SEISMIC ANALYSIS OF RC FRAMED STRUCTURES RETROFITTED WITH STEEL BRACES

SEISMIC ANALYSIS OF RC FRAMED STRUCTURES RETROFITTED WITH STEEL BRACES Ciro FAELLA Full Professor University of Salerno Via Ponte don Melillo, 8484 Fisciano (SA), Italy c.faella@unisa.it Carmine LIMA Research Assistant University of Salerno Via Ponte don Melillo, 8484 Fisciano (SA), Italy clima@unisa.it Enzo MARTINELLI Assistant Professor University of Salerno Via Ponte don Melillo, 8484 Fisciano (SA), Italy e.martinelli@unisa.it Roberto REALFONZO Associate Professor University of Salerno Via Ponte don Melillo, 8484 Fisciano (SA), Italy rrealfonzo@unisa.it* Abstract Existing Reinforced Concrete (RC) structures designed for gravitational loads only are generally vulnerable to seismic events. They do not generally comply with the more advanced seismic safety standards and are often in need for retrofitting. The introduction of diagonal steel bracings is among the most common technical solution for improving seismic performance of existing RC structures. Nevertheless, several issues dealing with both analysis and design of RC frames strengthened by steel bracings under seismic action are still open. This paper presents the numerical simulation of existing RC frames retrofitted by using steel bracing with different arrangement and distribution throughout the structure. The nonlinear analyses performed in OpenSEES by using the model generated by CDSwin focuses on RC structures retrofitted with concentric X-braces which are often employed for seismic strengthening of existing structures. After a short overview of the most recent contributions on the above mentioned aspect, the paper outlines the numerical models employed for simulating the behaviour of both RC frames and steel bracings. Then, the results of seismic nonlinear analyses are carried out for demonstrating the facility and effectiveness of the two software in modelling and simulating nonlinear behaviour of diagonal steel braces. Moreover, the effect of bracing patterns is investigated and the most effective one in the case of a relevant case-study is pointed out. Keywords: Existing RC frames, steel bracings, earthquake, retrofitting, structural scheme 149

1. Introduction Existing Reinforced Concrete (RC) structures built during the last decades in seismic regions (such as a wide part of Italy and the Mediterranean area) do not generally comply with the more advanced seismic codes currently adopted in the same regions [1][2] and are often in need for retrofitting. Several seismic retrofitting techniques are currently available and employed in practical applications, even though issues are still open (or not completely solved by the same codes) about the rational design of these retrofitting interventions. A thorough State-of-the-Art Report collecting the most well-established techniques for seismic retrofitting of RC structure is available in [3]. In particular, several member-level techniques (basically aimed at enhancing the capacity in terms of strength and/or ductility of single elements of the existing structures) are described and functionally distinguished by the so-called structurelevel techniques. The latter ones mainly aim at reducing the demand on the existing structure by introducing further elements (i.e., RC shear walls) or substructures (e.g., steel bracings) able to resist the seismic excitation. A rational strategy for a possible synergic application of both techniques has been also conceived and presented in the scientific literature [4]. Bracing systems are widely utilised in steel buildings and several models are currently available for describing their response under the cyclic actions induced by seismic excitation [5]. Moreover, using steel bracing systems in seismic retrofitting of existing RC structures is actually an attractive technique, as it is characterized by high architectural and functional compatibility with respect to the original purposes of the existing structure. This is the key motivation for a series of recent studies aimed at investigating the possible strengthening of RC frames by means of dissipative steel bracings [6][7]. As a matter of principle, the design of steel bracing in RC frames can be approached according to the well-established capacity design philosophy. Moreover, the key aspect of connection overstrength needs to be completely revisited in the case of steel braces connected to RC joints [8]. Another issue of concern deals with the distribution of steel braces throughout the existing RC frame and the definition of rational structural schemes for bracing systems to be employed in seismic retrofitting. Few recent studies actually addressed this topic by either proposing experimental and numerical results on steel frame with different braces configurations [9], or examining different bracing patterns for a given RC structures considered as a case-study [1], or approaching the problem of defining an optimal bracing configuration [11]. The present paper is also intended at investigating the effect of different bracing configurations on the seismic response of retrofitted RC frames. In particular, the study focuses on concentric X-braces which are often employed for seismic strengthening of RC existing structures. Thus, Section 2 presents an existing RC frame which is considered as a case-study. Moreover, the same section reports the key steps in the design procedure of steel braces intended for retrofitting and the various possible bracing configurations considered in this study. Finally, Section 3 outlines the key aspects of numerical models employed for simulating the behaviour of both RC frames and steel bracings and summarizes the results of the seismic analyses carried out on those retrofitted structures pointing out the influence of the bracing configuration on the seismic demand of the existing concrete members. Moreover, insights about the action values at the foundation level are also considered and the main favourable and unfavourable aspects of the various possible configurations are pointed out. 2. Presentation of the case-study This paper addresses a critical issue in designing steel bracings for seismic retrofitting of existing buildings: it investigates the influence of brace distribution throughout the existing frame. A 4-storey school building lying in the neighbourhood of L Aquila is examined as a case-study (Figure 1 shows its floor plan and the 3D model developed in CDSwin [1]). 15

