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A computer program for linear analysis of two-dimensional semi-rigid frames

Yıl 2022, Cilt 13, Sayı 2, 351 - 358, 28.06.2022
https://doi.org/10.24012/dumf.1087793

Öz


It is usual to assume that a displacement caused at any point in a structure is linearly dependent on the magnitude of the loads applied. This paper focuses on the linear analysis of 2-D frames with flexural connected beam-column members considering shear displacements. A computer program was written in MATLAB for this purpose. To achieve the above purpose, first, the element stiffness matrix with linear flexural springs at its ends has been obtained by using relevant differential equations, considering shear deformations. In the analysis of the stiffness methods, it has been observed that the loading vector can be obtained by means of the loads applied between the joint points. It is found that the presents of an axial load in a member affect the values of the fixed-end forces, and these are the subject of another paper. For linear cases, the semi-rigid end forces have been obtained for a uniformly distributed load, an unsymmetrical point load, a linearly distributed load, an unsymmetrical trapezoidal distributed load, and an unsymmetrical triangular distributed load. To prove the validity of the computer program, some problems in the literature have been solved differently. There was a good agreement between the relevant results.

Kaynakça

  • [1] Görgün,H., “Semi-rigid Behaviour of Connections in Precast Concrete Structures” University of Nottingham (1997), Ph.D. Thesis.
  • [2] A. R. Monforton, and T. S. Wu, “Matrix analysis of semi-rigidly connected frames”, Journal of Structural Division, ASCE, 1963, 89, pp. 13-42.
  • [3] R. K Livesley, “Matrix methods of structural analysis”, Permagon Press, Inc., 1964, New York, N.Y.
  • [4] K. M. Romstad, and C. V. Subramanian, "Analysis of Frames with Partial Connection Rigidity", Journal of Structural Division, ASCE, 96, pp. 2283-2300, November, 1970.
  • [5] M. R. Ackroyd. and K. H: Gerstle, "Elastic Stability of Flexibly Connected Frames", Journal of Structural Engineering, ASCE, Vol. 109, No. 1, pp. 241-245, January, 1983.
  • [6] T. W. Stelmack, M.J. Marley, and K. R: Gerstle, "Analysis and Tests of Flexibly Connected Steel Frames", Journal of Structural Engineering, ASCE, Vol. 112, No. 7, pp. 1573-1588, July, 1986.
  • [7] C. R. Yu, and N. E: Shanmugam, "Stability of Frames with Semi-Rigid Joints", Comput. Struct., Vo1. 23, No. 5, pp. 639-648, 1986.
  • [8] R. Cunnigham, "Some Aspects of Semi-Rigid Connections in Structural Steelwork", The Structural Engineer, Vol. 68, No. 5, pp.85-92, March, 1990.
  • [9] A. Azizinamini, and J. B. Radziminski, "Static and Cyclic Performance of Semi-Rigid Steel Beam-To-Column Connections", Journal of Structural Engineering, ASCE, Vol. 115, No.12, pp. 2979-2999, December, 1989.
  • [10] O. Aksogan, and F. Akkaya, "A Computer Program for the Analysis of Flexibly Connected Frames", Ç.Ü J.Fac.EngArch., Vol. 6, No. 2, pp.25-41, December, 1991.
  • [11] O. Aksogan, and H. Görgün, "The Nonlinear Analysis of Planar Frames Composed of Flexibly Connected Members", Ç.Ü J. Fac. Eng. Arch., Vol. 8, No. 2, pp.117-129, December, 1993.
  • [12] O. Aksogan, S. S. Akavcı,. and H. Görgün, "Analysis of Frames with Flexible Connections", Ç. Ü J. Fac. .Eng. Arch., Vol. 20, No. 1, pp.1-11, June, 2005.
  • [13] H. Erdem, “Yarı Rijit Bağlantılı ve Rijit Uc Bölgeli Düzlemsel Cercevelerin Nonlineer Analizi”, Turkish J. Eng. Env. Sci. 26, 2001, pp. 209–218.
  • [14] H. Görgün, O. Aksogan, and S. Yılmaz, “The linear analysis of planar frames composed of flexibly connected members taking shear deformations into consideration” Çukurova Üniversitesi, Mühendislik-Mimarlık Fakültesi Dergisi, 2008, 23, 1, pp:1-14.
  • [15] J. D. Aristizabal-Ochoa, “Matrix method for stability and second-order analysis of Timoshenko beam-column structures with semirigid connections”, Eng. Struct., 34, 2012, pp. 289-302.
  • [16] D. De Domenico, Giovanni F. and R. Laudanib. “Probability-based structural response of steel beams and frames with uncertain semi-rigid connections” Structural Engineering and Mechanics, 2018, Vol. 67, No. 4, pp. 439-455.
  • [17] M. Artar and A. T. Daloğlu, “Optimum design of composite steel frames with semi-rigid connections and column bases via genetic algorithm”, Steel and Composite Structures, 2015, Vol. 19, No. 4 pp. 1035-1053.
  • [18] A. N. T .Ihaddoudènea, M. Saidanib, and J. P. Jaspartc, “Mechanical model for determining the critical load of plane" frames with semi-rigid joints subjected to static loads”, Engineering Structures,145, pp. 109-117.
  • [19] M. Ghassemieh,; M. Baei; A. Kari, A. Goudarzi, and D. F. Laefer “Adopting flexibility of the end-plate connections in steel moment frames”, Steel and Composite Structures,18, 5, pp:1215-1237.
  • [20] B Du, W Jiang, Z He, Z Qi, C Zhang- “Development of a modified low-cycle fatigue model for semi-rigid connections in precast concrete frames”, Journal of Building Engineering, Volume 50, 1 June 2022.

