HYSTERETIC BEHAVIOUR OF AN IMPROVED PSEUDO-VISCOUS FRICTIONAL DAMPER

Size: px

Start display at page:

Download "HYSTERETIC BEHAVIOUR OF AN IMPROVED PSEUDO-VISCOUS FRICTIONAL DAMPER"

Mervyn Waters
5 years ago
Views:

1 3 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August -6, 4 Paper No. 99 HYSTERETIC BEHAVIOUR OF AN IMPROVED PSEUDO-VISCOUS FRICTIONAL DAMPER Bin WU, Jigang ZHANG, Jinping OU 3 and Martin WILLIAMS 4 SUMMARY Hysteretic behavior of an improved pseudo-viscous frictional damper (IPVFD) is studied through testing and numerical analysis. Test results show that () the fatigue performance and energy dissipation capacity of IPVFDs are much better than those of the previous version of the dampers due to some amendments on their construction; and () the tension force of IPVFDs is remarkably lower compared to that of Pall-typed frictional dampers, which is beneficial for reducing the pressure of adjacent columns and hence improving their ductility. The numerical computation results considering geometry nonlinearity induced by IPVFDs frictional mechanism agree with the test results.. INTRODUCTION Passive control systems have been successfully used for reducing the dynamic response of structures subjected to earthquakes or strong wind. Friction dampers have often been employed as components of these systems because they present high energy-dissipation potential at relatively low cost and are easy to install and maintain. A lot of friction devices have been studied experimentally and/or theoretically, e.g. Pall and Marsh [], Aiken and Kelly[], Grigorian and Popov [3], Nims et al. [4], Wu et al. [, 6], and many of them have been implemented in buildings around the world, e.g., see Balazic et al. [] and Soong and Spencer [8]. In China, several buildings are armed with friction dampers to reduce earthquake effects. Among them, two school buildings in Yunnan were incorporated with friction dampers [9,]; Pall dampers were used in the retrofit of a government building in Shenyang []. Viscous dampers are another type of popular dampers with many applications in civil engineering structures [8]. When incorporated in structures, viscous dampers can provide high additional damping ratio but do not change the frequency of the structures, thus significantly reduce the acceleration as well as displacement response[], which improves the safety of structures and foundations. Another particularly desirable feature of viscous damper is that the damping force is out-of-phase with the displacement. If dampers are included in the structure in such a way that there is a column axial force component due to the damper force (i.e., with a diagonal brace), then the out-of-phase peak damper force means that the peak column School of Civil Engineering, Harbin Institute of Technology, China. bin.wu@hit.edu.cn School of Civil Engineering, Harbin Institute of Technology, China. jgzhang@hit.edu.cn 3 School of Civil Engineering, Harbin Institute of Technology, China. oujinping@hit.edu.cn 4 Department of Engineering Science, Oxford University, UK. martin.williams@eng.ox.ac.uk

2 moment is less than if the peak damper force occurred at peak displacement [3]. The reduced column axial force may also results in the enhancement of ductility capacity of the column. An effort had been made by the first three authors to combine the advantages of friction dampers and viscous dampers. As a result, a pseudo-viscous friction damper (PVFD) was developed with similar hysteretic loops to viscous dampers but through friction mechanism [6]. The construction of the pseudoviscous dampers is shown in Figure. On one face of the crisscross plate of the PVFD, there are two convexities; correspondingly, on the inner face of the two horizontal links, there is a brass convexity, which contrasts with the flat faces of the crisscross plate and horizontal links of the Pall dampers [4]. It is this difference that makes the PVFD a novel ED mechanism. As seen in Figure, there is a clip force in the slip bolt which is passed through the horizontal link over the brass convexity, brass pad plate and crisscross plate. Hence, the compression force between the brass convexity and the crisscross plate and that between the brass pad plate and the crisscross plate, produces initial slip force in the PVFD. When the seismic load reaches a certain quantity, the PVFD will overcome the initial slip force and deform. The shape of the PVFD changes from rectangular to rhomboidal when the brass convexity slides down the convexity of the crisscross plate, which makes the distance between them short so that the clip force in the slip bolt decreases. Therefore, the restoring or friction force of the PVFD reaches minimum value at maximum displacement and reaches maximum value at zero displacement, i.e. it is out-of-phase with displacement. This is very similar to the behavior of viscous dampers, so we call it a pseudo-viscous frictional damper. A A 4 (a)assemblage (b)crisscross plate (c)a A.crisscross plate.curve slot 3.brass pad 4.brass block.slip bolt 6.horizon link.vertical link Figure Construction of pseudo-viscous dampers However, the hysteretic test showed the low fatigue performance due to the high local stress on the convexities of the damper [6]. As a result of the same reason, the capacity of the damper could not be high enough to meet the need of practical application. This paper presents an improved PVFD (IPVFD) which is intended to overcome the shortcomings of PVFDs. The behavior test is described and numerical simulation is conducted thereafter.. DEVELOPMENT OF IMPROVED PSEUDO-VISCOUS FRICTION DAMPERS (IPVFDS). IPVFD... Configeration A possible plan to improve PVFDs is shown in Figure. The damper in Figure is named as IPVFD which is to differentiate IPVFD as will described later in Section. The most significant feature of IPVFD compared to the previous PVFD is the two wedge parts of crisscross plate. It is through the 6 4 3

