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Thin-Walled Bars

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Part of the book series: Mechanics of Elastic Stability ((MEST,volume 13))

Abstract

There exists a great variety of possible buckling modes of thin-walled bars. Besides Euler’s buckling and lateral buckling we mention here, first of all, torsional buckling, and a combination of these phenomena. The above buckling modes, called jointly “the overall buckling”, may be investigated under the assumption of undeformable cross-sectional profiles. However, in fact, the profiles may also be subject to deformation, and we mention here local buckling of plate or shell elements of thin-walled bars, lateral buckling of individual elements and various possible combinations. Overall buckling modes are more typical for bars with open profiles and local buckling modes — for closed profiles, but this is not a general rule.

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References

  1. Andriyenko, A.I., Ryabchenko, V.M., On evaluation of parameters in the problem of optimal design of thin-walled stiffened structures (in Russian), Optimalnoe Proektir. Avyats. Konstr. 1, Kuybyshev 1973, 3 – 9.

    Google Scholar 

  2. Armand, J.L., On peculiarities of the problem of optimal thickness distribution in a thin wing under a given speed of divergence (in Russian), Izv. AN SSSR, Mekh. Tverd. Tela (1977), 2, 174.

    Google Scholar 

  3. Azad, A.K., Baluch, M.H., Minimum weight design of tapered steel I — columns, Eng. Optimization 7(1983), 1,1 – 6.

    Google Scholar 

  4. Balovnev, G.G., Evaluation of optimal dimensions of thin-walled profiles for elements subject to compression (in Russian), Stroit. Mekh. Rasch. Sooruzh. (1962), 6, 40 – 44.

    Google Scholar 

  5. Balovnev, G.G., Trofimov, G.S., On rational cross-sectional forms of thin-walled profiles (in Russian), Vestnik Mashinostr. (1959), 4, 3 – 10.

    Google Scholar 

  6. Balovnev, G.G., Trofimov, G.S., Choice of rational cross-sectional forms for thin-walled profiles (in Russian), Vestnik Mashinostr. (1960), 9, 3 – 7.

    Google Scholar 

  7. Balovnev, G.G., Ustilovsky, S.Ya., Choice of rational cross-sectional dimensions of thin-walled beams under bending (in Russian), Izv. VUZov, Mashinostr. (1966), 9, 40 – 44.

    Google Scholar 

  8. Balyk, V.M., Litvinov, V.S., Solution to optimization problems of thin-walled structures based on methods of multicriterial optimization (in Russian), Sb. Nauchn. Trud. Tashkentskogo Polit. Inst. 319(1981), 46 – 52.

    Google Scholar 

  9. Barnett, R.L., Optimum prestressed tubular columns, Proc. ASCE, J. Structur. Div. 96(1970), ST2, 291 – 301.

    Google Scholar 

  10. Benito, R., Sridharan, S., Mode interaction in thin-walled structural members, J. Struct. Mech. 12(1984 – 5), 4, 517 – 542.

    Google Scholar 

  11. Bentley, K., Lateral stability of beams, Proc. 4th Congr. Int. Assoc. Bridge and Struct. Engng., Cambridge 1952, 419.

    Google Scholar 

  12. Bergfelt, A., Design of plate girders without stiffeners, Paper 5.3 of Working Group VIII/3 of E.C.C.S. (1974).

    Google Scholar 

  13. Bijlaard, P.P., Fisher, G.P., Interaction of column and local buckling in compression members, NACA TN 2640 (1952).

    Google Scholar 

  14. Biryuk, V.I., On the problem of optimal structural design of a wing under strength and aeroelastic constraints (in Russian), Ucheb. Zap. Centr. Aerogidr. Inst. 3(1972), 2, 114 – 119.

    Google Scholar 

  15. Bisplinghoff, R.L., Ashley, H., Halfman, R.L., Aeroelasticity, Addison-Wesley, Reading Mass. 1955.

    MATH  Google Scholar 

  16. Bobrin, V.A., Design of bars of minimal weight allowing for local stability and manufacturing constraints (in Russian), Trudy Khabarovsk. Inst. Inzh. Zhel.-Dor. Transp. 40(1971), 274 – 279.

    Google Scholar 

  17. Braham, M., Grimault, J.P., Massonnet, Ch., Mouty, J., Rondal, J., Buckling of thin-walled hollow sections. Case of axially loaded rectangular sections, Acier — Stahl — Steel (1980), 1.

    Google Scholar 

  18. Bronowicki, A.J., Felton, L.P., Optimum design of continuous thin-walled beams, Int. J. Numer. Meth. Engng. 9(1975), 3, 711 – 720.

    MATH  Google Scholar 

  19. Budrin, S.B., Optimal parameters of a thin-walled box section stiffened by longitudinal ribs (in Russian), Podyemno-Transp. Mashiny, Tula 1976, 9 – 14.

    Google Scholar 

  20. Budrin, S.B., Tserlin, L.G., Parametric optimization of a box section of portal crane structures (in Russian), Leningr. Polit. Inst., Leningrad 1977, 1 – 25.

    Google Scholar 

  21. Cadambe, V., Krishnan, S., Minimum weight design of thin-walled cells in torsion, J. Roy. Aero. Soc. 59(1955), 120 – 126.

    Google Scholar 

  22. Cadambe, V., Krishnan, S., Note on the minimum weight of thin walled cells in combined bending and torsion, J. Roy. Aero. Soc. 60(1956), 541, 65 – 66.

    Google Scholar 

  23. Chilver, A.H., Some simple models for torsional creep buckling, Proc. IUTAM Symp. Creep in Structures, Stanford 1960, Springer 1962, 339 – 354.

    Google Scholar 

  24. Chong, K.P., Optimization of unstiffened hybrid beams, Proc. ASCE, J. Struct. Div. 102(1976), ST2, 401 – 409.

    Google Scholar 

  25. Chudzikiewicz, A., Ogolna teoria statecznosci pretow cienkosciennych z uwzglednieniem odksztalcalnosci przekroju poprzecznego, Rozpr. Inz. 8(1960), 3, 421 – 461; 4, 803 – 842.

