Аннотації
25.06.2018
Представлено дослідження стійкості сталевих портальних рам з двотаврів зі змінною висотою стінки. Залежно від жорсткості вузлів і умов закріплення елементів в рамах досліджено стійкість колон. Пропонується підхід для визначення стійкості рам через стійкість колон на пружних опорах. Жорсткість вузлів і пружність опор визначається із статичного розрахунку рами. Розглянуто п'ять різних випадків стійкості пружних стрижнів при різних крайових умов закріплення колон на пружних опорах. Проведено чисельні дослідження коефіцієнтів розрахункової довжини елементів портальних рам при змінності перерізу і жорсткості колон. Розвинений підхід до визначення стійкості елементів рам з площини рам залежно від піддатливості системи в'язів, проведений аналіз стійкість будівлі з комп'ютерним моделюванням і з обчисленням коефіцієнтів стійкості, фактору впливу системи в'язів рами на стійкість ригелів з площини портальних рам.
Представлено исследование устойчивости стальных портальных рам из двутавров с переменной высотой стенки. В зависимости от жесткости узлов и условий закрепления элементов в рамах исследована устойчивость колонн. Предлагается подход для определения устойчивости рам через устойчивость колонн на упругих опорах. Жесткость узлов и упругость опор определяется из статического расчета рамы. Рассмотрено пять различных случаев устойчивости упругих стержней при различных краевых условий закрепления колон на упругих опорах. Приведены численные исследования коэффициентов расчетной длины элементов портальных рам при переменности сечения и жесткости колонн. Развит подход к определению устойчивости элементов рам из плоскости рам в зависимости от податливости системы связей, проведен анализ устойчивость здания с компьютерным моделированием и с вычислением коэффициентов устойчивости, фактора влияния системы связей рамы на устойчивость ригелей из плоскости портальных рам.
Presented is the research of the stability of portal frames made of variable I cross-sections, depending on supports fastening factors and frames elements unfastening. In the process of mathematical research examined were five different cases of fixing columns nodes of portal frames resiliently mounted in each case, the stability criteria having been defined. In addition, conducted were studies to determine the coefficients of the portal frames elements effective length calculation in finding critical load on the column. Coefficients of the effective length factor of the welded variable I cross-section columns have been obtained. The influence of brace systems on stiffening of the whole structure, stability of the unit frames as well as the overall stability of the building with computer simulation and calculation have been studied, the coefficients of the influence of the frame structure on the stability of the unit frames having been obtained.
1. Bazhenov V.A. Budivelna mekhanika i teoriia sporud. Narysy z istorii (Construction mechanics and the theory of structures. Essays on history) / V.A. Bazhenov, Yu.V. Vorona, A.V. Perelmuter. – K.: Karavela, 2016. – 428 p. (in Ukrainian)2. Al-Sadder, S.Z. (2004). “Exact expressions for stability functions of a general non-prismatic beam-column member”). Journal of Constructional Steel Research, Vol. 60, No. 11, pp. 1561–1584. 