Effect of out-of-plane loading on in-plane behaviour of unreinforced infilled RC frames

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1 icccbe 2010 Nottingham University Press Proceedings of the International Conference on Computing in Civil and Building Engineering W Tizani (Editor) Effect of out-of-plane loading on in-plane behaviour of unreinforced infilled RC frames J S Kuang & Y P Yuen Hong Kong University of Science and Technology, Hong Kong Abstract The behaviour of infilled frames subjected to in-plane loading has been extensively studied, whereas few studies have been done on the behaviour of infilled frames under the action of combined in-plane and out-of-plane loads. In this paper, the effects of out-of-plane loads on the in-plane behaviour of infilled frames are investigated. Pushover analysis is performed with a detailed discrete model using 3-D elements incorporating damage-plasticity material models established by ABAQUS. It is found that the diagonal bracing action of the infill wall to the bounding frame can be significantly softened by out-of-plane loads owing to the P-δ effect. The in-plane load capacity of infilled frames can then be reduced up to 30% under the action of out-of-plane loading. Keywords: infilled frame, out-of-plane loading 1 Introduction Poor seismic performance of masonry infilled RC frame buildings has been reported in almost every destructive earthquake events in the world, which include 1999 Chi-Chi earthquake in Taiwan, 1999 Kocaeli earthquake in Turkey, 2007 Central Peru earthquake, and 2008 Sichuan earthquake in China. In design practice, masonry infill panels bounded by frame in buildings are usually regarded as nonstructural elements. However, the present of infill panels may significantly modify the structural behaviour of the adjacent structural elements and dynamic properties of the buildings. Hence these structural action modifications can be detrimental to the seismic performance of the buildings. The in-plan behaviour of unreinforced masonry infilled frames have been extensively studied in the literature, whereas few studies on the behaviour of infilled frames under the combined in-plane and out-of-plane action have been done, though it is not an uncommon case in the realistic buildings under seismic excitation. This paper presents an investigation of the effect of out-of-plan loads on the in-plan behaviour of RC infilled frames. Pushover analysis is conducted, where a detailed discrete model using 3-D elements with damage-plasticity material models is established by ABAQUS. 2 The prototype model The prototype model shown in Figure 1 is a bay of an exterior frame at the ground floor of a typical 5- storey RC frame designed to Chinese seismic code GB The design fortification intensity level for the building is 7 in Category 1, which corresponds to a design peak ground acceleration of 0.10g. Following the design practice, the effect of infill panels is ignored. The grades of concrete,

2 longitudinal and transverse reinforcement adopted in this design are C30, HRB-400 and HPB-235, respectively. A full height unanchored masonry infill wall is bounded by this bay of frame. The infill wall is composed of mm grade MU15 masonry bricks and 10 mm thick grade MU5 mortar joints. Figure 1, Dimensions and reinforcement details of prototype model (mm) 3 Finite element modelling The detailed 3-D finite element model for the infilled frame prototype model is established to investigate the behaviour of the structure under combined in-plane and out-of-plane action. The FE model mainly consists of five parts: bounding concrete frame, steel reinforcement, infill wall, rigid base, and loading element, as shown in Figure 2, to which where the lateral load was applied before the loading transfer to the frame in order to prevent the stress concentration occurring in the major element. (a) bounding frame and base (b) reinforcement detailing (c) infill wall (d) assembly and meshing Figure 2, Finite element model of an infilled RC frame

