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MINISTRY OF EDUCATION AND TRAINING NATIONAL UNIVERSITY OF CIVIL ENGINEERING Phan Van Hue EFFECTS OF MASONRY INFILLS ON THE RESPONSES OF REINFORCED CONCRETE FRAME STRUCTURES UNDER SEISMIC ACTIONS Major: Civil Engineering Code: 9580201 SUMMARY OF DOCTORAL DISSERTATION Ha Noi - 2020 The Dissertation has been completed at the National University of Civil Engineering Academic advisor: Assoc Prof Dr Nguyen Le Ninh Examiner 1: Prof Dr Nguyen Tien Chuong Examiner 2: Assoc Prof Dr Nguyen Ngoc Phuong Examiner 3: Dr Nguyen Dai Minh The doctoral dissertation will be defended before Doctoral Defence Committee held at the National University of Civil Engineering at ……… on ……………….…………, 2020 This Dissertation is available for reference at the Libraries as follows: - National Library of Vietnam - National University of Civil Engineering’s Library PREFACE REASON FOR SELECTING THE TOPIC Earthquake researches and engineering site observations over the past seven decades show that masonry infills (MIs) significantly affect response of the surrounding frame structures under seismic actions The modern seismic standards, including TCVN 9386:2012, admit this phenomenon, but the design regulations for the infilled frames still have many shortcomings: (i) Conflicts between design of the whole structure (ignoring the interactive forces with the MIs) and design of structural members locally (considering the interactive forces with the MIs); (ii) The models to calculate the infilled frames are unclear and uncompleted Therefore, the study on "Effects of masonry infills on the responses of reinforced concrete frame structures under seismic actions" is necessary and meaningful RESEARCH PURPOSES (i) To establish the behavior model of the MIs and to employ this model to determine the seismic behavior of infilled frames; (ii) To study how to control the failure mechanisms of reinforced concrete (RC) frames under seismic actions, considering the interaction between the frame and the MIs; (iii) To study the effects of the MIs on the control of the local response of RC frame columns under seismic actions RESEARCH OBJECTS AND SCOPE OF WORK 3.1 Research objects Multi-storey monolithic RC frames with MIs in the frame plane: (i) The frames are designed according to the modern seismic conception; (ii) Unreinforced MIs (solid and hollow clay bricks, AAC bricks) without openings are constructed after the hardening of the RC frames The MIs are in contact with the frame (i.e without special separation joints) but without a structural connection to it 3.2 Scope of work: (i) Impacts are in the frame plane; (ii) The aspect ratio of MIs: αm = hm/lm ≤ 1.0 SCIENTIFIC BASIS OF THE TOPIC (i) Research results of infilled frames in the last seven decades; (ii) The modern seismic design conception; (iii) Regulations on designing the RC frames subjected to earthquakes in some common building codes worldwide, including Vietnam RESEARCH METHODOLOGY Theoretical research and numerical simulation analysis are used NEW CONTRIBUTIONS OF THE DISSERTATION (i) Established the nonlinear behavior model of the MIs and employed this model to determine the seismic behavior of infilled RC frames; (ii) Established the condition to control failure mechanisms of the RC frames and proposed the method to design RC frames when considering the interaction with the MIs based on the modern seismic design conception; (iii) Proposed a method to determine the interactive forces between the frame and the MIs as well as a method to design RC frame columns in shear considering these interactive forces LAYOUT OF DISSERTATION The thesis consists of preface, four chapters, and conclusions, presented in 116 pages with 29 tables, 55 figures, 149 references (Vietnamese: 10, English, Romanian: 139) The appendix has 21 pages CHAPTER INTERACTION BETWEEN FRAMES AND MASONRY INFILLS AND DETERMINATION OF RESPONSES OF THE MASONRY INFILLED RC FRAMES UNDER LATERAL IMPACT 1.1 INTRODUCTION Contrary to the previous conception that considers MIs as nonstructural elements, the field observation results showed that MIs are the cause of failures: columns, beam-column joints, and the collapse of buildings, etc under seismic action This issue has attracted many studies worldwide 1.2 INTERACTION BETWEEN FRAMES AND MASONRY INFILLS AND BEHAVIOR OF MASONRY INFILLED RC FRAMES UNDER LATERAL IMPACT 1.2.1 Interaction between frames and MIs under lateral impact The behavior of MIs in the frames under lateral impact can be divided into two stages At the first stage, before the frame-MI contact surfaces are cracked, the structure behaves like a) b) a monolithic vertical cantilever; and at Figure 1.3 The behavior of MI RC the second stage after the contact frames and interactive forces in the surfaces are cracked at the unloaded contact regions corners (Figure 1.3a) In the remaining contact regions, interactive forces appear (Figure 1.3b) 1.2.2 Consequences of frame-MI interaction for the behavior of MI RC frames 1.2.2.1 RC frames are designed not according to the seismic standards The impact of the frames-MIs interaction forces has resulted in failure of MIs and of the frame components Types of failure in MIs: (i) Shear cracking (cracking along mortar joints, stepped cracks or horizontal sliding; diagonal cracks); (ii) Compression failure (failure of the diagonal strut; corner crushing) Types of failure of RC frames: (i) Flexural failure (at member ends; in span length); (ii) Failure due to axial force (yielding of the longitudinal reinforcement; bar