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N-
ESTABLISHING GLOBAL-STIFFNESS MATRIX
[S] x [D] + [P ]= 0
After beam, column, and
foundation elements are placed in general stiffness matrix
in directions of their global stifnesses, general stiffness
matrix is established.
General stifness matrix is arranged in a variable band and
does not take into account regions with zeros. STA4 makes a
special point optimization that provides economical usage of
memory to solve equilibrium equations at high speed. This
optimization technique of STA4 minimizes band matrix by use
of minimum global matrix size. Variable band matrix, which
can be seen in disc shape on diagonal during analysis,
provides economical usage of memory. Use of Gauss
elimination, blocking technique, and 16 digits (8 bytes)
reduce error making percentage in multi-unknowns that occurs
because of numeric operations.
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O- MODAL ANALYSIS
Modes and periods of system
are found by modal superposition. While finding periods of
structure, deflections without vibration and stiffnesses in
rotation directions are also considered.
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STA4 programme forms global rigidity matrix by taking into
account effects of a nonorthogonal structure on rigidities of
foundation and soil.
[K] KA matrix is obtained by eliminating part of [K]
matrix that consists of non-vibrating deflections and rotations
( qx, qy, dz components at joint point of structure and
foundation). Therefore matrix that considers
structure+foundation interaction participates in modal analysis.
The matrix that is obtained is story matrix.
Getting special values:
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R- TRANSFORMING FROM FREQUENCY EQUATION TO SPECIAL VALUES
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Special
values are obtained from above determinant
by Jakobi method.
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These equations are solved and special vectoral matrices of each
mode are found.
a)
Analysis option according to earthquake code
If T.D.Y. is applied, special period of structure is found by
solving only 1. mode. By this special period;
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b) Dynamic analysis option by modal superposition
In the same way, earthquake forces of floors in accordance with
T.D.Y. are obtained. Calculating ratios for each i mode;
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Sa
and Sd (acceleration or displacement) spectrum values of each
mode are taken from soil acceleration spectrum curves.
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Matrices of force of inertia are found for each mode. Elastic
earthquake forces are calculated for each mode.
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If
earthquake force found by dynamic analysis to earthquake force
found by equivalent earthquake load method ratio is smaller than
1, in accordance with minimum equivalent earthquake method,
increased by;
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S- CALCULATING MAXIMUM VALUES OF BEAMS
Maksimum moment and shear
forces at end points of beams are classified in following
groups:
a) Dead
load (1. Combination)
Mg : Beam dead
load end moment
Mdg : Beam dead load reduction moment
b)
Moving load (2-7 Combinations)
Mpu : Maximum live
load end moment
Mdpu : Maximum live load reduction moment
Mpa : Minimum live load end moment
Mdpa : Minimum live load reduction moment
c) Soil Effect (8. Combination)
Mz : Soil effect
end moment
Mdz : Soil effect reduction moment
d)
Earthquake load (9-12 Combinations)
Me : Earthquake
loading end moment
Mde : Earthquake loading reduction moment
e) Wind load (13-16 Combinations)
Shear forces are
found in the same way according to maximum values and load
combinations.
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T- DEFINING BEAMS THAT ARE CONNECTED TO THIN SHEAR WALLS AS
ELASTIC SUPPORTS
If elastic supporting that
occurs due to local deformations in shear walls is to be
considered in beams that are connected to thin shear walls
perpendicularly by fixed supports, from options part of the
programme first REINFORCED CONCRETE OPTION then BEAM REINFORCED
CONCRETE OPTION is selected.
In 'elastic support at beam ends option' of menu, programme
makes analysis according to the method offered by Muzaffer IPEK
(Refer to bibl. 19) that takes into account fictitious column
width as follows. However, due to rigidity assumption analysis
is performed according to rigid connection assumption.
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Due to tests made by STAAD-III programme;
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Results that are obtained by considering local deformation
effects of the beam that is connected tp wide shear walls by
fixed supports in the above figure on the column that functions
as a vertical slab due to elastic support hypothesis and results
that are obtained by STA4CAD are compared below.
Elastic support analysis by STAAD-III
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d) Analysis of wide shear wall column by considering slab
element as finite elements;
Evaluation of results;
Beams that are put on
strong columns perpendicularly are analysed by STAAD-III and
STA4 programmes and analysis results are compared. In
analyses that consider fictitious column widths and elastic
supports, STA4 programme gets accurate results in accordance
with values in (d) choice. Therefore, STA4 programme makes
analysis by finite elements method in accordance with both
elastic support and fictitious column width hypotheses.
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