COMPARISON OF LABVIEW WITH SAP2000 AND NONLIN FOR STRUCTURAL DYNAMICS PROBLEMS

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1 International Journal of Civil Engineering and Technology (IJCIET) Volume 8, Issue 2, February 2017, pp Article ID: IJCIET_08_02_025 Available online at ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed COMPARISON OF LABVIEW WITH SAP2000 AND NONLIN FOR STRUCTURAL DYNAMICS PROBLEMS Palash Rajepandhare M.Tech. Scholar, Department of Civil Engineering, NIT, Raipur, India Govardhan Bhatt Assistant Professor, Department of Civil Engineering, NIT, Raipur, India Abhyuday Titiksh PhD Scholar, Department of Civil Engineering, NIT, Raipur, India ABSTRACT Structural dynamics is a module of structural analysis that encapsulates the behavior of structures subjected to dynamic loadings. The problems of structural dynamics can be categorized as SDOF, MDOF or Continuous systems. LabVIEW is simulating software possessing extensive graphical representation and data acquisition capabilities. It is of particular interest to the engineers working in the general area of structural health monitoring. The graphical user interface and the capability to acquire & process real time data makes it the ideal choice of programming language. In this study, an attempt has been made to develop a dynamic system using a SDOF model in LabVIEW. The results were compared with NONLIN program and SAP2000 software. Parametric study has been done using Newmark β method and the results were plotted for accelerations, velocities and displacements. Key words: LabVIEW, SAP2000, NONLIN, SDOF, Validation of LabVIEW. Cite this Article: Palash Rajepandhare, Govardhan Bhatt and Abhyuday Titiksh, Comparison of LabVIEW with SAP 2000 and NONLIN for Structural Dynamics Problems. International Journal of Civil Engineering and Technology, 8(2), 2017, pp INTRODUCTION A typical SDOF system, shown in Fig. 1(a), consists of a mass 'm', a weightless frame which provides lateral stiffness, and a viscous damper (called a dashpot) for dissipating the vibrational energy of the entire system. The beam and columns are assumed to be axially inextensible. In this system, all these properties are concentrated in three separate components: mass component, stiffness component, and damping component. This structure has only one DOF when it is idealized with mass concentrated at one location. Thus we call this a single degree of freedom (SDOF) system. However in case of mass distributed throughout the height of the structure, as shown in Fig. 1(b), multi degree of freedom editor@iaeme.com

2 Palash Rajepandhare, Govardhan Bhatt and Abhyuday Titiksh systems are considered for analysis [1]. In our study, earthquake-induced ground motions of Loma Prieta (1989), San Fernando (1971) and Santa Monica (1994) earthquakes are provided to the SDOF system. LabVIEW was introduced some 30 years ago and since then, it has become one of the most reliable and dominant programming language. It is commonly used for works like instrumentation, data acquisition and control [2]. LabVIEW offers the user a chance to integrate the creation of user panel interface to the development cycle. The biggest advantage that the software has to offer is its capability to allow non-programmers to build programs simply by dragging and dropping virtual connections of equipments or formulae. However it also has a drawback; the programming language adopted in LabVIEW is G, which can prove very tricky to understand in complex situations. As far as the performance is concerned, LabVIEW produces results at a slightly slower rate when compared to other hand coded applications such as C or Fortran. However, high degree of precision can be achieved using dedicated toolkits for certain tasks. It is essentially a proprietary product, developed and owned by National Instruments, Texas and is not conforming to any other third party standards such as ANSI, IEEE or ISO. This therefore, raises the question of its application in solving complex problems of Structural Dynamics. Figure 1 (a) Idealized SDOF Figure 1 (b) MDOF systems So a comparative study is prepared, SAP2000 and NONLIN, by taking up a SDOF system. It is subjected to three different earthquake excitations using past as mentioned before and the response of the SDOF system is obtained using time domain analysis which comes under LDP. For systems that have irregular mass or stiffness distributions & irregular geometries, the demands predicted by a LDP analysis are more accurate than those predicted by the Linear Static Procedures (LSP).In this study, the response of the system is obtained by assuming that the system remains in a linear range (i.e. elastic range). As opposed to Nonlinear Dynamic Procedure (NDP), LDP is less time consuming if the system is responding in nearly elastic manner to seismic ground motions. In time domain analysis there are many methods to obtain the response of the structure. Newmark's β method (a kind of Numerical method) is adopted here Objectives of this Study To model a SDOF system in LabVIEW and analyze it using LDP. The response of the SDOF system in terms of acceleration, velocity and displacement is to be plotted against time. To model the same SDOF system in SAP2000 and NONLIN with the same parameters and obtain the responses of the system as mentioned above. Studying the variations in the above responses of the SDOF system editor@iaeme.com

