HALİL GÖRGÜN, Senem YILMAZ, Orhan AKSOĞAN

The nonlinear analysis of planar frames composed of flexibly connected members taking shear deformations into consideration

Bu çalısmada, kayma deformasyonlarının etkisi de göz önüne alınarak düğüm noktalarına dönel yaylarla bağlı çubuklardan olusan çerçevelerin nonlineer analizi yapılmıs ve bu konuda bir bilgisayar programı hazırlanmıstır. Önce, ikinci mertebe teorisi kullanılarak ve kayma deformasyonları hesaba katılarak uçlarında dönel yaylar bulunan çubuklara ait eleman rijitlik matrisi elde edilmistir. Daha sonra, diferansiyel denklemler yardımıyla üniform yayılı yük, tekil yük, doğrusal yayılı yük, simetrik yamuk seklinde yayılı yük ve simetrik olmayan üçgen seklinde yayılı yük için ankastrelik uç kuvvetleri bulunmustur. Hazırlanan bilgisayar programı yardımıyla incelenen örneklerde yay katsayılarının değisimine bağlı olarak bazı elastostatik büyüklüklerin değisimi incelenerek grafiklerle sunulmustur.

Kesme kuvvetini hesaba katarak elastik bağlı çubuklardan oluşan düzlemsel çerçevelerin nonlineer analizi

In this study, the nonlinear analysis of frames composed of members flexibly connected to the nodes has been carried out taking into consideration the effect of shear deformations and a pertinent computer program has been prepared. First, using second order theory, the member stiffness matrix for a bar with rotational springs at the ends was obtained, taking shear deformations into consideration. Then, using pertinent differential equations, the fixed end forces were found for a uniformly distributed load, a concentrated load, a linearly distributed load, a symmetrical trapezoidal distributed load and a nonsymmetrical triangular distributed load. The validity of the implemented computer program was proved by solving some example problems in different ways and showing the match between the results. Problems in the literature, which were special cases of the problems treated in this study, were solved by the present computer program and the match of the results was observed. Using the implemented computer program and solving some examples, the variations of some elastostatic quantities with spring constants were examined and presented graphically.

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1. Monforton,A.R. and Wu,T.S., "Matrix Analysis of Semi-Rigidly Connected Frames", Journal of Structural Division, ASCE, Vol.89, pp.13-42, December, 1963.
2. Livesley,RK., Matrix Methods of Structural Analysis, Permagon Press, Inc., New York, N.Y., 1964.
3. Romstad,KM. and Subramanian,C.V., "Analysis of Frames with Partial Connection Rigidity", Journal of Structural Division, ASCE, Vol.96, pp.2283-2300, November, 1970.
4. Ackroyd,MR. and Gerstle,K.H. "Elastic Stability of Flexibly Connected Frames", Journal of Structural Engineering, ASCE, Vol.109, No.1, pp.241-245, January, 1983.
5. Stelmack,T.W., Marley,MJ. and Gerstle,KR., "Analysis and Tests of Flexibly Connected Steel Frames", Journal of Structural Engineering, ASCE, Vol.112, No.7, pp.1573-1588, July, 1986.
6. Yu,CR. and Shanmugam,N.E., "Stability of Frames with Semi-Rigid Joints", Comput. Struct., Vo1.23, N05, pp.639-648, 1986.
7. Cunnigham,R., "Some Aspects of Semi-Rigid Connections in Structural Steelwork", The Structural Engineer, Vol.68, N05, pp.85-92, March, 1990.
8. Azizinamini,A. and Radziminski,J.B., "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.
9. Aksogan,O. and Akkaya,F., "A Computer Program for the Analysis of Flexibly Connected Frames", Ç.Ü J.Fac.EngArch., Vol.6, No.2, pp.25-41, December, 1991.
10. Aksogan,O. and Dinçer ,R., "Nonlinear Analysis of Planar Prames with Linear Prismatic Members Having Rigid End Sections Taking Shear Deformation info Consideration", Ç.Ü J.Fac.EngArch., Vol.6, No.1, pp.125-137, June, 1991.
11. Aksogan,O. and Görgün,H., "The Nonlinear Analysis of Planar Frames Composed of Flexibly Connected Members", Ç.Ü J.Fac.EngArch., Vol.8, No.2, pp.117- 129, December, 1993.
12. Aksogan,O., Akavcı,S.S. and Görgün,H., "Analysis of Frames with Flexible Connections", Ç.Ü J.Fac.EngArch., Vol.20, No.1, pp.1-11, June, 2005.