SEISMIC PERFORMANCE ENHANCEMENT OF TRUSS TOWERS WITH VISCOUS FLUID DAMPERS

Transcription

1 5th International Congress on Computational Mechanics and Simulation, December 2014, India SEISMIC PERFORMANCE ENHANCEMENT OF TRUSS TOWERS WITH VISCOUS FLUID DAMPERS ABSTRACT K. Rama Raju 1, R.R. Aathish Narayanan 2, Nagesh R Iyer 3 1 Chief Scientist, 2 Project Student, Vibration Control Group, 3 Director, CSIR-Structural Engineering Research Centre, Taramani, Chennai , India. 1 krraju@serc.res.in, 2 aathish555@gmail.com, 3 director@serc.res.in Retrofitting methodology for seismic performance enhancement of a 3D truss tower with scissorjack linear- and nonlinear- viscous fluid dampers (VFDs) subjected to four types of ground excitations (El Centro, Kobe, Northridge and Taft) with their PGA normalized to 0.2g is described. The developed iterative retrofitting methodology is used for effective distribution of the scissor-jack linear- and nonlinear- VFDs with different capacities and stroke lengths along the height of the tower for satisfying the prescribed constraints on roof displacement, inter-bay drifts and permissible stresses in the members with the available VFDs. This method uses analytical formulae for effective damping ratios for linear- and nonlinear-vfds for arriving at damping coefficients in scissor-jack linear- and nonlinear- VFDs placed at different bays of the tower. The procedure involves the linearand nonlinear- modal time history analyses of bare 3D truss tower and the tower with scissor-jack linear- and nonlinear- VFDs along the height of the tower. Keywords: 3D Truss towers; viscous fluid dampers; passive energy dissipation devices, Linear- and Nonlinear- damper distribution methodologies; Scissor-jack mechanisms; Seismic retrofit. Introduction Conventional seismic design of structures relies on the inherent ductility of the structure to dissipate seismically generated vibration energy, while accepting a certain level of structural damage. Recent R&D efforts are directed towards finding methods to enhance the structural energy absorption capacity while avoiding/minimizing damage in structural components. Large tower structures such as television transmitting towers and electricity transmitting towers are generally more flexible. They normally have small stiffness and possess low inherent structural damping. Extreme dynamic loads such as earthquakes, strong winds, impacts, or blasts on these towers induce excessive vibrations which may result in fatigue, damage or even failure of structural members and cause overall failure of the structure. Apart from physical damage, serviceability requirement for displacements and accelerations required to be met to prevent antennae outages or damage to tower equipment (Walsh et al., 2012, Qu WI et al., 2001). To protect truss tower structures and the equipment they support, passive devices, such as viscoelastic dampers, viscous fluid dampers, friction dampers, metallic dampers, tuned mass dampers, and tuned liquid dampers can be used (Qu WI et al., 2001). One of these methods, to dissipate energy and prevent catastrophic failure of a truss towers is installing passive dampers such as viscous fluid dampers (VFDs) within the structure c 2014 ICCMS Organisers. Published by Research Publishing. All rights reserved. ISBN: doi: /

2 A Viscous fluid damper is a device, which dissipates energy by applying resisting force over a finite displacement, either by shear deformation of fluids or by pushing fluid through an orifice. VFDs greatly reduce the effects of earthquake excitation on a structure and permit it to remain linearly elastic during a seismic event. The addition of fluid dampers to a structure does not significantly alter its natural period, but it increases damping from about 2 to 5% of critical (which is usual for structures) to anywhere between 20% and 40%, and sometimes even more (Haskell and lee, 2007). It is important to note that damping beyond 30% critical damping results in small decrease in response, and such increases would not, in general, lead to economical use of dampers (Hanson and Soong, 2001). The current codes of practices do not provide procedures or guidelines for optimal configuration of energy dissipation devices. However, systematic design procedures for optimal sizing and placement of these device systems in structural systems are needed