2nd International Conference on Earthquake Engineering and Post Disaster Reconstruction Planning 25 – 27 April, 2019, Bhaktapur, Nepal Study on the Effect of Mass and Stiffness Irregularities on Fundamental Period of Infilled RC Framed Buildings Mahesh Raj Bhatt1, Prachand Man Pradhan2 and Sudip Jha3 Abstract Reinforced concrete (RC) frames infilled with unreinforced masonry are quite common all across the globe since many decades. In this study the special moment resisting RC framed buildings with vertical mass and stiffness irregularities have been analysed with modal analysis using ETABS 2016. Regular model having regular distribution of mass and stiffness in elevation were analysed and designed as per IS 1893:2002 by equivalent static method. Comparison has been done among the fundamental periods of 6th, 9th and 12th storeys among regular, irregular and bare framed buildings. Results show that there is significant contribution of infill in fundamental periods and there is significant effect of location and magnitude of irregularity in fundamental period. The fundamental periods of the irregular buildings were found longer than regular and shorter than bare frame buildings. Furthermore, it has been found that there are positive correlation between elevation of mass irregularity & fundamental time period and negative correlation between elevation of stiffness irregularity and fundamental period. Fundamental period was longest with mass irregularities in top storey and stiffness irregularities in second storey. There was not significant effect in fundamental period when mass irregularity was in bottom portion of building and stiffness irregularity was in top portion of the building. Keywords: Infilled RC frames; Fundamental period; Mass irregularity; Stiffness irregularity 1. Introduction The structural irregularities can be broadly classified as plan and vertical irregularities as per (IS 1893:2002). Irregularity arises due to sudden reduction of stiffness or strength and sudden increase of mass in a particular storey. For high seismic zone area, irregularity in vertical elevation is a great challenge to structural engineers. A large number of vertically irregular buildings exist in modern urban infrastructures. Among them, open ground storey is common these days in urban cities in Nepal, for parking and storing purposes. As per (IS:1893, 2002), a storey in a building is said to contain mass irregularity if its mass exceeds 200% than that of the adjacent storey. Furthermore, a soft storey is one in which the lateral stiffness is less than 70% of that in the storey above or less than 80% of the average lateral stiffness of the three stories above. A storey is said to be an extreme soft storey if the lateral stiffness is less than 60% of that in the storey above it or less than 70% of the average stiffness of the three stories above. Many reasons like the presence of swimming pool in particular elevation, storing of heavy mechanical equipment & machines, parking of vehicle in particular storey etc., may cause the storey to be mass irregular. The elimination of infill in interior part of the building for application purpose, reduction of beam and column size in uppers storey, increasing the height of the particular storey, elimination of shear wall in particular level etc., may cause a particular storey to be soft storey (Varadharajan, 2014). It was observed that there were severe damages in vertical irregular structures in Gorkha Earthquake-2015; especially Open ground RC buildings were affected during earthquake (Gautam et. al., 2016). In Nepal the common types of failures in RC construction were identified as the soft storey, pounding, shear failure, and other failures associated with construction as well as structural 1Department of Civil & Geomatics Engineering, Kathmandu University, Dhulikhel, Nepal, maheshrajbhatt2014@gmail.com 2Department of Civil & Geomatics Engineering, Kathmandu University, Dhulikhel, Nepal, prachand@ku.edu.np 3Department of Urban Development & Building Construction, Government of Nepal, Ilam, Nepal, sudip.jha@ku.edu.np 195 2nd International Conference on Earthquake Engineering and Post Disaster Reconstruction Planning 25 – 27 April, 2019, Bhaktapur, Nepal deficiencies like building symmetry, detailing and others (Gautam et al., 2016). Earthquakes namely San Fernando (1971), North Ridge (1994), Bingol (2003), Kashmir (2011) etc. caused the major damage in the vertical irregular buildings (Varadharajan, 2014). After the visual observation during Jabalpur earthquake (1997), the performance of RC buildings with brick infill having no abrupt change in stiffness have been very satisfactory i.e. unreinforced masonry contributed positively, but RC frames with open ground storey has shown poor performance (Jain et al., 1997). Due to many reasons, the outcomes of the calculations of fundamental time period are scattered. Besides, the infill-frame interaction and the height of the construction, several other parameters affect the fundamental period of vibration, such as the irregularity in plan and elevation, the number of storeys, the number of spans (and respective dimensions), the presence of openings within infills and the rigidity of storeys (Asteris et al., 2015). This paper compares time period obtained from the finite element modeling of regular, bare frame and mass and stiffness irregular infilled RC buildings. Pradhan et al. (2012) states that, the fundamental period of vibration reduces significantly due to infill in RC frame. In this study infill is considered with central opening of 30% of panel area for the analysis. 