**2. Case studied**

A two story RC framed building was studied, (Figure 1a), which contains internal staircase and 220 m2 total plan area. This structure represents a common typology used for residential buildings in Venezuela, for prone seismic zones. The structure was designed and detailed for a high ductility value (response reduction factor of 6).

**Figure 1.** Low rise RC building(a) 3D view (b) Plan view

The building was modeled according its original design, called *original building (OB)*, with plan asymmetry (Figure 1b) and one way 25 cm depth slabs in *X* direction. A second model was designed adjusted to seismic performance requirements formulated by Herrera *et al.* [12], called *resizing building (RB)*, which presents equal geometrics and mechanics character‐ istics than *OB* model, but considering the "strong column-weak beam" condition. It was also used the displacement-based seismic design procedure of *Priestley et al.* [13] in order to de‐ sign of a third model, called *displacement-based design building (DBDB)*. These three models differ only in the dimensions of its structural elements (Table 1).


**Table 1.** Geometric characteristics of elements from each modeled building

## **3. Assessment method**

quadrants method, which leads to the rapid assessment of the seismic capacity of a structure through its non-linear response [10]. Results of the research shown that the current design of this kind of structures is not safe when they are under the maximum seismic actions prescribed by codes, then it is necessary to review the design procedures in order to find more realistic

A two story RC framed building was studied, (Figure 1a), which contains internal staircase and 220 m2 total plan area. This structure represents a common typology used for residential buildings in Venezuela, for prone seismic zones. The structure was designed and detailed for

designs that fulfill the goals of the performance-based design.

284 Engineering Seismology, Geotechnical and Structural Earthquake Engineering

a high ductility value (response reduction factor of 6).

(a)

(b)

**Figure 1.** Low rise RC building(a) 3D view (b) Plan view

**2. Case studied**

The Quadrants Method is based on the results of the non-linear static analysis (Pushover analysis). This analysis results are plotted in a displacement vs. base shear format, this generate the capacity curve which represents the overall capacity of the whole structure against lateral forces. In order to evaluate the capacity curve two of the main structural parameters are taken into account. The first one is the design elastic shear, obtained from the elastic analysis of the structure using the elastic design spectrum. The second parameter is the threshold that defines the Repairable Limit State, obtained from [14] for RC framed buildings with similar charac‐ teristics to the studied ones. The thresholds have been computed from characteristic values of three levels of damage proposed in [15] and are showed in Table 2. Both values are used to define two axes over the capacity curve, the elastic base shear defines an horizontal axis and the damage threshold defines a vertical axis, then Capacity Curve is divided in four spaces or quadrants, see Figure 2.


**Table 2.** Inter-storey drifts adopted for the damage thresholds determination

The performance point is a common procedure accepted among the scientific community to evaluate the seismic performance of a structure under a specific demand. It is usually obtained from the idealized shape of the Capacity Curve as is shown in the Figure 2 [16]. The Quadrants Method also uses this parameter in order to define the roof displacement of the case studied, defined according to the N2 method [5]. If the performance point is under the axis defined by the elastic base shear (Quadrants III or IV), the design does not meet the basic objective of the seismic design because the building does not have enough lateral strength. If the performance point is on the right side of the vertical axis (Quadrant I) means that the building has adequate stiffness, otherwise (Quadrant II) it means that the stiffness is very low and the displacements can be longer than the displacements that can produce advanced structural damage, techni‐ cally or economically irreparable. These lateral displacements are usually computed from the dynamic response of the structure submitted to a strong motion with a return period of 475 years, or an occurrence probability of 10% in 50 years [17].

**4. Nonlinear analysis**

maximum capacity [20].

diverges.

in the following expression:

The structures are modeled by incorporating the structural response when it incurs in the material and geometrical non-linear range, produced by high deformations caused by accidental excitations (earthquakes) [11]. The analyses were performed using ZEUS-NL software [18], which allows to model complex structures with "n" number of finite elements, thus to know the elements in the building which are most vulnerable to damage. Each building is modeled in two dimensions, spitting each frame to get a more detailed response for the

Seismic Evaluation of Low Rise RC Framed Building Designed According to Venezuelan Codes

http://dx.doi.org/10.5772/55158

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The static Pushover analysis is performed once the frames have been subjected to action of gravity loads, based on the pseudo-static application of lateral forces equivalent to displace‐ ments of seismic action [5]. The pattern of lateral seismic loads consist in increasing loads with height (triangular distribution) applied in a monotonic way until the structure reaches its

This procedure applies a solution of equilibrium equations in an incremental iterative process

Where *Kt* is the tangent stiffness matrix, *Rt* is the restorative forces at the beginning of the

While this procedure is applied, the strength of the structure is evaluated from it is balance internal conditions, updating at each step the tangent stiffness matrix. Unbalanced loads are applied again until it can satisfy a convergence criterion. Then, a new load increase is applied. The increases are applied until a predetermined displacement is reached or until the solution

From the capacity curve provided in this analysis, it is determined the structural ductility (μ) by the quotient between the ultimate displacement and cadence point displacement, as shown

Where ∆u is Ultimate displacement and ∆y is the global yield displacement. Both values are

By the other hand, the dynamic analysis is an analysis method that can be used to estimate structural capacity under seismic loads. It provides continuous response of the structural

*K RF tx t* D + =D (1)

, KΔ<sup>u</sup> (2)

μ=Δ /Δ u y (3)

form. In small increments of linear loads, equilibrium is expressed as:

Rt =Σ Kt

increased load. These restorative forces are calculated from:

computed from the idealized capacity curve of the structure.

seismic behavior of each frame; a 3D dynamic analysis was applied to the ER model.

**Figure 2.** Capacity curve and the axis that define the Quadrants Method

The Quadrants Method can provide an objective criterion in order to upgrade the seismic capacity of a structure. If the performance point is on the Quadrant I, the structure has enough lateral strength and stiffness, so does not need to be reinforced. If the structure is on the Quadrant II, it is necessary to provide additional stiffness by using conventional procedures like RC or steel jacketing. If the performance point is on Quadrant III, the structure requires a more radical intervention, adding stiffness and lateral strength. In this case it is possible to combine some traditional reinforcement techniques with new ones like FRP jacketing. In this case the columns are the subject of the main intervention. Finally, if the performance point is on the Quadrant IV, the structure does not has enough lateral strength and then the reinforce‐ ment technique must be FRP jacketing.
