Comparative Analysis of Seismic Load Methods on Structures Using EC8

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Abstract

This research examines the effects of the seismic load to a structure. The paper discusses the main methods of the definition and practical application of the seismic load based on the Standard Eurocode 8 (EC8). The similar structure is compared using all the different four methods that will be mentioned. A simple 2-storeys concrete frame with fixed joints was selected. As an alternative way, many calculations were done to define different model whose beams are rigid. The second model can be used for hand-calculations as a cantilever with two masses.

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The paper describes main dynamic properties of the selected structure. Seismic load was defined by Lateral Force Method, Modal Response Spectrum, Non-linear Time-History Analysis (Dynamic Analysis) and Pushover Analysis (Nonlinear Static Analysis). The time-history analysis is represented by accelerograms. There were made linear and non-linear calculations.

Introduction

The sudden waves emerge from sudden movements in a rapture or crack zone in the earth’s crust, in the case of an earthquake.

The various types and velocities of waves move through certain paths before approach the site of building and subjecting the local ground to different movements. No sooner had the waves reach the site of building, than the ground start moves quickly forth and back covering all directions horizontally and vertically. As a result, the footings or foundations of the building follow these forced movements and cause a huge vibration to the whole structure. In addition, the vibrations of the building that occurred without any damages are in plastic deformation of the structure and once they exceed the plastic deformation, the substantial damage with local failures will happen in extreme cases collapse.

Moreover, the huge magnitudes of earthquakes considered to be as giant natural disasters, as this case causes that hundreds of people to be killed, thousands of people to be homeless and in addition to the losses of the country’s economic.

Methodology

The most common use for a calculation of seismic response is the linear state of stress. For large or huge buildings or structures, the non-linear method is most commonly to be used and according to the Eurocode 8 (EC8), the upcoming four analysis method are defined as:

Lateral Forced Method Analysis
Modal Response Spectrum Analysis
Dynamic Analysis (Nonlinear Time-History Analysis)
Pushover Analysis (Nonlinear Static Analysis)

This upcoming section is regarding the background about the analysis methods used. The first method which is used is the Lateral Force, it is calculated using horizontal loads as a seismic load and this method is a static and linear. Thus, because of this lateral force method, there is no definitive impact for the high frequency could have. Moreover, each direction could identify the base shear force besides the allocation of horizontal forces is linearly increase or considered to be related to the eigenvalues. The R factor according to Eurocode 8 EC8 is assumed to be 5.85 whereas in the ECP-201, R factor is selected to be 7 in the former for ductile RC moment resisting frames.

In addition, the second method is the Modal Spectrum Analysis and it is follows the identical geometrical rules as the previous method (Lateral Force Analysis Method). Furthermore, 90% at least of the total mass should use the eigenmodes. The unsimilar directions’ responses can be merged using The Square Root of The Sum of The Square (SRSS) or using The Complete Quadric Combination (CQC) method and this is conceivable only if eigenmodes are mutually independent.

The third method used is the Dynamic Analysis (Nonlinear Time-History Analysis) is mostly recommended by codes of seismic design especially if these buildings are irregular and more than 15 storeys. This method analysis is based on direct numerical integration of the differential equation of motion and accelerograms represented the base motion. Due to the very short duration used in digitization of accelerograms, dynamic analysis considered to be costly and time-consuming method.

The fourth and last analysis method type from the Eurocode 8 (EC8) is the Pushover Analysis Method (Nonlinear Static) and the N2 method is the mostly used version besides this analysis method defines three procedures. The first procedure in the N2 analysis is the determination of the structure’s ductility, stiffness and strength. Moreover, the multiple degree of freedom system is the first mathematical model with linear horizontal increasing load is used. Furthermore, the second procedure should define the single degree of freedom system for the structural and must act similar as the multiple degree of freedom system. In addition, the ratio among the top-displacement and base shear force is the base for nonlinear characteristics. Lastly, the third procedure covers the calculation of extreme displacement.

