Retrofitting/upgrading of reinforced concrete elements with buckling restrained bracing elements

S. BORDEA, D. DUBINA

Steel Structures and Structural Mechanics(CMMC) Politehnica University of Timisoara

Piata Victoriei nr. 2 ROMANIA

dan.dubina@ct.upt.ro, sorin.bordea@ct.upt.ro, aurel.stratan@ct.upt.ro http://cemsig.ct.upt.ro/cemsig/index.php

Abstract: - The main aim of the study is to evaluate the performance of a gravity load designed reinforced concrete frame retrofitted with buckling restrained bracing (BRB) systems as a dissipative and retrofitting device. The BRB system wish to be applied for reinforced concrete frames located in seismic areas which have been designed previous to the appearance of a seismic code. This analysis represents the main topic of STEELRETRO project Steel Solutions for Seismic Retrofit and Upgrade of Existing Constructions of the Research Fund for Coal and Steel (RFCS) [13]. In order to analyze and confirm BRB system effectiveness as a strengthening solution for poor seismic resistant RC Frames, a benchmark building was proposed for modeling. Key-Words: reinforced concrete frame, moment resisting frame, retrofitting, buckling restrained braces (BRB), dissipative device, nonlinear pushover analysis, target displacement. 1 Introduction The reinforced concrete building chosen to be as a reference benchmark structure is located in Italy and was design according to an old design code. The design code assumed in the design process is the Royal Decree n.2229 November 16th, 1939 issued in Italy for the construction of reinforced and not reinforced concrete building. It was decided to adopt this old design standard because many reinforced concrete buildings were design according to its rules in the 50 to early 70 of the XX century in Italy [13]. Common materials used in the 1950-s, as concrete with characteristic compressive strength fck=20N/mm2 and a characteristic yield strength for reinforcement of fsk=230N/mm2 were considered. The detailing of the reinforcement is characteristic for design practice of that period, as it follows: poor anchorage length of the rebars at the external beam column joint, the use of plane (not ribbed) rebars, inclined reinforcement used for shear force resistance, largely spaced stirrups (15 cm for columns, 25 cm for beams) in potential plastic zones.

2 RC Building description (geometry and loads) 2.1 Frame geometry

In this paper 3 story RC building is analyzed before and after retrofitting it by BRB system. The dimensions of the whole building in plane 23.4 x 18.4 m and it is 11.95 m high.

Fig. 1: STEELRETRO reference benchmark RC

building model and BRB system distribution

It was chosen that in the model the ground floor columns to start from 0,00 (foundation level) and to be fixed in Y direction (4 spans) and hinged in X direction (5 spans). The axes of beams were considered to start from the upper level (see Fig. 2). In this manner a span of 5 m was choose for X direction with 3 m in the middle span and 4.5 m for the span in Y direction.

Fig. 2: External frame in X direction (5 spans) and

interior central frame in Y direction (4 spans)

Proceedings of the 11th WSEAS International Conference on Sustainability in Science Engineering

ISSN: 1790-2769 407 ISBN: 978-960-474-080-2

The heights of the stories are 3.9 m at the ground floor, 3.4 m at the first level, 3.35 m at second level and 0.9 respectively 1.8 for the rafters eave.

Fig. 3: Plan view of the first and second floor and

direction of ribs in the floor

The elements cross sections are displayed in Table 1, in addition it should be noticed that all elements are foresaw with single 6 mm hoops spacing 25 cm for beams and 15 cm for columns.

Table 1. Beam and column cross sections

2.2 Loads

In the first step, the existing RC building was verified for ULS (dead, imposed, snow and wind loads) and seismic load in accordance with [4], [5], [6] and [7] [13]. To compute self weight of the elements, a 25 KN/m3 was chose as reinforced concrete specific weight, and it was applied as a uniform distributed load on the element. Dead load (DL) was distributed only on the beams which are perpendicular in the direction of the ribs (from the floor, see Fig. 4).

Fig. 4: Dead Load (DL) distribution on stories

The self weight of concrete roof and concrete floors were assumed to be 3 KN/m2 [13]. They consist of concrete in-situ cast parallel ribs (15 cm ribs + 5 cm slab) with 15 cm thick bricks see Fig. 5 [13].