anchorage failure); (iii) Shear failure of columns; (iv) Beam-column joint failure 1.2.2.2 The RC frames are designed according to modern seismic standards The extensive experimental researches by the authors: Mehrabi et al (1996), Kakaletsis and Karayannis (2008), Morandi et al (2014-2018), Basha (2017) gave the failure types as follows: Types of failures in MIs: Strong MIs-strong frames: diagonal sliding shear and compression failure Weak MIs-strong frames: sliding shear failure along the diagonal or in the midheight of MIs Types of failure of RC frames: a) Column: Plastic hinges appear at the ends of columns; shear cracks occur simultaneously with flexural cracks b) Beams: Flexural and shear cracks rarely appear Frame beams behave more stiffly when considering the interaction with MIs 1.3 MODELING OF BEHAVIOR OF MIs UNDER LATERAL LOADING 1.3.1 Behavior models of MIs in frames 1.3.1.1 Macromodels Replace MIs with one or more equivalent diagonal struts Single-strut models (Figure 1.8): parameters of diagonal struts: width wm and thickness tm (tm is equal to a) Deformation due to b) The equivalent diagonal MI’s thickness) lateral force strut model Multiple-strut models: Figure 1.8 The equivalent diagonal strut model Divide a diagonal strut into multiple equivalent struts (Figures 1.9 and 1.10) 1.3.1.2 Micromodels Based on finite element methods (Figures 1.13 and 1.14) 1.3.1.3 Remarks: The single strut macromodels are simple, easy to apply They give approximate results, but no results for local effects The Figure 1.9 Chrysostomou’s Figure 1.10 micromodels are more model El-Dakhakhni’s model accurate, but calculation volume is large and it is difficult to determine the model's parameters 1.3.2 Main results achieved in macromodeling 1.3.2.1 Results achieved in determining the diagonal width wm In the world: a) The approaches for determining wm depend on the geometric properties of MIs: Figure 1.13 Mallick Figure 1.14 Mehrabi and Severn’s model and Shing’s model The following authors have given the expressions for determining wm by a fixed fraction of the length of the panel diagonal dm: Holmes [1/3] (1961), Smith [0.1÷0.25] (1962), Moghaddam and Dowling [1/6] (1988), Smith and Coull [1/10] (1991), Paulay and Priestley [0.25] (1992), Angel et al [1/8] (1994), Fardis [0.1÷0.2] (2009), etc (The values in [] indicate the proposed wm/dm ratios) b) The approaches for determining wm depend on both the geometric and mechanical properties of frames and MIs: The following authors have proposed the methods for determining wm in this way: Mainstone (1974); Abdul-Kadir (1974), Henry (1998); Nguyen Le Ninh (1980); Bazan and Meli (1980); Liauw and Kwan (1984); Decanini and Fantin (1986); Govindan (1986); Dawe and Seah (1989); Decanini et al (1993); Durrani and Luo (1994); Flanagan and Bennet (2001); Al-Chaar (2002); Tucker (2007); Amato et al (2009); Tabeshpour et al (2012); Chrysostomou and Asteris (2012); Turgay et al (2014), etc In Vietnam: Ly Tran Cuong (1991) and Dinh Le Khanh Quoc (2017) proposed the methods of determining wm in the direction of group b) Remarks on the results achieved in determining wm: The width wm depends on: (i) The mechanical and geometric properties of components of infilled frames; (ii) The degree of deterioration of their strength and stiffness; (iii) Time of determining wm Therefore, values of wm are completely different from the authors Among the proposed methods, the method proposed by Nguyen Le Ninh (1980) can be applied to consider all the above factors 1.3.2.2 Results achieved in establishing a simple nonlinear behavior model of MIs Many authors studied this model: Decanini, Bertoldi and Gavarini (1993); Panagiotakos and Fardis (1994); Kappos and Figure 1.15 Model of Decanini et al Stylianidis (1998); Chronopoulos (2004); Stavridis et al (2017), etc The curve shapes of these models are basically the same as Figure 1.15 However, the model parameters including the stiffness and strength of the MIs are different Although there are many advantages, their application is very limited 1.4 EFFECTS OF FRAME-MI INTERACTION IN THE SEISMIC STANDARDS 1.4.1 The rules take into account the influence of MIs TCVN 9386:2012 and EN 1998-1:2004; FEMA 356 (2000); ASCE 41-13 (2013) and ASCE 41-17 (2017); NZSEE (2017) provided the rules to consider the effects of MIs on behavior of RC frames under seismic action 1.4.2 Remarks on the rules in the design standards • All standards state that MIs have detrimental effects on the frames, but they separate the local response calculation from the overall calculation The design rules of beams, columns and beam-column joints not take into account the influence of interactive forces with MIs, but when examining the columns in shear, this interactive forces must be considered • When calculating the local response, the standards require the use of a single diagonal strut model, but there are no instructions on how to set the model (especially TCVN 9386:2012), so it is difficult to implement 1.5 REMARKS ON CHAPTER 1 The frame-MI interaction causes the typical types of failure in RC frames designed according to the modern seismic conception: flexural and shear failures either at the ends or in the middle of columns; beams are often increased in stiffness, and MIs are often failed by sliding shear along the diagonal or in the midheight of MI and diagonal compression The simple model using an equivalent diagonal strut is relevant to determine the overall response of the infilled frames While recognizing the important influence of the