Proceedings of the 5th International Conference on Integrity-Reliability-Failure, Porto/Portugal 24-28 July 2016 Editors J.F. Silva Gomes and S.A. Meguid

Publ. INEGI/FEUP (2016)

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PAPER REF: 6409

ANALYSIS OF THE EFFECT OF THE REINFORCEMENT DETAILS

FOR STRUCTURES SUBJECTED TO SEISMIC LOADING

Ioana Olteanu1(*)

, Mihai Budescu1, Radu Marian Canarache

2, Virgil Breanban

3

1Technical University Gheorghe Asachi of Iasi, Faculty of Civil Engineering and Building Services, Romania 2INICAD DESIGN S.R.L., Bucharest, Romania 3Fast Consult SRL, Constanta, Romania (*)Email: olteanuioa@yahoo.com

ABSTRACT

Advanced engineering problems arise in special situations, when detailed models are required in order to obtain adequate response of a joint or a member. One of the main design concepts is weak beam-strong column, which is strongly affected by the seismic action. Even though a simplified approach of the pushover analysis does not take into account the details of reinforcement, but only the cross section capacities. This paper presents two case studies which were modelled in detailed in ATENA 3D computer software.

The first one presents the influence of the slab stiffness on the plastic hinge development. A 3-D ground floor structure was considered with different details for the slab connectivity in the corners. The reinforcement was introduced accurately and comparative analyses were made in order to obtain the optimum global behaviour.

The second case study considers a 2D frame structure with 2 opening and 4 levels for which the overlapping of the reinforcement is studied. The influence of the overlapping length is analysed for columns, and the anchorage length for beams. The results show that the overlapping length is more important for the column elements, that the anchorage length for beam elements.

Keywords: stiffness, plastic hinge, reinforcement, overlapping, anchorage length

INTRODUCTION

The non-linear analysis became of great importance in the seismic vulnerability assessment of

buildings, when the performance based evaluation became more popular (ATC-40 Report). Frame structure are recommended in seismic areas because can dissipate energy through

vibration in the elastic range. As the earthquake induces higher inertial forces on the structure, a ductile plastic mechanism is formed designed to avoid brittle collapse.

First nonlinear methods were based on empirical relationships, statistical data and experts’ opinions and were introduced in the design codes in the 80s. Today the statically nonlinear methods are often used and was developed and enhanced since 1981.

The graphical representation of the relation between force and displacement is called capacity curve. This can be obtained through computer programs which have implemented the pushover analysis.

The simplified hypotheses from strength of materials are used in order to simplify the computation algorithm. There are also programs using the analysis with finite elements on

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assembly, subassembly or even on structural elements, analysing the materials separately. Thus the results characterize directly the cracking state, the stresses and the deformations in the concrete and in the reinforcement. In this paper, for the considered case studies, ATENA 3-D was used, allowing us to model in details the reinforcement of the elements.

NONLINEAR STATIC ANALYSIS

The nonlinear analysis can be classified according the definition of the seismic action or the considered structural model. From the nonlinear methods, the dynamic analysis is considered to be the most accurate as represents the behavior of the structure in time. Is difficult to use this method, because the input data are very complex (sets of seismic recordings, damping coefficients, hysteretic models for the inelastic behavior, etc.) and the output are difficult to interpret and to use in the daily design process (stress and displacement variation in time, absorbed energy, etc.) (Luca et al, 2014).

Among the nonlinear procedures, the pushover analysis is widely used because combines the advantage of considering the failure mechanism and the inelastic deformations with simplified static loading pattern providing low uncertainties in the results and practical to use in care of structures with complex geometry (Penelis and Kappos, 2001).

The pushover analysis is defined in the Federal Emergency Management Agency document 273 as a nonlinear static approximation of the response a structure will undergo when subjected to dynamic earthquake loading. Increasing the loads on the structure the weak structural members and the failure mechanisms is identified. Usually the loading pattern is an inverted triangle, fig. 1 (Saidii and Sozen, 1981), but can also be an increasing load at the roof of the structure, which is the case considered for the studied models in this paper. The loading pattern is actually an equivalence of the relative accelerations associated with the first mode of vibration.