Fig. 5: First and second floor/roof

In the 1st, 2nd and 3rd a distributed dead load of 0.8 KN/m2 for partitions was considered. The self weight of the exterior walls/cladding assumed to be 2.5 KN/m2 and its effect is transmitted only on the columns due to arch effect. In accordance to [5] the building is considered in category C1 as office areas of 3 KN/m2, and a category H for not accessible roof of 0.4 KN/m2. The imposed loads (IL) distribution is considered in the same way as dead load distribution (see Fig. 4). Regarding the snow load (SL), was considered to be as 0.8 KN/m2 [5] while the wind load (WL) is distributed perpendicular on the columns in both directions as 0.69 KN/m2 pressure and -0.29 KN/m2 in X direction, respectively 0.74 KN/m2 pressure and -0.40 KN/m2 in Y direction [13]. The imperfections were considered as global inclination angles [6] on both X and Y directions of the building. The seismically mass was taken into account according to [8] as a gravity load combination represented as (G+0.6x0.8xQ, where G=DL and Q = IL). Also, the accidental torsional effect (eai=+/-0.05) was considered for the reinforced concrete building. The seismically load was defined both in X (Ex) and Y direction (Ey) as an elastic spectrum [8] with a peak ground acceleration (PGA) of 0.23g, gI=1.0, TB=0.15 s, TC=0.5 s, TD=2.0 s, S = 1.2. For the reinforced concrete

Proceedings of the 11th WSEAS International Conference on Sustainability in Science Engineering

ISSN: 1790-2769 408 ISBN: 978-960-474-080-2

structure a seismic reduction factor q=1.5 was used and for retrofitted reinforced concrete structure (with BRB) q=6 (see Fig. 6).

0

1

2

3

4

5

6

7

0 1 2 3T[s]

4

Sd(T

)Se

(T),

TB TC

TD

q=1.5

TB TC

TD

q=6

Fig. 6: Elastic and design response spectrum [8]

According to [4] the following load combination resulted (see Fig. 7)

Fig.7: Load combinations [8]

The lateral forces for pushover analysis were considered modal distribution, and were determined as example Equation 1 below:

i ii

i i

m hFm h= (1)

where, hi = the height of level i relative to the base of the frame and mi = the mass at level i computed from the fundamental combination G+0.6x0.8xQ and distributed in the main nodes. The modal pattern force distribution resulted with the following values: f1=0.19, f2=0.337, f3=0.319, fr=0.155 (1 first floor, 2 second floor, 3 third floor, r roof level). All these normalized forces were applied in mass center of each story (in the middle of reinforced concrete floors). 3 RC Building modeling 3.1 Materials Concrete material was modeled as nonlinear based on Kent and Park model (see Fig. 7.a) with no tension [11]. The concrete was considered as unconfined due to [9] according to, if the hoops are spaced at a distance > d/3 the component is unconfined, where d - distance from extreme compression fiber to center of tension

reinforcement. According to [6] and corresponding to this type of concrete a young modulus of 29000 MPa was used. Reinforcement was modeled as modified Park nonlinear using a yield strain of 0.015 and an ultimate strain from 0.2 to 0.3 corresponding to yield strength of 230 MPa and an ultimate strength of 350 MPa (see Fig. 7.b). These limits were obtained from [3], corresponding on Romanian plane rebars OB37 which have a characteristic strength of 235MPa.

Fig. 7: a. Reinforced concrete material nonlinear model

based on Kent and Park; b. modified Park nonlinear model of steel reinforcement

3.2 RC elements (beams and columns) Reinforced concrete elements were modeled as plastic hinges concentrated at the ends of the elements. With the specification that in case of beams plastic hinges were concentrated in all points were the rebars change their number from the upper part to the lower part of the cross section and reverse (see Fig. 8 and Fig. 9).

Fig. 8. Reinforce concrete beam element definition

function of cross section

Fig. 9. Element splitting and plastic hinges location on rc

elements in X direction and Y directions Fig.12

Proceedings of the 11th WSEAS International Conference on Sustainability in Science Engineering

ISSN: 1790-2769 409 ISBN: 978-960-474-080-2

Plastic hinges were define as load deformation relationship following [2]/[9] model as a deformation controlled (ductile) typology (see Fig.10).

