Elastik bağlı çerçevelerin kesme kuvvetini dikkate alarak nonlineer analizi

Öz

Bu çalışmada, kesme kuvvetini hesaba katarak uçlarında dönel yaylar bulunan çubuklardan oluşan düzlemsel çerçevelerin nonlineer analizi yapılmış ve bu konuda bir bilgisayar programı hazırlanmıştır. Önce, ikinci mertebe teorisi kullanılarak ve kayma deformasyonları hesaba katılarak uçlarında dönel yaylar bulunan çubuklara ait eleman rijitlik matrisi elde edilmiştir. Daha sonra, aynı etkiler altında diferansiyel denklemler yardımıyla üniform yayılı yük, tekil yük, doğrusal yayılı yük, simetrik yamuk şeklinde yayılı yük ve simetrik olmayan üçgen şeklinde yayılı yük için ankastrelik uç kuvvetleri bulunmuştur. Hazırlanan bilgisayar programı yardımıyla incelenen örneklerde yay katsayılarının değişimine bağlı olarak bazı elostostatik büyüklüklerin değişimi grafiklerle sunulmuştur.

Anahtar Kelimeler

• Çerçeve sistemi, Doğrusal olmayan analiz, Kayma deformasyonu, Rijitlik matrisi, Bilgisayar programı

The nonlinear analysis of frames composed of flexibly connected members considering shear deformations

Abstract

In the current analysis and design of steel frames, and reinforced precast concrete frames the actual behaviour of beam-to-column connections are generally idealized either pinned or fully rigid. The rigid connection idealization indicates that relative rotation of the connection does not exist and the end moment of the beam is entirely transferred to the columns. In contrast to the rigid connection assumption, the pinned connection idealization indicates that any restraint does exist for rotation of the connection and the connection moment is zero. Although these idealizations simplify the analysis and design process, the predicted response of the frame may be different from its real behaviour 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

Keywords

• Frame system, Nonlinear analysis, Shear deformation, Stiffness matrix, Computer program