    MathSciNet  Google Scholar 

  26. Culver, C.G., Preg, S.M., Elastic stability of tapered beam-columns, Proc. ASCE, J. Struct. Div. 94(1968), ST2, 455 – 470.

    Google Scholar 

  27. Cywinski, Z., Techniczna teoria pretow cienkosciennych o zmiennych otwartych przekrojach zlozonych, Zesz. Nauk. Polit. Gdanskiej, Budown. Lad. 18(1968), 91 pp.

    Google Scholar 

  28. Cywinski, Z., Rownania wyboczenia skretnego preta dwuteweogo o zmiennym przekroju bisymetrycznym, Zesz. Nauk. Polit. Gdanskiej, Budown. Lad. 21(1970), 19 – 41.

    Google Scholar 

  29. Cywinski, Z., Kollbrunner, C.F., Drillknicken dünnwandiger I-Stäbe mit veränderlichen, doppelsymmetrischen Querschnitten, Inst. für Bauwissensch. Forschung, Verlag Leemann 18, Zürich 1971.

    Google Scholar 

  30. Cwik, R., Optymalne wymiarowanie belek zginanych o przekroju zamknietym skrzynkowym o jednakowej grubosci scianek, Zesz. Nauk. Polit. Slaskiej, Mechanika 52, (1973), 75 – 81.

    Google Scholar 

  31. De Miranda, F., Berardi, C., Progetto di sezioni composte in acciaio sollecitate a sforzo normale eccentrico col criterio delia massima economica, Acciaio e Costruz. Metall. 9(1957), 4, 154 – 162.

    Google Scholar 

  32. De Wolf, J., Pekoz, T., Winter, G., Interaction of postcritical plate buckling with overall column buckling of thin-walled members, 9th Congr. Int. Assoc. Bridge and Struct. Engng., Rapp. Prelim., Zürich 1972, 91 – 100.

    Google Scholar 

  33. Demokritov, V.N., Optimization of crane girders allowing for local wall stability (in Russian), Izv. VUZov, Mashinsotr. (1974), 8, 120 – 123.

    Google Scholar 

  34. Dharmarajan, S., McGhie, R.D., Optimization of composite columns of various cross sections, Proc. 6th Symp. Compos. Mater. Eng. Des., St. Louis 1972, Matals Park, Ohio 1973, 402 – 416.

    Google Scholar 

  35. Djubek, J., Stabilita stien nosnikov a ich hospodarne navrhovanie, Stav Casopis 9(1961), 2, 65 – 88.

    Google Scholar 

  36. Djubek, J., Kodnar, R., Skaloud, M., Limit state of the plate elements of steel structures, Veda — Birkhäuser, Praha — Basel 1983.

    Google Scholar 

  37. Doroshenko, O.P., On the choice of optimal cross-sections of structural elements by the search and geometric programming methods (in Russian), Issled. Optim. Metallokonstr. i Det. Pod.-Transp. Mashin, Vol. 1, Kuybyshev 1976, 68 – 83.

    Google Scholar 

  38. Dzyuba, A.S., Lipin, E.K., Optimal design of minimal volume structures under strength and stability constraints (in Russian), Ucheb. Zap. Centr. Aerogidr. Inst. 11(1979), 1, 58 – 71.

    Google Scholar 

  39. Elizarov, A.F., On the problem of design of minimal weight structures (in Russian), Trudy Tomsk. Inzh.-Stroit. Inst. 14(1968), 7 – 20.

    MathSciNet  Google Scholar 

  40. Elizarov, A.F., On the theory of optimal structural design (in Russian), Issled. po Stroit. Mekh. i Rasch. Sooruzh., Tomsk 1969, 4 – 16.

    Google Scholar 

  41. Elizarov, A.F., On minimal volume design of bars subject to loss of stability (in Russian), Issled. po Stroit. Mekh. i Stroit. Konstr., Tomsk 1974, 16 – 18.

    Google Scholar 

  42. Emero, D.H., Spunt, L., Optimization of multirib and multiweb wing box structures under shear and moment loads, J. Aircraft 3. (1966), 2, 130 – 141.

    Google Scholar 

  43. Endo, K., Buckling phenomenon of the plate element of the girder with varying cross-section, Trans. Japan Soc. Civil Eng. 91(1933).

    Google Scholar 

  44. Endo, K., Stability problem of the beam with gradually varying cross-section under uniform bending moment, Trans. Soc. Mech. Eng. Japan 46(Feb. 1943), 311.

    Google Scholar 

  45. Esslinger, M., Krautwurst, O., Zur Stabilität von auf Biegung beanspruchten I-Trägern, Stahlbau 19(1950), 4.

    Google Scholar 

  46. Farkas, J., Festigkeitseigenschaften von geschweissten auf Biegung optimal bemessenen I-und Kastenträgern, Acta Techn. Acad. Sci. Hung. 66(1969), 4, 427 – 439.

    Google Scholar 

  47. Farkas, J., Optymalne wymiarowanie belek zginanych o przekroju zamknietym cienkosciennym z pasow polkolistych i srodnikow pionowych, Dozor Techniczny (1971), 3, 3 – 6.

    Google Scholar 

  48. Farkas, J., Optimalbemessung und Vergleich von biegebeanspruchten dünnwandigen Trägern mit Kasten-, Kreisrohr-und Ovalquerschnitt, Acta Techn. Acad. Sci. Hung. 72(1972), 3/4, 377 – 388.

    Google Scholar 

  49. Farkas, J., Optimum design of compressed columns of constant welded square box cross section considering the effect of residual welding stresses, Acta Techn. Acad. Sci. Hung. 84(1977), 3/4, 335 – 348.

    Google Scholar 

  50. Farkas, J., Minimization of the cross section area of welded I- and box beams loaded in bending and shear by means of the “SUMT” nonlinear programming method, 8th Int. Kongr. Anwend. Math. Ingenieurwiss.,Weimar 1978, Bd. 1, Erfurt 1978, 319 – 324.

