An engineering Approach for 3-D Numerical Earthquake Analysis
JPBN Derks*
FE IT Consultant, Etten-Leur, Netherlands
Submission: January 22, 2019; Published: February 07, 2019
*Corresponding Author:JPBN Derks, FE IT Consultant, Etten-Leur, Netherlands
How to cite this article:JPBN Derks. An engineering Approach for 3-D Numerical Earthquake Analysis. Civil Eng Res J. 2019; 7(2): 555708. DOI: 10.19080/CERJ.2019.07.555708
Opinion
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].
References
- Bathe K J (2017) Finite Element Procedures. (2nd edn), K J Bathe Watertown MA, Massachusetts, USA, p. 1065.
- Petersen C, Werkle H (2018) Dynamics of Building Constructions. (2nd edn), Springer Vieweg, Germany.
- Wilson EL (2008) Three Dimensional Static and Dynamic Analysis of Structures A Physical Approach with Emphasis on Earthquake Engineering. Computers and Structures Inc, California, USA.
- Wilson EL, Der Kiureghian A, Bayo EP (1981) A Replacement for the SRSS Method in Seismic Analysis. Earthquake Engineering and Structural Dynamics 9(2): 187-192.