Elastik bağlı çerçevelerin kesme kuvvetini dikkate alarak nonlineer analizi

Yıl 2011, Cilt: 2 Sayı: 1, 19 - 31, 01.06.2011

Halil Görgün Senem Yılmaz Sevgi Seval Karacan

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

Öz

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

Anahtar Kelimeler

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