    Google Scholar 

  51. Farkas, J., Minimization of the cross section area of welded unstiffened plate and box girders subjected to bending and shear, Acta Techn. Acad. Sci. Hung. 87(1978), 3/4, 293 – 304.

    Google Scholar 

  52. Farkas, J., Optimum design for bending and ultimate shear strength of hybrid I-beams, Acta Techn. Acad. Sci. Hung. 90(1980), 3/4, 259 – 273.

    Google Scholar 

  53. Farkas, J., Szabo, L., Optimum design of beams and frames of welded I-sections by means of backtrack programming, Acta Techn. Acad. Sei. Hung. 91(1980), 1/2, 121 – 135.

    Google Scholar 

  54. Farrar, D.J., The design of compression structures for minimum weight, J. Roy. Aero. Soc. 53(1949), 1041 – 1052.

    Google Scholar 

  55. Feigen, M., Minimum weight of a tapered round thin-walled column, J. Appl. Mech. 19(1952), 3, 375 – 380.

    Google Scholar 

  56. Felton, L.P., Structural index methods in optimum design, ASME Structural Optimization Symposium, L.A. Schmit, Ed., (1974),

    Google Scholar 

  57. Felton, L.P., Dobbs, M.W., Optimum design of tubes for bending and torsion, Proc. ASCE, J. Struct. Div. 93(1967), ST4, 185 – 200.

    Google Scholar 

  58. Felton, L.P., Nelson, R.B., Optimized components in frame synthesis, AIAA Journal 9(1971), 6, 1027 – 1031.

    ADS  Google Scholar 

  59. Fleischer, W.H., Design and optimization of plate girders and weld-fabricated beams for building construction, Eng. J. USA 22(1985), 1, 1 – 10.

    MathSciNet  Google Scholar 

  60. Fox, R.L., Miura, H., Rao, S.S., Automated design optimization of supersonic airplane wing structures under dynamic constraints, AIAA Paper No. 333 (1972), 16 pp.

    Google Scholar 

  61. Frayman, F.I., Optimal design of thin-walled box section of a beam under pure oblique bending (in Russian), Prikl. Mekh. 7(1971), 11, 96 – 104.

    Google Scholar 

  62. Frayman, F.I., A particular case of optimal design of a thin-walled box beam under oblique bending (in Russian), Prikl. Mekh. 8(1972), 2, 135 – 138.

    Google Scholar 

  63. Frayman, F.I., Optimal design of a box beam under compression with bending (in Russian), Prikl. Mekh. 16(1980), 2, 88 – 94.

    Google Scholar 

  64. Galoussis, E., On an optimum design of cover plated beams, Civ. Eng. Pract. and Des. Eng. 3(1984), 4, 327 – 346.

    Google Scholar 

  65. Gerard, G., Optimum number of webs required for a multicell box under bending, J. Aero. Sci. 15(1948), 1, 53 – 56.

    Google Scholar 

  66. Gibczynska, T., Wyznaczanie optymalnych wymiarow przekroju skrzynkowego belki zginanej, Przeglad Mechaniczny 35(1976), 12, 404 – 408.

    Google Scholar 

  67. Gibczynska, T., General analysis of optimal design of a box-section under bending, Bull. Acad. Pol., Ser. Sci. Techn. 27(1979), 8/9, 379 – 390 (extensive English summary);

    Google Scholar 

  68. Gibczynska, T., General analysis of optimal design of a box-section under bending, Arch. Bud. Maszyn 25(1978), 2, 325 – 339 (Polish full text).

    Google Scholar 

  69. Gibczynska, T., Optymalne ksztaltowanie przekroju skrzynkowego przy obciazeniach zlozonych, Zesz. Nauk. AGH Krakow 103(1979), 51 – 67.

    Google Scholar 

  70. Gibczynska, T., Formation optimale de la section en caisson dans le cas de la flexion pure, Rev. Roum. Sci. Techn., Mec. Appl. 25(1980), 5, 751 – 758.

    MATH  Google Scholar 

  71. Gibczynska, T., Zagadnienia optymalnego ksztaltowania przekroju cienkosciennych dzwigarow skrzynkowych, Zesz. Nauk. Polit. Krakowskiej, Mechanika 4, Krakow 1980.

    Google Scholar 

  72. Gibczynska, T., Optymalne ksztaltowanie przekroju skrzynkowego preta rownoczesnie zginanego i skrecanego, Rozpr. Inz. 28(1980), 2, 237 – 254.

    MATH  Google Scholar 

  73. Gibczynska, T., Wyznaczanie optymalnych wymiarow hybrydowego przekroju skrzynkowego, Przeglad Mechaniczny 41(1982), 13, 5 – 8.

    Google Scholar 

  74. Gibczynska, T., Oziemski, S., Ksztaltowanie przekroju skrzynkowego w przypadkach obeiazen zlozonych, Przeglad Mechaniczny 42(1983), 18, 5 – 9.

    Google Scholar 

  75. Gioncu, V., Ivan, M., Interaction between flexural buckling and torsional-flexural buckling in thin-walled compression members, in [0.296], 359 – 376.

    Google Scholar 

  76. Goldberg, J.E., Bogdanoff, J.L., Glauz, W.D., Lateral and torsional buckling of thin-walled beams, Proc. Int. Assoc. Bridge Struct. Eng. 24(1964), 91 – 100.

    Google Scholar 

  77. Gopak, K.N., Optimal beam under the constraint of lateral buckling (in Russian), Primenenye Elektron. Vych. Mashin v Stroit. Mekh., Kiev 1968, 431 – 434.

    Google Scholar 

  78. Gopak, K.N., Optimal beam under the constraint of lateral buckling (in Russian), Gidroaeromekh. i Teoria Uprug. 11(1970), 113 – 120.

    Google Scholar 

  79. Gorski, S., Optymalizacja projektowania stalowych dwugaleziowych pretow sciskanych osiowo, Inzynieria i Budownictwo 25(1968), 12, 465 – 469.

