Civil Engineering Research Journal
This approximate calculation method is developed and
designed for replacement of the arbitrary Non-Linear Push-Over (NLPO)
method. The proposed rational methodology is an intermediate engineering
approach between the Linear-Elastic Dynamic Modal Response Spectrum
method and Non-Linear Dynamic Time Domain (History) method and comprises
six steps, i.e.
A. Step 1
Perform a numerical 3-D Linear-Elastic Dynamic Modal
Response Spectrum calculation based on the relevant Horizontal Elastic
Ground Acceleration Response Earthquake (Seismic) Spectrum (input).
Utilize the Complete Quadratic Combination (CQC) method instead of the
Square-Root-of-Sum-of-Squares (SRSS) method. Because it is well-known
for a long era that application of the Square-Root-of-Sum-of-Squares
(SRSS) method in seismic analysis for combining modal maxima can yield
significant errors.
B. Step 2
Extract the numerically determined (calculated) total component support reactions FX, FY and FZ. A global Cartesian (X, Y, Z components) right-handed coordinate system is adopted.
C. Step 3
Resolve the numerical calculated mass of the structure mstructure. It is tacitly assumed that the sum of the effective (participating) modal masses for the vibration modes taken into
account amounts to 100% of the total mass of the structure, i.e. meffective (participating) modal mass = mstructure.
D. Step 4
Calculate the Cartesian component accelerations. aX = FX / mstructure, aY = FY / mstructure and aZ = FZ / mstructure.
E. Step 5
Execute a numerical 3-D Non-Linear (Physical and
Geometric) Static calculation with the retrieved Cartesian component
accelerations aX, aY and aZ.
F. Step 6
Compare the acquired numerical results with a
conventional (EUROCODE) 3-D Non-Linear Push-Over (NLPO) earthquake
calculation method and 3-D Non-Linear Dynamic Time Domain (History)
(NLTH) calculation [1-4].
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