345 35x5 135 345 345 35x5 35x5 35x5 y 35x5 x 35 35 35 35 35 35 35 35 35 35 35 Figure 1. Typical floor plan with braced frames A nominal life of 5 years and functional type III (C u = 1.5) have been assumed according to NTC 28 [13]. Moreover a site class C and the topographic category T1 have been also considered for defining the design spectra for the four relevant Limit States (Table 1). Spectral dates Table 1: Parameters of the seismic design spectra Limit States of Service Ultimate Limit States SLO SLD SLV SLC P Vr 81% 63% 1% 5% T R [years] 45 75 712 1462 a g [m/s 2 ].98 1.155 2.792 3.574 a g /g.93.118.285.364 F 2.347 2.317 2.385 2.419 T C * [s].277.291.351.365 C C 1.6 1.58 1.48 1.46 S S 1.5 1.5 1.29 1.17 S 1.5 1.5 1.29 1.17 T B [s].148.153.174.178 T C [s].444.459.521.534 T D [s] 1.97 2.71 2.739 3.58 2.1 Design of a steel bracing sub-structure The steel bracings have been designed for retrofitting the structure under consideration by performing a static linear analysis [13]. Table 2 reports the values of masses and horizontal static forces used in designing steel bracings according to NTC 28 [13] and using a force reduction factor q=4. 151

Table 2: Masses and forces used in design steel bracings Floor Masses [ton] h [m] H [m] Forces [kn] 4 239.4 3.8 13.9 936.6 T =.36 s 3 388.43 3.8 1.1 114.21 S d (T) = 2.15 m/s 2 2 385.84 3.3 6.3 684.17 F h = 338.88 kn 1 371.74 313.89 1385.41 Table 3 summarises relevant data about steel diagonals in the bracing substructure. Table 3: Relevant data about the steel bracings Floor Forces [kn] Bracings in tension [kn] Section Overstrength 4 34.4 49.55 HEA1 1.36 3 358.87 934.85 HEB14 1.2 2 222.36 116.6 HEB16 1.22 1 12.1 1293.17 HEB18 1.32 2.2 Alternative distributions of the steel braces within the existing RC frame Three alternative patterns have been considered even though the number of diagonals placed on each level has been kept constant. The sections designed and reported in table 3 have been introduced in the models developed by using CDSwin [1] at each floor by considering the distributions reported in Figure 2. Façade X Façade Y Bracing distribution Figure 2: Distributions of steel bracings on the two facades Pattern 1 Pattern 2 Pattern 3 The following analyses are intended at investigating the seismic response of the structures retrofitted by means of the bracings distributed according three different patterns depicted in Fig 1. Particularly, their influence on relevant response parameters, such as displacement demand, foundation actions and the internal forces distribution, is particularly addressed. 3. Numerical analysis Nonlinear Time History (NLTH) analyses have been carried out on the 3D structural model by using the OpenSees computer program [14]. Indeed, a tcl input file has been generated by CDSwin [1] and then it has been processed in OpenSEES [14]. Non-linear behaviour of RC beams and columns has been simulated through a lumped plasticity model by introducing plastic hinges at both ends of each element (in particular the beamwithhinges element has been adopted by using the OpenSEES default library introducing Concrete1 and Steel1 materials for concrete and steel, respectively [14]). Moreover, the buckling effect has been considered in modelling steel bracings [15]: in particular, the non-linear behaviour has been implemented through truss elements by using the Uniaxial Hysteretic Material currently available in OpenSees [14]; a threshold for the axial action, both in tension and compression, has been evaluated according to NTC 28 provisions [13]. Pinching factors equal.8 and.2 have been used for simulating the reduction in terms of deformation and force capacity, respectively. 152

