EFFECTS OF OPENINGS ON COLLAPSE RISK OF INFILED RC BUILDINGS

Transcription

1 EFFECTS OF OPENINGS ON COLLAPSE RISK OF INFILED RC BUILDINGS V. H. Akansel 1 and A. Yakut 2, P. Gülkan 3 1 Graduate Student and Research Assistant, Department of Civil Engineering, Middle East Technical University, Ankara, (on leave from Muğla Sıtkı Koçman University), vesileakansel@gmail.com 2 Prof. Dr., Department of Civil Engineering, Middle East Technical University, Ankara, ayakut@metu.edu.tr 3 Prof. Dr., Middle East Technical.University NCC, 99738, Kalkanlı, Güzelyurt, Northern Cyprus, Mersin 10, Turkey, pgulkan@metu.edu.tr ABSTRACT: Infill wall arrangements affect the failure mechanism and create localised damages. Such effects include increased axial forces on columns due to overturning, concentrated shear forces at the ends of beams and columns, and localised deformations in columns surrounded by discontinuous infills. In this study, we concerned the effects of openings, such as doors and windows in the infill walled reinforced concrete buildings on the failure mechanisms and collapse risk. Analytical models assembled in which the infill walls modelled with macro modelling approaches. OpenSEES software was used for modelling and comparison of the numerical models with experiments. Reliable and accurate infill wall model that simplifies modelling and decreases computational effort will be preferred. 3, 5 and 8 story frames were modelled. Bare frame results compared with fully infilled and infilled frames with openings. Failure mechanisms are investigated for different infill wall arrangements. Engineering demand parameters such as base shear capacities, inter-story and roof drift are investigated. Computed demands compared with the design parameters defined in TEC 2007 (Turkish Earthquake Code). KEYWORDS: Infill Wall, Openings, MRF, RC, Design. 1. INTRODUCTION The interaction of infill walls with reinforced concrete or surrounding frames is a state-of-art topic for researchers. Infill walls affect the strength, stiffness, ductility with a non-deniable level when the reports of the significant earthquakes are investigated. The experimental studies, done by many researchers, support the contribution of the infills (Panagiotakos and Fradis (1996), Dolsek and Fajfar (2005, 2008) and Furtado et.al. (2015). There are several ways to model the infill walls with reinforced concrete frames. These methods divided into two part such as micro modelling and macro modelling. Micro-modeling approach considers bricks, mortar and plaster (if it exists) separately and use contact definitions between each of them and surrounding frame (Redmond et.al. (2015)). Macro modelling approach considers only the total response and not interested in the damage pattern in infill wall. Equivalent compression-only struts are used to construct the macro modelling (Smith and Carter (1970)). Macro models differ from each other regarding the number of struts and material constitutive relationship