3 3.1 Loading A sequential loading analysis is performed. Frame members and the infill wall are first loaded with the design gravity loads; then the infill wall is loaded with a prescribed constant out-of-plane load. After all the constant loads have been applied, in-plane lateral pushover analysis is carried out. Four cases of different out-of-plane loads are analyses for the infilled frame. The loads which are applied to structural members prior to pushover analysis are given in Table 1. Table 1. Loads applied to structural members Column load Beam load Wall gravity load Out-of-plane loads on (kn) (kn/m) (kn/m 3 ) infill wall (kn/m 2 ) , 5, 10, Elements and meshing The concrete, brick and mortar are modelled with linear 8-node, 3D solid elements (C3D8R). The reduced integration technique with average strain kinematics split method is employed. The reinforcement is modelled with 2-node 3-D truss elements (T3D2), and steel bars are embedded to the surrounding concrete element. Progressive refinement of meshing size has been conducted to obtain convergent analysis results. The finial meshing obtained is shown in Figure 2(d). The maximum meshing size for the frame and steel bars is not greater than 100 mm and the mesh is refined to 60 mm at the member ends and joint cores where high stress gradient is expected, while for the infill panel the meshing size is approximately 120 mm. 3.3 Constitutive models of materials Concrete The constitutive model adopted for concrete and brick is the damage-plasticity model for quasi-brittle material (Lubliner et al. 1989; and Lee and Fenves 1998) which has been implemented in ABQUS. Two independent scalar internal damage variables, d t and d c are introduced in the model to characterise the damage of material fabric under tensile and compressive actions, respectively. The constitutive rule is written as el pl σ (1 d)d 0 : (ε ε ) = (1) el where σ = Cauchy stress tensor; D 0 = initial elastic stiffness tensor; ε pl = plastic strain tensor; d = stiffness reduction variable and can be expressed in terms of the two damage variables d t and d c as (1 d) = (1 sd )(1 s d ) 0 s, s 1 (2) t c c t t c where s t and s c = variable depend on stress state to represent unilateral effect or stiffness recovery associated with stress reversals. The yield function is given (Maekawa et al., 2003) by pl 1 pl ˆ ˆ pl F(σ,ε % ) = ( q 3 αp+ β( % ε ) σmax γ σmax ) σ c(ε % ) (3) 1 α where p is the effective hydrostatic stress; q is Mises equivalent effective stress; ˆ σ max is the maximum eigenvalue of effective stress tensor in which the notation < > is the Macauley bracket; the parametersα, β and γ can be calibrated by the ratio of the biaxial to uniaxial compressive strengths, uniaxial tensile stress-strain/displacement relation and the ratio of Mises equivalent effective stress on the tensile meridian to that on the compressive meridian of the yield surface under triaxial compression respectively.

4 Since concrete is a friction material, the flow rule should be non-associated and the flow potential is typical Drucker-Prager hyperbolic function. The parameters and stress-strain curves proposed by Chen (1982) and Hsu and Mansou (2005) are adopted for calibrating of the concrete constitutive model, where the hardening/softening rules and evolution rules of damage variables as a function of inelastic strain or cracking strain of the concrete. Since the embedded steel bars provide tension stiffening to the concrete, the tensile stress-cracking strain adopted has greater fracture toughness than plan concrete to account for this effect. Regarding the unilateral effect, the stiffness of the damaged concrete is assumed to be full recovery when loading changes from tension to compression and there is no recovery from compression to tension. Table 2 presents the material parameters Table 2. Material parameters for concrete Young modulus (GPa) Poisson ratio Density (kn/m 3 ) Dilation angle Flow potential eccentricity Biaxial/uniaxial compression pla-stic strain ratio /3 Deviatoric stress invariant ratio Steel It has been recognised that embedded steel bras has lower tensile yield strength under macroscopic averaging due to the tension stiffening effect. A smeared uniaxial stress-strain for the embedded steel bars and the zoning approach are adopted Brick The material model for brick is the same as that for the concrete with some modifications to account for the more brittle stress-strain behaviour. The uniaxial compressive response of the bricks is assumed to behave as linearly elastic up to the peak strength and drop immediately to the residual strength of 1% of the peak strength. The muti-axial compressive behaviour is assumed to be the same as the concrete, while the uniaxial tensile behaviour is expressed in terms of stress and crack displacement so that the localised fracture effect can be accounted (Lourenco et al., 2005). The material properties for the calibrating the model are shown in Table 3. Table 3. Material parameters for brick Young modulu s (GPa) Poisso n ratio Density (kn/m 3 ) Dilatio n angle Flow potential eccentricit y Peak compressive strength Peak tensile strength Critical crack displacement (mm) Mortar The extended Drucker-Prager yield surface is used to model the mortar behaviour. Since the head joints are usually much weaker than the bed joins due to the difficulty in the construction quality control, the strength of head joints is deducted by half. Regarding the plastic flow, the dilatation angle of mortar is usually much smaller than the friction angle and it decreases with increasing shear displacement. Therefore, the plastic flow must be non-associated and is assumed as non-dilatant flow. Table 4 shows the material parameters of mortar for bed joint. Table 4. Material parameters for mortar (bed joint) Young modulus (GPa) Poisson ratio Density (kn/m 3 ) Dilation angle Friction angle Initial hydrostatic tension strength Compressive strength