and they are not yet available (Wongprasent and symans, 2004). In the present study, a design procedure is evolved using analytical and numerical studies for seismic performance enhancement of the 3D truss tower (Figures 1a and 1b) modeled as 3D model using SAP2000. Types of viscous fluid dampers Viscous fluid dampers provide a force that always resists the structural motion. The forces in viscous fluid dampers are expressed as: ) (1) Where is the damper output force, is the velocity and is damping coefficient with units of force per velocity, α is a real positive exponent (with typical values in the range of 0.35 to 1.2), sgn( ) is the signum function and is velocity in the damper. In Equation (1), if α=1, the damper is linear and if α is other than one, the damper is nonlinear. Design, analysis and distribution techniques of VFDs in structures The important factors need to be considered in seismic resistant design of structures are, the characteristics of the structure (type, height and base dimensions, damping, importance and ductility of the structure) and the location of the structure (earthquake zone in which the structure is located - gives characteristics of the earthquake ground motion represented by amplitude of ground motion i.e., Peak Ground Acceleration (PGA) and the site soil conditions). The technique for placing VFDs in lateral loading system for a given structure begins with the assumption that the lateral force resisting system will remain linearly elastic within the design level earthquake excitation (the 475 year event). This means there is no permanent deformation of any structural member, and no structural repair required after the event (Haskell and Lee, 2007). The time history analysis of the lateral loading structural system is required to design the damping system. This means analysis determines the inter-story velocities at which the viscous fluid dampers need to operate, as well as the required stroke lengths and force levels. Once the inter-storey velocities are determined, approximate lateral force (shear force) demand is assumed to be equal to 3% to 5% of the building weight above the plane of the VFDs (Haskell and Lee, 2007). The developed design methodology is used for finding the scissor-jack linear- and nonlinear- VFDs of different capacities and stroke lengths along the height of tower. In the present study, the methodology for finding storey shears, using linear- and nonlinear- modal time history analyses for truss with scissor-jack linear- and nonlinear- dampers is described. Once the maximum velocity and approximate force level are found, the size of the VFDs can be determined. An iterative method is developed based on 5th International Congress on Computational Mechanics and Simulation 1293

3 the effective damping requirement in the first mode of the building, for finding the number, capacity and distribution of dampers fitted in different configurations (Chevron, toggle and scissorjack mechanisms) in twenty storey benchmark building (Rama Raju et al., 2013) for the prescribed performance enhancement requirements. It was found that low intensity earthquakes with PGA 0.2g, fitting dampers in the ground floor is enough with Chevron, upper toggle and scissor-jack configurations. Walsh et al., 2012, studied the feasibility of seismic performance enhancement of the 3D flexible tower (Figures 1a and 1b) with scissor-jack dampers with an ELEVATION=0 m ELEVATION=8m ELEVATION=16m ELEVATION=20m equivalent 2D lumped-mass model with three DOF. The responses of the tower subjected to El Centro, Hachinohe, Northridge and Kobe ground motions with PGA of 3.417, 2.25, and m/s 2, respectively are found. It was observed that the system is effective in reducing both displacement and acceleration response of the tower without exceeding the damper stroke capacity in most cases, but the damping level and earthquake intensity are important factors in the consideration of scissor-jack dampers for flexible structures subjected to seismic loads. Since, the tower is subjected to very high intensity earthquakes such as Northridge and Kobe, and the members are not satisfying the permissible stresses in compression as given in codes of practice (Viz. IS ), the truss tower cannot be retrofitted with VFDs. In the present study, the sections are modified in the truss tower and three additional bays