2 (Thiruvengadam (1985), Chrysostomou (1991) and Crisafulli et. al. (1997 and 2000)). Equivalent strut method is a wise way to calculate the strength and displacement capacity of the infills quickly. Smith and Carter (1970) was the first of authors studied with the concept of the relative stiffness of frame to infill panel. They used some charts to calculate equivalent strut width via contact length definition. Thiruvengadam (1985), Chrysostomou (1991) and Crisafulli et. al. (1997 and 2000) studied a three compression-only strut model for each direction to consider the interaction of infill wall with the surrounding frames. Many researchers did experimental studies to understand the contribution of infills to the total response. Mehrabi et.al. (1996), Bertoldi et.al (1993) and Kakaletsis and Karayannis (2008) and Ezzatfar et.al. (2014) are some of the researchers who tested reinforced concrete frames with infills. Openings in infill walls decrease the strength capacity and should be considered in modelling. Dawe and Seah (1989) use a factor to reduce the strength capacity of the infills with opening In this study, the macro-modeling approach was preferred. Equivalent strut widths and contact lengths were calculated according to ASCE 41, and three compression-only struts were defined for each direction. The material constitutive relationship was constructed using the studies of Bertoldi et.al (1993) and Zarnic and Gostic (1997). The strength capacity of the infills will be reduced by a factor which is suggested by Dawe and Seah (1989). 2. MODELING OF NUMERICAL MODEL AND VERIFICATION The Open System for Earthquake Engineering Simulation (OpenSees, McKenna, (2011)) was used for simulation of the analytical models. Force-based elements were preferred for beam and columns. Fiber sections were defined to represent the cross section of structural elements. The CONCRETE07 material model for reinforced concrete and the STEEL02 material model for reinforcing steel was used. The BONDSP01 material model was used for anchorage slip at the bottom of the columns. In Figure 1b, the modelling technique is given. Shear aggregated into the each fiber section with elastic GA stiffness. Infill walls were modelled with an equivalent strut, macro-modeling technique. ASCE 41 equivalent strut modelling approach was preferred to calculate the strut width and contact length between infill and surrounding frame. Due to the interaction of infill wall and surrounding structure, Thiruvengadam (1985) proposed the use of multiple strut models. Chrysostomou (1991) and Crisafulli et. al. (1997 and 2000) studied a three compressiononly strut model for each direction. In Figure 1, the three compression-only strut model proposed by Chrysostomou (1991) was given, and this modelling technique was used in this study. a) b) Figure 1. a) The Three Strut Model for Each Direction proposed by Chrysostomou (1991); b) Opensees Finite Element Model Equivalent strut width and contact length parameters were calculated according to given formula from Eq.1 through Eq3.

3 a = (λ 1 h col ) 0.4 r inf λ 1 = [ E inf t inf sin (2θ) z = 1/4 ] 4 E fr I col h inf π 2 λ 1 (1) (2) (3) where; h col : Column height between centerlines of the beam h inf : Height of infill panel E fr : Expected modulus of elasticity of frame material E inf : Expected modulus of elasticity of infill materials which is calculated as 550*f m. I col : Moment of inertia of column r inf : Diagonal length of the infill panel t inf : Thickness of infill panel and equivalent strut : Angle whose tangent is the infill height-to-length aspect ratio, in radians. z: Contact length (in calculations half of the calculated values were used.) Calculating the equivalent strut model is not enough to model the infill behaviour. Therefore, a material constitutive law is necessary to use. Panagiotakos and Fardis (1996) and Bertoldi et.al (1993) proposed some similar material constitutive relationships for the infill strut model. In this thesis, the material constitutive model from Bertoldi et.al (1993) was studied with some modifications. Force-deformation relationship is used in the modelling, as given in Figure 2. This material constitutive law modified with new formula for F m, infill strength capacity, by Zarnic and Gostic (1997). This formula includes wall ratio in a way with C 1 factor and calculates max axial load capacity of the strut. The formula given in Eq 4; where f tp is the cracking strength of the infill, obtained from a diagonal compression test, whereas L in and H in are the lengths and the height of the infill. F m = L int w f tp (1 + C 2 C 1 + 1), C 1 = L in (4) 1 H in Secant stiffness, K m at F m is calculated from Eq. 5 which is proposed by Klingner (1976). S m is the maximum displacement calculated as the ratio of the F m to K m. Figure 2. Modified from Bertoldi et.al. (1993) K m = E mw w t w cos 2 θ, d S m = F m K m (5)

