structural response control of rcc moment resisting

International Journal of Civil Engineering and Technology (IJCIET) Volume 8, Issue 1, January 2017, pp. 900–910 Article ID: IJCIET_08_01_106 Available online at http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=8&IType=1 ISSN Print: 0976-6308 and ISSN Online: 0976-6316 © IAEME Publication

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STRUCTURAL RESPONSE CONTROL OF RCC MOMENT RESISTING FRAME USING FLUID VISCOUS DAMPERS A.K. Sinha Professor and Centre Director, Earthquake Safety Clinic and Centre, Department of Civil Engineering, National Institute of Technology Patna, Bihar, India Sharad Singh Research Scholar, Structural Engineering, Department of Civil Engineering, National Institute of Technology Patna, Bihar, India ABSTRACT Frequent earthquakes round the globe and large no of structures vulnerable to it have necessitated the need for structural response control to gain pace in application around the globe. This paper discusses the use and effectiveness of one such device, fluid viscous dampers, for response control of structures and to reduce damping demand on structural system. In this paper a non-linear time history analysis has been carried out on a 3D model of a 12 story RCC MRF building using 3-directional synthetic accelerogram. Two different cases of building models with and without supplemental damping have been analyzed using ETABS. The story responses in terms of absolute maximum displacement and story drift have been compared. Time history response plots for the two models have also been compared for various responses viz. roof displacement and acceleration, base shear and story shear forces, along with the various energy components and damping behavior. The results of the time history analysis are in close conformation with previous investigations and represent the effectiveness of dampers in improving the structural response as well as damping demand on structural systems. Key words: Structural response control, Non-linear time history analysis, Fluid Viscous dampers. Cite this Article: A.K. Sinha and Sharad Singh, Structural Response Control of RCC Moment Resisting Frame Using Fluid Viscous Dampers. International Journal of Civil Engineering and Technology, 8(1), 2017, pp. 900–910. http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=8&IType=1

1. INTRODUCTION The concept of structural response control has been widely spread in the structural engineering community [1-4, 7, 8, 14, 23]. Methods of response control like seismic isolation (SI) and energy dissipation (ED) have shown significant progress in controlling the response of structures. The structural control using energy dissipation can be achieved in many ways of which fluid viscous damping has gained prominence [1-3, 8, 14, 23]. Fluid Viscous Damper (FVD) is installed in structures to dissipate the input energy of vibration due to external excitation and thereby reduce the

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damping demand on members of the structure. The dynamic behavior of the structure installed with FVD can be represented by equation (1). M + {C + | | [ ]} +Ku=−M g (1) Where M is the mass matrix, C is the damping coefficient matrix, C0 is the damping constant for FVD, is piston velocity of the FVD, sgn is signum function, is damping exponent, K is stiffness matrix, is acceleration, is velocity, u is displacement, and g is ground acceleration. The mass and stiffness contribution of dampers to the dynamic behavior of structures is usually neglected due to small values as compared to those of structural members. Even though very small, the mass and stiffness contributions of damper brace system attached to the structure should be incorporated in analysis. Investigations have been carried out to use FVD in RC buildings for dynamic response control. Multi storey buildings specially the major lifeline buildings like hospitals, emergency centres, schools and administrative buildings need to adopt response control devices for improved performance levels [12]. In this context a study has been carried out to observe the behavior of RC frame buildings with FVD installed for structural response control. A comprehensive review of Passive Energy Dissipation (PED) concepts and application shows that addition of PED devices to structural system reduces the excessive deformation and ductility demands and at the same time enhances its energy dissipation capacity. The PED devices have been found to be effective for both shock loads as well as earthquake forces [3, 4, 7, 14, 23]. Among the viscous energy dissipation devices, FVD have been widely used in vibration control as PED devices [2, 5-9, 11, 13, 19, 21-23, 25]. FVD enhance the performance of structures not only by reducing the deformation demand but also the force demand. Non-linear FVDs have been proposed for control of seismic response of structural system [13, 19]. Non-linear FVD achieves the same reduction in response but with significant reduced damper force as compared to linear damper. While using Chevron braced frame with non-linear FVD in near-fault ground motion, it has been found that the energy dissipated by them prevents the buckling of braces and helps the frame members to remain within elastic limits [9]. In a diagonal brace damping systems the deformation of the device is proportional to the relative displacement between the floors i.e. the inter-storey drift. Analytical study of a ten story steel frame structure where viscous damping has been incorporated in modal damping has presented positive results [25]. The study shows the viscous diagonal damper to be effective in reducing floor displacements and inter-storey drifts against seismic loadings. Extensive research on viscous dampers reveals that viscous damping provides an accurate representation of energy dissipation characteristics of viscous dampers [1]. The analytical results using viscous damping within a linear elastic analysis approach has good correlation with experimental results, such that displacements and story shears typically are within 10%. Viscous dampers can reduce the drift of a MRF by as much as 50% without significantly increasing the base shear demand or floor accelerations. Herein the design of viscous damper dose not incorporates the stiffness of the structure. There are two important issues involved in application of viscoelastic damping for seismic loads i.e. significant higher levels of damping needed to be effective against seismic load and the damper has to undergo significant large deformations during severe seismic response. Earthquake simulator tests for diagonal viscous dampers with varied vibration inputs further demonstrate effectiveness of adding energy dissipation using viscous dampers [1-2]. It is found that viscous dampers supplement the structural damping at all levels of excitation unlike friction or inelastic deformation dampers, as damping increases with level of response. The analysis shows that 20% added damping is optimum and that the temperature changes in the dampers are small and can be disregarded.