5 4 Results Five pushover analyses are performed, including one for the bare-frame and four for the unreinforced infilled frame subjected to four sets of combined loads. Table 5 summarises the peak base shears, the corresponding storey drifts, and out of plane displacements at the centre of the infill walls. Table 5. Peak base shear and corresponding storey drift Specimen Out-of-plane load (KPa) Peak in-pane base shear (kn) Drift (mm) Out-of plane displacement (mm) Bare frame Infilled frame Infilled frame (1.07)* Infilled frame (2.14)* Infilled frame (4.28)* * The initial out-of-plane centre displacement of infill walls before in-plane loading is applied. 4.1 Behaviour under pure in-plane action The infill wall can significantly stiffen up the bare frame. Under in-plane action, the initial stiffness of the unanchored infilled frame is 1.7 times greater then that of the bare frame. The in-plane strength of the infilled frame is increased by about 1.9 times. However, the infilled frame is more brittle than the bare frame. The bare frame failed in a ductile mode where plastic hinges formed at the members ends then crushing of the concrete at the hinges with the reinforcing bars buckled, as shown in Figure 3(a). On contrast, the failure mode of the infilled frame is brittle shear failure at the region near the frame coroner where is the contact region between the frame and infill wall as shown in Figures 3(b)- 3(e). Moreover, the rotation of plastic hinges in the beam is restricted by the wall, and therefore the beam is suffered only little damage when the column concrete is seriously spoiled. As a result, the beam lost its primary function to dissipate energy. The brittle failure of the infilled frame leads to a sharp decrease in the load carrying capacity in the post peak region, as shown in Figure 4. (a) bare frame (b) out of plane load = 0 kpa (c) out of plane load = 5 kpa (d) out of plane load = 10 kpa (e) out of plane load = 20 kpa Figure 3, Damage pattern and deformation shape at post-failure stage of bare and infilled frames 4.2 Effect of out-of-plane loads on behaviour of infilled frame A small, initial out-of-plane elastic deformation is induced by the prescribed out-of-plane loads before the pushover analysis. When the structure is loaded laterally, the small initial out-of-plane deflection is significantly magnified by the secondary moment induced by the diagonal compressive thrust as a result of the P-δ effect. The apparent in-plan lateral stiffness of the infill wall and therefore the

6 imposed bracing action on the bounding frame are weakened, as shown in Figure 4. The in-plane strength of the infilled frame is degraded by 15% up to as most as 30% when the unanchored infill wall is subjected to out-of-plane loads of 5 kpa and 20 kpa respectively. As the lateral in-plane loading is kept increasing, extra damage of the infill walls is incurred, thus the bracing stiffness being further reduced and the P-δ effect being aggravated. Eventually, part of the wall lost its stability and buckled, as shown in Figure kpa 5 kpa 10 kpa 20 kpa Bare Frame Base shear (kn) Storey drift (mm) (a) in-plane pushover curves (b) buckling of infill wall under combined in- and out-of-plane loads Figure 4, Pushover curves of unanchored infilled frame and buckling of infill wall under combined loads 5 Conclusions Infill walls can significantly alter the structural behaviour of their hosting frame in terms of stress distribution, failure mode and ductility. The weak beam/strong column seismic design rule for RC frame structures may become unrealistic with the present of infill walls. Under combined in-plane and out-of-plane loads, even small initial out of plane deflection can be significantly magnified owing to the P-δ effect. The diagonal compressive thrust induced by the lateral load and gravity loads on the infill wall act as destabilising forces that incur the buckling of the wall. The bracing action on the bounding frame can be significantly weakened by the out-ofplane action, thus reducing both of in-plane lateral strength and stiffness. Buckling of the infill wall reflects as disintegration and falling off of the wall components in the realistic situation that impose risk to the public. The effect of combined in-plane and out-of-plane loads in accessing the performance of RC infilled frames should be considered in design practice. Acknowledgement The support of Hong Kong RGC under grand No is generally acknowledged. References CHEN, W.F., Plasticity in Reinforced Concrete. New York: McGraw-Hill HSU, T.C. and MANSOUR, M., Behavior of reinforced concrete elements under cyclic shear: II. Theoretical model. Journal of Structural Engineering, ASCE, 131(1), LEE, J. and Fenves, G.L., Plastic-damage model for cyclic loading of concrete structures. Journal of Engineering Mechanics, ASCE, 124(8), LOURENCO, P.B., ROTS, J.G. and BLAAWENDRAAD, J., Continuum model for masonry: Parameter estimation and validation. Journal of Structural Engineering, ASCE, 124(6), LUBLINEAR, J., Oliver, J, Oller, S, and Oñate, E., A Plastic-Damage Model for Concrete. International Journal of Solids and Structures, 25(3),