2. Code Provision of Fundamental Time Period Nepal National Building Code (NBC-105, 1994), Indian Standard (IS: 1893, 2002), Uniform Building Code (UBC 1997), National Building Code of Canada (NBCC 2005), International Building Code (IBC 2012) & American Society of Civil Engineer (ASCE, 7-05) recommendation for time period are given in Table 1. Table 1. Mass and stiffness irregularity limitations and empirical time period as per different codes Code Mass Irregularity Stiffness Irregularity Time Equation (T) 0.09 ℎ IS 1893:2002 Mi>200 Ma Si<0.7 Si+1 Si<0.8( Si+1+Si+2+Si+3)/3 UBC 1997 Mi>150 Ma Si<0.7 Si+1 Si<0.8( Si+1+Si+2+Si+3)/3 Ct h0.75 Mi>150 Ma Si<0.7 Si+1 Si<0.8( Si+1+Si+2+Si+3)/3 0.01N NBCC 2005 NBC 105:1994 IBC 2012 ASCE 7-05 Mi>150 Ma Mi>150 Ma Si<0.7 Si+1 Si<0.8( Si+1+Si+2+Si+3)/3 Si<0.7 Si+1 Si<0.8( Si+1+Si+2+Si+3)/3 √𝑑 0.09 ℎ √𝑑 Ct hnz Ct hnz where, Mi, Ma, Si, Si+1, Si+2, Si+3 are Mass of irregular storey, Mass of adjacent storey, stiffness of ith , i+1th , i+2nd and i+3rd storey, Ct constant which varies as per different codes, h is total height of the building, N is the numbers of storey and, d is bay width in earthquake direction. It is seen that the fundamental time period is influenced by various factors like height of the building, number of span and span width, number of storey, presence of infill or not, size and property of material used in the building frame etc. Some of the codes provide simple empirical formulas for the estimation of the fundamental period of vibration (T) of construction simply related to the overall height and base width of the buildings and some are based upon overall structural height of the building irrespective of the width. 196 2nd International Conference on Earthquake Engineering and Post Disaster Reconstruction Planning 25 – 27 April, 2019, Bhaktapur, Nepal 3. Modelling and Analysis In this study Beam, column and strut were modeled in ETABS 2016 as frame element with prismatic section with specific defined material properties of concrete, steel and masonry. The foundation level was assumed fixed and meshing of the shell element i.e. slab and shear wall was done manually. Concrete grade of M25 and steel of grade Fe415 were assigned as materials for beam, column, slab and shear wall. Slab and shear walls were modeled as shell element with slab having rigid diaphragm in each storey level. Mechanical properties of the materials are explained in Table 2. Three different building height categories, ranging 6, 9 and 12 stories (Fig. 2.), with a similar storey height of 3.5m and in both directions number of three bays are considered for the present study. The mass ratio is varied to 200% and 300%. For the mass irregularity of 200%, live load is assigned up to 21.10 kN/m2 uniformly distributed in slab and for the mass irregularity of 300% the live load assigned is 48.24 kN/m2 uniformly distributed in slab in irregular storey. Stiffness irregularity is introduced by replacing all the infill struts in particular storey. Fig. 1. Typical plan and elevation of 6-storey building model Fig. 2. (a), (b) and (c) ETABS 6th, 9th and 12th storey building 3D models Equivalent diagonal compression strut of width, w, given by the Eq. (1), recommended by (FEMA 356, 2000) is considered 𝑤 = 0.175 𝑑-./ (𝜆2 ℎ3 )56.7 𝜆2 = 8 F 9: ;<=> ?-.@A G 79B CB D<=> 197 E (1) (2) 2nd International Conference on Earthquake Engineering and Post Disaster Reconstruction Planning 25 – 27 April, 2019, Bhaktapur, Nepal Where, hc= Column height between centerlines of the beams, hinf = Height of infill panel, Ec is Expected modulus of elasticity of frame material, Em= Expected modulus of elasticity of infill material, Ic = Moment of Inertia of Column, Linf = Length of the infill panel, dinf = Diagonal length of the infill, tinf = Thickness of infill panel and equivalent panel, θ = Angle whose tangent is the infill height-to-length aspect ratio in radians, λ1= Coefficient used to determine equivalent width of infill strut. Reduction factor proposed by (Al-Chaar, 2002), given in Eq. (3) is adopted in the study. J @ J 𝑅/ = 0.6 8JK E − 1.6 8JK E + 1 (3) 𝑓P = 0.433 𝑓S 6.T7 𝑓PU 6.VT (4) L L Where, Ao=Area of the Opening, Ap =Area of the infill panel and Rf = In plane reduction factor for the infill opening. External infill is considered with 30% central openings. Modulus of elasticity Em (in MPa) of masonry wall as Em=550 fm , where fm is the compressive strength of the masonry prism (in MPa) obtained as per (IS:1905, 1989) and is given by Eq. (4). where, fb = compressive strength of brick along its thickness (MPa) and fmo =compressive strength of mortar (MPa). As per (IS:1077, 