frame-MIs interactive forces, the standard design regulations of infilled frames are still inadequate and unclear CHAPTER MODELING OF NONLINEAR BEHAVIOR OF MASONRY INFILLED RC FRAMES UNDER SEISMIC ACTIONS 2.1 SELECTING THE METHODS TO MODEL MASONRY INFILLED RC FRAMES From the literature review, the following models are selected for the analysis of infilled frames: a simple model to simulate bending behavior in critical regions of the RC frame and the equivalent diagonal strut model to simulate the behavior of MIs 2.2 BEHAVIOR MODEL OF THE RC FRAMES 2.2.1 At the material level: Use the behavior models of concrete and reinforcement specified in EN 1992-1-1:2004 2.2.2 At structural element level: Use the concentrated-plasticity modeling approach The behavior of plastic hinges is controlled through the modified Takeda model and its force-displacement curve is taken according to ASCE 41-13 (Figure 2.2) a) b) c) Figure 2.2 a) Plastic b) The modified Takeda c) Generalized M–θ deformation concentrated hysteresis rule relationship at plastic on the frame components hinges of RC frame components 2.3 ESTABLISH THE NONLINEAR BEHAVIOR MODEL OF THE MIs IN RC FRAMES 2.3.1 Setting up the force-displacement relationship of the model The behavior of the MIs in the frame is modeled as a curve shown in Figure 2.3 In the frame model, the MIs are shown in Figure 2.4 Figure 2.3 The force-displacement relationship Figure 2.4 Position of plastic of the MI’s behavior model hinges in the model of infilled frames 2.3.2 Define the basic parameters of the model 2.3.2.1 The stiffness of MIs According to Nguyen Le Ninh (1980), the width wm = e m (1− n ) wm (2.1) with wm = dm = (2.2); λh ( λh h + λl l + k ) Em tm lm = ; λl Ec I c hm2 4 Em tm hm (2.3) Ec I b lm2 where n = H/Hu, H is the lateral force and Hu is the lateral force at the time when MI reaches the ultimate strength; m and k are coefficients depending on the type of masonry; other parameters indicate the geometric and mechanical properties of frames and MIs (Figure 1.8) From the width wm, determine the stiffness of the MI at the beginning of the crack (2.4) and when reaching to the ultimate strength (2.5): K my e0.4 m wm tm Em wm tm Em ∗ K my = cos θ cos θ = = (2.4); K mu (2.5) dm dm e0.4 m 2.3.2.2 The strength of the MIs The ultimate strength of masonry infill Vmu is determined from the condition Vmu = (Vms ,Vmc ) (2.6), where: a) Vms is the sliding shear strength of MIs selected from approaches of following authors: Rosenblueth (1980); Smith and Coull (1991); Paulay and Priestley (1992); Decanini et al (1993); Panagiotakos and Fardis (1994), Fardis (2009); Zarnic and Gostic (1997); FEMA 356 (2000), AlChaar (2002), ASCE 41-06, ASCE 41-13; Galanti et al (1998), EN 19981:2004; FEMA 306 (1998); EN 1996-1-1:2005; according to TCVN 5573:2011 (2.10) Vms = f bs tm lm − 0.72n1µ tgθ (2.10) b) Vmc is the diagonal compression strength of MIs selected from approaches of following authors: Smith and Coull (1991); Decanini et al (1993); Galanti et al (1998); FEMA 306; AlChaar (2002); Tucker (2007); ASCE 41-13 In order to select the appropriate strengths for MI’s model, comparative analyses are performed on the infilled RC frame consistent with the object and objectives of the research The results are Figure 2.9 Variation of Vms determined by different the curves representing approaches associated with hm/lm relationships of Vms and Vmc associated with the common hm/lm ratios of MIs in Figures 2.9 and 2.10 Since then, choose the strength Vms according to TCVN 5573:2011 (2.10) and the strength Vmc according to ASCE 41-13: Figure 2.10 Variation of Vmc determined by h Vmc = f mc m tm cos θ (2.11) different approaches associated with hm/lm The yielding strength of the masonry infill Vmy is selected from approaches of following authors: Nguyen Le Ninh (1980), Dolsek and Fajfar (2008); Decanini et al (1993); Panagiotakos and Fardis (1994); Saneinejad and Hobbs (1995), FEMA 306; Tucker (2007); Stavridis (2009) Similarly, from the results in Figure 2.12, choose Vmy = 0.6Vmu (2.12) as suggested by Nguyen Le Ninh and Dolsek and Fajfar (2008) Figure 2.12 Variation of Vmy determined by The residual strength of different approaches associated with hm/lm the masonry infill Vmr: (2.13) ≤ Vmr ≤ 0.1Vmy 11 3.1.3 Design RC frames according to current seismic standards To carry out the above design principles, the capacity design method is used By using this method, the forces used to design a frame must be as follows, for example, according to TCVN 9386:2012 (the “so-called” basic design principle of strong columns - weak beams): a) Beam: The bending moment M and the axial force N are taken from the results of structural analysis, while the shear force Q is determined from the bending resistance of the beam b) Column: The bending moment M is redefined from the following condition: M Rc ≥ 1.3 M Rb (3.1) ∑ ∑ in which: ΣMRc is the sum of the minimum design values of the moment resistances of the columns framing to the joint, taking into account the column axial force N in the seismic design situation; ΣMRb is the sum of the design values of the moment resistances of the beams framing to the joint Shear force Q is redefined from the flexural strength of columns Remarks: (i) The frame design process must follow a very strict process; (ii) Frame design rules not take into account frame-MI interaction 3.2 EFFECTS OF MIs TO THE BEAM RESPONSE Experimental studies on the infilled frames show that the interactive forces with the MIs make the beams behave more stiffly than that of bare