NORMA COVENIN (Review ). YEAR: Approved December 9, Reviewed March GENERAL REMARKS: The Norm is mandatory by law. COVENIN 82 seismic code and seismic risk analysis data were used to construct the response spectrum. Furthermore, the earthquake time duration. Mapa de zonificación sísmica para el Occidente de Venezuela, Norma Covenin En general, los valores predichos por la Norma para estas ciudades.

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June 5th Reviewed: November 21st Published: Along its history, Venezuela has been severely affected by destructive earthquakes [ 1 ]. Then it is essential to continuously make progress and research in the field of earthquake engineering and upgrade the seismic design codes.

Seismic upgrade requires the evaluation or predictions of the expected damage to structures at the time of an earthquake of a certain severity occur. From this 7156 it can be defined solutions for the reduction of structural vulnerability [ 3 ].

### GT Descriptor_PC: Alejandría BE b3

The damage occurred in buildings after an earthquake indicates the need for reliable methodologies for the evaluation of seismic behavior of the existing buildings.

According to current technical and scientific advances, seismic evaluation of reinforced concrete RC structures can be 175 by two different approaches: The current tendency of earthquake engineering in the evaluation of structural behavior is the application of simplified mechanical methods based on performance, involving the capacity spectrum [ 5 ], because there are developed refined models and detailed analysis.

This study used a covenni method that involves non-linear analysis with deterministic and probabilistic approaches, as well as procedures of analysis based on Limits States defined by displacements [ 6 ], in order to evaluate the behavior of a low rise RC building with plan irregularity, designed according to Venezuelan codes [ 7 ]-[ 9 ] and subjected to seismic action effect.

Through the use of mathematical models and computational tools, seismic behavior of the building is obtained in a suitable way. Among these tools any procedure was chosen: 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 designs that fulfill the goals of the performance-based design.

A two story RC framed building was studied, Figure 1awhich contains internal staircase and m 2 total plan area.

This structure represents a common typology used for residential buildings in Venezuela, for prone seismic zones. The structure was designed and ocvenin for a high ductility value response reduction factor of 6. The building was modeled according its original design, called original building OBwith 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. It was also used the displacement-based seismic design procedure of Priestley et al.

These three models differ only in the dimensions of its structural elements Table 1. 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. 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 characteristics 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. The performance point is a covebin 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 covenim 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 IVthe 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, technically or economically irreparable.

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 reinforcement technique must be FRP jacketing.

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

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 displacements of seismic action [ 5 ].

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

The pattern of lateral seismic loads consist in increasing loads with height triangular distribution applied in a monotonic way until the structure reaches its maximum capacity [ 20 ]. This procedure applies a solution of equilibrium equations in an incremental iterative process form.

In small increments of linear loads, equilibrium is expressed as:. Where Kt is the tangent stiffness matrix, Rt is the restorative forces at the beginning of the increased load.

These restorative forces are calculated from:. 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 covenon a convergence criterion. Then, a new load increase is applied. The increases are applied until a predetermined displacement is reached or until the solution diverges. Both values are computed from the idealized capacity curve of the structure.

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 system from elastic range until it reaches collapse. In this method the structure is subjected to one or more seismic records scaled to intensity levels that increase progressively. The maximum values of response are plotted against the intensity of seismic signal [ 21 – 22 ].

The procedure to perform the dynamic analysis from the seismic signal is:. To study a seismic record for the dynamic analysis of a structural model parameterized to measure earthquake intensity. The non-linear dynamic analyses provide a set of curves which are a graphical representation of the evolution of the drifts respect time.

Results let to compute the damage lumped in specific elements of the structure, but these cofenin are beyond the objective of this Chapter. For the dynamic analysis the structures were subjected to seismic action see Table 2 defined by accelerograms built on the fovenin of a likely value covsnin maximum acceleration of the coveinn and the hazard level associated with the location of the structure and other covrnin characteristic design parameters [ 16 ]. Non-linear dynamic analysis was applied to all buildings in order to verify if the performance evaluated by the Quadrants Method is reliable in order to evaluate the fulfilment of the thresholds defined in the precedent section.