2. IDEALIZATION OF FVD A typical idealized load deformation curve for a damper is shown (Figure 1). The equivalent stiffness and damping of any damper can be computed using the curve as:


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Structural Response Control of RCC Moment Resisting Frame Using Fluid Viscous Dampers

=

∆

=

(2)

∆

!"

$%& ∆$%&

#

'

(3)

Figure 1 A generalized force displacement curve for dampers to represent formulation of equation (2) and (3) for linear dampers (dashed straight line) and for non-linear dampers (solid bilinear curve)

Where F is the force and Δ is the displacement. Empirical expressions for and depends upon material properties and characteristics. Fluid viscous dampers exhibit viscoelastic behavior. This behavior is best predicted with the Maxwell model [20, 24].It is described as a spring in series with a dashpot using equation (4). ()*+ + -

./)0+ .0

=

.1)0+

(4)

.0

Where ‘P’ is damper output force, ‘λ’ is relaxation time, ′ ′ is damping constant at zero frequency, and ‘u’ is displacement of piston head with respect to damper housing. The relaxation time for damper is defined as -=

34

(5)

56

where′ ′ is damping constant at zero frequency and ′ ′ is storage stiffness of damper at infinite frequency. A more general Maxwell model [20] is described by equation (6). ()*+ + .7

.7 /)0+ .0 7

=

.8

.8 1)0+

(6)

.0 8

where.0 7 and .0 8 are fractional derivatives of orders r and q, based on material properties. When r=q=1 the model becomes Maxwell model described in equation (4).

2.1. Linear Fluid Viscous Dampers The model described by above equation has been simplified to obtain a more useful model of linear viscous damping. The device parameters, λ and , are obtained from experimental tests [5]. If frequency of vibration is below cut-off frequency, the second term in equation (4) drops out and model of damper is simplified as ()*+ =

.1

(7)

.0

where is independent of frequency. With this model damper behaves as linear viscous dashpot. An important feature of linear viscous model equation is that damper force is a function of velocity. Hence if the device is loaded with a sinusoidal function, displacements may be a sine function and http://www.iaeme.com/IJCIET/index.asp

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then will be out of phase with velocity and damper force, which will be a cosine function. Again this is beneficial if structure remains elastic, since dampers will reduce drifts and shear forces without creating greater column axial forces in combination with column bending moments.

2.2. Nonlinear Fluid Viscous Dampers As the current study uses nonlinear fluid viscous dampers the model represented for linear fluid dampers has to be made more general to include nonlinear damping, to explain non-linear fluid viscous dampers. This generalized form is as follows [5, 11, 13, 19, 20, 21, 24] ()*+ =

.1

9 9 .0

.1 .0

'

(8)

Where, ‘α’ is a real positive exponent that ranges from 0.1 to 2, and sgn is signum function. When α is unity, equation reduces to linear viscous dashpot model described for linear fluid viscous damping. It has been suggested that a design with value of α=0.5 should be used for situations when a structure is subjected to extremely high velocity shocks, or near-field earthquakes, because this type of damping will limit peak force in damper.