frames To clarify this phenomenon, consider a RC frame without MI (bare frame) as shown in Figure 3.2a The external force H causes the bending moment at the ending section C of the beam: Ih Hh 3ω ω= b (3.2) where: (3.3) M bC , H = Icl 6ω + a) Bare frame; b) Infilled frame; c) Equivalent infilled frame Figure 3.2 Models for calculation of the frame The curvature of the beam at the end C has the following value: M bC , H Hh 3ω (3.4) = ρbC , H = Ec I b Ec I b 6ω + 12 When MI is available, the model to calculate an infilled frame is as shown in Figure 3.2b, where Rm is the compression force in the diagonal strut with the area of cross-section of wmtm Replace the model in Figure 3.2b with the equivalent model in Figure 3.2c (Vm is the horizontal projection of the compression force Rm in the diagonal strut) With this model, we have the moment and curvature of the beam when taking into account the interactive force with MIs: ( H - Vm ) h 3ω (3.5) M bC , H -Vm = 6ω + ρbC , H -Vm = M bC , H -Vm ( H - Vm )h 3ω = < ρbC , H Ec I b 6ω + Ec I b (3.6) Thus, the interaction with MIs makes the beam stiffer Let Ibm ( >Ib) be the equivalent moment of inertia of the beam when considering interaction with MIs Similarly (3.4), we will get the curvature of the beam in this case: * M bC I h 3ωm Hh ,H * (3.7), where: ωm = bm (3.8) ρbC , H = = Icl Ec I bm Ec I bm 6ωm + Considering (3.3) and (3.8), we obtain the coefficient k= Ib I bm ωm = Ib ω (3.9) which indicates the increase in moment of inertia (flexural stiffness) of the beam when interacting with MIs Balancing the curvatures (3.6) and (3.7), we establish the relationship: 6ωm + H = 6ω + H − Vm (3.11) From the relationship between horizontal force H and Vm established on the basis of the calculation diagrams in Figures 3.2b, 3.2c, and from (3.11), we set the ratio ωm/ω With this result, determine the coefficient kIb (3.9) at the ultimate time (wm = wm0 when n = 1.0 see Chapter 2) when considering the interaction with MIs: k Ibu = I bmu h3 w m 0tm Em cos 2θ 3ω + = 1+ Ib Ec I c d m 72ω (3.18) Equation (3.18) shows that, when considering the interaction with MIs, the moment of inertia of the beam Ibmu is increased by kIbu times: Ibmu = kIbuIb This means that the cross-section height of the beam is increased to hbmu = hb k Ibu (3.19) called the equivalent cross-section 13 height The increase in the cross-section height of the beam leads to an + − and negative M Rb for increase in its bending resistance both positive M Rb the considered sense of the seismic action In the general case, at any column-beam joint: − + − + M Rbmu =M Rbmu + M Rbmu > M Rb =M Rb + M Rb (3.21) ∑ ∑ where ΣMRbmu and ΣMRb are the sums of the design values of the moments of resistance of the beams framing the joint when considering and not considering the interaction with MIs for the considered sense of the seismic action, respectively Thus, when considering the interactive forces with MIs, the moments of resistance of the beams are increased by the following coefficient: + M Rbmu M Rbmu + M Rbmu (3.22) = k Mb = > + M Rb M Rb + M Rb ∑ ∑ 3.3 METHODS TO DESIGN THE RC FRAMES FOR EARTHQUAKE RESISTANCE WHEN CONSIDERING THE INTERACTION WITH THE MIs 3.3.1 Condition to control the failure mechanism of the RC frames From the above mentioned research results, in cases taking into account of the interaction with MIs, the condition to control the plastic failure mechanism (3.1) of a frame in TCVN 9386:2012 may not be M Rb in the right-hand side is increased via kMb This accurate, because ∑ also means that the columns may be failed before the beam and the soft story failure mechanism may appear unintentionally Therefore, to let the infilled frames be failed plastically as the design purpose, the design conditions (3.1) shall be rewritten as follows: M Rcmu ≥ 1.3kMb M Rb (3.23) ∑ ∑ in which ΣMRcmu is the sum of the minimum design values of the moment resistances of the columns framing to the joint, taking into account the column axial force N in the seismic design situation at the ultimate limit state of MIs With this condition, whether the MIs are available or not, the design principle of "strong columns - weak beams" will be guaranteed and the frames will be failed in plastic mechanisms under strong earthquakes 3.3.2 The method to design RC frame structures under seismic actions when considering the interaction with the MIs Step Design and detail of RC beams in accordance with current seismic design standards 14 Step Determine kIbu in (3.18) and the equivalent cross-section height of beam hbmu in (3.19) Then determine the moment resistances of the − and equivalent beams when considering the interaction with MIs M Rbmu + M Rbmu Determine kMb in (3.22) Step Determine the bending moment to design the columns M ∑ Rcmu in the proposed condition (3.23) Then design and detail the longitudinal reinforcement of columns according to the rules of the current seismic design standard 3.4 CALCULATION EXAMPLES 3.4.1 The calculation data A 3-storey cast-in-place RC frame building with dimensions as shown in Figure 3.4 The exterior beams of 25x45 cm, the interior beams of 25x50 cm, the slab thickness of 15 cm Materials: concrete B30, longitudinal reinforcement type CB400-V, stirrup reinforcement type CB240-T The KB and KE frames are filled with solid brick masonry 20 cm thick, burnt clay bricks M100, cement mortar M75 Vertical load (permanent load g and imposed load q) at each floor (including roof): g + ψ2q = kN/m2 The building is built in a region with the reference peak ground acceleration on type A