Kesme kuvvetini hesaba katarak uçlarında rijit bölgeler bulunan elastik bağlı çerçevelerin doğrusal olmayan analizi

Yıl 2012, Cilt: 3 Sayı: 2, 61 - 74, 01.12.2012

Halil Görgün Asım Çelik Sercan Kaymak

Öz

Bu çalışmada, kayma deformasyonlarının etkisi de göz önüne alınarak sonsuz rijit kısımları
bulunan elastik bağlı çubuklardan oluşan düzlemsel çerçevelerin doğrusal olmayan analizi yapılmış
ve bu konuda bir bilgisayar programı geliştirilmiştir. Önce, her iki ucunda rijit bölgeler ve dönel
yaylar bulunan bir çubuk için rijitlik katsayıları elastik bölgesindekiler cinsinden elde edilmiştir.
Daha sonra, ikinci mertebe teorisi kullanılarak ve kayma deformasyonları hesaba katılarak rijitlik
katsayıları çıkarılmıştır. En sonunda, doğrusal prizmatik bir çubuğun üniform yayılı yük, tekil yük,
doğrusal yayılı yük, simetrik yamuk şeklinde yayılı yük ve simetrik olmayan üçgen şeklinde yayılı
ara yükler için değiştirilmiş ankastrelik uç kuvvetleri elde edilmiştir. Literatürde bulunan bazı
sonuçlarla karşılaştırmalar yapılmış ve aralarında çok iyi uyum olduğu görülmüştür.

Anahtar Kelimeler

Rijit uçlu bölgeler, Çerçeve sistemi, Doğrusal olmayan analiz, Kayma deformasyonu, Rijitlik matrisi, Bilgisayar programı.

The non-linear analysis of frames composed of semi-rigidly connected members with rigid end sections considering shear deformations

Öz

In present study, the geometrical nonlinear analysis
of frames with linear prismatic members, which may
have rigid end sections and rotational semi-rigid
end connections, has been carried out taking into
account the effects of shear deformations.
In the analysis and design of reinforced precast
concrete frames, and steel frames the real behaviour
of beam-to-column connections are generally
idealized either pinned or fully rigid. The notions of
the two alternatives either pinned or fully rigid
connections are simply the extreme cases of the
actual connection behaviour, and experimental
works up to date, many of which are referred to in
section of previous studies of this paper show
without doubt that true connections exhibit
characteristics over a wide spectrum between these
two extreme cases. 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. Most connection normally
regarded as fully rigid often display some flexural
flexibility, while connections which are regarded as
pinned, implying no moment transfer, posses some
flexural stiffness. It would therefore seem more
correct that to classify all the behaviour of beam-tocolumn
connections in reinforced precast concrete
frames, and steel frames under the heading of semirigid
connections, while keeping in mind that pinned
and fully rigid connections as extreme cases.
In this study, the nonlinear analysis of planar
frames with semi-rigid connections and rigid end
sections is performed. Modified stiffness coefficients
in the shear wall axis of the beam connected to the
shear wall are obtained with assumption that the
rigid strain would be at the part between the elastic
beam end and the shear wall axis.
The matrix stiffness method of analysis was
modified to allow for flexible connections and rigid
end parts.
The stiffness matrices are modified by correction
matrices and the resulting linear equations are
solved for as in the normal stiffness method. The
advantages of the matrix stiffness method are that it
can be programmed so that relatively large frames
can be analyzed with ease and that the use of
interactive techniques would permit the inclusion of
improvements in the end restraint representation.
The current paper considers the nonlinear
structural analysis of planar frames with flexibly
connected members having rigid end sections taking
into consideration the effect of shear deformations
and a computer program has been prepared for the
pertinent design purposes. To accomplish the
foregoing goal, first the stiffness coefficients of the
stiffness matrix of linear prismatic members has
been found using pertinent differential equations
assuming there are rigid sections of arbitrary
lengths and rotational beam-to-column connections
at the both ends. This kind of members, which may
have rigid end sections, show up when there are
lintel beams connecting shear walls and column
connecting high beams. Then, the stiffness
coefficients of the stiffness matrix of beams itself
have been obtained, taking shear deformations into
consideration. Finally, the fixed end forces have
been found for a uniformly distributed load, a
concentrated load, a linearly distributed load, a
symmetric trapezoidal distributed load and a
nonsymmetrical triangular distributed load.
A computer program has been prepared for the
numerical applications of the analytical results. This
program carries out the second order structural
analysis of planar frames and pierced shear walls
using modified stiffness matrix method, taking shear
deformations into considerations, not only the effects
of bending and axial deformations, but also due to
shear, as well. Solving some problems in different
ways, the validity of the pertinent computer program
has been proved by the close match of the results.
Some examples from the literature have been treated
by the present method and a perfect match has been
observed between the corresponding numerical
results.

Anahtar Kelimeler

Rigid end sections, frame system, nonlinear analysis, shear deformation, stiffness matrix, computer program.