3 Comparison of LabVIEW with SAP 2000 and NONLIN for Structural Dynamics Problems Commenting on the suitability of LabVIEW for applications in the solving complex problems of structural dynamics Newmark's β method Linear equation of motion for a SDOF system is given as: = () (1) where, M = Mass, C = Damping, K = Stiffness, a = acceleration, v = velocity, d = displacement, F(t) = External force at time t The Newmark's β method is adopted in solving such differential equations. It is a method of numerical integration and is widely used in numerical evaluation of the dynamic response of structures and solids. The method is named after Nathan M. Newmark (former Professor of Civil Engineering at the University of Illinois) who developed it in 1959 for use in the field of structural dynamics. Newmark's β method uses a step-by-step numerical integration scheme. The equation of motion at (i+1) th step is evaluated by using acceleration, velocity & displacement at the i th step and external force at (i+1) th step, assuming linear acceleration in small time step. Optimum values of this time interval 'dt' should be chosen to obtain the fastest converging results with required degree of precision. The biggest limitation with Time stepping methods is that the total error goes on accumulating as the calculation proceeds [3]. In order to keep Newmark s β method stable, the time step should be taken such that the ratio where To = 2π/ω, is the time period of the SDOF system [4]. Displacement and velocity equations given by Newmark are: = + [(1 ). ]. + (. ). (2) = +. + [(0.5 ).. ]. + (.. ). (3) where, β, γ = Newmark's parameter. Here constant (average) acceleration is considered for which γ = ½ & β = ¼. To avoid iteration, incremental form of equations were introduced by Newmark [5]. = (4) = (5) =.... (6) Here, dd, dv & da are the incremental values of displacement, velocity & acceleration. Adding these incremental values of displacement, velocity & acceleration at i th step to previously obtained values at i th gives values at (i+1) th step [5], [6]. = + (7) = + (8) = + (9) 2. MODELLING OF THE SYSTEMS Modelling in LabVIEW For the purpose of modelling, zero initial conditions were assumed, damping (c) was taken as 5%, incremental time interval (dt) was taken as 0.02 s, and unit mass was considered for the SDOF system. SI system of measurement was followed in the entire study. The records of three different earthquakes as mentioned before were taken up for time history analysis. The SDOF system with above mentioned editor@iaeme.com

4 Palash Rajepandhare, Govardhan Bhatt and Abhyuday Titiksh properties is subjected to earthquake ground accelerations as obtained from PEER Ground Motion Database [7], [8]. The stiffness of the system was taken as N/m. The module developed in LabVIEW for the above stated problem statement is shown below in Fig. 2. Figure 2 Block Diagram for the flow of information in LabVIEW 2.1. Modelling in NONLIN Developed by Advanced Structural Concepts, Inc., NONLIN is software specially prepared for earthquake related analysis. It has a default option of SDOF system and hence required values of parameters can be directly entered in it [9]. Same parameters were selected as in the case of modelling in LabVIEW. Time History data present in the software was selected for the before mentioned earthquakes and analysis was done to obtain the response plots in terms of acceleration, velocity and displacement Modelling in SAP2000 Preparing the damped SDOF system and analyzing it by Newmark's β method, in SAP2000, was done by giving a special joint at the axis intersection. Same parameters were selected as in the case of modelling in LabVIEW. This joint was assigned with mass and stiffness parameters in the same direction and degree of freedom (DOF) was also assigned in the same direction. Time History functions were added from files along the direction of DOF. These files contained records of past earthquakes and were obtained from PEER Ground Motion Database [7], [8]. Linear direct integration was done and acceleration parameter was used to apply the loads. Other factors such as scale function for time history loads and damping (c = 0.05) was provided as default values provided in the software and Newmark's β method was selected for the purpose of analysis. 3. VALIDATION To validate the accuracy of results obtained from LabVIEW, two sample problems were solved. For the first problem, the parameters entered for SDOF system were taken from a solved example in editor@iaeme.com