Case Study of the Structure Building

The following are some dimensions and parameters for the model structure. The model is a simple concrete frame consists of 2 storeys and the fixed joints was selected. The structure has 6 m width with 4 m height for each story which mean that the total height of the structure is 8m. The concrete frame has two cross-sections and the selected columns are 40x40 cm square cross-section. The reinforcement is symmetrical distributed to all sides and the diameter of the bar is Φ20. Moreover, the cross-section of the beams chosen are rectangular 40x60 cm with a reinforcement placed at the bottom and on the top of cross-section. The 3Φ20 is used for one side and the shear reinforcement is neglected.

The main parameters of materials were defined for linear and nonlinear actions according to the Eurocode 8 (EC8) section 3.1 and 3.2. Furthermore, the following are the crucial parameters for nonlinear analysis of the concrete:

Compressive Strength fck = 30 MPa
Tension Strength (5% fractile) fctk(0.05) = 2 MPa
Design Strain = 0.077%

For reinforcement, the yield strength fyk = 500 MPa and strain = 2.5%

For the vertical load, the frame is loaded by the self-weight (6KN/m) for the column with a uniformly distributed load of 10 KN/m’. the safety factors are not considered and one combination only was defined for the simplification.

For seismic load, it was defined by horizontal elastic response spectrum according to the Eurocode 8 (EC8) section 3.2.2.2. Due to the structure is fictional, the initial conditions were randomly selected:

The design peak ground acceleration (PGA): 0.8 m/s that is 0.0815 g.
The frame is based in the ground type B (corresponds to the gravel, very dense sand or very stiff clay).
Average shear wave velocity (Vs,30) = 360 m/s
Importance class of structure: Class II (indicates ordinary building with importance factor (ℽI = 1). With a comparison of ECP 201, the importance factor ℽI= 1.20
Behaviour factor, q= 1
Effective damping according to the Eurocode 8 (EC8) = 5%

Lateral Force Method Analysis

This is a static analysis as aforementioned using linear behaviour of the of the material where the seismic load, which is in the form of horizontal forces, act to the structure’s joints. According to the Eurocode 8 (EC8) section 4.3.3.3, the following are the results:

Design Spectrum Sd(T1)= 2.4 m/s2
Base Shear Force Fb= 57.6 KN

Since the values of design spectrum and base shear force reach the horizontal forces, it is acting to the whole storeys and here are the results:

Force of first storey (F1) = 24.16 KN
Force of second storey (F2) = 33.44 KN

Finally, the displacement for storey 1 and storey 2 are U1 = 0.00109 m and U2 = 0.00172 m, respectively.

Modal Response Spectrum Analysis

The response spectrum and structure’s input values are similar or in the same way as in EC8 section 2.2.2 and 3.1. The following are the results for the first and second procedures by hand calculations. In the first procedure, the first eigenmode of horizontal force was:

F1= 22.98 KN and F2= 31.78 KN

Whereas in the second eigenmode of horizontal force was:

F1= 4.32 KN and F2= 2.73 KN

In the second procedure, for the first eigenmode’s horizontal displacements were:

U1= 0.001037m and U2= 0.00003m

Whereas the second eigenmode’s horizontal displacements were:

U1= 0.00003m and U2= 0.000022m

By using the SRSS (Square Root of the Sum of the Squares) method that previously mentioned, the total displacements were calculated and the results were:

U1= √((0.00003)^2+(0.001037)^2 ) = 0.001038m

U2= √((0.000022)^2+(0.001639)^2 ) = 0.001639m

Case Study Results

For a simple concrete frame, the research compared flexible and rigid beam behaviors under seismic loads, finding that flexible beams exhibited higher horizontal displacement. This underscores the importance of material behavior in seismic response.

Analysis Method	Maximum Displacement (m)
Flexible Beam	0.00209002
Rigid Beam	0.00157214

Table 1. Displacement Comparison between Flexible and Rigid Beams

Conclusion

The integration of CR technology and IoT offers a promising approach to water and irrigation management, addressing the global water crisis by allowing precise control over resource usage. The comparative analysis of seismic load methods provides insights into optimizing structural design against seismic forces, highlighting the need for advanced analysis techniques in high-risk areas.