ground (rock) agR = 0.1097g, ground type D, importance factor γI = 1.2; ductility class medium (DCM) according to TCVN 9386:2012 a) Plan view of the typical floor b) Elevation of the frame Figure 3.4 Models for the frame structure 3.4.2 Design the RC frame structures according to the regulations of TCVN 9386:2012 The reinforcement details of typical frame KE are shown in Figure 3.5 15 Figure 3.5 Reinforcement details of frame KE 3.4.3 Determine responses of frame KE designed according to TCVN 9386: 2012 Figure 3.6 Behavior of frame KE designed according to TCVN 9386:2012 a) Step b) Step 22 Using nonlinear pushover analysis is to determine responses of frame KE Behavior models of materials and frame components are taken from EC2 and ASCE 41-13 The analysis results show that the frame is failed in agreement with the plastic mechanism as the design goal set out (Figure 3.6) The capacity curve is shown in Figure 3.7 (solid line) c) Step 48 d) Step 102 Figure 3.7 Capacity curves of frame KE in different cases 16 3.4.4 Determine responses of frame KE designed according to TCVN 9386:2012 when considering the interaction with MIs Calculation results for force-displacement relations of the MIs are shown in Figure 3.8 a) 1st-floor b) 2nd to 3rd floors Figure 3.8 Force-displacement relationship in the behavior model of MIs The pushover analysis in Figure 3.10 shows that the plastic deformation process starts from the MIs to beams and the bases of columns on the first floor The capacity curve (dashed line) in Figure 3.7 shows that the frame stiffness drops suddenly and varies irregularly when the base shear force reaches its maximum value of V = 626.27 kN and ∆ = 0.023 m in step 10 because the MIs on the first and second floors are failed considerably Until the target displacement ∆ = 4% H = 0.36 m (step 108) is achieved, the plastic deformations are almost focused on the bases of columns on the foundation surface and the top of columns on the first floor, the MIs on the first floor are no longer capable of bearing (Figure 3.10) The infilled RC frame is failed in agreement with the “soft storey” mechanism a) Step b) Step 10 c) Step 15 d) Step 108 Figure 3.10 Behavior of frame KE when considering the interaction with MIs Comparing the capacity curves of frame KE in Figure 3.7 (without considering (solid lines) and considering (dashed lines) the interaction with MIs) shows that the interaction with MIs has greatly increased the stiffness, horizontal bearing capacity, and energy dissipation capacity of the frame in the initial elastic phase 3.4.5 Design and detail the RC frame structures considering the interaction with MIs using the proposed method The design of the frame structure shown in Figure 3.4 is implemented using the method proposed in section 3.3.2 17 Step 1: Calculate beam reinforcement of frame KE and calculate their flexural resistance MRb as design results in section 3.4.2 (Figure 3.5) Step 2: Determine kIbu = 2.508 and the equivalent cross-section height hbmu = 680 mm, thereby determine bending resistance of the beams and the coefficient kMb = 1.14 Step 3: Determine the required bending moment to design the columns yc from the proposed condition (3.23), from which design and M Rcmu ∑ arrange longitudinal reinforcement of the columns Compared with the standard design results (Figure 3.5), the cross-section height of columns on the first floor (C1 and C4) must be increased by 50mm while the reinforcement of all columns remains the same Figure 3.11 Behavior of frame KE designed using the proposed condition (3.23) a) Step 11 b) Step 17 c) Step 113 Performing pushover analysis is to determine responses of infilled frame KE with behavior models of materials, structural members, and MIs used in the calculation example in section 3.4.4 The analysis results show that the frame designed using the proposed method isn’t failed corresponding to the soft storey mechanism (Figure 3.11) The capacity curves in Figure 3.7 show that frame KE designed using the proposed method with the condition (3.23) (dashed double-dot line) has superior behavior compared with the case designed according to the condition (3.1) of TCVN 9386:2012 3.5 REMARKS ON CHAPTER The increasing coefficients of flexural stiffness kIbu and flexural resistance kMb of beams are quantified when considering the interaction with MIs On this basis, the condition that controls failure mechanism (3.23) is proposed to replace the condition (3.1) of TCVN 9386:2012 which is no longer accurate when considering the interaction with MIs Then a method to design RC frame structures for earthquake resistance is proposed Specific calculation examples have demonstrated the reliability of the performed theoretical research: the model of MIs, the method to design RC frame structures for earthquake resistance when considering the interaction with MIs, etc 18 CHAPTER CONTROL OF LOCAL FAILURES OF RC FRAMES UNDER SEISMIC ACTIONS CONSIDERING THE INTERACTION WITH THE MIs 4.1 CONTROL OF LOCAL FAILURES OF RC FRAMES IN CURRENT SEISMIC DESIGN STANDARDS 4.1.1 Control of shear failure in RC frames Shear failure is a brittle failure mode, so it must be prevented, and is not allowed to occur before flexural failure For frame columns, according to TCVN 9386:2012, the design shear force is determined from the bending resistance of the column (called Figure 4.1 Diagram of determining column shear force the capacity shear force) (Figure 4.1)   M   M   γ Rd  M Rc ,1  ∑ Rb  + M Rc ,2  ∑ Rb    ∑ M Rc   ∑ M Rc     1  2  VCD , c = (4.3) lcl , c where lcl,c is the