3. Al-Sarraf, S.Z. (1979). “Elastic instability of frames with uniformly tapered members.”).Structural Engineer, Vol. 57, No. 13, pp. 18–24.4. Arbabi, F. and Li, F. (1991). “Buckling of variable cross-section columns: integral-equation approach.”). Journal of Structural Engineering, Vol. 117, No. 8, pp. 2426–2441, DOI: 10.1061/(ASCE)0733-9445(1991) 117:8(2426).CrossRef5. Avraam, T. P. and Fasoulakis, Z.C. (2013). “Nonlinear postbuckling analysis of frames with varying cross-section columns.”). Engineering Structures, Vol. 56, pp. 1–7, DOI: 10.1016/j.engstruct.2013.04.010.CrossRef6. Bilyk S.I. Effective length of elements of steel frames from developed I-beams with variable height of wall / S.I. Bilyk // Strength of materials and theory of structures. - K.: Budivelnik, 1989. - Vip. 55. - P. 93-96.7. Bilyk S. I. Stability analysis of bisymmetrical tapered I-beams / S. I. Bilyk // Progress in Steel, Composite and Aluminium Structures Proceeding of the XI international conference on metal structures (ICMS–2006): Pzeszow, Poland, 21–23 June 2006-p. – Pzeszow, 2006. – С.254–255.8. Leites SD Stability of elastic fixed compressed bars, the stiffness of which varies according to a power law / Leites S.D. // Materials on metal structures. - M .: Stroyizdat, 1973. - Vol. 17. - P. 127-148.9. Banerjee, J.R. (1987). “Compact computation of buckling loads for plane frames consisting of tapered members.” Advances in Engineering Software, Vol. 9, No. 3, pp. 162–170. 10. Bazhenov V. The heterogeneous prismatic finite element with variable crosssectional area and taking into account the variability of components of metric tensor / V. Bazhenov, А. Shkril’, S.Piskunov, D.Bogdan // Strength of Materials and Theory of Structures. – 2010. – Issue. 85. – P. 3- 22.11. Bazeos, N. and Karabalis, D. L. (2006). “Efficient computation of buckling loads for plane steel frames with tapered members.”). Engineering Structures, Vol. 28, No. 5, pp. 771–775, DOI: 10.1016/j.engstruct. 2005.10.004.CrossRef12. Bleich, F. (1952). Buckling strength of metal structures (1st ed.), McGraw Hill Text.13. Bulut, G. (2013). “Effect of taper ratio on parametric stability of a rotating tapered beam.”).European Journal of Mechanics- A/Solids, Vol. 37, pp. 344–350. 14. Chan, S. L. (1990). “Buckling analysis of structures composed of tapered members.”). Journal of Structural Engineering, Vol. 116, No. 7, pp. 1893–1906. 15. Chen, W.F. and Lui, E. M. (1991). Stability Design of Steel Frames (1st ed.), CRC Press. CRC Press, 1991. P.39416. Coşkun, S.B. and Atay, M.T. (2009). “Determination of critical buckling load for elastic columns of constant and variable cross-sections using variational iteration method.”).Computers and Mathematics with Applications, Vol. 58, No. 11–12, pp. 2260–2266. 17. Dynnyk A. Using Bessel functions for tasks The theory of elasticity. Part 2: vibration theory/ AN Dynnyk. - Ekaterynoslav: Printing house E. I. Kogan, 1915. - 137 p.18. Dynnyk A.N. Longitudinal bending and its application in engineering / AN Dynnyk, VN Leskov. - Kharkiv-Dnipropetrovsk: Tech. published., 1932. - 164 p.19. Dynnyk A. Stability of elastic systems / A.N. Dynnyk . - M .: ONTI, 1935. -183 p.20. Eisenberger, M. and Reich, Y. (1989). “Static, vibration and stability analysis of non-uniform beams.”). Computers and Structures, Vol. 31, No. 4, pp. 567–573. 21. Ermopoulos, J.C. (1986). “Buckling of tapered bars under stepped axial loads.”). Journal of Structural Engineering, Vol. 112, No. 6, pp. 1346–1354. 22. Ermopoulos, J.C. (1988). “Slope-deflection method and bending of tapered bars under stepped loads.”). Journal of Constructional Steel Research, Vol. 11, No. 2, pp. 121–141.23. Ermopoulos, J.C. (1997). “Equivalent buckling length of non-uniform members.”). Journal of Constructional Steel Research, Vol. 42, No. 2, pp. 141–158. 