3. ANALYTICAL CONSIDERATIONS ETABS 2015 has been used to carry out this study. The building under consideration in this study is a 12 storey RCC special moment resistant frame as per the guidelines of IS 1893:2002 for seismic zone V and site class I (rocky or hard soil). The schematics of building plan and elevation are shown in figure 2 and 3. The total height of the building is 40.2 m. The height of 1st floor from ground floor is 3.2 m and the foundation is at 2 m below the ground floor. All other storey heights above the 1st floor are 3.5 m. Frame sections used for modeling depend upon design requirements. The base is fixed to restrain in all 6 DOFs. A rigid diaphragm action has been considered for all the floors. A panel zone has been considered for beam column connectivity with local axes along column, with inbuilt auto inelastic properties. Non-linear hinges have been considered for frame elements [9, 10, 15-18]. For the design of frame guidelines in IS 875 Part 1, 2 and 5 for dead load, imposed load and load combinations have been used to define gravity loads and IS 1893:2002 has been used to define seismic load on the building. Natural time period of building T=1.1974 sec; seismic zone factor Z=0.36; Importance factor I=1.5; Response reduction factor R=5. The torsional effect has been considered due to accidental eccentricity. The mass source definition includes default definition of elemental selfmass and additional mass. The modal case used in preliminary modeling and design process of original building follows eigenvalue method with default definitions [15]. The product which has been taken into account for development of FVD model in this study is 67DP1892101- type-A damper manufactured by Taylor Devices Inc., USA [11]. The dampers have been installed in even bays only in the exterior throughout the height of the building as shown in figure 3. It is modeled as a link element with link type damper-exponential. The damper is modeled only along one longitudinal direction and restrained in other two transverse directions, in its local coordinate system. Non-linearity is considered along the active direction U1. Rotation has been restrained. Following values have been used to model the damper (table 1). Table 1 Damper properties used in modeling Mass

Weight

Effective Stiffness*

(Kg) 511.84

(KN) 5.016

(KN/m) 28144.86

Effective Damping ( :) ⁄;+3 420

Damping Exponent (α) =#

)

0.8

*Stiffness provided by bracings


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Non-linear dynamic analysis has been performed to study the effect of FVD on seismic behavior of structure. The time history analysis method adopted in this study uses a tri directional ground motion. Response spectrum function has been defined using IS 1893: 2002 for a damping of 5% [15]. The accelerogram record used in this study is the SYLMARFF county hospital parking lot record of the 1994 Northridge Earthquake. A set of three records at 0o, 90o and Z direction have been used with PGA values of 826.76 cm/s2, 592.639 cm/s2, and 524.985 cm/s2 respectively. This time history function data has been matched to response spectrum function, to generate synthetic accelerogram for the assumed site condition. The spectral matching has been done in frequency domain. The matching parameter is set in a frequency range of 0.01 cycles/sec to 100 cycles/sec. The 3 synthetic accelerogram in 3 directions (U1, U2 and U3) are applied simultaneously, to create realistic ground motion condition [24].

Figure 2 Plan view of building model

Figure 3 Elevation view of building model with and without dampers


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4. RESULTS AND DISCUSSION The modal analysis has been carried out for 12 modes and following time periods have been noted down for various modes (tables 2) in each case for frame with and without supplemental damping. Since the frequencies are just the inverse of time period hence they have not been specifically noted down here. From the table for time period it can be easily seen that the time period of the oscillation of the structure has shifted to lower values on addition of dampers to the system. The variation along the modes is considerable. Other modal results have not been considered for comparison as the study strictly focuses on investigations of non-linear time history analysis. Table 2 Time period for buildings with and without supplemental damping for various modes

4.1. Results of Non-Linear Time History Analysis The results of non-linear time history analysis to be hereafter referred as THA have been studied for both storey responses in terms of storey v/s storey response as well as time history functions of the responses. The storey responses considered here are absolute maximum storey displacement to be hereafter referred as AMSD and absolute maximum storey drift to be hereafter referred as AMSd. 4.1.1. Absolute Max. Storey Displacements (mm) The AMSD of different stories have been plotted for THA in both X and Y directions. The observations reveal the effectiveness of dampers in controlling the story displacement response of the building. In both the cases the maximum displacement is at the roof level and minimum at the base level storey. Observations for AMSD comparing the models with and without supplemental damping shows that models with dampers have lower response as compared to model without dampers. For building model with damper the maximum storey displacement attained at top story is 152.848 mm in global X-direction and 120.514 mm in global Y-direction as compared to 174.218 mm and 149.635 mm for building model without damper at top story in global X and Y directions respectively. For ground story there is not any difference in AMSD of two models which increases up to top story. A lower AMSD value for building with damper shows the effectiveness of dampers in controlling the response of the structure. 4.1.2. Absolute Max. Storey Drift (Unit less) The Absolute maximum storey drift in terms of inter-story drift ratio (IDR) of different stories has been obtained for both global X and Y directions. The code suggests a limiting value of 0.004 times


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the storey height for drift in any storey i.e. 0.014 m [3]. The IDR values has been obtained using the following formula IDR= (Dn+1 – Dn)/Hn (9) th Where, Dn+1 is the displacement of upper floor or n+1 floor, Dn is the displacement of lower floor or nth floor and Hn is the storey height or floor separation for the given storey.

