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Perception of stiffness trend in city residential buildings

In this project, a descriptive research was carried out in order to analyze, evaluate and detail the behavior of buildings between 4 and 18 floors of residential use in the City of San José de Cúcuta, Colombia, at the moment they are subjected to forces produced by earthquakes. For this purpose, a sample of 40 buildings framed in the above-mentioned characteristics was used by means of the SAP 2000 software. The seismic analysis of each building was made and the displacements of these were obtained when they are submitted before an earthquake. With this information, it was possible to calculate the drifts and evaluate them based on the requirements that determine the stiffness conditions present in the buildings. Finally, a document was drawn up identifying those buildings that are susceptible to significant damage in the event of a seismic movement and recommendations, due to the fact that they represent a social risk.


Introduction
An earthquake is a sudden movement of the ground that is usually caused by slipping along fault lines that results in the sudden release of energy in the earth's crust, generating seismic waves and in turn, give their energy to the foundations and then to the structure [1]. As a result of these earthquakes, human lives are lost that are proportionally linked to the vulnerability of buildings in this natural event, increasing their mortality rate due to the number of people who live and work in buildings [2]. After the occurrence of an earthquake, the information collected from the collapsed building should be done in a timely manner to be used as an effective implementation guide at the time of the emergency rescue [3].
Falls of buildings cause almost 95% of the victims in this natural catastrophe, therefore, it is important to study the damage to buildings in earthquakes [4]. One of the reasons that affect the constructions at the moment of an earthquake are the inadequate materials used in the construction (mud, stone, briquette, blocks of soft stone, among others), either by their low quality or because they do not fulfill the standards against the seismic forces [5], besides the materials used it is the method of realization at the moment of constructing, being United States and Japan, one of the countries using base insulation, a passive structural control technology with the aim of reducing earthquake damage to structures by isolating the soil superstructure using flexible bearings (seismic isolation bearings), which have some stiffness and are inserted between the foundation and superstructure, thus separating the seismic energy in the structure [6].
In the city of San José de Cúcuta, Colombia, a tendency to the construction of buildings with a considerable number of floors has been evidenced, orienting the city to a vertical urban growth; In addition it is located in a region characterized by its a zone of high seismicity on the frontal fault of the eastern mountain range of Colombia, with an effective horizontal peak design acceleration of 0.30 g [7], which confirms because there was an earthquake in 1875; achieving this natural event a countless number of homeless people, causing a total halt of all economic activities for a long time, which in turn chained an increase in poverty indicators [8]. In this order of ideas one of the parameters of great importance is the present rigidity in the buildings which contributes to the resistance of seism, limiting the displacement caused by the action of the forces applied on these, for such reason, a study is made on the tendency of rigidity that contain the buildings of residential use that possess between 4 and 18 floors.

Methodology
The sample is made up of all residential buildings between 4 and 18 floors in San José de Cúcuta, Colombia, in the time interval from 2008 to 2015; in this way 40 buildings were obtained that met these requirements. Information was collected through project [9] and [10], SAP 2000 software and curatorship's 1 and 2, the latter being acquired: name of the project, location, height of the building, number of floors, dimensions, structural system and date of issuance of license; in order to classify buildings that meet the standards required by the NSR-10 [11].

Calculation of the design spectrum
The elastic acceleration spectrum of each building in the project was calculated taking into account the following considerations: Zone of high seismic risk, corresponding to the city of San José de Cúcuta, Colombia, C soil profile, which are regulated by NSR-10 [11]; they are determined by the coefficient that represents the effective horizontal peak acceleration Aa, the coefficient that represents the effective horizontal peak velocity Av; according to these two standard coefficients of each capital city, the level of seismic threat AE and AD is determined; the coefficient of amplification that affects the acceleration in the zone of short periods, Fa, the coefficient of amplification that affects the acceleration in the zone of intermediate periods  The calculation process to determine the value of K (stiffness value) and Sa (value of the design acceleration spectrum for a given vibration period) is performed by means of the Ta value (characteristic periods of the spectrum) and the Equation (1), Equation (2) and Equation (3). Ta > 2.5; K = 2 (3) Table 1 shows the values of Sa and K of different buildings in the city of San José de Cúcuta, Colombia, that comply with the parameter of 4 and 18 floors, it being understood that the buildings do not have high values of Sa and K proportionally, as in the case of Barcelona Apartment that has the highest value of rigidity, its Sa is the lowest.