    ADS  Google Scholar 

  80. Graves-Smith, T.R., The ultimate strength of locally buckled columns of arbitrary length, Thin-Walled Structures, Crosby Lockwood, London 1969, 35.

    Google Scholar 

  81. Graves-Smith, T.R., The effect of initial imperfections on the strength of thin-walled box columns, Int. J. Mech. Sci. 13(1971), 11, 911 – 925.

    Google Scholar 

  82. Gubaydulin, R.G., Method of determination of optimal cross-section of columns under central compression (in Russian), Izv. VUZov, Stroit. i Arkhitekt. (1969), 2, 12 – 18.

    Google Scholar 

  83. Gusev, K.P., Optimal shape of an I-section of a steel column (in Russian), Stroit, Mekh. Rasch. Sooruzh. (1960), 1, 34 – 38.

    Google Scholar 

  84. Gwin, L.B., Taylor, R.F., A general method for flutter optimization, AIAA Journal 11(1973), 12, 1613 – 1617.

    ADS  MATH  Google Scholar 

  85. Gwin, L.B., Optimal aeroelastic design of an oblique wing structure, AIAA Paper No. 349 (1974).

    Google Scholar 

  86. Haftka, R.T., Parametric constraints with application to optimization for flutter using a continuous flutter constraint, AIAA Journal 13(1975), 4, 471 – 475.

    ADS  MATH  Google Scholar 

  87. Haftka, R.T., Starnes, J.H.Jr., Barton, F.W., Dixon, S.C., Comparison of two types of structural optimization procedures for flutter requirements, AIAA Journal 13(1975), 10, 1333 – 1339.

    ADS  Google Scholar 

  88. Hamayoshi, F., On the torsion of I-beam with variable web-height of second order, Proc. 10th Japan Nat. Congr. Appl. Mech. (1960), II – 18, 105 – 108.

    Google Scholar 

  89. Hancock, G.J., Local, distortional and lateral buckling of I-beams, Proc. ASCE, J. Struct. Div. 104(1978), ST11, 1787 – 1798.

    Google Scholar 

  90. Hemp, W.S., The theory of flat panels buckled in compression, Aero. Res. Council Rep. and Memo. 2178. June 1945.

    Google Scholar 

  91. Isabayev, Sh.L, Optimal dimensions of box-section of a beam under oblique bending (in Russian), Izv. VUZov, Stroit. i Arkhitekt. (1981), 1, 19 – 22.

    Google Scholar 

  92. Janiczek, R., Sciskana osiowo rura cienkoscienna o minimalnym ciezarze, Zesz. Nauk. Polit. Czestochowskiej, Nauki Podst. 6(1964), 51 – 72.

    Google Scholar 

  93. Juhas, P., Economical design of steel beams with account of stability of the web, 3rd Bulgar, Congr. Theor. Appl. Mech., Varna 1977, Vol. 1, 616 – 621.

    Google Scholar 

  94. Juhas, P., Optimalny navrh ocelovych nosnikov s prierezom i so zahrnutim vplyvu vybocovania steny., Stavebn. Cas. 26(1978), 8, 639 – 654.

    Google Scholar 

  95. Juhas, P., Optimalny navrh i prierezu ocelovych nosnikov pri uvazeni vplyvu vybocovania steny, Inz. Stavby 27(1979), 5, 221 – 228.

    Google Scholar 

  96. Kachanov, L.M., Lateral stability of a beam beyond the elastic limit (in Russian), Prikl. Mat. Mekh. 15(1951), 2, 195 – 206; 5, 637–641; 6, 762–764.

    Google Scholar 

  97. Kamenomostsky, A.I., Determination of minimal weight and optimal parameters of a stringer for channel section (in Russian), Dinam, Vynosl. i Nadezh. Avyats. Konstr. i Sistem, Moskva 1978, 2, 119 – 124.

    Google Scholar 

  98. Kappus, R., Drillknicken zentrisch gedrückter Stäbe mit offenem Profil im elastischen Bereich, Luftfahrtforschung 14(1937), 9, 444; NACA Tech. Memo. 851 (1938).

    Google Scholar 

  99. Kartvelishvili, V.M., Mironov, A.A., Optimization problems of effective torsional stiffness of nonuniformly heated and prestressed bars (in Russian), Izv. AN SSSR, Mekh. Tverd. Tela (1979), 5, 150 – 161.

    Google Scholar 

  100. Kiselev, V.G., Optimization of a thin-walled bar subject to forces and moments acting at its ends (in Russian), Mat. II Nauchn. Konf. Molodykh Uch., Gorky 1977, 1, 105 – 120.

    MathSciNet  Google Scholar 

  101. Klinov, S.I., Choice of optimal cross-sections of steel I-beams (in Russian), Metal. Konstr. i Ispyt. Sooruzh., Leningrad 1979, 115 – 123.

    Google Scholar 

  102. Klöppel, K., Scheer, J., Beulwerte ausgesteifter Rechteckplatten, H. Band, Ernst und Sohn, Berlin-München 1968.

    Google Scholar 

  103. Klöppel, K., Schmied, R., Schubert, J., Die Traglast mittig und aussermittig gedrückter dünnwandiger Kastenträger unter Verwendung der nichtlinearen Beultheorie, Stahlbau 35(1966), 11, 321 – 337;

    Google Scholar 

  104. Klöppel, K., Schmied, R., Schubert, J., Die Traglast mittig und aussermittig gedrückter dünnwandiger Kastenträger unter Verwendung der nichtlinearen Beultheorie, Stahlbau 38(1969), 1, 9 – 19; 3, 73 – 83.

    Google Scholar 

  105. Kluyev, B.N., On the problem of evaluation of optimal depth of steel beams with cylindrical X-shaped webs (in Russian), Arkhit. i Strait. 3, Alma — Ata 1974, 11 – 15.

    Google Scholar 

  106. Kochetov, V.P., Determination of minimal cross-sectional area of a column under central compression (in Russian), Strait. Mekh. Rasch. Sooruzh. (1978), 6, 62 – 68.