Linear analysis of two-dimensional semi-rigid frames

Yıl 2022, Cilt 13, Sayı 2, 351 - 358, 28.06.2022
https://doi.org/10.24012/dumf.1087793

Öz

It is usual to assume that a displacement caused at any point in a structure is linearly dependent on the magnitude of the loads applied. This paper focuses on the linear analysis of 2-D frames with flexural connected beam-column members considering shear displacements. A computer program was written in MATLAB for this purpose. To achieve the above purpose, first, the element stiffness matrix with linear flexural springs at its ends has been obtained by using relevant differential equations, considering shear deformations. In the analysis of the stiffness methods, it has been observed that the loading vector can be obtained by means of the loads applied between the joint points. It is found that the presents of an axial load in a member affect the values of the fixed-end forces, and these are the subject of another paper. For linear cases, the semi-rigid end forces have been obtained for a uniformly distributed load, an unsymmetrical point load, a linearly distributed load, an unsymmetrical trapezoidal distributed load, and an unsymmetrical triangular distributed load. To prove the validity of the computer program, some problems in the literature have been solved differently. There was a good agreement between the relevant results.

Kaynakça

  • [1] Görgün,H., “Semi-rigid Behaviour of Connections in Precast Concrete Structures” University of Nottingham (1997), Ph.D. Thesis.
  • [2] A. R. Monforton, and T. S. Wu, “Matrix analysis of semi-rigidly connected frames”, Journal of Structural Division, ASCE, 1963, 89, pp. 13-42.
  • [3] R. K Livesley, “Matrix methods of structural analysis”, Permagon Press, Inc., 1964, New York, N.Y.
  • [4] K. M. Romstad, and C. V. Subramanian, "Analysis of Frames with Partial Connection Rigidity", Journal of Structural Division, ASCE, 96, pp. 2283-2300, November, 1970.
  • [5] M. R. Ackroyd. and K. H: Gerstle, "Elastic Stability of Flexibly Connected Frames", Journal of Structural Engineering, ASCE, Vol. 109, No. 1, pp. 241-245, January, 1983.
  • [6] T. W. Stelmack, M.J. Marley, and K. R: Gerstle, "Analysis and Tests of Flexibly Connected Steel Frames", Journal of Structural Engineering, ASCE, Vol. 112, No. 7, pp. 1573-1588, July, 1986.
  • [7] C. R. Yu, and N. E: Shanmugam, "Stability of Frames with Semi-Rigid Joints", Comput. Struct., Vo1. 23, No. 5, pp. 639-648, 1986.
  • [8] R. Cunnigham, "Some Aspects of Semi-Rigid Connections in Structural Steelwork", The Structural Engineer, Vol. 68, No. 5, pp.85-92, March, 1990.
  • [9] A. Azizinamini, and J. B. Radziminski, "Static and Cyclic Performance of Semi-Rigid Steel Beam-To-Column Connections", Journal of Structural Engineering, ASCE, Vol. 115, No.12, pp. 2979-2999, December, 1989.
