/223, 256/262, 279/284, 306/314. T.Google Scholar
3. Mathar, J. Beitrag zur Frage der Beplankung von Flugzeugen. Jb. wiss. Ges. Luftf. (1929), S.205/210. V.Google Scholar
4. Timoschenko, S. Stability and strength of thin-walled constructions. Verhandl. 3. int. Kongr. techn. Mechanik. Bd.3, S.3/15. Stockholm 1930. Z.Google Scholar
5. Kuhn, P. A summary of' design formulas for beams having thin webs in diagonal tension. N.A.C.A. Techn. Note 469, Washington 1933. Z.Google Scholar
6. Karman, T. v. Analysis of some typical thin-walled structures. Aeron. Engng. Bd.5 (1933), Heft 4. S.155/158. ZGoogle Scholar
7. Sechler, E. E. Strength of thin metal structures beyond the stability limit. Aeron. Engng. Bd.5 (1933), Heft 4, S. 151/153. Z.CrossRefGoogle Scholar

References

Relative to the strength of isotropic circular cylindrical partial shells under axial pressure

1. Redshaw, S. C. The elastic instability of a thin curved panel. Aeron. Res. Comm. Rep. and Mem. 1565, London 1934. T.Google Scholar
2. Cox, H. L. Summary of the present state of knowledge regarding sheet metal construction. Aeron. Res. Comm. Rep. and Mem. 1553, London 1933. Z.Google Scholar
3. Pollard, H. J. Some developments in aircraft construction. J. Roy. Aeron. Soc. Bd.38 (1934), S.651/686. Z.CrossRefGoogle Scholar

References

Relative to the strength of isotropic cylindrical partial shells under shear.

1. Wagner, H. Über Konstruktions- und Berechnungs-fragen des Blechbaues. Jb. wiss. Ges. Luftf. (1928). S.113/125. TV.Google Scholar
2. Smith, G. M. Strength in shear of thin curved sheets of alclad. N.A.C.A. Techn. Note 343, Washington 1930. V.Google Scholar

References

Relating to the strength of stiffened cylindrical partial shells under pressure.

1. Lundquist, E. E. Comparison of three methods for calculating the compressive strength of flat and slightly curved sheet and stifiener combinations. N.A.C.A. Tech. Note 455, Washington 1933. TZ.Google Scholar
2. Newell, J. S. The strength of aluminium alloy sheets. Airway Age, Vol. 11 (1930), pp. 1420/1424, 1467, 1548/1551, 1574. V.Google Scholar

References

Relating to the strength of isotropic cylindrical solid shells under axial compression.

1. Lorenz, R. Achsensymmetrische Verzerrungen in diinnwandigen Hohlzylindern. Z. VDI Bd.52 (1908), S.1706/1713. T.Google Scholar
2. Lorenz, R. Die nicht achsensymmetrische Knickung diinnwandigen Hohlzylinder. Physik Z. Bd.12 (1911), S.241/260. T.Google Scholar
3. Timoschenko, S. Einige Stabilitätsprobleme der Elastizitätstheorie. Z. Math. Physik Bd.58 (1910), S.337/385. T.Google Scholar
4. Southwell, R. V. On the general theory of elastic stability. Philos. Trans. Ser. A Bd.213 (1914), S.187/244. T.CrossRefGoogle Scholar
5. Dean, W. R. On the theory of elastic stability. Proc. Roy. Soc. Lond. Ser. A Bd.107 (1925), S.734/760. T.CrossRefGoogle Scholar
6. Foppl, L. Achsensymmetrische Ausknicken zylindrischer Schalen, Sitzungsber, Bayer, Ak. Wissensch. math.-naturwiss. Abt. (1926), S.27/40. T.CrossRefGoogle Scholar
7. Geckeler, J. W. Plastisches Knicken der Wandung von Hohlzylindern und einige andere Flatungserscheinungen an Schalen und Blechen. Z. angew. Math Mech. Bd.8 (1928), S.341/352. T.CrossRefGoogle Scholar
8. Sanden, K. v. und Tolke., F. Über Stabilitätsprobleme dunner, kreiszylindrischer Schalen. Ing.-Arch. Bd. 3 (1932), Heft 1, S.24/66. TZ.CrossRefGoogle Scholar
9. Fliigge, W. Die Stabilitat der Kreiszylinderschale. Ing.-Arch. Bd.3 (1932), Heft 5, S.463/506. TV.CrossRefGoogle Scholar
10. Donnell, L. H. A new theory for the buckling of thin cylinders under axial compression and bending. Trans. Amer. Soc. mech. Engr. Bd.56 (1934), Heft 11, S.795/806. T.CrossRefGoogle Scholar
11. Robertson, A. The strength of tubular struts. Aeron. Res. Comm. Rep. and Mem. 1185, London 1929. V.Google Scholar
12. Rhode, R. V. und Lundquist., D. F. Strength tests on paper cylinders in compression, bending and shear. N.A.C.A. Techn. Note 370. Washington 1931. V.Google Scholar
13. Lundquist, E. E. Strength tests of thin-walled duralumin cylinders in compression. N.A.C.A. Techn. Report 473, Washington 1933. V.Google Scholar
14. Prescott, J. Applied elasticity. London 1924, Verlag Longmans, Green and Co. Z.Google Scholar
15. Geckeler, J. W. Elastostatik. Handbuch der Physik, Bd.6, Berlin 1928, Verlag J. Springer. Z.CrossRefGoogle Scholar
16. Timoschenko, S. Stability and: strength of thin-walled constructions. Verhandl. 3. int. Kongr. techn. Mechanik. Bd.3, S.3/15. Stockholm 1930. Z.Google Scholar
17. Timoschenko, S. Stabilitätsprobleme der Elastizität. Handbuch der physikalischen und technischen Mechanik Bd.4, 1. Halite, 2. Teil. Leipzig 1931, Verlag J. A. Barth. Z.Google Scholar
18. Cox, H. L. Summary of the present state of knowledge regarding sheet metal construction. Aeron. Res. Comm. Rep. and Mem. 1553, London 1933. Z.Google Scholar
19. Pollard, H. J. Some developments in aircraft construction. J. Roy. Aeron. Soc. Bd.38 (1934), S.651/686. Z.CrossRefGoogle Scholar