Fig. 1 - Transforming a MDF system in a SDF system in a capacity curve

The engineering community did not paid special attention to the pushover method until the

mid-90s. Nowadays there are several methods that include the pushover analysis as: the capacity spectrum method, the coefficient method and the improved N2 method.

The structure behaviour is expressed by graphical representation of the displacement at the top of the structure in respect to the shear force at the base, also called the pushover or capacity curve. The failure mechanism appears due to plastic hinge formation, which passes

through different stages as the lateral load increases. In FEMA 356 three performance stages are defined: immediate occupancy (IO), life safety (LS) and collapse prevention (CP). These stages are graphically represented on the capacity curve from figure 2.

The plastic hinges are geometrically predefine in the initial stages of the modelling, in the regions where it is known that they could appear (for a frame structure the beams and

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columns ends are considered plastic potential areas). Considering their evolution conclusion are drawn on the deformed mechanism of the studied structure.

Fig. 2 - Pushover curve and structural performance stages

The considered cases were analyzed in ATENA 3D computer software. The program has a computing platform based on the graphical user interface through which all the input is entered. The computation is based on Lagrange formula. The software is designed for spatial nonlinear analysis of solids. The properties and characteristics of the nonlinear materials are complex and can be defined manuals or takes from the software data base (Cervenka et al., 2002).

The program has three main functions: pre-procession (where are defined the geometry of the elements including the spatial position of the reinforcement by grid coordinates, the nonlinear characteristics for the materials, load assignment, bounding conditions for the materials, finite element meshing and various parameters used for the analysis), analyze (where the results can be monitored and accessed in real time, as the analysis passes from one step to another) and the post-procession (which provides access to the results expressed graphically and numerically).

Modelling in ATENA 3D is more complex, but a complete virtual model can be achieved. The precise positioning of the reinforcement in the concrete gives an idea about the problems that may occur and allows to find solution in the design stage in case of unfavorable situations. The potential plastic areas can be characterized directly through stress development until it reaches the yield limit and through crack development for concrete.

CASE STUDIES

The first case study analyses the plastic hinge development for a 3D ground floor reinforced

concrete frame structure. The openings on both direction are of 6 m and the level height is 3 m. Cross sections of 50x50 cmxcm were considered for the columns and cross sections of 30x50 cmxcm for the beams, with reinforcement bars as in Fig. 3. The slab thickness is of 15 cm with reinforcement of 8 mm diameters placed at a distance of 10 cm on both directions. The used material properties are resumed in Table 1. The vertical loads are represented by the self-weight of the structure and additional uniformly distributed load of 2 kN/m2 on the slab. For the frame without slab an additional load was applied on the beams equal to 3.75 kN/m, which represents the load transmitted from the slab. In order to apply the horizontal loading a supplementary steel plate was introduced at one of the beam face.

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Different analysis were performed considering only the bared frame, the general situation of the frame with the slab and with some changes like reducing the reinforcement around the edge of the slab, introducing a material with lower characteristics in the corner or a bitumen layer in the corners. The pushover procedure was applied in 50 steps, with a constant step size of 20 kN. The total horizontal load was of 1000 kN.

a) b)

Fig. 3 - Considered cross-sections for: a) beams; b) columns

Table 1 - Materials properties

Materials E(GPa) � ft (MPa) fck (MPa) fyk (MPa)

Concrete C20/25 –SR EN 2 30 0.2 1.5 20 -

Longitudinal reinforcement PC 52 20 0.3 - - 355

Stirrups OB 37 20 0.3 - - 235

Concrete C12/15 –SR EN 2 27 0.2 1.1 12 -

The analysis showed a flexible structure for the column-beam case and the plastic hinges had developed first in the beams, according to current regulations. The influence of the slab is to stiffen the frame model and to direct the plastic hinges in the columns.

In order to avoid the unwanted failure mechanism several constructive measures were

analyzed: reduce reinforcement on a distance of 50 cm on the slab margin, changing the concrete in the slab corners with a lighter material and introducing a joint 5 mm thick and 50

cm long in each of the corners of the slab, Fig. 4.

a) b) c)

Fig. 4 - Studied cases: a. reduced reinforcement; b. material replacement in the corners; c. 5 mm

joint in the corners.