Figure 4 AMSD for building with and without supplemental damping in Global X and Y directions

Figure 5 IDR v/s storey plot for building with and without supplemental damping in Global X and Y Directions

The plot of IDR shows that this value is exceeded in both the cases. The maximum value of IDR for building without damper is 0.0068 and 0.0055 in global X and Y directions respectively at story 4. Whereas the maximum value for building with damper is 0.0054 at story 4 in global X-direction and 0.0042 at story 8 in global Y-direction. The value of IDR has exceeded the limiting value of 0.004 in both the cases. In case of building without damper this value exceeds at 3rd, 4th, 5th, 6th, 7th, and 8th storey in both directions whereas in case of building with damper this value exceeds at stories 3rd, 4th, 5th, 6th, 7th, and 8th in global X-direction and at 5th and 8th storey in global Y-direction. Even though the drift values exceed the limiting value for building with dampers it is comparatively lower than the drift values for building without damper observable in either direction.

4.2. Time History of Responses The responses of the structure for THA have been obtained as time history functions of response against time. The TH functions give better insight into the response behavior of structure at each time step of analysis. The time history plots have been represented for following responses viz. Roof


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displacement, Roof Acceleration, Base Shear force, storey shear force and plot for input energy and damped energy. 4.2.1. Time History of Roof Displacement and Roof Acceleration Roof displacement and acceleration are important parameters to analyze the behavior of structure under dynamic loading. It presents a better insight into performance of the structure as a whole. Plots of roof displacement v/s time period and roof acceleration v/s time period for two building models with and without supplemental damping under seismic loading have been obtained. The displacement plots reveal that displacement values for building without dampers is as high as 174.218 mm which is subsequently lower for building model with dampers with maximum displacement as high as 152.911 mm. The use of dampers has not successfully reduced the displacement values at all-time instances in comparison to building without dampers but has managed to keep the overall displacement of building within a limited range with smooth transitions preventing sudden reversal of displacement load. Similar interpretation can be made for roof acceleration time history response. The roof acceleration for building with damper is as high as 6.34 m/sec2 which is even higher than the maximum roof acceleration of 5.99 m/sce2 for building without dampers. But the transition of roof acceleration over time and overall roof acceleration response is within a controlled range.

Figure 6 Roof displacement and acceleration v/s time plots in global X-direction for building with and without supplemental damping

Figure 7 Base shear force v/s time plot in global X-direction for building with and without supplemental damping


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Figure 8 Storey Shear force v/s time plots in global X-direction at story 1, 5, 9 and 12 for building with and without supplemental damping

4.2.2. Base Shear Force in X Direction The base shear force in X direction against time period has been plotted for building models with and without supplemental damping. It can be seen from the time history of base shear force that the overall effect of damper in reducing the base shear is significant even though the maximum shear value of 11089.34 KN for building with damper is more than the shear value of 10645.89 KN for building without damper. As can be seen the base shear for building with damper against the building without damper has higher values for small fraction of time indicating that on the time scale of the event the building experiences less amount of force over the run of the event. The increased force in case of the building with damper can be attributed to increased mass due to addition of dampers in the building. 4.2.3. Time History of Storey Shear Force The storey shear plot is a very important parameter to study to observe the resistance provided at different stories against storey displacement. The resistance offered with time can be visualized from TH plots for storey shear. The TH of storey shear for stories 1, 5, 9 and 12 for both the building cases has been compared. In each case the maximum value of story shear at given stories is higher for building with dampers. Another trend in story shear values to observe is decrease in story shear from bottom to top of the building in both the cases. Even though the maximum story shear forces for building with dampers is higher than that for building without damper the overall effect is similar to time history plot of base shear force. Over the time scale of the event different stories of the building with damper experience lesser force over the run of the event as compared to the building without http://www.iaeme.com/IJCIET/index.asp

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damper. Again as stated for base shear force the higher value of story shear in case of building with damper can be attributed to the increased mass by addition of dampers at each story level.

5. CONCLUSION The results of the non-linear modal time history analysis conducted on a 12 story RC frame structure with and without FVD, represented using story responses and time history plots for various parameters, demonstrate that the story response of the structure in form of AMSD and AMSd have been reduced considerably by use of dampers. The time history plot of roof acceleration show considerable reduction over the time scale of the event by use of dampers against the building without supplemental damping. The effectiveness of dampers is evident in form of reduced stress demands on structural elements. The time history plot of roof displacement over the time scale of event by use of dampers shows overall reduction in maximum displacement value. The displacement values are within limited range desired proving the effectiveness of dampers in reducing the displacement response of the structure. The time history plots of base shear and story shears for stories 1, 5, 9 and 12 have similar pattern as to time history plot of roof acceleration. The dampers have been effective in reducing shear forces in the structure. Even though the FVDs have significantly reduced the responses, the damping demand of structure can be further reduced by optimum selection and installation of FVDs at various critical locations.

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