    Google Scholar 

  107. Koiter, W.T., Kuiken, G.D.C., The interaction between local buckling and overall buckling on the behaviour of built-up columns, Lab. Eng. Mech. Techn. Hogeschool Delft Rep. 447 (1971).

    Google Scholar 

  108. Koiter, W.T., Pignataro, M., An alternative approach to the interaction between local and overall buckling in stiffened panels, in [0.262], 133 – 148.

    Google Scholar 

  109. Koiter, W.T., Skaloud, M., Interventions, Comportement Postcritiqe des Plaques…, Mem. Soc. Roy. Sci. Liege 8(1962), 5, 64 – 68, 103 – 104.

    Google Scholar 

  110. Kolarov, I.G., Optimal design of a box section subject to bending and torsion (in Bulgarian), Godishnik Wis. Mash.-Elektr. Inst. 20(1966), 1, 29 – 36.

    Google Scholar 

  111. Kolarov, I., Optimal design of thin-walled beams (in Bulgarian), Stroitelstvo 17(1970), 11, 12 – 16.

    Google Scholar 

  112. Kolarov, L, Bestimmung der optimalen Querschnittsabmessungen doppel-symmetrischer Vollwandträger, Wiss. Z. Techn. Hochsch. Magdeburg (1976), 1, 51 – 55.

    Google Scholar 

  113. Kolarov, I., Evaluation of optimal dimensions of bisymmetric I-and box-sections under general bending (in Bulgarian), Mashinostr. 27(1978), 5, 213 – 219.

    Google Scholar 

  114. Kolarov, I., Zarvenkov, N., Bestimmung der optimalen Querschnitte von Vollwand-Kastenträgern, Hebezeuge und Fördermittel 3(1963), 7.

    Google Scholar 

  115. Krishnan, S., Cadambe, V., A note on the minimum weight design of a thin-walled stiffened rectangular cell subjected to torsion, J. Aero. Soc. India 7(1955), 3, 43 – 47.

    Google Scholar 

  116. Krishnan, S., Shetty, K.V., On the optimum design of an I-section beam, J. Aero/Space Sci. 26(1959), 9, 599 – 600.

    Google Scholar 

  117. Krzys, W., Optimum design of the box-section of a beam bent in elastic-plastic range, Bull. Acad. Pol. Sci., Ser. Sci. Techn. 12(1964), 5, 321 – 331 (English extensive summary);

    Google Scholar 

  118. Krzys, W., Optimum design of the box-section of a beam bent in elastic-plastic range, Zesz. Nauk. Polit. Krakowskiej (1966), 2, 39 – 50 (Polish full text).

    Google Scholar 

  119. Krzys, W., Optimale Formen gedrückter dünnwandiger Stützen im elastisch-plastischen Bereich, Wiss. Z. Techn. Univ. Dresden 17(1968), 2, 407 – 410.

    Google Scholar 

  120. Kulish, V.I., Korpan, P.P., Optimal design of thin-walled composite box-beams joined with a reinforced concrete plate (in Russian), Issled. Mostov. Konstr., Khabarovsk 1972, 125 – 137.

    Google Scholar 

  121. Lianis, G., Torsional creep buckling of open tubes having arbitrary cross-sections, School of Aero. Engng. Purdue Univ. Rep. No. 5 – 59 – 1, Dec. 1959.

    Google Scholar 

  122. Lindner, J., Mindeststeifigkeiten für den Kippsicherheitsnachweis beim Traglastverfahren, Bauingenieur 47(1972), 7, 238 – 240.

    Google Scholar 

  123. Lukhanin, V.E., Ryabchenko, V.M., Toporov, V.G., Weight optimization of thin-walled skeletal bars with nonlinear state diagrams of carrying elements (in Russian), Optim. Proekt. Avyats. Konstr., Kuybyshev 1973, 1, 101 – 110.

    Google Scholar 

  124. Lundquist, E.E., On the strength of columns that fail by twisting, J. Aero. Sci. 4(1937), 249.

    Google Scholar 

  125. Manandian, L.T., Determination of optimal parameters of a thin-walled column (in Russian), Izv. VUZov, Mashinostr. (1975), 7, 175 – 177.

    Google Scholar 

  126. Maquoi, R., Massonnet, Ch., Interaction between local plate buckling and overall buckling in thin-walled compression members — theories and experiments, in [0.262], 365 – 382.

    Google Scholar 

  127. Maquoi, R., Rondal, J., Optimum cross-sectional properties for unstiffened plate girders, Sec. Int. Coll. Stability of Steel Struct., Liege 1977, 155 – 156.

    Google Scholar 

  128. Martin, G., Optimierung kastenförmiger Querschnitte bei exzentrisch angreifenden Kräften, Konstruktion 17(1965), 12, 486 – 488.

    Google Scholar 

  129. Massonnet, Ch., Le flambage des barres a section ouverte et a parois minces, Homm. Fac. Sci. appl. Liége a l’occasion de sa centenaire (1947), Liege, Georges Thone.

    Google Scholar 

  130. Massonnet, Ch., Various approaches to optimal design of stiffened box girders, Rapp. Fin. 10th Congr. Int. Assoc. Bridge and Struct. Engng. Tokyo 1976, 161 – 163.

    Google Scholar 

  131. Massonnet, Ch., Zagadnienia inzynierskie statecznosci konstrukcji, in [0.288], 193 – 340.

    Google Scholar 

  132. Massonnet, Ch., Rondai, J., Le dimensionnement optimal des structures, Ann. Travaux Publ. Belgique 6(1976).

    Google Scholar 

  133. Matsui, K., On the optimum design of I-section beam subject to pure bending… Does the solution exist? (in Japanese), Toke Denki Dajgaku Rikogakubu kie 1(1979), 29 – 32.

    MathSciNet  Google Scholar 

  134. Mazurkiewicz, S., Zyczkowski, M., Optimum design of cross-section of thin walled bar under combined torsion and bending, Bull. Acad. Pol., Ser. Sci. Techn. 14(1966), 4, 273 – 281 (extensive english summary);

    Google Scholar 

  135. Mazurkiewicz, S., Zyczkowski, M., Optimum design of cross-section of thin walled bar under combined torsion and bending, Rozpr. Inz. 14(1966), 2, 199 – 213 (Polish full text).