For this purpose they has been computed three synthetic elastic design spectrum-compatible accelerograms by means of the PACED program [ 23 ]. In Figure 3 are shown the Venezuelan rigid-soil elastic design spectrum with the response spectra covenn from the synthetic accelerograms. These three earthquakes were applied to all frames from the three buildings evaluated, in order to obtain maximum displacement that can be reached by each one.

In the software used [ 18 ], it was required the implementation of dynamic loads in direction X and the assignation of a control node located in the gravity center of the roof level. The 3D non-linear dynamic analysis is based on the procedure explained in [ 20 ]. The RB building is analyzed, defining its geometry, materials and sections, serviceability loads in Y direction in all beams-columns joints, and dynamic loads on outer nodes with directions and combinations shown in Table 4.

One direction ribbed slabs 175 modeled as rigid diaphragms in its plane by using additional elements with no flexural coveniin Figure 4. Once built the model, there covdnin applied all the accelerograms with the combinations shown in Table 3for the interstorey drifts and maximum torsional moments on supports.

These combinations are based on the Venezuelan seismic code [ 7 ] and following established by [ 24 ] about the seismic response of asymmetric structural systems in the inelastic range. By the other hand, in the DBDB building were not performed drifts verifications, since it was designed based on the method performed in [ 13 ], where the generated seismic forces are originally limited to not exceed the limit value of drift specified in the applied code.

To determine the values of structural ductility it was necessary to plot the idealized curve in function of the capacity curve obtained from non-linear pseudo-static analysis 17566 analysisin order to know the point at which the structure begins to yield. Figure 5 shows an example of the normalized capacity curve with the idealized bi-linear curve of Frame C of OB.

Structural ductility for each evaluated building values are presented in Table 5. From this Table it is evident that the original building, designed according to current Venezuelan codes has ductility values lower than the redesigned and the displacement-based buildings.

From the obtained capacity curves there were computed the Performance point Pp of every frame covejin each evaluated building. Table 5 presents the values of Pp of all the frames of evaluated buildings. From dynamic analyses, there were determined global and interstorey drifts of each frame from all three models studied.

Both types covenun drifts were calculated on the basis of the application of synthetic accelerograms with different intensities, representing the lateral forces applied to frames in order to generate their respective maximum displacements.

Similarly, interstorey drifts for applied earthquakes, R1, R2 and R3 with its three intensities, were obtained. It were verified for each Limit State considered in this study. Prevention of Collapse Limit State; -: Checks the Venezuelan seismic code. According to results obtained, interstorey drifts in 2D and 3D modeled buildings differ greatly from each other, for this reason it is important to take into account the 3D analysis in order to evaluate the drifts of buildings, because irregularities can produce lateral displacements that does not match with the obtained in 2D analysis.

In the 2D model greater drifts were obtained, while in 3D model the drifts were reduced by the contribution of the diaphragms.

In Figure 13 have been plotting torsional moments in function of time for the four combinations, where nodes appointed by n until the n are corresponding to supports, while Figure 14 shows the maximum torsional moment range for each column from three-dimensional analysis.

It is evident that for the accelerograms used, the maximum torsional moments occurs in the extreme columns and in the columns located in the intersection of the structure.

This is an important feature that confirms the negative effect of the irregularity combined with the seismic action. The torsional moments for the other seismic combinations used in this study were obtained using the same procedure.

In order to know the seismic response of the studied building it were used analytical methods considering the seismic hazard level and structural regularity criteria.

The elastic analysis applied to the OB building identified elastic displacements greater than maximum value of interstorey allowed by Venezuelan seismic code. From the resizing model RB it was obtained interstorey drifts that satisfied the maximum value established in the code.

Thus, the cocenin of the structural elements of OB are insufficient to properly control the damage caused by seismic forces. From dynamic analysis there were computed the global and interstorey drifts for all three evaluated models determining the dynamic response of these structures and controlling the damage level reached in them. With the global drifts, it was evaluated the threshold cvoenin the collapse Limit State, which corresponds to the maximum value of 2.

RB and DBDB buildings reached drifts values below this limit, proving good seismic performance on both buildings; OB presented drifts values which exceeded this limit. In the verification of interstorey drifts it was generally noted that interstorey drifts of OB building were longer than the considered by hazard levels, while the two resized buildings reached values within the thresholds established for each Limit State.