References

Relative to the strength of isotropic cylindrical solid shells under bending.

1. Brazier, L. G. The flexure of thin cylindrical shells and other ” thin “ sections. Aeron. Res. Comm. Rep. and Mem. 1081, London 1927 und Proc. Roy. Soc. Lond. Ser. A Bd.116 (1927). S.104/114. TV.Google Scholar
2. Chwalla, E. Reine Biegung schlanker, diinnwandiger Rohre mit gerader Achse. Z. angew. Math. Mech. Bd.13 (1933) Heft 1, S.48/53. T.CrossRefGoogle Scholar
3. Mossman, R. W. und Robinson., R. G. Bending tests of metal monocoque construction. N.A.C.A. Techn. Note 357. Washington 1930. V.Google Scholar
4. Lundquist, E. E. Strength tests of thin-walled duralumin cylinders in pure bending. N.A.C.A. Techn. Note 479, Washington 1933. V.Google Scholar
5. Younger, J. E. Principle of similitude as applied to research on thin-sheet structures. Aeron. Engng. Bd.5 (1933), Heft 4, S. 163/169. V.CrossRefGoogle Scholar
6. Timoschenko, S. Stability and strength of thin-walled constructions. Verhandl. 3. int. Kongr. techn. Mechanik. Bd.3, S.3/15. Stockholm 1930. Z.Google Scholar

References

Relative to the strength of isotropic cylindrical solid shells under torsion.

1. Schwerin, E. Die Torsionsstabilitat des diinnwandigen Rohres. Verhandl. 1. int. Kongr. techn. Mechanik. S.255/265, Delft 1925, und Z. angew. Math. Mech. Bd.5 (1925) S.235/243. T.CrossRefGoogle Scholar
2. Sezawa, K. und Kubo., K. The buckling of a cylindrical shell under torsion. Aeron. Res. Inst. Tokyo Univ., Report 76 (1931). TV.CrossRefGoogle Scholar
3. Sanden, K. v. und Tölke., F. Über Stabilitätsprobleme diinner, kreiszylindrischer Schalen. Ing.-Arch. Bd.3 (1932), Heft 1, S.24/26. T.CrossRefGoogle Scholar
4. Sezawa, K. The nature of the torsional stability of a monocoque fuselage. J. Roy. Aeron. Soc. Bd.37 (1933), S.411/422. TV.CrossRefGoogle Scholar
5. Donnell, L. H. Stability of thin-walled tubes under torsion. N.A.C.A. Techn. Report 479. Washington 1933. TV.Google Scholar
6. Lundquist, E. E. Strength tests of thin-walled duralumin cylinders in torsion. N.A.C.A. Techn. Note 427, Washington 1932. V.Google Scholar
7. Younger, J. E. Principle of similitude as applied to research on thin-sheet structures. Aeron-. Engng. Bd.5 (1933), Heft 4, S.163/169. V.CrossRefGoogle Scholar

References

Relating to the strength of isotropic cylindrical solid shells under composite stresses.

1. Bridget, F. J. Jerome, C. C. und Vosseller., A. B. Some new experiments on buckling of thin-wall constructions. Trans. Amer. Soc. mech. Engr. Bd.56 (1934), Heft 8, S.569/578. V.CrossRefGoogle Scholar

References

Relating to the strength of orthotropic circular cylindrical solid shells under composite stresses.

1. Yamana, M. On the elastic stability of aeroplane structures. J. Fac. Engng. Tokyo Univ. Bd.20 (1933) Heft 8, S.163/224. TV.Google Scholar