    Google Scholar 

  136. McIntosh, S.C., Ashley, H., On the optimization of discrete structures with aeroelastic constraints, Computers and Structures 8(1978), 411 – 419.

    MATH  Google Scholar 

  137. Mcintosh, S.C., Eastep, F.E., Design of minimum-mass structures with specified stiffness properties, AIAA Journal 6(1968), 5, 962 – 964.

    ADS  Google Scholar 

  138. Meshcheryakov, V.B., On the problem of stability of thin-walled bars with variable cross-section subject to multiparameter loadings (in Russian), Tr. Mosk. Inst. Inzh. Zhel-Dor. Transp. 155(1962), 138 – 142.

    Google Scholar 

  139. Meyer, J.J., Neut, A., van der, The interaction of local buckling and column failure of imperfect thin-walled compression members, Report VTH-160, Dept. of Aero. Engng., Techn. Hogeschool Delft, 1970.

    Google Scholar 

  140. Mezhlumyan, R.A., Spatial stability of structures undergoing elastic-plastic deformations, (in Russian), Inzh. Sbornik 14(1953). 31 – 72.

    Google Scholar 

  141. Michell, A.G.M., Elastic stability of long beams under transverse forces, Phil. Mag. 48(1899), 298.

    Google Scholar 

  142. Mioduchowski, A., Thermann, K., Optimale Formen des dünnwandigen geschlossenen Querschnitts eines auf Biegung beanspruchten Balkens, Z. Angew. Math. Mechanik 53. (1973), 3, 193 – 198.

    MATH  Google Scholar 

  143. Muratov, A.F., On the problem of optimal design of a centrally compressed I-section column made of steels of various strengths (in Russian), Tr. Gorkov. Inzh.-Stroit. Inst. 67(1974), 93 – 102.

    Google Scholar 

  144. Nedovodeyev, V.Ya., Demokritov, V.N., Optimal design of continuous steel crane beams (in Russian), Issled. Optim. Metallokonstr. i Det. Podyemno-Transp. Mashin, Vol. 1 Kuybyshev 1976, 49 – 60.

    Google Scholar 

  145. Nelson, R.B., Felton, L.P., Thin-walled beams in frame synthesis, AIAA Journal 10(1972), 1565 – 1569.

    ADS  Google Scholar 

  146. Neut, A. van der, The sensitivity of thin-walled compression members to column axis imperfection, Int. J. Solids Structures 9. (1973), 999 – 1011.

    Google Scholar 

  147. Neut, A. van der, Mode interaction with stiffened panels, in [0.262], 117 – 132.

    Google Scholar 

  148. Nylander, H., Drehungsvorgänge und gebundene Kippung bei geraden, doppelt-symmetrischen I-Trägern, Ing. Vetenskaps Akad. Handlingar 174, Stockholm 1943.

    Google Scholar 

  149. Orel, F.N., On a certain algorithm of determination of optimal cross-sectional parameters of steel columns (in Russian), Izv. VUZov, Stroit. i Arkhit. (1976), 12, 19 – 24.

    Google Scholar 

  150. Oshchipko, L.J., Ivankiv, K.S., Application of geometric programming to weight optimization of thin-walled structures (in Ukrainian), Visnik Lwiw. Univ., Ser. Mekh.-Mat., 11(1976), 81 – 84, 128.

    Google Scholar 

  151. Ostenfeld, A., Politecknisk Laeranstalts Lab. for Bygningsstatik Meddelelse Nr. 5, København 1931.

    Google Scholar 

  152. Oziemski, S., Optymalizacja konstrukcji nosnych maszyn roboczych ciezkich, Przeglad Mechaniczny 10(1974), 339 – 343.

    Google Scholar 

  153. Pestriakov, V.P., Construction of an optimal design operator for an eccentrically compressed bar under stability constraint (in Russian) Tr. Gorkov. Inzh.-Stroit. Inst. 67(1974), 86 – 93.

    Google Scholar 

  154. Peterson, W.S., Minimum-cost design for corrugated containers under top-to-bottom compression, Techn. Assoc. Pulp Paper Ind. 63(1980), 2, 143 – 146.

    Google Scholar 

  155. Prandtl, L., Kipperscheinungen, Diss., Nürnberg 1899.

    Google Scholar 

  156. Proctor, A.N., A rational design of steel H-columns, Civil Eng. 16(1962), 9, 479 – 484.

    Google Scholar 

  157. Rajasekaran, S., Murray, D.W., Coupled local buckling in wide-flange beam-columns, Proc. ASCE, J. Struct. Div. 99(1973), ST6, 1003 – 1023.

    Google Scholar 

  158. Ramberg, W., Levy, S., Instability of extrusions under compressive loads, J. Aero. Sci. 12(1945), 485.

    Google Scholar 

  159. Rezvin, M.P., Ryabchenko, V.M., Optimization of stiffening rings by the method of generalized Lagrangian multipliers (in Russian), Vopr. Optimiz. Tonkost. Silov. Konstr. 3(1977), 21 – 27.

    Google Scholar 

  160. Richards, D.M., Optimum design of stiffened shear webs with supplementary skin stabilization, Int. J. Solids Structures 12(1976), 11, 791 – 802.

    Google Scholar 

  161. Rockey, K.C., Plate girder design — flange stiffness and web plate behaviour, Engineering 184(1957), 4789.

    Google Scholar 

  162. Rondal, J., Maquoi, R., Optimization of unstiffened hybrid I beams with stability constraints, Proc. Reg. Coll. Stability of Steel Struct., Budapest-Balatonfüred 1977, 373 – 382.

    Google Scholar 

  163. Rondal, J., Maquoi, R., Etude d’une gamme optimale de profils creux carrés et rectangulaires, Ann. Inst. Techn. Bât. Travaux Publ., Constr. Met. 91, 409(1982), 63 – 72.