  • [10] O. Aksogan, and F. Akkaya, "A Computer Program for the Analysis of Flexibly Connected Frames", Ç.Ü J.Fac.EngArch., Vol. 6, No. 2, pp.25-41, December, 1991.
  • [11] O. Aksogan, and H. Görgün, "The Nonlinear Analysis of Planar Frames Composed of Flexibly Connected Members", Ç.Ü J. Fac. Eng. Arch., Vol. 8, No. 2, pp.117-129, December, 1993.
  • [12] O. Aksogan, S. S. Akavcı,. and H. Görgün, "Analysis of Frames with Flexible Connections", Ç. Ü J. Fac. .Eng. Arch., Vol. 20, No. 1, pp.1-11, June, 2005.
  • [13] H. Erdem, “Yarı Rijit Bağlantılı ve Rijit Uc Bölgeli Düzlemsel Cercevelerin Nonlineer Analizi”, Turkish J. Eng. Env. Sci. 26, 2001, pp. 209–218.
  • [14] H. Görgün, O. Aksogan, and S. Yılmaz, “The linear analysis of planar frames composed of flexibly connected members taking shear deformations into consideration” Çukurova Üniversitesi, Mühendislik-Mimarlık Fakültesi Dergisi, 2008, 23, 1, pp:1-14.
  • [15] J. D. Aristizabal-Ochoa, “Matrix method for stability and second-order analysis of Timoshenko beam-column structures with semirigid connections”, Eng. Struct., 34, 2012, pp. 289-302.
  • [16] D. De Domenico, Giovanni F. and R. Laudanib. “Probability-based structural response of steel beams and frames with uncertain semi-rigid connections” Structural Engineering and Mechanics, 2018, Vol. 67, No. 4, pp. 439-455.
  • [17] M. Artar and A. T. Daloğlu, “Optimum design of composite steel frames with semi-rigid connections and column bases via genetic algorithm”, Steel and Composite Structures, 2015, Vol. 19, No. 4 pp. 1035-1053.
  • [18] A. N. T .Ihaddoudènea, M. Saidanib, and J. P. Jaspartc, “Mechanical model for determining the critical load of plane" frames with semi-rigid joints subjected to static loads”, Engineering Structures,145, pp. 109-117.
  • [19] M. Ghassemieh,; M. Baei; A. Kari, A. Goudarzi, and D. F. Laefer “Adopting flexibility of the end-plate connections in steel moment frames”, Steel and Composite Structures,18, 5, pp:1215-1237.
  • [20] B Du, W Jiang, Z He, Z Qi, C Zhang- “Development of a modified low-cycle fatigue model for semi-rigid connections in precast concrete frames”, Journal of Building Engineering, Volume 50, 1 June 2022.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik, Ortak Disiplinler
Bölüm Makaleler
Yazarlar

Senem YILMAZ ÇETİN> (Sorumlu Yazar)
DICLE UNIVERSITY
0000-0002-7282-6413
Türkiye


Halil GÖRGÜN>
DİCLE ÜNİVERSİTESİ
0000-0002-4357-0009
Türkiye


Derman KAYA>
sosyal güvenlik kurumu
0000-0002-5779-736X
Türkiye

Erken Görünüm Tarihi 28 Haziran 2022
Yayımlanma Tarihi 28 Haziran 2022
Yayınlandığı Sayı Yıl 2022, Cilt 13, Sayı 2

Kaynak Göster

IEEE S. Yılmaz Çetin , H. Görgün ve D. Kaya , "A computer program for linear analysis of two-dimensional semi-rigid frames", Dicle Üniversitesi Mühendislik Fakültesi Mühendislik Dergisi, c. 13, sayı. 2, ss. 351-358, Haz. 2022, doi:10.24012/dumf.1087793
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