Address for Correspondence

Research Article EXPERIMENT STUDY OF DYNAMIC RESPONSE OF SOFT STOREY BUILDING MODEL C. S. Sanghvi 1, H S Patil 2 and B J Shah 3 Address for Correspondence 1 Associate Professor, Applied Mechanics Department, L.D. College of Engineering, Ahmedabad, Gujarat, India 2 Professor, Department of Applied Mechanics, S V National Institute of Technology, Surat, Gujarat, India 3 Associate Professor,Applied Mechanics Department, L.D. College of Engineering, Ahmedabad, Gujarat, India ABSTRACT The study of structural dynamics in civil engineering is commonly perceived to be a difficult exercise because of the mathematical nature of the subject. One of the most effective ways to simplify this would be development of a suite of simple experimental set ups which would enable the study of basic issues related to acceleration, velocity, displacement, damping, natural frequency, mode shape, natural period, etc. Study of dynamic response of building is carried out on two stories regular and irregular `building. Regular consists of symmetrical plan as well as elevation and irregular consists of soft storey. Model made up with steel bars and plate. Upon completion of the, static stiffness tests and free vibration tests are perform to determine the actual properties of the such as stiffness, damping ratio, and natural frequencies of vibration. Comparison of the system properties identified experimentally with those predicted by the theory or simulated numerically. Shake table is used for excitations and corresponding response of the physical is measured in terms of natural frequency, acceleration, phase angle. Such experimental results are compared with SAP 2000 software. KEYWORDS: Dynamic response of building, Shake table Testing, Stiffness, Damping, Frequency 1. INTRODUCTION Recently, several sizeable earthquakes have caused severe damage in civil structures all over the world, including Northridge, California (1994), Kobe, Japan (1995), Kocaeli, Turkey (1999), Chi-Chi, Taiwan (1999), and Bhuj, India (2001), Indonesia (2004), Kashmir (2005), Haiti (2010), Japan (2011) etc. To protect civil structures from significant damage, the response reduction of civil structures under such severe earthquakes has become an important topic in structural engineering. Study of the response of structure is very important. So effort is made to study the behavior of a two story regular building and stiffness irregular building frame subjected to harmonic base motions. This experiment also enables the understanding of occurrence of resonance phenomenon in multi-degree of freedom (MDOF) systems. The frame of is rectangular in plan as well as in elevation. The building without stiffness irregularity and with stiffness irregularity is used for the testing. Regular consists of symmetrical plan as well as elevation and irregular consists of stiffness irregularity. 2. OBJECTIVE OF STUDY 1. To find out stiffness of building experimentally. 2. To find out dynamic properties of the like damping, natural frequency with free vibration test. 3. To find out dynamic properties of like acceleration, natural frequency, time period, phase angle, mode shapes, with shake table testing. 4. Comparison of dynamic responses of from shake table test with SAP 2000 software. 3. GEOMETRIC DEFINATION The plan & elevation of and 3D are shown in figure 1, 2 & 3. Two storey of building is regular in plan as well as in elevation and other with stiffness irregularity is considered. The frame of is rectangular in plan as well as in elevation. Model is made up with steel bars and plates. Material used to construct along with its dimensions are given below. Materials: 1. 23 x 18 of 2mm mild steel base plate. 2. 20 x 14 of 3.12 mm mild steel top plate. 3. 6.8 mm diameter rod (Mild steel). 4. 2 diameter top of MS rod with 3.92 mm thickness. Figure 1 Plan view of Figure 2 Elevation of regular and irregular