5 Comparison of LabVIEW with SAP 2000 and NONLIN for Structural Dynamics Problems Dynamics of Structures [1]. El Centro earthquake records were used with a maximum acceleration of g. Damping (c = 0.02) and unit mass (m = 9.81 N) were provided and a time step of 0.02 s was selected. Results for different time periods (T 1 = 0.5 s, T 2 = 1.0 s and T 3 = 2.0 s) as obtained from LabVIEW and as presented by Chopra, 1995 are shown below in Fig. 3. For the second problem, the parameters entered for SDOF system were taken from a solved example in Dynamics of Earthquake Analysis : NPTEL Courses [3]. Here again El Centro earthquake records were used with a maximum acceleration of g. Damping (c = 0.02) and unit mass (m = 9.81 N) were provided and a time step of 0.02 s was selected. Results for time period (T = 1.0 s) as obtained from LabVIEW and as presented by Jangid, 2013 are shown below in Fig. 4. For both the sample problems considered, almost identical results were obtained, thus validating the LabVIEW program presented in this paper. (a) Figure 3 For the first sample problem, results obtained through: (a) LabVIEW, (b) Chopra, 1995 (b) (a) (b) Figure 4 For the second sample problem, results obtained through: (a) LabVIEW, (b) Jangid, editor@iaeme.com

6 Palash Rajepandhare, Govardhan Bhatt and Abhyuday Titiksh 4. RESULTS & DISCUSSIONS In this paper, a comparative analysis is presented for a SDOF system using LabVIEW, SAP2000 and NONLIN. The parameters considered for the system were c = 0.05, dt = 0.02 sec and m = 9.81 N. The system was subjected to three different earthquake excitations of Loma Prieta (1989), Santa Monica (1994) and San Fernando (1971) earthquakes. The response of the system was obtained using time domain analysis in terms of acceleration, velocity & displacement. Note PA Max = Peak Acceleration (+ve) (m/s 2 ) PA Min = Peak Acceleration (-ve) (m/s 2 ) PV Max = Peak Velocity (+ve) (m/s) PV Min = Peak Velocity (-ve) (m/s) PD Max = Peak Displacement (+ve) (m) PD Min = Peak Displacement (-ve) (m) 4.1. Responses of Loma Prieta Earthquake Table 1 Variation of Responses for Loma Prieta Earthquake Santa Monica PA (m/s 2 % variation % variation % variation ) PV (m/s) PD (m) LabVIEW NONLIN SAP Figure 5 Response in terms of Acceleration (m/s 2 ) for Loma Prieta Earthquake Figure 6 Response in terms of Velocity (m/s) for Loma Prieta Earthquake editor@iaeme.com

7 Comparison of LabVIEW with SAP 2000 and NONLIN for Structural Dynamics Problems Figure 7 Response in terms of Displacement (m) for Loma Prieta Earthquake The responses obtained from LabVIEW are same as that of responses obtained from NONLIN with negligible difference. In case of SAP2000, the phase (pattern) of the responses and peak values of responses are differing slightly. As per SAP200, the peak acceleration is 11.05% higher, peak velocity is 14.21% higher and peak displacement is 10.81% higher as compared to the respective responses obtained through LabVIEW. Also the phase is slightly varying in the region of 17 sec to 30 sec Responses of San-Fernando Earthquake Table 2 Variation of Responses for Santa Monica Earthquake Santa Monica PA (m/s 2 % variation % variation % variation ) PV (m/s) PD (m) LabVIEW NONLIN SAP The responses obtained from LabVIEW are same as that of responses obtained from NONLIN with negligible difference. In case of SAP2000, the phase of the responses and peak values of responses are differing slightly. As per SAP200, the peak acceleration is 13.19% higher, peak velocity is 11.37% higher and peak displacement is 11.11% higher as compared to the respective responses obtained through LabVIEW. Also the phase is slightly varying in the region of 10 sec to 20 sec. Figure 8 Response in terms of Acceleration (m/s 2 ) for San Fernando Earthquake editor@iaeme.com