4 Yield parameters are calculated according to given formula in Eq. 6. G in is the tangential elastic modulus of masonry infill. K y = K 1 = G int in L in H in, F y = 0.8 F m = f tp t in L in, S y = F y K y (6) Ultimate displacement is calculated according to Eq. 10. K 3, softening stiffness is in the range of 0.005K 1 K 3 0.1K 1 according to Uva et.al. (2012), Bertoldi et.al (1993) and Panagiotakos and Fardis (1996). Dolsek and Fajfar (2005, 2008) suggested that S m can be considered as 0.2% in the case of no openings in infill walls and 0.1% for the infill walls with openings. S u = S m + F m K 3 (7) In this study, the method proposed by Dawe and Seah (19889) was preferred for the calculation of the infill strength. Dawe and Seah (1989) used a factor, as given in Eq 8, to calculate the strength capacity of infill wall. λ o = L opening L infill (8) Material constitutive law, which is created using the formulas given in Eq. 1 to 7, were converted to the stressstrain relationship to use in the numerical model. Strain compatibility was considered while transforming to stressstrain relationship. For verification and validation of the modelling technique, experimental studies can be useful. In this study, the experimental study of Kakaletsis and Karayannis (2008) was used. Kakaletsis and Karayannis (2008) tested 1/3 scale one-bay, one-story one bare, two fully infilled and four infilled with openings frames. They considered two types of infills, regarding strength, such as weak and strong. The authors investigated the effects of openings and compressive strength of masonry parameters and designed almost same shear strength. In Figure 3, the details of the test specimen are given from the study of Kakaletsis and Karayannis (2008). The compressive strength of the infills is 2.63 MPa for weak infill and 15.8 MPa for strong infill. Elastic modulus is 661 MPa and 2837 MPa correspondingly for weak and strong infills. The thickness of the weak infill is 60 mm and 52 mm for strong infill walls. The compressive stress of concrete was MPa, and the yield stress of the longitudinal and transverse reinforcements was tested as MPa and MPa correspondingly. Friction coefficients for weak and strong infills are and correspondingly. In Eq. 9, the shear stress calculation for the cohesion test is given. τ = τ o + μσ (9) where τ is the shear stress (f tp ), τ o is the cohesive strength, μ is the friction coefficient an σ is the normal stress under the vertical load.the cohesive strength is arround MPa for weak and 0.17 MPa for strong infills. K 3 stiffness, for degradation part in material constitutive law, is taken as 0.1K 1 both for E m= 660 MPa and Em=550*f m for the comparison od the weak infill response. In Figure 4a and Figure 5a, E m was considered as given by Kakaletsis and Karayannis (2008) and in Figure 4b and Figure 5b, E m was calculated as E m=550f m which is consistent with FEMA 273 and ASCE 41.

5 Figure 3. Kakaletsis and Karayannis (2008) from Figure 1, (a) reinforcement detailing of the R/C frame model (mm); (b) weak masonry (cm); (c) strong masonry (cm) In Figure 4 and Figure 5, the results of the Specimen DO2 and WO2 from the experimental study of Kakaletsis and Karayannis (2008) compared with the analytical ones. DO2 is the specimen for weak infill with the door opening, and WO2 is the specimen for weak infill with the window opening. In Figure 4a, the analytical model has a good match with the experimental study, however, using the E m as given in the experimental study makes the cyclic behaviour non-degrading regarding strength after the peak. In Figure 4b, the numerical model shows degrading in strength and has a good match with experimental results. In Figure 5, the strength capacity is obtained approximately 15% less for weak infill with window opening and degrading behaviour is possible only if we use E m=550f m. a) b) Figure 4. Results for Specimen DO2;a) E m= E exp and f t=(f t) exp; b) E m=550f m and f t=(f t) exp a) b) Figure 5. Results for Specimen WO2;a) E m= E exp and f t=(f t) exp; b) E m=550f m and f t=(f t) exp