clear length of the column; MRc,i is the design value of the column moment resistance at the end i (i = 1, 2) in the sense of the seismic bending moment under the considered sense of the seismic action; ( M Rb / M Rc )i ≤ where ∑MRc and ∑MRb are the sums of the design ∑ ∑ values of the moment resistances of the columns and the sum of the design values of the moment resistances of the beams framing into the joint, respectively; γRd is the factor accounting for overstrength The values of MRc,i and ∑MRc should correspond to the column axial force in the seismic design situation for the considered sense of the seismic action 4.1.2 Verification of column shear failure in seismic standards TCVN 9386:2012 and EN 1998-1:2004 require checking and detailing of columns in shear considering the interaction with MIs through the (4.4) condition: VRd , c ≥ VEd , c ,lc Figure 4.2 Acting shear on the columns due to MIs 19 in which VRd,c is the shear resistance at the ends of the columns designed according to the standard; VEd,c,lc is the increased design shear due to the horizontal strut force acting at the column ends (Figure 4.2): VEd , c ,lc = (VEd , c , ms ;VEd , c , M ) (4.5) = V= Am f mv (i) VEd , c , ms m where: (4.6) with Am = tmlm and fmv is the shear strength of the MIs; (ii) VEd , c , M = 2γ Rd M Rd , c lc (4.7) Other countries' standards are the same 4.1.3 Remarks on the rules for verification of shear failure There is a high agreement among the standards: the interaction with the MIs is not considered when designing overall the frame but the interactive forces with the MIs are considered when verifying the columns in shear The instructions in TCVN 9386:2012 and EN 1998-1:2004 are rather ambiguous, Figure 4.3 The interactive leading to various interpretations when they forces between frame and MI are applied, e.g the diagonal strut width wm, the length of contact regions lc, etc 4.2 FRAME - MI INTERACTIVE FORCES AND LOCAL RESPONSE OF RC COLUMNS UNDER INTERACTIVE FORCES According to Nguyen Le Ninh, the contact lengths zh and zl between the MI and the frame change when the infilled frame is subjected to lateral load At the ultimate time of MI (n = 1.0): zh = β 0π 2λh and zl = β 0π 2λl (4.14) with: β0 = dm wmk ( λh h + λl l + k ) (4.13) Figure 4.4 The distribution of strut’s force on frame’s elements Along the contact regions zh and zl, interactive stresses which are assumed to be linearly distributed appear, causing the force Rm in the equivalent diagonal strut (Figure 4.3) According to Tassios et al (1988), it is possible to divide Rm into parts as shown in Figure 4.4 At the ultimate state of the MI (n = 1.0), the interactive forces at the contact regions of column and beam with the MI are determined by the following expressions (Figure 4.5): 20 qh = 0.8Vmu zh (4.17) ql = 0.4Vmu tgθ zl (4.18) where Vmu is the horizontal projection of the force in the diagonal strut Rmu From the force qh0, determine the column shear force due to the local interaction with the MI (Figure 4.5): Vc , mA = qh zh qh zh30 qh zh40 − + (4.19) 4lcl ,c 10lcl3 ,c  q z3 q z4 Vc , mB = −  h 02 h − h h  4l 10lcl ,c  cl ,c    Figure 4.5 Local effects on columns due to MIs (4.20) 4.3 METHOD TO DESIGN THE RC COLUMNS IN SHEAR WHEN CONSIDERING THE FRAME-MI INTERACTIVE FORCES 4.3.1 Condition to control the column shear failure When considering the interactive forces with the MIs, the capacity design shear of columns, VCD,c,m is determined in (4.3) in which ∑MRcmu is determined by increasing kMb times using the proposed method in section 3.3, Chapter So it will be greater than VCD,c determined according to TCVN 9386:2012 However, this increase in shear force is only caused by the stiffening effect of the beams, not counting the interactive forces between the MIs and the columns Therefore, the design shear of columns will be determined from the following proposed condition: VEd ,c , m = max(VCD ,c , m ;Vc , pt , m ) (4.23) where Vc , = Vc , pt + Vc , m (4.24) is the column shear force determined pt , m from structural analysis considering the local interaction with the MIs; Vc,pt is the column shear force determined from the structural analysis without considering the interaction with the MIs; Vc,m is the column shear force due to the local interaction with the MIs determined by (4.19) and (4.20) The condition of controlling column shear failure in the case of considering the interactive forces with the MIs is as follows: (4.25) VRd ,c , m ≥ max(VCD ,c , m ;Vc , pt , m ) where VRd,c,m is the shear resistance of the column when considering the interaction with the MIs 21 4.3.2 Method to design columns in shear when considering frame-MI interactive forces Continuing with the frame design steps proposed in section 3.3.2, the design of columns in shear is carried out as follows: Step Determine the capacity design shear of columns VCD,c,m in (4.3) from the result in step Step Determine the interactive force qh0 in (4.17) and local shear forces in columns Vc,mA, Vc,mB in (4.19) and (4.20) Step Determine VEd,c,m in (4.23) in which Vc,pt,m is taken from (4.24) Step Design and detail the columns in shear according to TCVN 9386:2012 and EN 1992-1-1:2004 from VEd,c,m in step Step Check the columns in shear according to conditions (4.25) 4.4 CALCULATION EXAMPLES 4.4.1 Design of columns in shear according to TCVN 9386:2012 The analytical results in the seismic design situation produce the shear force diagram Vc,pt in frame KE as shown in Figure 4.6 From the flexural strengths of columns and beams determined in the calculation example