Figure 3 Photograph of Regular and Irregular Note: Dimension of the bracing 12 mm width & 2 mm thick 4. INSTRUMENT USED IN EXPERIMENTS Instrument used in the experiment is given below 1. Shake table 2. Accelerometer 3. Sixteen channel vibration analyzer instrument 4. Data acquisition system 5. Shake table speed controller 6. Stiffness calculation assembly 5. EXPERIMENTAL SETUP: Following test were carried out during experimental work. a) Determination of Property of Model. b) Determination of Stiffness of the c) Free Vibration Test. d) Shake Table Test. a) Determination of Property of Model: The modulus of elasticity of material used in is very useful to determine the natural frequency of structure for manual calculation as well as input for software. Sample of material used in is tested in the universal testing machine and a graph of stress versus strain graph is plotted to find out the modules of elasticity Modules of elastic of =20500 N/mm 2 b) Stiffness Experiment: This experiment was designed to measure the inter-story stiffness of the three dimensional which will be tested on Shake Table. Equipments: 3D Model, steel platform, fix frame, nut and bolt, Steel bracket, dial gauge with magnetic base, load Cell, weights Procedure: (1) Prepare steel platform for experiment. (2) Screw one bracket in the frame just above each floor level (Figure 4). (3) Place the 3D on the steel platform, close enough to the frame, to clamp each floor to the bracket. (4) Clamp 3D to the steel platform with nut bolt. (5) Attach the dial gauge with magnetic base. (6) Connect the with steel wire (7) Place weight to generate initial tension in steel wire. (8) Adjust dial gauge to zero position. (9) Gradually increase the load and measure gauge reading. (10) Determine K 1 (the stiffness between the base and Floor 1). (11) After determine K 1, fixed first floor with vertical wall with bracket and place gauge at top floor and repeat step at (6) to (9). (12) Determine K 2 (the stiffness between the first floor and second floor). Figure 4 Stiffness experiment Figure 5 Schematics setup c) Free vibration test: This experiment is designed to determine the damping ratio of the 3D. The damping ratio is important input in the SAP 2000. The damping ratio characterizes the rate of decay of motion of the system. It is not possible to analytically determine the damping coefficient c or damping ratioξ for a structure, there is considerable interest in evaluation of damping from experiments. The results of the preceding section provide a basis for evaluating amount of damping from free vibration experiments. The natural period of vibration T of the structure can also be determined from these experiments. Equipments:

3D Model, Accelerometer, Sixteen channel vibration analyzer instrument, Laptop Procedure: (1) Fix on shake table. (2) Place accelerometer in direction of pull. (3) Attach accelerometer to instrument. (4) Disturb the structure from its equilibrium position through some displacement u (0) and release the structure. (5) Record the free vibration of the structure to obtain the acceleration vs. time plot as shown in Fig.13. (6) Measure the time required to complete one cycle of vibration to obtain the vibration period T. (7) Measure successive peaks (8) Damping ratio can be determined from the following equation [Chopra, 2000]: 1 u&& i ξ = ln * 2π u&& j i + j Where j denotes the number of cycles during which successive peaks ü i, ü i+1 ü i +j are used in the calculation as shown in Figure. Also record acceleration vs. frequency in FFT graph and finally compute natural frequency of. the response amplitudes along x-axis versus time. (10) Find out natural frequency, acceleration and natural period of structure (11) Also find natural frequency and acceleration in other direction by placing in y- axis and repeat step from (1) 6. RESULTS OF EXPERIMENTS: Result of Stiffness Experiment: First Floor Figure 7 Displacement verses tension graph Stiffness in kn/m= 12.61 Table 1 Stiffness test results: First storey Sr. No. Gauge Reading Disp. (mm) Tension (gm) Figure 6 Damping ratio determined by logarithmic decrement d) Shake table test: The vibration properties of a structure are determined by varying the frequency of the shake table through appropriate range. The amplitude of the steady state acceleration of the structure at each forcing frequency is measured. Frequency-response curves, in the form of acceleration amplitude vs. forcing frequency, may be plotted directly from the measured data. The natural frequency of vibration, acceleration and time period can be determined from frequency-response curves Equipments: 3-D Model, shake table, accelerometer, sixteen channel vibration analyzer, laptop. Procedure: (1) Securely attach the 3-D to shake table. (2) Place accelerometer on 3-D. (3) Start NVgate software and run it (4) Arrange the experimental setup as shown in figure 3. Note that the accelerometer needs to be placed on slab in such a way that acceleration along x-direction can be measured. (5) Connect accelerometer to vibration analyzer instrument. (6) Run the base motion (7) Identify the frequencies at which the structure undergoes resonance by observing the variation of response amplitudes with change in frequency of shake table. (8) At resonance conditions, note the amplitude of acceleration at slab level. (9) Plot 1 110 1.1 1414 2 220 2.2 2828 3 330 3.3 4242 4 440 4.4 5656 5 550 5.5 7070 Result of Stiffness Experiment: Second Floor Figure 8 Displacement verses tension graph Stiffness in kn/m = 27.27 Result of Free Vibration Test ξ = ( 1 / 2 * 3.14 * m) ln( Vn ) Vn + m m =Number of cycle required for calculation Vn=Peak value of graph in m/s^2 Table 2 Free vibration test results First floor m 1 4 V n 4.623 V n+m1 3.694 Damping 0.00893 Damping (%) 0.893 Natural frequency First mode w (rad/sec) 16.642 f (cycle/sec) 2.65