    Google Scholar 

  164. Rondal, J., Maquoi, R., On the optimum design of square hollow compression members, in [0.296], 333 – 344.

    Google Scholar 

  165. Rosen, W.B., Analysis of ultimate strength and optimum proportions of multiweb wing structures, NACA TN 3633 (1956).

    Google Scholar 

  166. Rudisill, C.S., Bhatia, K.G., Optimization of complex structures to satisfy flutter requirements, AIAA Journal 9(1971), 8, 1487 – 1491.

    ADS  Google Scholar 

  167. Rutecki, J., Niestatecznosc preta cienkosciennego o otwartym przekroju z uwzglednieniem odksztalcenia profilu, Arch. Mech. Stos. 3(1951), 3/4, 437 – 460.

    MathSciNet  Google Scholar 

  168. Rutecki, J., Skrecanie cienkosciennych pretow zbieznych o stalej grubosci scianek, Arch. Mech. Stos. 7(1955), 2, 231 – 246.

    MATH  Google Scholar 

  169. Ryabchenko, V.M., Toporov, V.G., Lukhanin, V.E., On a certain algorithm of rational choice of nonlinearly deforming thin-walled skeletal bars (in Russian), Samoletostr. i Tekhn. Vozd. Flota 31(1973), 77 – 85.

    Google Scholar 

  170. Rzhanitsyn, A.R., Stability of thin-walled skeletal bars beyond the elastic limit (in Russian), Tr. Lab. Stroit. Mekh. CNIPS, Moskva 1949.

    Google Scholar 

  171. Saelman, B., A note on the optimum design of I-section beams, J. Aircraft 4(1967), 5, 477.

    Google Scholar 

  172. Schilling, C.S., Optimum properties for I-shaped beams, Proc. ASCE, J. Struct. Div. 100(1974), ST12, 2385 – 2401.

    Google Scholar 

  173. Schlechte, E., Die günstigste Wanddicke des mittig gedrückten einteiligen Stabes aus Stahl mit einfachsymmetrischen offenem Querschnitt, Bauplanung – Bautechnik, 14(1960), 10, 461 – 466.

    Google Scholar 

  174. Schlechte, E., Goeben, H.E., Untersuchungen über die Wahl statisch günstiger einteiliger Stabquerschnitte für Fachwerk-konstruktionen, Wiss. Z. Hochsch. Bauwesen Leipzig 11(1965), 1, 41 – 50.

    Google Scholar 

  175. Schleusner, B.A., Kippsicherheit eines gleichmässig belasteten Trägers mit linear veränderlicher Hohe, Stahlbau 22(1953), 3.

    Google Scholar 

  176. Schuette, E.H., McCulloch, J.C., Charts for the minimum weight design of multiweb wings in bending, NACA TN 1323 (1947).

    Google Scholar 

  177. Seyranian, A.P., Problem of minimum weight design of a wing under the constraint of divergence speed (in Russian), Uch. Zap. Centr. Aero-Gidrodin. Inst. 10(1979), 6, 81 – 89.

    Google Scholar 

  178. Seyranian, A.P., Sensitivity analysis and optimization of characteristics of aeroelastic stability (in Russian), Inst. Problem Mekh. AN SSSR, Preprint No. 162(1980), 58 pp.

    Google Scholar 

  179. Shanley, F.R., Optimum design of eccentrically loaded columns, Proc. ASCE, J. Struct. Div. 93(1967), ST4, 201 – 226.

    Google Scholar 

  180. Sofronov, Yu.D., Minimum weight design of beams with respect to lateral stability (in Russian), Tr. Kazan Avyats. Inst. 168(1974), 34 – 43.

    Google Scholar 

  181. Solovev, E.G., Suchkov, V.N., Optimal design of statically indeterminate thin-walled beams for postbuckling behaviour of walls due to shear (in Russian), Issled. po Teorii Plastin i Obol. 9(1972), Kazan, 303 – 316.

    Google Scholar 

  182. Solovev, E.G., Suchkov, V.N., Optimal design of thin-walled skeletal structures of maximal stiffness with stability of elements taken into account (in Russian), Prochnost i Zhestkost Tonkost. Konstr., Leningrad 1975, 187 – 193.

    Google Scholar 

  183. Solovev, E.G., Suchkov, V.N., Minimal weight design of thin-walled skeletal structures allowing for strength and stability of elements (in Russian), Stroit. Mekh., Leningrad 1975, 138 – 145.

    Google Scholar 

  184. Spunt, L., Weight optimization of the postbuckled integrally stiffened wide column, J. Aircraft 7(1970), 4, 330 – 333.

    Google Scholar 

  185. Spunt, L., A dimensionless programming approach to optimal structural design, AIAA Paper 344 (1973).

    Google Scholar 

  186. Spunt, L., A programming approach to optimal structural design using structural indices, AIAA Journal 12(1974), 6, 865 – 868.

    ADS  Google Scholar 

  187. Srinivasa, C.N., Optimum properties for I beams with varying degrees of lateral restraint, J. Inst. Eng. India, Civ. Eng. Div. 59(1978), 1, 43 – 45.

    Google Scholar 

  188. Strasser, G., Optimization of multiweb beams under combined bending and torsional loading, J. Aero/Space Sci. 25(1958), 8, 529.

    Google Scholar 

  189. Studnicka, J., Mistni a celkova stabilita tlacenych prutu, Stav. Cas. 28(1980), 8, 587 – 598.

    Google Scholar 

  190. Studnicka, J., Mistni a celkova stabilita ohybanych prutu, Stav. Cas. 28(1980), 11, 813 – 825.

    Google Scholar 

  191. Svensson, S.E., Croll, J.G.A., Interaction between local and overall buckling, Int. J. Mech. Sci. 17(1975), 4, 307 – 321.

    MATH  Google Scholar 

  192. Szymczak, Cz., Optymalizacja sciskanych osiowo pretow cienkosciennych, Zesz. Nauk. Polit. Gdanskiej 294, Bud. Lad. 32 (1978), 43 – 50.

