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The
dynamic analysis of the structure is carried out
three-dimensional as provided in the Earthquake
Code.
The
method used in the determination of modal values
in the dynamic analysis is the Vianello Stodola
method. The free vibration calculation of single
mass systems can be made definitely by this
method. First, the flexibility matrix belong to
the lateral displacement components of the
structure in the related seismic direction is
formed. Afterwards, the building mass matrix is
obtained by the story weights. Starting out from
these two matrices and the initial characteristic
vector, special angular frequency and
characteristic vectors for every mode are obtained
as a result of consecutive approach calculations.
The obtained characteristic vectors are normalized
by means of certain coefficients. Thus, the
normalized free vibration modes and special
angular frequencies and periods of the structure
are determined.
Generally
the below sequence is followed when dynamic
analysis by modal superposition method is
performed:
The
number of modes to be considered in the dynamic
analysis are determined.
The
lateral stiffness matrix of the structure is
formed. The necessary arrangements are made on
this matrix and the non-vibrating vertical
displacements and rotations are eliminated. Thus,
the reduced stiffness matrix response of
vibrations in the story slab perpendicular to each
other is obtained. If desired, the vibrations of
the structure can be reduced to a single direction
in the horizontal plane.
The
diagonal mass matrix is formed.
Special
angular frequencies are calculated for every mode
by means of reduced lateral stiffness matrix and
diagonal mass matrix for the structure.
The
characteristic vectors are found by means of
iteration.
The
necessary division coefficients for normalization
are found and the contribution coefficients of the
modes are calculated.
The
maximum behavior spectral accelerations for every
mode are calculated or read from the curve.
The
modal loads acting on the story level are found
for every mode.
The
maximum story loads are calculated for every story
by CQC (Complete Quadratic Combination) method.
It’s
continued to the system analysis under lateral
loads by the obtained story loads (for both two
directions), considering the minimum story torsion
condition. |