24. Ermopoulos, J.C. (1999). “Buckling length of non-uniform members under stepped axial loads.”). Computers and Structures, Vol. 73, No. 6, pp. 573–582.25. Ermopoulos, J.C. and Kounadis, A. N. (1985). “Stability of frames with tapered built-up members.”). Journal of Structural Engineering, Vol. 111, No. 9, pp. 1979–1992. 26. Euler, L. (1778). Die altitudinecolomnarum sub proprioponderecorruentium, Acta Academiae Scienti arum Imperialis Petropolitan (in Latin).27. Fraser, D.J. (1983). “Design of tapered member portal frames.”). Journal of Constructional Steel Research, Vol. 3, No. 3, pp. 20–26. 28. Galambos, T.V. Surovek А. Structural stability of steel: concepts and applications for structural engineers / Theodore Galambos, Andrea Surovek./ Copyright © 2008 John Wiley & Sons, Inc. P.373.29. Gere, J.M. and Carter, W.O. (1962). “Critical buckling loads for tapered columns.”). Journal of the Structural Division, Vol. 88, No. 1, pp. 1–12.30. Huang, Y. and Li, X.-F. (2010). “A new approach for free vibration of axially functionally graded beams with non-uniform cross-section.”). Journal of Sound and Vibration, Vol. 329, No. 11, pp. 2291–2303. 31. Huang, Y. and Li, X.-F. (2011). “Buckling analysis of nonuniform and axially graded columns with varying flexural rigidity.”). Journal of Engineering Mechanics, Vol. 137, No. 1, pp. 73–81. 32. Iremonger, M.J. (1980). “Finite difference buckling analysis of nonuniform columns.”).Computers and Structures, Vol. 12, No. 5, pp. 741–748. 33. Karabalis, D.L. and Beskos, D.E. (1983). “Static, dynamic and stability analysis of structures composed of tapered beams.”). Computers and Structures, Vol. 16, No. 6, pp. 731–748. 34. Konstantakopoulos, T.G., Raftoyiannis, I.G., and Michaltsos, G.T. (2012). “Stability of steel columns with non-uniform cross-sections.”). The Open Construction and Building Technology Journal, Vol. 6, pp. 1–7.35. Kounadis, A.N. and Ermopoulos, J.C. (1984). “Postbuckling analysis of a simple frame with varying stiffness.”). ActaMechanica, Vol. 54, No. 1, pp. 95–105. 36. Lee, B.K., Carr, A.J., Lee, T.E., and Kim, I..J. (2006). “Buckling loads of columns with constant volume.”). Journal of Sound and Vibration, Vol. 294, Nos. 1–2, pp. 381–387. 37. Li, G.Q. and Li, J.J. (2004). “Buckling analysis of tapered lattice columns using a generalzed finite element.” Communications in Numerical Methods in Engineering, Vol. 20, No. 5, pp. 479–488. 38. Li, G.Q. and Li, J.J. (2000). “ "Effects of shear deformation on the effective length of tapered columns with I-section for steel portal frames.”). Structural Engineering and Mechanics, Vol. 20, pp. 479–489. 39. Li, Q.S. (2000). “Buckling of elastically restrained non-uniform columns.”). Engineering Structures, Vol. 22, No. 10, pp. 1231–1243. 40. Li, Q.S. (2003). “Buckling analysis of non-uniform bars with rotational and translational springs.”). Engineering Structures, Vol. 25, No. 10, pp. 1289–1299 .41. Marques, L., Taras, A., Simões da Silva, L., Greiner, R., and Rebelo, C. (2012). “Development of a consistent buckling design procedure for tapered columns.”). Journal of Constructional Steel Research, Vol. 72, pp. 61–74. 42. O’Rourke, M. and Zebrowski, T. (1977). “Buckling load for non-uniform columns.” Computers and Structures, Vol. 7, No. 6, pp. 717–720. 