Fig. 10. Deformation controlled action model with

nonlinear load-deformation parameters and acceptance criteria ([2]/[9])

In the case of beams a moment rotation relationship for unconfined concrete was described following acceptance criteria values from [2]/[9] tables, basing on efforts obtained from gravity loads (see Fig. 11.a.). It should be precise that after insertion of the inverted V BRB system, the plastic hinges defined in beams at their intersection with braces elements, were defined as moment rotation curves at different stages of the axial force (P-M-M) see Fig. 11.b. In the same way were defined all plastic hinges for the columns, only that the moment rotation relation was defined differently for each direction of column cross section.

Fig 11. a. Moment rotation relation following FEMA

procedure; b. P-M-M surface interaction

As an observation, for more accurately results the shear capacity of the elements need to be checked. 3.3 Modeling hypothesis Due to the existence of a linear modeling of plastic hinges (from A to B from Fig. 10) in terms of moment-rotation curve, component effective stiffness corresponds to the secant value to the yield point of the component. In our case, following [2]/[9] table, the stiffness of beams and columns should be reduced by 50%, due to the fact that beams are nonprestressed and columns have axial compression, due to design gravity load,

coefficient u/y was found using formulas from [1], see Equation 3:

max

max

C = T

and maxfysc

T = f A

(3) where fysc= is the measured yield strength of the steel core. BRB member behaves according to a bilinear force-deformation relationship with hardening. In Fig. 14 and Fig. 15 is presented BRB behaviour model and the corresponding areas of the steel core in dissipative zone. As an observation the steel core (active zone) was considered to be Lcore=2m for all 3 storeys in both directions.

BRB behavior model - X direction

-1000

-750

-500

-2500

250

500

750

1000

-20 -15 -10 -5 0 5 10 15 20

Displacement [mm]

Forc

e (C

ompr

esio

n/Te

nsio

n)

[KN

]

ground floor - A=(30 x 100)mm21'st floor - A=(20 x 100)mm22'nd floor - A=(20 x 50)mm2

Fig.14. BRB behavior model in X direction BRB behavior model - Y direction

-350

-250

-150

-50

50

150

250

350

-20 -15 -10 -5 0 5 10 15 20

Displacement [mm]

Forc

e (C

ompr

esio

n/Te

nsio

n)

[KN

]

ground floor, 1'st floor & 2'nd floor - A=(20 x 50)mm2 Fig.15. BRB behavior model in Y direction

5 Performance assessment In Table 2 are presented the first three eigen modes function of their value, direction and type, both for non-retrofitted frame (RC) and for retrofitted one (RC+BRB).

Table 2. Modal response of RC vs. RC+BRB

Following nonlinear static (pushover) analysis, it was observed the order of plastic hinges in elements (attaining of CP, FEMA acceptance criteria) and the effect of BRB retrofitting technique on RC building. In Tables 3, 4 and 5 basing on FEMA assumption of 50% stiffness reduction, for both non-retrofitted frame (RC) and for retrofitted one (RC+BRB), in X and Y directions, are presented the elements from each storey (columns, beams and braces in case of retrofitted building). In this manner, it may be followed the order of plastic hinges attaining collapse prevention (CP), their corresponding top displacements (D) and base shear forces (F) (see tables 3, 4 and 5).

Table 3. Plastic hinges (CP) order and corresponding F and D values from pushover analysis for columns

Table 4. Plastic hinges (CP) order and corresponding F and D values from pushover analysis for beams

Table 5. Plastic hinges (CP) order and corresponding

F and D values from pushover analysis for BRB

In order to have a reference for the stage of the elements, the target displacement of the RC and RC+BRB building was computed according to [8]. Analysis of the original RC showed an unsatisfactory seismic response. Ultimate rotations in plastic hinges corresponding to collapse prevention state are first reached in columns followed by the ones in beams. Because columns attain CP at a top displacement roughly smaller than the top displacement demand result a very limited global ductility of non-retrofitted building.