of horizontal members (H 2) are incorporated to support the scissor-jack linear- and nonlinear- VFDs, instead of hourglass systems reported in Walsh et al [1]. In the seismic retrofitting strategy for the modified 3D truss tower (Figures 1a and 1b), the tower is modeled as 3D model with scissor-jack linear- and nonlinear- VFDs. The analytical and numerical studies are carried out for seismic performance enhancement of the truss tower. The retrofit methodology developed uses analytical formulae for effective damping ratios for linear- and nonlinear-vfds for arriving at damping coefficients in scissor-jack linear- and nonlinear- VFDs placed at different bays of the tower. The procedure involves the linear- and nonlinear- modal time history analysis (is also called Fast Nonlinear Analysis) of bare 3D truss tower and the tower with scissor-jack linear- and nonlinear- VFDs along the height of the tower. The retrofit methodology proposed in the present study is general, and can be used for the seismic design of existing and new structures with linear- and nonlinear- VFDs. This methodology considers general performance requirements required for the design of truss towers. Optimum seismic performance depends on intensity of earthquake time histories the truss tower subjected to and performance limits prescribed for the design or retrofit ELEVATION=4m ELEVATION=12m Z ELEVATION=24m =Node =Mass All dimensions are in 'm' (a) (b) (c) (d) Figure 1 Truss Model (a) Elevation View of original truss, (b) Node Coding, (c) Truss tower with scissor-jack dampers on both sides and (d) 3D model of truss with scissor-jack dampers X th International Congress on Computational Mechanics and Simulation

4 The time histories of accelerations to be considered for time history analysis Among the two methods used for finding time histories accelerations, in first method, the site specific earthquake design spectra are found from the relevant codes of practice by the country in which the structure is located by deterministic or probabilistic seismic hazard analysis methods and generate consistent time histories. In the second method, for the time-history analysis a minimum of three acceleration time histories are required for the given project site, generated by a geotechnical expert (Haskell and lee, 2007). Guidelines given in 1993 by the Passive Energy Subcommittee of the Structural Engineers of Northern California require the engineer to use the worst (maximum stress and deflection case) of the three events in the design. In the present study, method two is used. The PGA of the place where the truss tower is located is assumed to be 0.2g. The 3D truss tower is subjected to four typical ground excitations (viz., N-S components El Centro, N-S component of Kobe, N-S component of Northridge, and S-E component of Taft) with their PGA normalized to 0.2g. These are considered as the design basis earthquakes at the place where the truss tower located. Modeling and analysis of the 3D truss tower with VFDs The modelling of linear- and nonlinear- dampers is same as used by Scheller and Contantinou [32]. They have carried out time history analysis of a 3-Storey quarter length scale steel model using SAP2000 and the results were compared with the results from other programs, 3D BASIS and ANSYS, and the experimental results. They found in general, the results using SAP2000 are in good agreement with other programs and they are also found to be in good agreement with experimental results. For modeling linear- and nonlinear- dampers, NLINK element in SAP2000 is used. The inputs for the same are effective stiffness ( and effective damping ( ). The value of for both linear and nonlinear cases is assumed to be zero. The value of stiffness, k, in nonlinear damper case is assumed to be large enough to ensure that the element behaves as a pure damper. This nonlinear modal time history analysis is used for comparing the experimental results of moment resisting frame with toggle bracing mechanisms fitted with magneto-rheological dampers modelled as nonlinear viscous fluid dampers subjected to two types of seismic excitations [33]. In the present study, twelve scissor-jack systems are provided in truss tower in all the six bays, with one on each side of the tower as shown in Figures 1(c) and 2. The retrofitting methodologies are carried out for the 3D truss tower