43. Ozay, G. and Topcu, A. (2000). “Analysis of frames with non-prismatic members.”). Canadian Journal of Civil Engineering, Vol. 27, No. 1, pp. 17–25.44. Qiusheng, L., Hong, C., and Guiqing, L. (1995). “Stability analysis of bars with varying cross-section.” International Journal of Solids and Structures, Vol. 32, No. 21, pp. 3217–3228.45. Raftoyiannis, I.G. (2005). “The effect of semi-rigid joints and an elastic bracing system on the buckling load of simple rectangular steel frames.”). Journal of Constructional Steel Research, Vol. 61, No. 9, pp. 1205–1225. 46. Rezaiee-Pajand, M. Shahabian, F., Bambaeechee, M. Stability of non-prismatic frames with flexible connections and elastic supports. KSCE Journal of Civil Engineering March 2016, Volume 20, No. 2, pp 832–846.47. Saffari, H., Rahgozar, R., and Jahanshahi, R. (2008). “An efficient method for computation of effective length factor of columns in a steel gabled frame with tapered members.”). Journal of Constructional Steel Research, Vol. 64, No. 4, pp. 400–406. 48. Seyranian, A.P., Elishakoff, I. Modern Problems of Structural Stability. Springer Science & Business Media, 2003. Р. 394.49. Shooshtari, A. and Khajavi, R. (2010). “An efficient procedure to find shape functions and stiffness aatrices of nonprismaticeuler-bernoulli and timoshenko beam elements.”). European Journal of Mechanics A-Solids, Vol. 29, No. 5, DOI: 10.1016/j.euromechsol.2010.04.003.50. Siginer, A. (1992). “Buckling of columns of variable flexural rigidity.” Journal of Engineering Mechanics, Vol. 118, No. 3, pp. 640–643. 51. Smith, W.G. (1988). “Analytic solutions for tapered column buckling.”). Computers and Structures, Vol. 28, No. 5, pp. 677–681. 52. Taha, M. and Essam, M. (2013). “Stability behavior and free vibration of tapered columns with elastic end restraints using the DQM method.”). Ain Shams Engineering Journal, Vol. 4, No. 3, pp. 515–52153. Timoshenko, S. P. (1908). Buckling of bars of variable cross section, Bulletin of the Polytechnic Institute, Kiev, Ukraine.54. Timoshenko, S. P. and Gere, J. M. (2009). Theory of elastic stability, Dover Publications.55. Su L., Attard M. In plan stabilitiof variable cross-section columns with shear deformations/ From Materials to Structures: Advancement through Innovation/ CRC Press, p.207-21256. Valipour, H.R. and Bradford, M.A. (2012). “A new shape function for tapered three-dimensional beams with flexible connections.”). Journal of Constructional Steel Research, Vol. 70, pp. 43–50, DOI: 10.1016/ j.jcsr.2011.10.006.CrossRef57. Wang, C.K. (1967). “Stability of rigid frames with nonuniform members.”). Journal of the Structural Division, Vol. 93, No. 1, pp. 275–294.58. Wang, C.M. and Wang, C.Y. (2004). Exact Solutions for Buckling of Structural Members (1st ed.), CRC Press. Р. 224 CRC Press, 2004. P. 224 .59. Wei, D.J., Yan, S.X., Zhang, Z.P., and Li, X.F. (2010). “Critical load for buckling of non-prismatic columns under self-weight and tip force.”). Mechanics Research Communications, Vol. 37, No. 6, pp. 554–558.60. Bilyk S., TonkacheievV. / Determining sloped load limits inside von mises’ truss with elastic support/Journal Materiali in tehnologije / Materials and Technology/. Volume 52, N0.2, Mar.-Apr. 2018.pp. 105-110.doi:10.17222/mit.2016.08361. Bilyk S. Determination of critical load of elastic steel column based on experimental data // Підводні технології. Промислова та цивільна інженерія. міжнар. наук.-вироб. журн. К., КНУБА, Вип.04/2016, С.89-96. library.knuba.edu.ua/books/zbirniki/12/201604.pdf62. ANSYS Mechanical User’s Guide/ ANSYS, Inc.,2013 – pp.192-196.