top [m] stress / force Axial Force [kn] Figure 3 shows on the left the general behaviour of the elements employed in OpenSees [14] for simulating the cyclic response of dissipative elements taking into account the pinching effect. This general relationship has been specialized for the steel braces under consideration and their cyclic response is represented by the graph on the right of Figure 3. A clearly unsymmetrical behaviour can be observed therein as a result of the reduced strength in compression..8.6.4.2 -.2 -.4 -.6 -.8 - -.1-5 5.1 strain / displacement 1 4 1 2 1 8 6 4 2-2 -4 -.4% -.2% %.2%.4%.6%.8% Drift Figure 3: Hysteretic behaviour of steel bracings: OpenSees hysteretic model (on the left), bracing response (on the right). Nonlinear Time History analyses have been performed for the four Limit States (SLO, SLD, SLV and SLC) defined by NTC 28 [13]. Consequently, four sets of 7 accelerograms matching with the design spectra defined in table 1 have been selected by using Rexel v.3.2beta [16] for each Limit State and for the two main directions in plan. Thus, a total number of 56 accelerograms has been used for performing 14 analyses for each Limit States: 7 of those in X-direction with a 3% of the action in Y-direction and 7 analyses in Y-direction with a 3% of the seismic action in the X-direction. According to NTC 28 [13] the demand in terms of forces and/or displacements for each limit state and direction has been evaluated as mean of the response evaluated through the 7 dynamic nonlinear analyses. 3.1 Results in terms of displacement demand on the retrofitted structures Figure 4 outlines the displacement demand evaluated on the existing structure and the structures retrofitted with the three analysed patterns. It shows that the displacement demand on the existing members is evaluated for the retrofitted structures (regardless the particular pattern adopted for the bracing system) is much lower than the corresponding values obtained of the existing one..2.18.16.14.12.1.8.6.4.2 Existing SLO SLD SLV SLC SLO SLD SLV SLC Direction X Direction Y Figure 4: Displacement demand. 153

Floor Floor Floor Floor Moreover, among the various retrofitted structures, the one adopting bracing pattern n.3 (Figure 2) results in the lower values of displacement demand. The better performance of the same structure is also confirmed by the analysis in terms of the interstorey drifts (Figure 5) 4 Pattern 3 Pattern 2 Pattern 1 Existing 4 Pattern 3 Pattern 2 Pattern 1 Existing 3 3 2 2 1 SLD SLO %.2%.4%.6%.8% % 1.2% 1.4% Interstory drift - Direction X 1 SLC SLV %.5% % 1.5% % Interstory drift - Direction X Pattern 3 Pattern 2 Pattern 1 Existing Pattern 3 Pattern 2 Pattern 1 Existing 4 4 3 3 2 2 1 SLD SLO %.2%.4%.6%.8% % 1.2% 1.4% Interstory drift - Direction Y 1 SLC SLV %.5% % 1.5% % Interstory drift - Direction Y Figure 5: Interstorey drifts. 3.2 Actions at the foundation level due to the various bracings patterns Figure 6 shows the value of the axial forces in the columns at the first floor of the building. They have been evaluated at the Limit State of Life Safety for each of the three different patterns in Figure 2. The results are reported in terms of ratio between the axial force N Sd in the braced structures and the corresponding values N Sd,existing evaluated for the unstrengthened existing one. Those data are of interest for investigating the different demand induced by the seismic action on the foundation. Thus, the best behaviour observed in case of pattern 3 is confirmed by the values of the ratios N Sd /N Sd,existing which are lower than the ones evaluated for the first and the second bracing patterns. Obviously, the axial forces determined for the braced structures are greater than the ones evaluated for the existing structure (and the ratio on the y-axes of Figure 6 are often greater than the unit) because retrofitting leads to a significantly higher lateral strength of the structure. Further results in terms of actions at the foundation level for other Limit States and in direction Y are omitted for sake of brevity. Direction Y - SLV N Sd / N Sd,existing N Sd / N Sd,existing 5 1 15 2 25 3 5 1 15 2 25 3 Base Joints Base Joints Figure 6: Axial actions at the foundation level: X-direction (on the left) and Y-direction (on the right). 154