Proceedings of the 11th WSEAS International Conference on Sustainability in Science Engineering

ISSN: 1790-2769 411 ISBN: 978-960-474-080-2

In Fig. 16 and Fig. 17 may be observed the pushover curves resulting from nonlinear analysis in terms of top displacement and base shear force for both directions. In this manner, comparing RC and RC+BRB, it may be seen an increasing in strength of about 2.5 times, a large increase of stiffness and around 4 times reduction of the target displacement. These changes appeared due to BRB system and as it may be seen that BRB elements reach ultimate deformation state before columns. This strengthening solution reduced the overall damage in the structure, as less plastic hinges formed in reinforced concrete elements at the target displacement.

Fig. 16. Pushover curves for RC vs. RC+BRB and corresponding target displacement on X direction

Fig. 17. Pushover curves for RC vs. RC+BRB and corresponding target displacement on Y direction

6 Concluding Remarks A nonlinear static analysis was applied on the three dimensional model, with finite element method [12], of the reinforced concrete building before and after global retrofitting with BRB system. The applied system showed a good effect on global behavior of the RC building in terms of strength and stiffness. However, a better response capacity of BRB retrofitting system is expected if a local strengthening of the elements (especially columns) will be applied. The aim of this analysis was the illustration of performance base evaluation of BRB retrofitting procedure application, which it works only by local strengthening. Also, a better sizing of BRB member in balance with initial structural stiffness and strength may be performed. Local strengthening of columns, maybe beams too (with FRP), is needed due to the fact that

BRB system increase strength demand in RC members. In this manner a convenient distance it will obtain between reaching of BRB elements at ultimate deformation versus the members (beams and columns) of the structure. References: [1] AISC (2005) Seismic Provisions for Structural Steel

Buildings American Institute of Steel Construction, Inc. Chicago, Illinois, USA.

[2] ASCE/SEI 41-06 (2007) Seismic Rehabilitation of Existing Buildings, American Society of civil Engineering (formerly FEMA 356)

[3] Clipii T. et all. (1999) Beton armat, Romania, Editura Orizonturi Universitare, Timisoara.

[4] Eurocode 0 (April 2002) - Basis of structural design CEN - European Committee for Standardization.

[5] Eurocode 1 (April 2002) Actions on structures - Part 1-1: General actions - Densities, self-weight, imposed loads for buildings. CEN - European Committee for Standardization.

[6] Eurocode 2 (December 2003) Design of concrete structures - Part 1-1: General rules and rules for buildings FINAL DRAFT prEN 1992-1-1. CEN - European Committee for Standardization

[7] Eurocode 3 (2003). Design of steel structures Part 1-1: General Rules and Rules for Buildings CEN - European Committee for Standardization.

[8] Eurocode 8 - EN1998-1 - (December 2004) Design of structures for earthquake resistance - Part 1: General rules, seismic actions and rules for buildings, CEN - European Committee for Standardization

[9] FEMA 356, (2000) Prestandard and commentary for the seismic rehabilitation of buildings, Federal Emergency Management Agency, Washington (DC).

[10] Newell, J.& Higgins, C. (n.d.) Steel Confined Yielding Damper For Earthquake Resistant Design ,NHMJ Young Researchers Symposium June 21, 2003,http://cee.uiuc.edu/sstl/nhmj/ppt/Newell.ppt

[11] Park, R. & Paulay, T (1975) Reinforced Concrete Structures, New Zealand ,John Wiley & Sons, Inc., New York.

[12] Structural Analysis Program (SAP2000). [13] Steel Retro report (may-july 2008) Definition of the

reinforced concrete benchmark building for the execution of comparative performance analyses between steel intervention techniques (amended version 1.1), WP 3, 4, 5 and 6: Cost, performance and constructive analyses of steel solution for retrofitting vertical elements, floors, roofs and foundations RIVA Acciaio S.p.A. - Aurelio Braconi, Alessandro Osta, University of Pisa - Luca Nardini, Walter Salvatore

Proceedings of the 11th WSEAS International Conference on Sustainability in Science Engineering

ISSN: 1790-2769 412 ISBN: 978-960-474-080-2