Table 2 presents a synthesis of the results. The yield (dy) and ultimate displacement (du) are

given, as well as the yield force and the length of the plastic hinge in the beam.

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Table 2 - Analysis results

Analysed model Name Type of slab

reinforcement

Yield state Ultimate

state Length for the plastic hinge in the

beam (mm) dy (mm) fy (mm) du (mm)

Frame without slab C1 - 6,45 400 169,26 1200

Frame with slab C2 normal 6,05 560 39,75 600

Frame with slab with material replacement in

corners

C3 normal 5,36 520 42,10 625

C4 reduced 4,09 460 44,32 700

Frame with slab and 5 mm joint in corners

C5 normal 4.12 480 45.02 700

C6 reduced 4,03 440 50,35 825

Considering table 2 we can conclude that the maximum or ultimate displacement, du, is 4 times greater for model C1. The flexibility of this model is explained by the missing slab. For the same case, the yielding force, fy, is smaller with 40%, while the yield displacement, dy, is greater with 6% in comparison with C2. At the same time, it is clear that the plastic hinge length is double for C1 in comparison with C2. Comparing C2 with C3 the differences are not significant, in contrast with case C4, when the plastic hinge length increases with approximately 12%. If model C5 is compared with C4 no significant differences are noticed, but for C6 case the biggest increase in the plastic hinge length, approximately equal to 40%, is noticed.

Considering the two marked areas from fig. 5 it can be concluded that the introduction of the 5 mm joint in the corner area helps redirecting the plastic hinge from the columns to the beams.

a) b)

Fig. 5 - Plastic hinge development for case: a) C2 and b) C6

Fig. 6 presents the cracks evolution in beams and slab, for four of the studied cases. It can be

observed that for C4 model in the plastic area are more cracks. In C6 case cracks are lead beyond the joint. The second row of images represents the stresses from the reinforcement.

The ductility coefficient can be computed for all the analyzed cases. An increase in its value is noticed with each considered measure. The ductility factor, computed as the ratio between the du and dy, takes values from 6.5 for the C2 model to 12.5 for the C6 model.

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a) b) c) d)

Fig. 6 - Cracks and stress development for case: a) C1; b) C2; c) C4; d) C6.

Fig. 7 emphasizes the increase of the model stiffness when a slab is considered. The base shear force increases, while the displacement decreases for a load of 1000 kN. Comparing the capacity curves and the ductility factor values it is observed that the differences between model C1 and C2 are insignificant. Nevertheless the reduction in the slab reinforcement has a significant influence in the model behavior, increasing the flexibility of the model.

Fig. 7 - Capacity curves for frame without slab and frame with slab

The second case study analyses the influence of the reinforcement overlapping in columns and the anchorage length of beams, in the overall behavior of the structure (Canarache 2014). Both aspects are frequently seen during erection of structures and workers do not obey the project details.

A frame with 4 levels and 2 openings was analyzed with standard quality for concrete and reinforcement. The column cross section was of 60x60 cmxcm with a reinforcement of 12 bars of 25 mm diameter and stirrups of 8 mm diameter positioned every 10 cm. The beams cross section are 30x60 cmxcm with 6 bars of 20 mm diameter and same type of stirrups as

0

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400

600

800

1000

1200

0,00 0,05 0,10 0,15 0,20

Model C1

Model C2

Displacement [m]

Shea

r fo

rce

[kN

]]

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reinforcement. In Fig. 8 are presented the sections of interest and the load application in the pushover analysis.

Fig. 8 - General configuration of the frame considered in the case study

In order to analyze the influence of the anchorage length several dimensions were considered: 60 diameters (as in current regulations), respectively 50, 40 and 30 diameters. In all cases 42 steps of increasing horizontal loads were considered. Figures 9 and 10, and table 3 present the obtained results. The cracks in the concrete and the tensions from the reinforcement are compared. The differences for the analyzed situation are not significant.

Fig. 9 - Crack state and reinforcement cracks at the last load step for case of 60 diameters anchorage length.