3.3 Results in terms of actions of the RC frames and steel bracings The four diagrams reported in Figure 7 show the actions (N Sd, V Sd, M x,sd, M y,sd ) in beams and columns for the retrofitted structures adopting the three distributions of bracing. In particular, the retrofitted-to-existing ratio in terms of actions on the various members is reported on the y-axis. Since the curve which refers to the retrofitted solution adopting pattern 3 for the bracing distribution is always below of the other two curves, this diagrams demonstrate once again (and under another standpoint) the superior performance of pattern 3 solution with respect to the other considered ones. N Sd / N Sd,existing V ysd / V ysd,existing 5 1 15 2 25 3 Frame 5 1 15 2 25 3 Frame M xsd / M xsd,existing M ysd / M ysd,existing 5 1 15 2 25 3 Frame 5 1 15 2 25 3 Frame Figure 7: Actions in frames: axial force (on the top-left), shear (on the top-right), bending-x moment (on the bottom-left) and bending-y moment (on the bottom-right). 4. Conclusions In this paper the effects of alternative bracing configurations on the seismic response of retrofitted RC frames have been investigated. As a result the distribution of steel bracings in RC frames significantly affects the results in terms of optimizations of actions in RC frames and at the foundation level. In particular from a general point of view the three analysed patterns are characterized by increasing levels of distribution of steel bracing on RC frames. The third configuration generally leads to a superior performance under the various standpoints emphasized in section 3. In particular, the following aspects can be pointed out: - the lateral stiffness of the structure retrofitted by adopting the above mentioned pattern 3 is significantly higher than those obtained in the other cases: this effects is of key importance especially for the Limit State of SLO and SLD; - the axial stresses in beam-columns determined on pattern 3 retrofitted frame are generally lower than those induced on the same elements in the other retrofitted solution; this effect is also beneficial for foundation elements; - as a general trend, patterns 3 leads to the lowest values of stresses (in terms of axial, shear and bending stresses) in RC structures. As a concluding remark, the influence of the bracing configuration on the response of retrofitted RC frames is not negligible, as it controls the actual lateral stiffness of the 155

retrofitted structure. Although formulating general rules for a rational design of those steel bracings is not an easy task, the implications in terms of flexural and shear stiffening induced by the alternative configurations of braces should be carefully considered. 5. Acknowledgements The Authors gratefully acknowledge S.T.S. Software Tecnico Scientifico s.r.l. for providing CDSwin computer software. 6. References [1] CDSwin, Calcolo di strutture in c.a., acciaio e legno, S.T.S. Software Tecnico Scientifico s.r.l. [2] EN 1998-1 (24), Design of Structures for Earthquake Resistance - Part 1: General Rules, Seismic Action and Rules for Buildings, December 24 [3] EN 1998-3 (25), Design of Structures for Earthquake Resistance - Part 3: Assessment and Retrofitting of buildings, June 25 [4] fib, Seismic assessment and retrofit of reinforced concrete buildings, State-of-art report, bulletin 24, 23 [5] Faella C., Martinelli E., Nigro E., A rational Strategy for Seismic Assessment of RC Existing Buildings, 14th WCEE, Beijing (China), 12-17 Sept, Paper ID 5-3-28, 28 [6] Tremblay R., Inelastic seismic response of steel bracing members, Journal of Constructional Steel Research, 58, 22 [7] Bartera F., Giacchetti R., Steel dissipating braces for upgrading existing building frames, Journal of Constructional Steel Research, 6, 24 [8] Youssef M.A., Ghaffarzadeh H., Nehdi M., Seismic performance of RC frames with concentric internal steel bracing, Engineering Structures, 29, 27 [9] Maheri M. R., Ghaffarzadeh H., Connection overstrength in steel-braced RC frames, Engineering Structures, 3, 28 [1] Türker T., Bayraktar A., Experimental and numerical investigation of brace configuration effects on steel structures, Journal of Constructional Steel Research, 67, 211 [11] Komuro T., Hirosawa M., Analysis on elasto-plastic behaviour of an existing reinforced concrete building retrofitted by steel-framed braces in different arrangements and simplified evaluation method of horizontal bearing capacity of the retrofitted building, 13th WCEE, Vancouver, BC (Canada), 1-6 August, Paper No. 794, 24 [12] Aydin E., Boduroglu M. H., Optimal placement of steel diagonal braces for upgrading the seismic capacity of existing structures and its comparison with optimal dampers, Journal of Constructional Steel Research, 64, 28 [13] Italian Ministry of Public Work (28), Technical Code for Constructions (in Italian), Ordinary Supplement n. 3 to the Italian Official Journal of 4 February 28. [14] Mazzoni S., McKenna F., Scott M.H., Fenves G.L., OpenSees Open System for Earthquake Engineering Simulation, Pacific Earthquake Engineering Research Center, University of California. Berkeley (USA), 27 [15] Gomes A., Appelton J., Nonlinear Cyclic Stress-Strain Relationship of Reinforcing Bars Including Buckling. Eng. Struct., 19(1), 822 826, 1997. [16] Iervolino I., Galasso C., Cosenza E., REXEL: computer aided record selection for codebased seismic structural analysis, Bullettin of Earthquake Engineering, 8:339-362, 21. 156