with both scissor-jack linear- and nonlinear- VFDs. In nonlinear case, the damping exponent (α) of nonlinear dampers is assumed to be 0.5. In linear case, the damping exponent (α) is assumed to be unity (i.e., 1). Based on the value of damping exponent, the damper characteristics can be linear or nonlinear (Equation 1). Based on the characteristics of the dampers, for linear VFDs linear-, and for nonlinear VFDs, nonlinear- modal time-history analysis (modal nonlinear analysis is also called Fast Nonlinear Analysis) implemented in SAP2000 (Computers and Structures, Inc., Berkley, CA, USA) is used. Only nonlinear material behavior in LINK objects is considered and, the frame hinges and geometric nonlinearities are not considered in the analysis. 3D Truss tower model The finite element model of 3D truss tower used for the analysis is shown in Figure 1(a). The sections chosen in the present study for vertical, horizontal, diagonal truss members and scissor-jack members are given in Table 1. The sections have a modulus of elasticity of Pa. The entire mass of the structure is lumped at three bays corresponding to elevations 8, 16 and 24m, where each level has a mass of kg. In 3D truss model, one fourth of total mass is lumped in the centre of each of the horizontal members as shown in Figure 1(b). These masses represent the mass of the structural 5th International Congress on Computational Mechanics and Simulation 1295

5 components, non-structural components, and any supported equipment. From the modal analysis of the truss model, the fundamental period of the truss is found to be 2.16s. The design compressive stress, of axially loaded compression members is calculated as per clause of IS 800:2007 using Equation 2. (2) Where, =, Non-dimensional effective slenderness ratio = = Euler buckling stress= Where, Effective slenderness ratio, K=1 for truss members, = imperfection factor given in Table 7 of IS 800:2007, = partial safety factor for material strength. In the present study, the allowable inter-bay ratio, roof displacement and compressive stresses of a member are prescribed additionally as 0.4h%, H/400 and respectively, where, h and H are bay- and total- height of the tower, and is design compressive stress as per clause of IS 800:2007 using Equation 2. Retrofitting with scissor-jack linear- and nonlinear- dampers For retrofitting with scissor-jack damper systems, three additional bays with horizontal members are provided at elevations of 4, 12 and 20m as shown in Figures 1(b) to 1(d). The truss tower model is retrofitted with two scissor-jack damper systems placed at each of the six levels as shown in Figures 1(c) and 1(d). At these levels, an additional node at crossing of horizontal members is provided. These additional nodes provide connection points for the scissor-jack damper systems between subsequent levels of the truss tower. The sections chosen for each of these horizontal members are given in Table 1. Table 1 Member Cross Sections for 3D Truss tower Actual 3D Truss Additional bays Dampers Types of sections Vertical (V) Horizontal (H 1) Diagonal (D) Horizontal (H 2) Scissor-jack (SJ) 1800 A(mm Sectional ) (OD: 60; OW: (Section) ( ) ( ) ( ) (42.4 4) 30; t f: 29.9; t w: properties 14.9) (Tubular) KL(mm) r min(mm) KL/r min f cd(mpa) Performance limits Note: f cd: Allowable compressive stress calculated as per (clause of IS: ); KL/r min: effective slenderness ratios of members, where, K=1 for trusses, L is the length of the member and r min is minimum radius of gyration; V, D, H 1 and H 2 are steel tubular sections from IS: ; SJ is a rectangular tubular section with outside depth (OD), outside width (OW), flange thickness (t f) and web thickness( t w) th International Congress on Computational Mechanics and Simulation