6 In the following parts of this study, K 3 post peak stiffness was taken as 0.1K 1 and the f tp, tensile strength was calculated according to given formula in Eq.8 and τ o =0.267 MPa and μ=0.770 were taken in the calculations. This numbers are relevant with the Turkish construction material properties for infill (Begimgil (1991)). 3. CASE STUDIES AND RESULTS Building designs were made according to TEC2007, TS500 and TS498 and assumed as residential. Equivalent (Linear) earthquake load analysis performed for the design process. Soil class is Z1 (Ta=0.10 s and Tb= 0.30 s), and seismic zone assumed as 1. PROBINA v.18 software was used for design. High ductility systems were chosen (R=8) as specified in TEC2007, In Figure 6 through Figure 8, 3-story, 5-story and 8-story reinforced concrete frames with infill walls were given. The building is for 3, 5, and 8 story buildings are 160 m 2, 182 m 2, and 243 m 2.The compressive strength of reinforced concrete was f ck=25 MPa. Yield strength for longitudinal and transverse reinforcing steel was 420 MPa and 220 MPa, respectively. Young modulus of concrete and steel were MPa and MPa, respectively. Frames were selected from the first mode dominant direction and inner frames. Infill wall thickness was taken as 20 cm, the compressive strength of the infill wall was taken as f m=3 MPa. f tp is calculated according to Eq.8 on the change of the vertical stresses at each floor level. In Figure 6 - Figure 8, designed frames are given. Openings for windows are (1.1 m) x (1.0 m) and for doors are (0.9 m) x (1.90 m). All the opening are in the middle of the bay for doors and at the center of the bay for the windows. Three and five-story building frames both have windows and door openings, and the eight-story frame has door openings. a) b) c) Figure 6. 3-story, a) 3D view ; b) plan; c) FF axes frame a) b) c) Figure 7. 5-story, a) 3D view ; b) plan; c) FF axes frame

7 a) b) c) Figure 8. 8-story, a) 3D view; b) plan; c) FF axes frame Each frame is investigated for the cases of; bare frame, infilled with openings as given in Figure 6 through Figure 8 and fully infilled frames. The results are examined through pushover curves with immediate occupancy (IO) and collapse prevention (CP) limit states, and vertical irregularity identifier parameter n k was studied. IO limit state was chosen if the curvature in the member ends exceeds the yield curvature. CP limit state was chosen if the curvature at the member ends exceeds the fifteen times of yield curvature or 15% reduction in the base shear capacity. The failure mechanism is given for the CP limit state for all frames in Figure 9 through Figure 11. In Figure 9, the results of the three-story frame are given. n ki parameter is passing the limit of the TEC 2007 value for the CP limit state. The pushover curves for the infilled with openings and fully infilled cases are close to each other. Base shear capacity is increased almost five times of the bare frame for the infilled cases. In Figure 10, the results of the five-story frame are given. n ki parameter is close to the limit of the TEC 2007 value for the CP limit state, especially for a bare frame. The pushover curves for the infilled with openings and fully infilled cases are close to each other. Base shear capacity is increased almost 4 times of the bare frame for the fully infilled cases and 3 times for infilled with openings. In Figure 11, the results of the eight-story frame are given. n ki parameter is close to the limit of the TEC 2007 value for the CP limit state for a bare frame. The pushover curves for the infilled with openings and fully infilled cases are close to each other. Base shear capacity is increased almost four times of the bare frame for the fully infilled cases and three times for infilled with openings. Figure 9. 3-story Frame Results

8 Figure story Frame Results 4. CONCLUSIONS Figure story Frame Results In this study, the infilled reinforced concrete frames with openings were investigated, and design parameter n ki and n kj were checked for the infilled cases. n k values are lower than the proposed values in TEC 2007 at collapse limit for higher frames. Infill walls increase the base shear capacity even they have openings. Infill wall arrangement effects the failure mechanisms of the frames. All frames were checked for shear failure and not experienced in any columns. The method proposed by Dawe and Seah (1989) seems adequate for the cases when the opening is at the center. However, it is limited due to not considering the height of the opening and the location of the opening. 5. ACKNOWLEDGEMENT This research was supported by TUBITAK 2214 A Scholarship for International Research during PhD Program. 6. REFERENCES McKenna, F. (2011). OpenSees: a framework for earthquake engineering simulation. Computing in Science & Engineering, 13(4), Chrysostomou CZ, (1991), Effects of degrading infill walls on the nonlinear seismic response of two-dimensional steel frames, PhD thesis, Cornell University, Ithaca (NY).

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