Numerical analysis of a masonry residential building using AmQuake software

: Many masonry structures are located in seismically active areas where the action of seismic forces has revealed their vulnerability. Since such structures are built of composite materials, attention should be paid to all the structural elements that make it up. The objective of this paper is to present the procedure and analysis results for a masonry building in order to determine its seismic resistance. The AmQuake software, which facilitates the design and calculation of masonry buildings according to European standards and norms, was used for the analysis. By using the pushover method, the system response to an increasing horizontal force with a constant vertical load is monitored through the calculation. Based on the calculation results, a conclusion on the conducted analysis is given.


INTRODUCTION
Masonry, or laying stone or clay blocks on top of one another while binding them together with mortar if necessary, is the oldest construction technique that has been preserved to this day. The long tradition and worldwide spread of masonry are attributed to its simplicity and to the longevity of masonry structures, which is evident in many such buildings that are hundreds and even thousands of years old. The pyramids in Egypt dating from the period between 2800-2000 BC, the Parthenon in Greece from the fifth century BC, the Great Wall of China whose construction began in the fifth century BC, and the Colosseum in Rome from the first century AD are just some of the examples of such buildings that have also become symbols of some cultures.
Despite the simplicity that is manifested during construction of masonry structures, understanding and describing the mechanical behavior of such structures, especially under seismic loading conditions, is still a true challenge due to the nature of masonry, which shows complex and markedly nonlinear behavior caused by the presence of joints between blocks, which may or may not be filled with mortar. Many masonry structures are located in seismically active areas where earthquakes have revealed all their vulnerability. These earthquakes often damage masonry structures and monuments categorized as cultural heritage as well as modern masonry structures.
Modern masonry structures are widely popular due to their reasonable price, thermal insulation, fire protection, durability, ease of construction, and low maintenance costs. This type of structures behaves well under vertical loading due to its good compressive strength, however their resistance to horizontal actions is reduced.

AMQUAKE SOFTWARE FEATURES
AmQuake software is intended for the design of masonry structures according to Eurocode 6 and 8. It was developed as a result of close cooperation between the companies Červenka Consulting and Wienerberger, the largest European manufacturer of bricks and building systems. When calculating masonry structures, AmQuake uses the pushover analysis and equivalent frame method to verify the seismic safety of masonry structures.
The program has a database of products and national standards of 11 European countries. When creating a new project, the desired national standard can be selected and the parameters of the selected standard can be selected separately. Seismic zone, soil category, reference ground acceleration can be selected in the basic seismic load settings, while spectrum limits and other seismic parameters can be changed in the advanced settings. The program includes an extensive database of Wienerberger brick products with all technical characteristics of products. It is possible to define the type of masonry, reinforced, non-reinforced, confined and reinforced-concrete masonry. When entering walls and other structural elements (ring beams, lintels, ceilings), it is necessary to define the type of material of the individual element.
The model of the structure is entered in DXF format from a CAD program. The topology of the model is set in the CAD program, where the main geometric elements are walls, windows and ceilings. Each ceiling comprises a defined load, along with the corresponding safety factor that is automatically filled based on the national standard annex, but can be changed as necessary. After the model and corresponding loads are entered, a finite element mesh is automatically generated, and appropriate parameters can be manually set in the advanced options. After the model is calculated, the masonry structure is checked according to Eurocode 6, and the e-Zbornik 20/2020. Kustura, M., Matijević, I. Numerical analysis of a masonry residential building using AmQuake software reinforced concrete structure according to Eurocode 2. Seismic evaluation of the model is made according to Eurocode 8, and all results can be shown in RTF format.

General
The pushover method is a nonlinear static method for calculating existing or new structures. The basic principle of the method is to monitor the system response for an increasing horizontal force with a constant vertical load. The seismic resistance of the system can be determined from the obtained relationship between the horizontal force and the reference displacement.
The seismic load is gradually applied to the system that has previously been fully subjected to the action of vertical loads. The inertial forces that occur in the system during an earthquake load are simulated in this way. Increasing the load leads to failure of individual elements of the structure, which causes a decrease in the rigidity of the system. The method is based on the procedures for design and repair of damaged buildings, which comprise engineering concepts based on structural behavior.
It was realized that more attention should be devoted to damage control during design. This can be achieved only by introducing nonlinear calculation into the seismic calculation methodology. One of the most suitable approaches is to combine the nonlinear static pushover method with the spectral response methodology. The assessment of earthquake resistance is given on the basis of monitoring one characteristic node -the control node. The control node is usually the center of masses of the highest floor. The load-bearing curve, from which the seismic resistance of the system can be estimated, is constructed based on trajectory of the control node.