Fig. 10 - Crack state and reinforcement cracks at the last load step for case of 40 diameters anchorage length

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Table 3 - Concrete tensions distribution in section 2, last step of load

Section 60d 50d 40d 30d

2a

2b

2c

2d

Scale values

In order to analyze the influence of the overlapping length of the reinforcement in columns a

pushover analysis in 42 steps was performed considering 3 different overlapping lengths: 60, 40 and 20 diameters. In these case study the differences are more significant. This leads to the conclusion that a correct overlapping length estimation is essential, because the crack distribution changes and the global failure mechanism is influenced by small differences. The overall behavior of the 2 D reinforced frame structure is influenced, moving toward a no favorable failure mechanism.

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Fig. 11 - Capacity curves for the considered cased foe overlapping lengths in column reinforcement

Fig. 11 shows the capacity curves obtain with ATENA software in the considered situations. Based on these curves and the well-known methodology regarding the steps to follow to plot the vulnerability curves (Olteanu, 2011), Fig. 12 is realized.

In this graphic it is noticed that for a spectral displacement of 10 cm, an increase of approximately 10 % of the vulnerability index is obtained for each 20 diameters decrease of overlapping. The plastic hinges develop at smaller values of the base shear force. In exchange, the cracks distribution in the concrete and the tensions distribution in the reinforcement do not change very much.

Fig. 12 - Comparison between vulnerability curves for different overlapping lengths of column reinforcement

CONCLUSION

The pushover analysis can be used for an exact quantification of the effects of local mistakes

in reinforcement due to erection works or to the fact that sometimes old buildings are analyzed, which were designed based of previous regulations. Such analysis can be used in order to determine the “critical areas” of structures, such as connections between existing

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 0,1 0,2 0,3 0,4 0,5

Dam

age

index

, ID

(%)

Spectral displacement (m)

20d

40d

60d

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concrete elements with new ones by chemical anchors, coating of elements and so on. A great advantage for using ATENA software to perform the analyzed case studies is that the detailed definition of all reinforcement in the models can be introduced.

Considering the first case study it is noticed that the proposed constructive measures have an important influence on the global behavior of the model. They redirected the plastic hinge development from the columns to the beams. Considering the obtained results it can be stated that the most favorable constructive measure is represented by the combination of 5 mm joint with reduced reinforcement.

Considering the second case study it can be concluded that the anchorage length for the beam reinforcement does not influence significantly the final results. On the contrary the overlapping length for the column has a great influence on the overall behavior of the structure and on the failure mechanism.

Adequate detailing should be given by the designers and respected during the erection process in order to reduce additional stresses in the principal elements and in exceptional cases unwanted failure mechanisms.

REFERENCES

[1]-Cervenka V., Cervenka J., Pulk R., ATENA – A Tool for Engineering Analysis of Fracture in Concrete. Sădhană, 27, part 4, 485-492 (2002), printed in India.

[2]-Seismic Evaluation and Retrofit of Concrete Buildings. ATC-40 Report, Vols. 1 and 2, Appl. Technol. Council, Redwood City, California, 1996

[3]-Olteanu I., Evaluarea comportării structurilor în cadre din beton armat supuse la acţiuni seismice. Ed. Politehnium, Iaşi, 2011.

[4]-Penelis G.G., Kappos A.J., 3-D Pushover Analysis: The Issue of Torsion. Dept. of Civil Engng., Aristotle Univ. of Thessaloniki, Greece, 2001.

[5]-Luca S.G., Pastia C., Toma I.O., Budescu M., Control Strategies for Seismic Energy Dissipation, 14th SGEM GeoConference on Science and Technologies in Geology,

Exploration and Mining, SGEM2014 Conference Proceedings, ISBN 978-619-7105-07-0 /ISSN 1314-2707, Bulgaria, Vol I, pp. 435-442, 2014.

[6]-Federal Emergency Management Agency, Guidelines for the Seismic Rehabilitation of Buildings. FEMA 273, Publ. 273, 1997.

[7]-Saidii M., Sozen. M., Simple Non-Linear Seismic Analysis of R/C Structures. J. of the Struct. Div., ASCE, 107, 937-952 (1981).

[8]-Federal Emergency Management Agency, Prestandard and Commentary for the Seismic Rehabilitation of Buildings. FEMA 356, Washington D.C., 2000.

[9]-Canarache R.M., Unele aspect privind reabilitarea construcțiilor energetice, PhD thesis, Iași, 2014.