Basic data for structural models
The structural models developed for the seismic analysis by means of SAP 2000 software had the following data according to Table 2, where there are different variations in the measurements of floor heights, being the maximum among them of 4.36 m and plate height of 0.7 m, so that the building with more height in its floors and plate is "Fomanort" with 4.33 m and 0.7 m, respectively.

Areas of structural elements.
According to the results obtained from the seismic analysis of the buildings in Table 3, it was perceived that 47.5% of the 40 buildings in the sample were constructed with the requirements stipulated in the Colombian norm of resistant seismic construction NSR-10 [11], which stipulates that the minimum area of the column is 0.5 m 2 and 33 m 2 for the structural wall area.

Evaluation of requirements
The determination of the drift is made by means of Table 4, which stipulates what is the maximum drift that the construction can have to be accepted by NSR-10 [11] as earthquake resistant. In Table 5 and Table 6, it is shown that 27.5% of the buildings evaluated did not comply with the drift requirements in both directions (X,Y), as the maximum direction is 0.040 and 0.032 respectively, while 25% only met the drift requirements in one direction, exposing a great danger to an earthquake in the direction that has less rigidity with respect to the other, in addition to the fact that 20% of buildings with a floor height less than 3 m did not meet the necessary drift conditions; on the other hand, 63.33% of buildings with a height equal to or greater than 3 m were not fit to meet the derivatives.

Recommendations
Earthquakes are unpredictable events that can occur very frequently, such as in Japan and Haiti, but they are usually infrequent in the vast majority of the world, causing disastrous consequences; although they cannot be controlled at the time of execution, the damages can be mitigated [12], by means of construction norms for buildings that each country presents, the differences between them will depend on the seismic level that can occur; in Colombia, NSR-10 [11] is applied, stipulating for each region the seismic level and its constants and/or values of the building structure. Between floors containing the building, the requirements are stricter, so it is recommended that future buildings with a greater number of 3 floors comply with the specifications of drift, direction of X,Y, height of the floor and plate, value of resistance and spectral elasticity; Since these buildings are visited daily by thousands of people in the area who may be in danger when a high impact earthquake occurs and the structures are not adequate to withstand it, risking their lives for lack of ethics by eliminating building materials or speeding up the project to start making profits.

Conclusions
Within the net evaluated buildings, 16 were constructed before 2010, implying that their structural design was carried out with the requirements of the old Colombian norm for constructions earthquake resistant according to law 400, 1997, even so, 12 did not comply with the requirements demanded as regards drifts of the norm currently in force, while the buildings constructed from 2010 onwards have an indicator of 50% that do not comply with the requirement regarding drifts established by the Colombian regulation for constructions earthquake-resistant. The seismic analysis carried out for the 40 buildings resulted in the following: buildings with 4 floors 50%, 5 floors 50%, 6 and 7 floors 100%, 8 floors 80%, 9 floors 50%, 10 floors 33.33%, 11 floors 25%, 12 floors 100%, 13 floors 50%, 14 floors 66.67% and 16 floors 100% inefficient according to Colombian regulation established for constructions earthquake resistant; in summary, 65.22% of buildings with less than 10 floors and 47.06% with more than 10 floors do not comply with the standards of the Colombian seismic resistant construction regulations. Therefore, policy makers should adopt anti-seismic construction strategies, mainly in areas of high seismic risk.