in section 3.4.2, calculate the capacity design shears VCD,c of first floor Figure 4.6 Shear force diagram of frame KE determined from structural analysis in the columns according to (4.3): seismic design situation VCD,c = 125.698 kN for column C1 and VCD,c = 54.523 kN for column C4 From these capacity design shear forces, identify the stirrup reinforcement of the column C1 (Ф8, spacing sd1 = 110 mm in the critical regions) and the column C4 (Ф8, spacing sd1 = 120 mm in the critical regions) The stirrup reinforcement details of the columns are shown in Figure 3.5 Calculate the shear resistances of column C1: VRd,c = 140.742 kN and column C4: VRd,c = 66.283 kN 4.4.2 Design of columns in shear using the proposed method From the section 4.3.2, the design is carried out as follows: 22 Step Calculate the capacity shear force VCD,c,m using (4.3) in which ∑MRcmu was taken from step Results: column C1: VCD,c,m = 149.05 kN; column C4: VCD,c,m = 65.594 kN Step Calculate the interactive force qh0 = 519 N/mm and the local shear forces Vc,mA, Vc,mB caused by this force using (4.19) and (4.20) Step Calculate Vc,pt,m using (4.24) and design shear forces VEd,c,m using (4.23) Step Detail and dimension of columns in shear from VEd,c,m in step Results: column C1 – stirrup reinforcement Ф8, spacing sd1 = 130 mm in critical regions and column C4 - stirrup reinforcement Ф10, spacing sd1 = 120 mm in critical regions Therefore, the stirrup spacing of column C1 increases from 110 mm to 130 mm, while the stirrup diameter of column C4 increases from Ф8 to Ф10 compared with the design results according to TCVN 9386:2012 in section 4.4.1 Step The results of verification through the condition (4.25) show that columns designed using the proposed condition and method ensure shear resistances 4.4.3 Verification of the shear strength of columns when considering the interaction with the MIs in accordance with TCVN 9386:2012 4.4.3.1 Verification of the shear strength of columns designed according to TCVN 9386:2012 To be objective in checking columns in shear, choose the width of the diagonal strut wm = 0.125dm= 678 mm suggested by Fardis and fmv = 0.16 MPa according to Hak From (4.6) determine VEd,c,ms = 149.6 kN for columns C1 and C4 and from (4.7) determine VEd,c,M = 520.691 kN for column C1 and VEd,c,M = 236.134 kN for column C4 The results of verifying the condition (4.4) show that columns C1 and C4 on the 1st floor of frame KE are all failed in shear 4.4.3.2 Verification of the shear strength of columns designed by the proposed method To clarify the logic and effectiveness of the proposed design method, the inspection of columns in shear is carried out in accordance with TCVN 9386:2012 as the above calculation example The results show that column C4 is failed in shear while column C1 is not However, the difference is that VRd,c,m/VEd,c,lc = 76% compared with the frame designed according to the standard VRd,c,m/VEd,c,lc = 44% 23 4.5 REMARKS ON CHAPTER The interactive force between frame columns and MIs qh0 is clearly quantified Consequently, a method to design frame columns in shear is proposed This method is more logical and effective than that in the seismic design standards which are quite passive and illogical The guidelines for checking the column resistances in shear in TCVN 9386:2012 are still quite uncertain and difficult to apply CONCLUSIONS CONCLUSIONS The research results allowed quantifying the increase of flexural stiffness by kIbu and flexural resistance by kMb of frame beams when considering the interaction with MIs in form of a mathematical expression The increase in flexural resistance of frame beams considering the interaction with the MIs can cause the RC frame structures designed in accordance with the current seismic design standards (including TCVN 9386:2012) to be collapsed by the "soft storey" mechanism, missing the original design purpose The design of RC frame structures employing to M Rcmu ≥ 1,3kMb M Rb allows the proposed condition (3.23): ∑ ∑ controlling of failure mechanisms of frames when considering the interaction with MIs With this design condition, whether the MIs are available or not, the design of frames will be safer and more economical A simple model for nonlinear behavior of MIs is established using the approach of an equivalent diagonal strut Deterioration in stiffness and strength of the MIs and surrounding RC frames and the axial compression behavior of masonry are considered when determining the model parameters This model is calibrated corresponding to the results of various experiments published by foreign researchers These experiments were performed on masonry infilled RC frames designed according to the modern seismic conception, which is consistent with research objects and objectives The analytical results of the multi-bay, multi-storey RC frame structure designed according to TCVN 9386:2012 by nonlinear pushover analysis method with the proposed model show that: a) When the interaction with the MIs is not taken into account, the frames are collapsed in plastic mechanisms with flexible plastic hinges that appear first in the beams, which is fully in line with the original design goal; 24 b) The interaction between MIs and surrounding RC frame structures can lead to soft storey mechanisms and brittle collapses, which is completely consistent with the research results of the thesis and other researchers in the world in the recent decades; c) When the frames are designed using the proposed method with the condition of controlling the plastic failure