8 Palash Rajepandhare, Govardhan Bhatt and Abhyuday Titiksh Figure 9 Response in terms of Velocity (m/s) for San Fernando Earthquake Figure 10 Response in terms of Displacement (m) for San Fernando Earthquake 4.3. Responses of Santa Monica Earthquake Table 3 Variation of Responses for San Fernando Earthquake Santa Monica PA (m/s 2 % variation % variation % variation with ) PV (m/s) PD (m) LabVIEW LabVIEW NONLIN SAP The responses obtained from LabVIEW are same as that of responses obtained from NONLIN with negligible difference. In case of SAP2000, the phase of the responses and peak values of responses are differing slightly. As per SAP200, the peak acceleration is 23.46% lower, peak velocity is 16.62% higher and peak displacement is 12.12% higher as compared to the respective responses obtained through LabVIEW. Also the phase is slightly varying in the region of 5 sec to 15 sec editor@iaeme.com

9 Comparison of LabVIEW with SAP 2000 and NONLIN for Structural Dynamics Problems Figure 11 Response in terms of Acceleration (m/s 2 ) for Santa Monica Earthquake Figure 12 Response in terms of Velocity (m/s) for Santa Monica Earthquake Figure 13 Response in terms of Displacement (m) for Santa Monica Earthquake editor@iaeme.com

10 Palash Rajepandhare, Govardhan Bhatt and Abhyuday Titiksh 5. CONCLUSIONS An attempt has been made to compare the responses of a SDOF system in terms of acceleration, velocity and displacement. Ground motion data of three earthquakes was used and the results obtained using LabVIEW, NONLIN and SAP2000 were compared. Based on the above analytical study, the following conclusions can be drawn- Accurate results are obtained by the proposed program in LabVIEW. The results were validated through two sample problems and the final responses obtained are in line with the ones obtained through NONLIN. The time period obtained through LabVIEW, NONLIN and SAP2000 are exactly same (T = sec). However for certain intervals, a difference in the phase was observed in the case of responses through SAP2000. The responses obtained through SAP2000 were of slightly higher magnitudes as compared to the responses of LabVIEW. On an average, the acceleration varied by 15.9%, velocity varied by 14.06% and displacement varied by 11.34%. REFERENCES [1] A. K. Chopra, Dynamics of Structures - Theory and Applications to Earthquake Engineering. New Jersey: Prentice Hall, [2] G. W. Johnson, LabVIEW graphical programming : practical applications in instrumentation and control [3] R. S. (IIT B. Jangid, Dynamics of Earthquake Analysis, in NPTEL Courses, vol. 1, Mumbai, India: NPTEL, [4] A. K. Chopra, Elastic response spectrum: a historical note, Earthq. Eng. Struct. Dyn., vol. 36, no. 1, pp. 3 12, [5] C. Caprani, Structural Dynamics, in Structural Analysis IV - Lecture Notes for 2011/12, Dublin, Ireland: Dublin Institute of Technology (DIT), 2012, pp [6] S. Krenk, Non-linear modeling of solids and structures, First. Cambridge, UK: Cambridge University Press, [7] T. D. Ancheta et al., PEER NGA-West2 Database : A Database of Ground Motions Recorded in Shallow Crustal Earthquakes in Active Tectonic, 15th World Conf. Earthq. Eng., [8] P. E. E. R. C. PEER, PEER Ground Motion Database, Shallow Crustal Earthquakes in Active Tectonic Regimes, NGA-West2, [Online]. Available: [9] NONLIN 7.05 User s Manual. Advanced Structural Concepts, Inc. NONLIN7.05, Blacksburg, Virginia, pp , [10] Dharane Sidramappa Shivashaankar and Patil Raobahdur Yashwant, Design and Practical Limitations in Earthquake Resistant Structures and Feedback, International Journal of Civil Engineering and Technology (IJCIET) 5(6), 2014, pp editor@iaeme.com