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

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

Abstract

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.

Özet

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.