6 The approximate magnification factor of the scissor-jack damper is found out from the Equation (3) (Rama Raju et al., 2014): (3) where, is the magnification factor, Ψ is the angle between horizontal line and the center line of the damper mechanism and θ is the angle between hollow damper section and center line of the damper mechanism. The initial geometry of each scissor-jack damper systems are taken as Ψ i= , θ i = and l 1= m and the approximate magnification factor found from Equation (3) is 2.11 as shown in Figure 2. Figure 2 Scissor-jack configurations Effective supplemental damping ratios for Viscous Fluid dampers Damping provided by linear- and nonlinear- VFDs The effective additional damping ration ratio (ξ d) provided by linear viscous dampers for the primary mode can be obtained. (4) The equivalent additional viscous damping ratio (ξ d) provided by the nonlinear viscous dampers (Lin et al., 2008 and Hwang et al., 2008) for the primary mode can be obtained as Here, the summation over j extends over all bays, and the summation i extends over all reactive weights, Where, is the damping coefficient for nonlinear viscous damper at j th bay; α j is the velocity exponent for nonlinear viscous damper j, is gamma function, is maximum roof displacement, is magnification factor in horizontal direction; The equivalent damping ratio of linear viscous dampers (Equation 4) can be obtained by setting and. For nonlinear dampers (Equation 5), the damping exponent is assumed to be 0.5. Analysis of bare truss retrofitted with additional horizontal members Modal Analysis of the retrofitted bare truss tower with horizontal members Modal analysis of the bare truss retrofitted with additional horizontal members (Figure 1c) at three levels is carried out. With the incorporation of these horizontal members in the tower an scissorjack mechanism, the fundamental period (T 1) of the truss tower reduced from 2.16s to 1.34s. Modal displacement vector of six bays in the first mode of the bare truss is given by,. The modal displacements where modal masses are located are obtained as,. Methodologies for finding damping coefficient of scissor-jack linear- and nonlinear- VFDs Because of symmetry of 3D truss tower, torsional effects are not considered in this study. The methodology to find the maximum roof displacement (u roof) is described by Lin et al., In the (5) 5th International Congress on Computational Mechanics and Simulation 1297

7 present study the peak roof displacement of 3D truss tower subjected to the four earthquake time histories representing DBE is considered as the maximum roof displacement (u roof) and it is 0.237m. The damping coefficients of scissor-jack linear- and nonlinear- VFDs are assumed to be proportional to peak bay shears in truss along the height of the truss tower. The peak absolute accelerations in the three bays of the bare truss are found from the absolute accelerations corresponding to the peak base shear among the earthquakes considered. The absolute accelerations corresponding to the peak storey shear (in m/s 2 ) at bays, 6, 4 and 2, are found to be -1.11, and In the present study, the number and capacity of VFDs in the truss are distributed in proportion to the bay shears (Rama Raju K, Hemant GG et al., 2011). Because, masses in all three storeys are same, the storey shears are proportional to absolute accelerations without sign. i.e., in the present problem, the storey shears of bare truss at bays, 6, 4 and 2, are in the ratio of and they are 1:2.60:5.34. The effective damping coefficient, computed using Equation 5, can be obtained for 3D truss tower as, (6) For linear dampers, substituting, and, the damping coefficient (C 0) can be arrived (Equation 6). The damping coefficients of scissor-jack dampers in bays 1-2, 3-4 and 5-6 can be arrived at using the equations, C 01= C 0/4; C 02=C 0 C 2/4 and C 03=C 0 C 3/4 respectively. With the basic characteristics of bare truss tower determined, and, the dampers arranged in a scissor-jack mechanisms (at different levels of the truss tower), the damping coefficients are determined for the values of effective damping ratios in the tower system varying from 0.1 to 1 (with an increment of 0.1) and the same are given in Table 3. Different parameters used for finding the damping coefficients are peak roof displacement, 0.237m; scissor-jack magnification factor, f =2.11; time period in first mode, T 1=2.16s; ; and the lumped mass applied at nodal points at different bays (Figure 1b), mass in each storey, m is kg. Retrofitting methodology for truss tower In this section, by using the damping coefficients found with different effective damping ratios varying from 0.1 to 1 (given in Table 3), the linear- and nonlinear- modal time history analyses of the truss tower subjected to El Centro, Kobe, Northridge and Taft earthquakes (with PGA of 3.417, , 8.268, and 1.52 m/s 2 ) normalized to 0.2g, with scissor-jacks with linear- and nonlinear- Table 