    Google Scholar 

  193. Szymczak, Cz., Optymalne ksztaltowanie pretow cienkosciennych o bisymetrycznym przekroju dwuteowym z uwagi na wartosci wlasne, Zesz. Nauk. Polit. Gdanskiej 322, Bud. Lad. 35 (1980), 86 pp.

    Google Scholar 

  194. Szymczak, Cz., On torsional buckling of thin walled I columns with variable cross-section, Int. J. solids Structures 19(1981), 6, 509 – 518.

    Google Scholar 

  195. Skaloud, M., Interaktion der Ausbeulung von Wänden und der gesammten Formänderung gedrückter und gebogener Stäbe, Acta Techn. CSAV 7(1962), 1, 52 – 86.

    Google Scholar 

  196. Skaloud, M., Naprstek, J., Limit state of thinrwalled steel columns, Rozpravy CSAV, Rada Techn. Ved 87(1977), 2, 146 pp.

    Google Scholar 

  197. Thompson, J.M.T., Hunt, G.W., Dangers of structural optimization, J. Eng. Optimiz. 1(1974), 2, 99 – 110.

    Google Scholar 

  198. Thompson, J.M.T., Lewis, G.M., On the optimum design of thin-walled compression members, J. Mech. Phys. Solids 20(1972), 2, 101 – 109.

    ADS  Google Scholar 

  199. Timoshenko, S.P., Lateral buckling of beams (in Russian), Bull. St. Petersburg Inst. 45(1905 – 1906).

    Google Scholar 

  200. Toakley, A.R., Williams, D.G., The optimum design of stiffened panels subject to compression loading, J. Eng. Optimiz. 2(1977), 4, 239 – 250.

    Google Scholar 

  201. Tolmachev, K.Kh., Ishchenko, Z.B., Lanin, A.I., Application of nonlinear programming to minimum mass design of beams (in Russian), Izv. VUZov, Stroit. i Arkhit. (1979), 9, 106 – 109.

    Google Scholar 

  202. Tvergaard, V., Influence of post-buckling behaviour on optimum design of stiffened panels, Int. J. Solids Structures 9(1973), 12, 1519 – 1534.

    MATH  Google Scholar 

  203. Tvergaard, V., Needleman, A., Mode interaction in an eccentrically stiffened elastic-plastic panel under compression, in [0.262], 160 – 171.

    Google Scholar 

  204. Usami, T., Fukomoto, Y., Local and overall buckling of welded box sections, Proc. ASCE, J. Struct. Div. 108(1982), 525 – 542.

    Google Scholar 

  205. Usanov, S.I., Optimal I-section of steel columns under eccentric and central compression (in Russian), Prochnost i Ustoych. Inzh. Konstr., Barnaul 1978, 1, 80 – 86.

    Google Scholar 

  206. Vakhurkin, V.M., Design procedure for rational cross-sections of asymmetric I-columns under eccentric compression (in Russian), Mat. po Stalnym Konstr. (1957), 1, 54–63

    Google Scholar 

  207. Vasilenkov, F.B., Tumanov, B.A., Choice of optimal cross-sections and weight characteristics of steel I-beams (in Russian), Izv. VUZov, Stroit. i Arkhit. (1975), 3, 7–11.

    Google Scholar 

  208. Venkov, L., Optimal dimensioning of centrally compressed elements, consisting of composed I-sections (in Bulgarian), Stroitelstvo 23(1976), 3, 13–15, 22.

    Google Scholar 

  209. Vlasov, V.Z., Torsion and stability of thin-walled profiles (in Russian), Stroit. Promyshlennost (1938), 6.

    Google Scholar 

  210. Vlasov, V.Z., Torsion, stability and vibration of thin-walled bars (in Russian), Prikl. Mat. Mekh. 3(1939), 1, 3–30.

    Google Scholar 

  211. Volkersen, O., Ein Beitrag zum optimalen Bemessen von axial gedrückten Rohren und Integralplatten, VDI-Zeitschrift 108(1966), 26, 1281–1284.

    Google Scholar 

  212. Wagner, H., Verdrehung und Knickung von offenen Profilen, Festschrift 25 Jahre Technische Hochsch. Danzig, Kafermann 1929, 329; English transl.: NACA Tech. Memo. 807(1936).

    Google Scholar 

  213. Wanke, J., Wirtschaftliche Bemessung von Vollwandträgern mit parallelen Gurten, Stahlbau 36(1967), 11, 344–348.

    Google Scholar 

  214. Wilde, P., The torsion of thin-walled bars with variable cross-section, Arch. Mech. Stos. 20(1968), 4, 431–443.

    MATH  Google Scholar 

  215. Yoshida, H., Maegawa, K., The optimum cross section of channel columns, Int. J. Mech. Sci. 21(1979), 3, 149–160.

    MATH  Google Scholar 

  216. Young, J. McH., Landau, R.E., A rational approach to the design of deep plate girders, Proc. Inst. Civil Engrs., 4(1955), 3, 299–335.

    Google Scholar 

  217. Zapolsky, N.N., Andryienko, N.N., Galaktinov, E.Ts., Optimal design of telescopic crane jibs of rectangular cross-section (in Russian), Stroit. i Dorozhn. Mashiny (1976), 3, 23–25.

    Google Scholar 

  218. Zyczkowski, M., The “onefold optimum approximation” and some of its applications in mechanics, Bull. Acad. Pol., Ser. Sci. techn. 11(1963), 6 199–208 (extensive English summary);

    Google Scholar 

  219. Zyczkowski, M., The “onefold optimum approximation” and some of its applications in mechanics, Rozpr. Inz. 11(1963), 3, 463–490 (Polish full text).

    MATH  Google Scholar 

  220. Zyczkowski, M., Optymalne ksztaltowanie wytrzymalosciowe przy uwzglednieniu warunkow statecznosci, in [0.11], 466–555.

    Google Scholar 

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Gajewski, A., Zyczkowski, M. (1988). Thin-Walled Bars. In: Optimal Structural Design under Stability Constraints. Mechanics of Elastic Stability, vol 13. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2754-4_9

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