1992), compressive strength of the common burnt clay brick with Grade 35 is 35 MPa, and as per (IS:1905, 1989), minimum strength of mortar at 28 days Grade H1 is 10 MPa. Adopting these bricks and mortar, Modulus of elasticity of the masonry using Eq. (4) is obtained as 5309.48 MPa. Fig. 3. Typical placement of single strut in infill panel, (Bhatt et al., 2017) Regular model (having regular distribution of mass and stiffness along height) was designed as per (IS:1893, 2002), with load combinations for linear static and response spectrum method with medium soil type and seismic zone of V. After the design check for safety, the models were made irregular in both mass and stiffness. In this study the infill is modeled as macro modeling with equivalent single strut as per FEMA 356. Panel of infill is replaced by a single equivalent diagonal strut of thickness equal to that of infill wall and length equal to length of the diagonal between the two compression corners. 198 2nd International Conference on Earthquake Engineering and Post Disaster Reconstruction Planning 25 – 27 April, 2019, Bhaktapur, Nepal Table 2. Geometrical and mechanical properties of material used in analysis Parameters Characteristic Strength of Concrete (fck) Young’s Modulus of Concrete, (Ec ) Data Unit 25 MPa 25000 MPa Size of Beam (Depth X Breadth) 550 X300 (mm X mm) Size of Column (Breadth X Width) 450 X 450 (mm X mm) Moment of inertia of Column MOI, Ic Remarks (IS:456, 2000) 3417187500 mm4 Infill wall thickness (t) 230 mm Infill wall height (h) 2950 mm Length of Infill wall (L) 4550 mm 13422500 mm2 Characteristic strength of the infill wall (fm) 9.6536 MPa (IS 1893:2016) Young’s Modulus of masonry wall (Em) 5309.48 MPa (FEMA 356:2000) Angle made by strut with horizontal (θ) 32.957 Degrees Diagonal Length of the Infill (dinf) 5422.635 mm Height of the Storey/Column (hc) 3500 mm 4026750 mm2 Area of the infill (Ap) Open Area (Ao) Opening reduction factor ( Rf) 0.574 Equivalent Coefficient ( λ1) 0.0010254 30% opening (Al-Chaar, 2002) Eq. (2) Equivalent width of the Strut (w) 569.17 mm Eq. (1) Final modeled width of strut (w') 326.70 mm (Al-Chaar, 2002) 4. Results and Discussions The presence of infill walls resulted in a considerable increase in the global stiffness of the building that reduced the first mode time period. Because of increase in the lateral stiffness of the infilled frame it is expected to experience higher seismic forces. Some of the Parameters that may affect the time period of the infilled RC frames are e.g. number of the spans, stiffness of the masonry panel, opening ratio of the infill panel, position of the soft storey, soil type etc. Here, building having no mass and stiffness irregularity is named as regular frame, the building without infill is named as bare frame and building having irregularity is named as irregular building model. 4.1 Result discussions for the mass irregularities The location and magnitude of mass irregularity is considered for the fundamental time period comparison of regular, bare frame and irregular building models. In 6-storey case (Fig. 4), first mode time period of bare frame is maximum i.e. 0.796 sec and the first mode time period of regular frame building having regular distribution of storey weight is least among all irregular cases. When irregularity is in higher elevation the time period is increased. In 200% mass case, 13% and 17% are increased in time for irregular 5th and 6th storey respectively and in 300% irregularity, 25% and 33% is increased time period as compared to regular case model for irregular 5th and 6th storey respectively. Highest time period is observed when top storey is irregular. 199 2nd International Conference on Earthquake Engineering and Post Disaster Reconstruction Planning 25 – 27 April, 2019, Bhaktapur, Nepal Fig. 4. First mode time period comparison of 6-storey, mass irregular case Fig. 5. First mode time period comparison of 9-storey, mass irregular case Fig. 6. First mode time period comparison of 12-storey, mass irregular case İn 9-storey case, (Fig. 5), bare frame building model with 0.734 Sec. is highest value followed by irregular top storey. Irregularity in bottom one third part, do not have high influence compared to the irregularity in top part. Time period increasing rate is higher when the magnitude of the irregularity increase in that specific storey level. Irregularity in top increased the time period abruptly, while the base part irregularity does not have significant effect in time period. 20%, 26%, 10% & 13% are 200 2nd International Conference on Earthquake Engineering and Post Disaster Reconstruction Planning 25 – 27 April, 2019, Bhaktapur, Nepal increased time periods in both 300% and 200% irregular cases when irregularities were in 5th and 6th storeys. İn 12 storey case, (Fig. 6), bare frame has highest time period in first mode i.e. 1.756 Sec. followed by irregularity in top storey in both 200% & 300% irregular case. In 200% mass time period increased by 10% and 13% respectively when irregularity in 5th and 6th storey & 19% and 23% is increased time period when 5th and 6th storeys irregular by 300%. Linearly positive correlation is observed between position of irregularity and fundamental time period of the building. 