3 Damping coefficients (C 01, C 02, C 03) ξ C C C C C C Note: Effective Damping ratio (ξ), C 01, C 02 and C 03 are the damping coefficients in 1&2, 3&4, 5&6 bays respectively; : Damping exponent. dampers, are carried out. From the linear analysis of truss with linear dampers, it is observed that, there is no decrease in base shear beyond effective damping ratio of 0.3 (base shear found to be constant). From nonlinear modal time history analysis of the truss with nonlinear dampers, the base shear is found to be reducing even beyond the effective damping ratio of 0.3. Assuming internal th International Congress on Computational Mechanics and Simulation

8 damping of the truss tower to be 0.04, and initial added effective damping coefficient in dampers is assumed to be 0.14 for linear dampers and, 0.7 for nonlinear dampers for starting the iterations for finding the optimum damping coefficients to satisfy the performance criteria given in Section 3D Truss tower model. The methodologies for the same are explained in Table 4 and Table 5. Implementation of retrofitting methodologies in truss tower Recognizing that the higher mode responses will be highly suppressed when sufficient dampers are incorporated into a building (Rama Raju et al. 2011) the damping ratio of a building with added linear dampers is approximated by the first mode vibration in the direction of excitation considered. It is to be noted that the method is trial-and-error method (Table 4). This developed methodology is used for designing scissor-jack linear- and nonlinear- dampers to the required added effective damping in the building. The optimum design is arrived for the linear- and nonlinear- dampers by the least damping coefficients (C 01,C 02 and C 03) which satisfy the performance criteria. The iterations used for arriving at final effective damping ratio and corresponding effective damping coefficients along the height of the truss are given in Tables 5. At effective damping ratio of 0.16 for linear damper and effective damping ratio of 0.72 for nonlinear dampers, the performance criteria for interbay drift, allowable compressive stress and roof displacement for the 3D truss tower are found to be satisfied. For linear dampers the optimum performance is coming at lower effective damping ratio (0.16) in comparison with nonlinear dampers (0.72), but damping coefficients (C 01,C 02 and C 03) are much higher for linear dampers (385, 1000 and 2040 kns/m) in comparison with the nonlinear dampers (180, 470 and 960 kns/m) as shown in Table 5. The values of peak responses of bare truss tower by carrying out linear modal time history analysis. The decrease in the magnitude and percentage of reduction of peak base shear, peak bay drifts and peak absolute accelerations compared with bare truss, due the provision Table 4 Seismic retrofit design methodology for of 3D Truss tower with VFDs i. Choose damper configuration as Scissor-jack and calculate magnification factor of ii. Assume Damping in structure, to be Choose the additional effective damping required by provision of VFDs, to be 0.25 for linear damper and 0.5 for nonlinear dampers. Effective damping ratio = iii. Input the characteristics of the 3D truss tower, fundamental period T 1, and mode shape, ϕ 1, bay masses,, where n is number of bays. iv. Choose the number of dampers and their distribution in different floors of the truss tower. v. Calculate damping coefficient ( ) of dampers at each floor using the Equation (6) vi. Assign damping coefficient, to the dampers in different bays of the tower. vii. Find roof displacement, inter-bay drifts and section stress limits as given in Section 3D Truss tower model. viii. Carry out time history analysis of the building subjected to 4 types of earthquake loads (representing DBE) and find the peak inter-bay drifts, peak absolute accelerations where the base shears are maximum. ix. Check whether inter-bay drifts and roof displacements exceeds the limits calculated, if they exceed the limits, increase the value and go to step vi, otherwise decrease value and go to step vi, till it becomes smallest one which satisfy the limits. of scissor-jack linear- and nonlinear- VFDs for the optimum configurations ( at 0.16 for linear dampers and 0.72 for nonlinear dampers) are given in Table 6 and the same are shown in Figure 3. 5th International Congress on Computational Mechanics and Simulation 1299