Figure 9 Time vs. acceleration graph Figure10 Natural frequency Vs. Acceleration graph Results of Shake Table Test Irregular Model Mass at first floor : 16.265 kg Mass at second floor : 16.265 kg fz = Natural frequency. Ac 1 = Acceleration of first floor. Ac 2 = Acceleration of second floor D 1 = Displacement of first floor. = Displacement of second floor. Θ o = Phase angle Table 3 Shake table test results: First mode fz Time Period Ac 1 Ac 2 D 1 (Hz) (Sec) m/sec 2 m/sec 2 mm mm 2.95 0.339 2.56 2.88 6.97 7.97 Figure 11 Natural frequencies vs. acceleration graph first mode Figure 12 First floor and second floor acceleration

Regular Model fz (Hz) Table 4 Shake table test results: First mode Time Period (Sec) Ac 1 Ac 2 D 1 m/sec 2 m/sec 2 mm 4.24 0.236 8.77 8.88 1.0 2.0 Mm 7. SAP 2000 Model: Irregular Model Figure 13 First floor and second floor acceleration Figure 14 Object regular created in SAP 2000 Figure 15 Mode of regular and irregular Table 5 SAP 2000 results: First mode Frequency Time period D 1 A 1 A 2 (Hz) (sec) Mm Mm m/sec 2 m/sec 2 2.92 0.341 7.13 8.24 2.78 3.02 Figure 16 First floor and second floor acceleration Regular Model Figure 17 Object regular created in SAP 2000

Figure 18 First floor and second floor acceleration Table 6 SAP 2000 results Frequency Time period D 1 A 1 A 2 (Hz) (sec) mm Mm m/sec 2 m/sec 2 4.11 0.243 1.2 2.24 8.62 7.95 8. CONCLUSION Frequency & natural period calculated experimentally & SAP 2000 are very close. Amount of damping in steel structure from the free vibration test is found nearly 0.9 % instead of conventional 2 % damping in steel structure. Relative acceleration in first mode in regular building is almost 3.5 times as compared to irregular. Table 7 Acceleration results of experiment: First & second floor 5. Pankaj Agrawal & Manish Shrikhande, Earthquake resistant design of structure, Prentice-Hall India 2005. 6. Sabnis, Gajanan M., et al. Structural Modeling and Experiment Techniques. Englewood Cliffs: Prentice-Hall, Inc., 1983. 7. Shonkwiler Brenda E., Miller Thomas H. Small scale shake table experiments of simple three storey building, Oregon state university. Regular Irregular A 1 (m/sec 2 ) A 1 (m/sec 2 ) First Floor 8.77 2.56 Second Floor 8.88 2.88 Relative displacement in first mode in irregular building is increased almost 7 times as compared with regular with bracing. Table 9 Displacement results of experiment: First & Second floor Regular Irregular D 1 (mm) D 1 (mm) First Floor 1.0 6.97 Second Floor 2.0 7.97 It can be concluded that the soft storey building swing back and fort like inverted pendulum during earthquake shaking and column in the open ground storey are severely stressed due excessive deformation. REFERENCES 1. Chopra, A.K. (2001), Dynamics of Structures: Theory and Applications to Earthquake Engineering, Second Edition, Prentice Hall. 2. Chopra A. K., A Primer, Dynamic of structure Earthquake engineering research institute: 3. Clough, R.W. and Penzien, J. (1993). Dynamics of Structures, Second Edition, McGraw Hill. 4. Naeim Farzad, Seismic design hand book, 2 nd edition, Kluwer academic publication