Assumptions for pushover method
Some assumptions according to EN 1998-1: 2004: are used for pushover method.
 Zero post-yield stiffness can be assumed;  Longitudinal forces due to gravitational loading should be taken into account when calculating EN 1998-1;  Mean values should be used for material properties;  The value of transverse and bending stiffness of masonry and reinforced concrete is assumed as ½ of the actual one in order to simulate cracking of cross section;  As a minimum bi-linear force-deformation relationship should be used at the element level;  Spatial model should be made for irregular structures, and two analyses are necessary for two different directions. where it is not necessary to consider horizontal actions from two directions in a single calculation;  Transverse forces should be set at the center of masses, or at the center of floors with eccentricity set according to EN 1998-1 e ai = ±0.05L i Li -floor dimension perpendicular to earthquake action  Horizontal forces for the case of modal distribution are determined according to the expression:

The pushover method implementation procedure
The pushover method is carried out in the following steps:  Determining spectral acceleration from elastic response spectrum of a single-degree system;  Determining pseudoforce from spectral acceleration, and determining the relationship between spectral acceleration and spectral displacement;  Determining the target displacement of a single-degree system;  Transformation of a multi-degree system into an idealized single-degree system;  Making an idealized elastoplastic diagram;  Determining the period of the idealized system;  Determining the target displacement of the idealized system;  Determining the target displacement of the system. According to the calculation needs, the systems can be divided into single-degree and multi-degree systems. consists of an elevator and a two-flight staircase that extends to the top floor. The roof is made as a flat impassable roof with 80 cm high parapets. The building is founded on category B soil and is located in a seismically active area with expected design ground acceleration of 0.28 g for a return period of 475 years, and 0.14 g for a return period of 95 years.

Analysis of loads
The basic loads acting on the structure are permanent, variable and accidental actions.

Permanent action
Permanent action on the structure includes dead weight of the structure itself, and the additional permanent load. Additional permanent load for: -floor slab (POZ 100, 200, 300

Accidental action
For the relevant ground acceleration, the value was read from seismological maps for a return period of 475 years, and the load was finally set in two plan-view, mutually perpendicular directions (X and Y). Computational ground acceleration: a g = 0.28 g (T=475); g=9.81 m/s² Soil category: B Spectrum type: 1 Importance factor: II (common buildings, residential, without special importance) The behavior factor of the structure for confined masonry is q = 2.0 -3.0, and q= 2.5 was selected for the subject structure.

Calculation by the pushover method
The calculation using the pushover method was performed in the AmQuake program, which performs proof of seismic resistance by combining the equivalent frame method and the pushover method. Calculation results are affected by the settings related to finite element mesh, so it is necessary to choose individual options in the program with special attention. The basic idea is to model all load-bearing elements with 1D beam elements. This is related to vertical and horizontal elements such as walls, tie columns, ring beams, lintels above doors. The next assumption is concerned with floor structure, which is infinitely stiff in its plane, while out of that plane its stiffness is negligible.  The results show that the target displacement for the serviceability limit state (SLS) is 4.306 mm, while the capacity for SLS is 14.489 mm, which means that the design structure satisfies the serviceability limit state. The target displacement multiplied by factor 1.50 for the ultimate limit state (ULS) is 12.918 mm, while the capacity for ULS is 14.489 mm, which means that the design structure also satisfies the ultimate limit state. In Y direction, it can be observed that the target displacement for the serviceability limit state (SLS) is 2.703 mm, while the capacity for SLS is 8.691 mm, which means that the design structure satisfies the serviceability limit state. The target displacement multiplied by factor 1.50 for the ultimate limit state (ULS) is 8.109 mm, while the capacity for ULS is 8.691 mm and the design structure also satisfies the ultimate limit state.

CONCLUSION
The paper presents the calculation of a masonry residential building. Analysis of seismic resistance was performed using the pushover method implemented in AmQuake software. Based on the obtained results, we can conclude that the pushover method is an effective procedure for analyzing the seismic resistance of masonry buildings, which determines the load-bearing capacity and deformation of the structure due to the action of seismic forces. Assessment of seismic resistance for masonry buildings in seismic areas is greatly influenced by the regularity of the building in the plan view and in height, what the example of building presented in this paper is like.