mechanism (3.23) taking into account the interaction with the MIs, they are no longer collapsed by the soft storey mechanism, which is perfectly suitable for the research objectives The frame-MI interactive forces are clearly quantified, then we can determine its action effects on the columns Consequently, a method to design RC frame columns in shear according to the current seismic conception considering the interaction with the MIs is proposed This design method has the following main advantages: a) Be logical and strict, considering systematically the effect of interaction with the MIs on bending resistances of beams and columns and design shear force of columns; b) Allow controlling column shear failure actively, which is consistent with the capacity design principles widely used in current seismic design standards worldwide RECOMMENDATIONS Remaining safety and economy for RC frame buildings makes it necessary to study and apply the proposed frame design method with the condition to ensure the plastic failure mechanism (3.23) and the condition to determine the column shear force (4.23) into the design of RC frame structures for earthquake resistance as well as verification of seismic resistance of the existing frame buildings Currently, there are many types of constructed MIs which are different from those considered in the research content Therefore, in order to obtain suitable masonry strength for the behavior model of the MIs as well as to determine the frame-MI interactive forces, the experiments to determine their mechanical and physical properties are required Based on the research results of the thesis on the effects of solid MIs on the responses of the RC frame designed according to the current seismic conception, it is necessary to continue the study on the followings: a) MIs with openings (windows and doors) in the frame plane; b) The height of MIs is smaller than the clear length of columns; c) The bottom storey of frames has no MIs LIST OF PUBLISHED WORKS RELATED TO DISSERTATION A Scientific journals Nguyen Le Ninh, Phan Van Hue (2017), “The influence of masonry infills on the seismic response of reinforced concrete frame structures according to modern conception”, Science Journal of Architecture & Construction, Hanoi Architectural University, ISSN 1859-350X, (28/2017), pp 49-55 (in Vietnamese) Nguyen Le Ninh, Phan Van Hue (2017), “Analytical modeling of nonlinear behavior of masonry infills in reinforced concrete frame buildings under seismic action”, Journal of Science and Technology in Civil Engineering, National University of Civil Engineering, ISSN 1859-2996, vol 11 (6), pp 13-21 Phan Van Hue, Nguyen Le Ninh (2018), “The effect of masonry infills on the seismic local response in columns of reinforced concrete frame structures according to modern conception”, Journal of Structural Engineering and Construction Technology, Vietnam Association of Structural Engineering and Construction Technology, ISSN 1859-3194, (27), pp 105-116 (in Vietnamese) Phan Van Hue (2019), “Effects of masonry infills to the control of the failure mechanism of reinforced concrete frame structures under earthquake loading”, Journal of Science and Technology in Civil Engineering, National University of Civil Engineering, ISSN 2615-9058, vol 13 (4V, 9-2019), pp 58-72 (in Vietnamese) Phan Van Hue (2019), “A method of designing reinforced concrete frame columns subjected to shear force considering the frame – infill interaction according to the modern seismic concept”, Vietnam Journal of Construction, Ministry of Construction, ISSN 0866-8762, (618) (9-2019), pp 66-72 (in Vietnamese) B Scientific Conferences Nguyen Le Ninh, Phan Van Hue (2017), “The influence of masonry infills on the seismic response of reinforced concrete frame structures according to modern conception”, Proceedings of the International Scientific Conference on “Material, Structures, Construction Technology and Construction Inspection-MSC 2017”, State Authority for Construction Quality Inspection - Ministry of Construction and Hanoi Architectural University, 10/11/2017, Hanoi (in Vietnamese) Phan Van Hue, Nguyen Le Ninh (2017), “The effect of masonry infills on the seismic local response in columns of reinforced concrete frame structures according to modern conception”, Proceedings of the 30th National Conference on Structural Engineering and Construction Technology, Vietnam Association of Structural Engineering and Construction Technology, 15/12/2017, Hanoi (in Vietnamese) Hue Van Phan, Ninh Le Nguyen (2018), “The Influence of Masonry Infills on the Seismic Response of Reinforced Concrete Frame Structures according to Modern Conception”, Proceedings of The International Seminar of “NIT, Gifu College” and Partner Universities – Environmental Sustainability, Disaster Prevention and Reduction, and Engineering Education, National Institute of Technology, Gifu College, Gifu, Japan (March 18th – 19th 2018), Paper No O14 ... Examiner 3: Dr Nguyen Dai Minh The doctoral dissertation will be defended before Doctoral Defence Committee held at the National University of Civil Engineering at ……… on ……………….…………, 2020 This Dissertation... columns, beam-column joints, and the collapse of buildings, etc under seismic action This issue has attracted many studies worldwide 1.2 INTERACTION BETWEEN FRAMES AND MASONRY INFILLS AND BEHAVIOR... Chrysostomou and Asteris (2012); Turgay et al (2014), etc In Vietnam: Ly Tran Cuong (1991) and Dinh Le Khanh Quoc (2017) proposed the methods of determining wm in the direction of group b) 5 Remarks on