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

Yıl 2012, Cilt: 3 Sayı: 1, 5 - 19, 01.06.2012

Halil Görgün Sercan Kaymak Asım Çelik

Öz

Bu makalede, kayma deformasyonlarının etkisi de göz önüne alınarak sonsuz rijit kısımları bulunan elastik
bağlı çubuklardan oluşan düzlemsel çerçevelerin doğrusal 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 ankastrelik uç kuvvetleri elde edilmiştir. Literatürde bulunan
bazı sonuçlarla karşılaştırmalar yapılmış ve aralarında uyum olduğu görülmüştür.

Anahtar Kelimeler

Rijit uçlu bölgeler, Kayma deformasyonları, Elastik bağlı çubuklar, Düzlemsel çerçeveler, Doğrusal analiz.

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

Öz

In this study, the linear 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.
When analysing and designing 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.
Here, the linear 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 linear semi-rigid connection behaviour is used
to modify the member stiffness matrices and the
fixed-end forces vector.
The current paper considers the linear 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 linear and also 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, shear deformations, flexibly connected members, planar frames, linear analysis