9 The scissor-jack linear- and nonlinear- damper responses, Viz., forces, displacements and velocities are given in Table 7. Table 5 Iterations for optimum performance for linear & Nonlinear Damper C 0 (kns/m) Maximum stress obtained (MPa) Iterations ξ C 01 C 02 C 03 V D H 1 H 2 SJ Check Bare truss Unsafe Unsafe Safe 1 Safe and optimum Unsafe Safe 0.5 Safe and optimum Note: ξ: Damping ratio; C 01, C 02 and C 03 are the damping coefficients in 1&2, 3&4, 5&6 bays respectively; V, D, H 1, H 2 and SJ are different types of section and their allowable stresses (MPa) are given in Table 1. Table 6 Peak responses and their percentage of reduction of truss tower for initial model ξ Peak Responses % of Reduction Bay (m/s 2 ) (m) Drift (m) Base shear (kn) x Drift Base shear Note: Damping exponent; ξ: Damping ratio; : absolute accelerations; : Displacements. Table 7 Peak damper responses of initial model Bay Linear damper Nonlinear damper f d (kn) u d (m) v d (m/s) C 0 (kns/m) f d (kn) u d (m) v d (m/s) C 0 (kns/m) C C C C C C Note: f d: Damper Force; u d: Damper Displacements; v d: Damper Velocity; C 0: Damping coefficient; : Magnification factor th International Congress on Computational Mechanics and Simulation

10 g p Base shear (kn) Bare frame LA_LD NLA_NLD Bay Figure 3 Variation of storey responses Note: LD: linear damper; NLD: Nonlinear damper Bare truss LD 1 1 Bare truss 1 Bare truss LD LD NLD NLD Displacement (m) Bay Drifts (m) Absolute accelerations (m) Bay 3 Bay Table 8 Dampers chosen from Taylor devices for the peak damper displacement and forces Standard Taylor Devices Bay F pd C d MSL SL U pd Required SL MSL m Note: : damping exponent; C d: Damper Capacity; F pd: Peak damper force; U pd: Peak damper Displacements; MSL: Mid stroke length; MSL m: Modified mid stroke length (Equation A1); SL: Stroke Length. Finding forces and stroke lengths of scissor-jack linear- and nonlineardampers The maximum forces and displacements in the scissor-jack linear- and nonlinear- dampers for all the cases with corresponding analyses carried out are given in Table 8. The peak damper capacities and stroke lengths at different levels of the truss are chosen from the corresponding to the results of the linear- and nonlinear- analyses of the truss tower with both scissor-jack linear- and nonlineardampers. The dampers are selected from the available dampers of Taylor devices and the details are presented in Table 8. Since, the peak displacements of scissor-jack for linear- and nonlinear- dampers are less than the standard stroke lengths available, the mid stroke lengths of the dampers need not be increased as recommended by Taylor devices [43] (in Equation 7, MSL m is equal to MSL). If the peak 5th International Congress on Computational Mechanics and Simulation 1301

11 damper displacement exceeds the standard stroke length of the damper, the formula for calculating modified mid stroke length is given by, (7) Here, MSL m is the modified mid stroke length, MSL is the standard stroke length of the damper given by manufacturer and U pd is the peak damper displacement. The MSL of the damper chosen from Taylor devices are given in Table 8. Once mid stroke length of the dampers are known, the scissorjack configurations need to be changed. Initial and modified scissor-jack configurations, i.e. values of θ, Ψ, l 1 (shown in Figure 2) and magnification factors (f) are given in Table 9. The responses of scissor-jack linear- and nonlinear- dampers Viz., forces, velocities and displacements with the finally designed scissor-jack dampers are found to be almost equal to the initial scissor-jack linear- and nonlinear- VFDs arrived by design methodology. Table 9 Final scissor-jack damper configurations chosen with modified mid stroke lengths Model assumed Bay U D θ Ψ l 1 Initial - All Modified Note: f: Magnification factor; ψ, θ, l 1 are as shown in Figure 2, damping exponent (α) Summary and conclusions In the present study, a retrofitting methodology for seismic performance enhancement of a 3D truss tower with scissor-jack linear- and nonlinear- viscous fluid dampers (VFDs) subjected to four types of ground excitations (El Centro, Kobe, Northridge and Taft) with their PGA normalized to 0.2g (which represents the design basis earthquakes for the site the truss tower chosen to be designed) is described. The