4.2 Result discussions for the stiffness irregularities As time period is the fundamental parameter for the seismic lateral force calculation, in this case it is seen that the time period is highest in bare frame and least in the regular frame having full infill. Global stiffness of the building system is influenced by the presence of the masonry infill. The diagonal strut enhances the lateral stiffness of the structure which causes reduction in time period of the buildings systems. In all height of the building model i.e. 6th, 9th and 12th storey, the time period is highest among all irregularities when the 2nd storey is irregular (Fig. 7) and (Fig. 8). In stiffness irregular case, irregularity in lower one third portion yield increased in time period but irregular top one third parts do not show significant change in time periods. In 6-storey when irregularity is in 1st& 2nd storey the increase in time period is 13% and 18% respectively. In 9-Storey building, the increased percentage of time period is 46% & 56% when irregularities are in 1st and 2nd storey. Similarly, 12-Storey, (Fig. 8), 5% & 10% increase in time period was observed when irregularities are in 1st and 2nd storey respectively. Fig. 7. First mode time period comparison of 6-Storey, 9-Storey, Stiffness Irregular case Fig. 8. First mode time period comparison of 12-storey, Stiffness Irregular case For all the building height, the time period is highest when stiffness irregularity is in 2nd storey. Infill reduces the time period of the building, so the time period of the bare frame is highest and least 201 2nd International Conference on Earthquake Engineering and Post Disaster Reconstruction Planning 25 – 27 April, 2019, Bhaktapur, Nepal in the regular building. It is seen that the negative linear correlations between the elevation of stiffness irregularity and fundamental time period in all cases i.e. 6th, 9th and 12th storeys. 5. Conclusions Total of 60 models for mass irregularities and 33 model of stiffness irregularities were analyzed for the comparative study of fundamental time period. From this study, following conclusions are drawn: ü Magnitude (amount of irregularities) as well as location (elevation of the irregular storey) of the irregularities has significant role on fundamental time period of infilled RC frames. ü In both mass and stiffness irregular case the time period of the bare frame is highest and that of regular frame is least. First mode period of the building increased as the number of the storey increased. For the same storey building the mass irregularity magnitude increases the fundamental first mode time period when located in same position. That concludes the time period of the building is directly affected by the magnitude of the mass irregularity. When irregular mass is in higher elevation the time is increased and vice versa for the stiffness irregularity ü As per IS:1893, 2002 & NBC-105, 1994, the code calculated time periods for 6th, 9th and 12th storey are 0.488 Sec., 0.732 Sec., & 0.976 Sec. respectively in both X and Y-directions. These are nearly similar to the regular building model; however, the code specified formulae don’t satisfy for the irregular case with same building height and bay width. ü In case of mass irregularity, the location of mass irregularity for bottom one third parts don’t vary the time period significantly but when irregularity is in top one third parts the time period increases significantly. Similarly, in case of the stiffness irregularity, time period is maximum when irregularities in 2nd storey. An irregularity in bottom one third significantly increases the time period while an irregularity in top one third does not in case of stiffness irregular case. ü In case of mass irregularities, the positive correlation between the elevation of the mass irregularity and time period is observed. Similarly, negative correlation between the locations of the irregularity and time period is observed. Finally, in light of the above points it is concluded that, mass irregularity in top part of the building and stiffness irregularity in bottom part of the building significantly changes the fundamental time period of the RC infill building structures in comparison to the regular building. Acknowledgement University Grants Commission (UGC-Nepal), Sanothimi, Bhaktapur is acknowledged for the financial support, as the research is based on the work done for master’s thesis for the completion of the Masters degree in Structural Engineering from Kathmandu University, Nepal. References: Al-Chaar, G. (2002). Evaluating strength and stiffness of unreinforced masonry infill structures. US Army Corps of Engineers, Engineering Research and development center. Construction Engineering Research Laboratory. ASCE (2006). Minimum Design loads and for Buidling and other Structures (ASCE/sei-7-05). New York, USA: American Society of Civil Engineers. Asteris, P. G., Repapis, C. C., Tsaris, A. 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