developed iterative retrofitting methodology is used for effective distribution of the scissor-jack linear- and nonlinear- VFDs with different capacities and stroke lengths along the height of the tower for satisfying the prescribed constraints on roof displacement, inter-bay drifts and permissible stresses in the members with the available VFDs. The procedure for finding the optimum damping coefficients, for the scissor-jack linear- and nonlinear- dampers in bare 3D truss tower with scissor-jack linear- and nonlinear- VFDs arranged along the height of the tower is described. The retrofit methodology proposed in the present study is general, and can be used for the seismic design of existing and new structures with linear- and nonlinear- VFDs. This methodology considers general performance requirements required for the design of truss towers. Optimum th International Congress on Computational Mechanics and Simulation

12 seismic performance depends on intensity of earthquake time histories the truss tower subjected to and performance limits prescribed for the design or retrofit. The methodology inherently considers maximum base shear reduction in the truss tower. The methodology demonstrates practical aspects of choosing appropriate scissor-jack linear- and nonlinear- dampers along the height of the tower for the prescribed performance limits. The procedure for choosing damper forces, for the scissor-jack linear- and nonlinear- dampers using linear- and nonlinear- modal time history analyses of bare 3D truss tower and the tower with scissor-jack linear- and nonlinear- VFDs arranged along the height of the tower with the available dampers corresponding to optimum damper -forces and -displacements is also described. The responses of scissor-jack linear- and nonlinear- dampers Viz., forces, velocities and displacements with the finally chosen from dampers from Taylor devices are found to be almost equal to the initial scissor-jack linear- and nonlinear- VFDs arrived at by the retrofitting design methodology evolved. But dampers chosen are higher capacity and stroke lengths than the required, all performance limits are satisfied except inter-bay drifts. Acknowledgement This paper is being published with the kind permission of Director, CSIR-Structural Engineering Research Centre, Chennai , India. The authors thank staff of Vibration Control Group, CSIR- SERC for their help in various stages of this study. References Hanson RD and Soong TT. Seismic design with supplemental energy dissipation devices. EERI Publication No. MNO-8, Haskell G and Lee D. Fluid Viscous Damping as an Alternative to Base Isolation. accessed on Hwang JS, Huang YN, Yi SL and Song YH. Design Formulations for Supplemental Viscous Dampers to Building Structures. Journal of Structural Engineering ASCE 2008; 134(1): Lin YY, Chang KC, Chen CY. Direct displacement-based design for seismic retrofit of existing buildings using nonlinear viscous dampers. Bull Earthquake Engineering 2008; 6: Qu Wl, Chen Zh, Xu YL. Dynamic analysis of wind-excited truss tower with friction dampers. Computers & structures 2001; 79: Rama Raju K, Ansu M and Iyer NR. A methodology of design for seismic performance enhancement of buildings using viscous fluid dampers. Journal Structural Control and Health monitoring 2014; 21(3): , 17 APR 2013, DOI: /stc Rama Raju, K., Hemant G G, Rekha, K S, Iyer, N R Seismic Design of Buildings with Viscous Fluid Dampers- A Methodology, Journal of Institution of Engineers(India) 2011; Vol 92, pp Scheller J and Contantinou MC. Response History Analysis of Structures with Seismic Isolation and Energy Dissipation Systems. Verification Examples for Program SAP2000, Technical Report MCEER , National Center for Earthquake Engineering research (NCEER), State University of New York at Baffalo, Baffalo, N.Y, Walsh KK, Cronin KJ, Rambo-Roddenberry MD and Grupenhof K. Dynamics analysis of seismically excited flexible truss tower with scissor-jack dampers. Structural Control and health monitoring 2012; 19: th International Congress on Computational Mechanics and Simulation 1303

13 g p Wongprasert N and Symans MD. Application of Genetic Algorithm for Optimal Damper Distribution within the Nonlinear Seismic Benchmark Building. Journal of Engineering Mechanics ASCE.2004; Vol. 130, No. 4, pp th International Congress on Computational Mechanics and Simulation