3 wedge parts of crisscross plate other than the convexities that IPVFD imitates the hysteretic behavior of viscous dampers. Although the basic configuration of PVFD is similar to the previous PVFD, but the flat friction surface of IPVFD will make a big difference on the performance of PVFDs due to the absence of local stress concentration on the friction surface h w tw h (a) front view (b) crisscross plate (c) side view.crisscross plate.curve slot 3.friction pad 4.corner bolt.slip bolt 6.horizontal link.vertical link Figure Construction of PVFD The operation of IPVFD is shown in Figure 3. When brace forces are large enough to activate IPVFD, IPVFD will deform from rectangle to parallelogram. The centers of the horizontal links, as well as the clamping bolts or slip bolts move along the arc slot. The motion of the horizontal link relative to the crisscross plate can be divided into two components, i.e. horizontal one and vertical one. Let us focus on the vertical movement of the horizontal links. As the horizontal links move inwards to the center of the crisscross plate, relatively the wedge ends of crisscross plate move outwards. Thus the distance between horizontal links is shortened and part of stress in the clamping bolts and normal stress on the friction surfaces are released. Hence, the friction force is reduced as the deformation of the damper increases. In Sections.. and..3, we will discuss quantitatively hoe the friction force is reduced. h d A δ I t t' A (a) front view (b) side view (c) detail Figure 3 Operation of PVFD... Geometry analysis Based on geometry analysis, the vertical displacement of the horizontal links relative to crisscross plate with the damper deformation Äd is obtained as I δ = R R ( / ) = ( h h ) () d d The horizontal distance t h between the pair of horizontal links is shortened due to the relative movement between the horizontal links and crisscross plate. The shortened quantity is

4 I δ = th t h ' = δ tgγ = (h h d ) tgγ () where γ is the angle of the wedge and tgγ=t w /h w. Here h w is the height of the wedge and t w is the cut depth on the root of wedge part of the crisscross plate...3. Force analysis I The axial force in the clamping bolt will release because of the occurrence of δ. The releasing amount has relationship to tensile stiffness of champing bolt and the compression stiffness of vertical and horizontal links, friction pad, as well asδ. We designate K c as the composite stiffness of the relavent components, then the variance of axial force can be expressed as N = K c δ (3) Substituting Equation into Equation 3, we get N = K c ( h h d ) tgγ (4) Then the axial force of the clamping bolt or the normal compression force on the friction surface becomes N = N N () where N is the initial normal compression force when damper deformation Äd=. From Equations 4 and, friction force is obtained as I I F = µ N = F β ( h h d ) (6) I in which F =ìn is the initial friction force, and β = µ K c tgγ which is called slope coefficient of the wedge because of its relationship with wedge angle γ. From Equation 6, we clearly see that the friction force goes down with the increase of damper deformation... IPVFD Further improvement on the IPVFD can be made if its configuration is adapted as shown in Figure 4. One advantage of IPVFD is that it further reduces damper force or friction force, which can be illustrated by the operation of IPVFD as shown in Figure. From similar geometry analysis to IPVFD, The expression of δ of IPVFD can be written as δ = h h () I d (a) front view (b) crisscross plate (c) side view.t plate with wedge part.curve slot 3.friction pad 4.corner bolt.slip bolt 6.horizontal link.vertical link Figure 4 Construction of PVFD

5 d δ I (a) front view (c) side view Figure Operation of PVFD So δ I = δ I. Then the friction force or damper force of IPVFD can be express as I I F = F β ( h h d ) (8) where β I = β I. From the comparison of Equations 6 and 8, it can be seen that with the same d, I I F F (9) Another advantage of IPVFD is that fabrication of IPVFD is easier than IPVFD, since it has only one arc slot to machine and less connection bolts. The IPVFD used in the test to be dscribed in Section 3 is shown in Figure 6. Note that the multiple T plates are adopted to increase the capacity of the damper at the same clamping moment. The damper force of IPVFD in Figure 6 will be three times that in Figure (a) front view (b) crisscross plate (c) side view.t plate.curve slot 3.friction pad 4.corner bolt.slip bolt 6.horizontal link.vertical link Figure 6 PVFD used in the test 3. HYSTERETIC TEST OF IPVFD 3.. Test plan The experimental study was carried out at Mechanical and Structural Testing Center of Harbin Institute of Technology. The dimension of the dampers used in the test is shown in Figure 6, the corresponding setup is shown in Figure. The damper was scaled 3: of the prototypes which were used in a school building of Zhenrong Middle School, Yunnan Province, China. The braces were steel equal angles?3 3. Strain sensors were attached to the braces to measure the strain, hence the axial forces of the braces. The ratio of the axial force and the strain of the?3 3 was measured.6kn/ìå through a pretest. To study the influence of different wedge on the hysteretic feature of IPVFD, three dampers were manufactured with t

6 of mm, mm and 3mm. The different clamping forces were also considered in the test. The test cases are shown in Table. plain surface bearing 8 actuator brace brace 3 brace brace 4 94 support damper Figure Testing setup of IPVFDs Table Test case Case number Cut depth (mm) 3 3 Clamping moment (Nm) Test results The result of case, i.e., with cut depth t of 3mm and clamping moment of 6Nm, is shown in Figure 8. The other cases are referred to []. It is seen from Figure 8 that the damper force decreases with the Force (KN) Displacement (mm) (a)damper (b)brace Figure 8 Tested hysteretic loops of IPVFD (case) increase of frame displacement. Although the damper force does not reduce to zero, the IPVFD simulate one of the basic features of viscous dampers, i.e., the dampers force reach maximum at displacement of zero and reduce to zero at the maximum displacement when subject to harmonic excitation, or the damper force is out-of-phase with displacement. From Figure 8a, we also see that the peak damper forces of different cycles are almost the same which demonstrates the good fatigue property of IPVFD compared to previous PVFDs. It is seen from Figure 8b that the brace force decreases for quite a while after the damper overcomes initial friction force, but then start to increase at the frame displacement of 4mm. The Force (KN) - Displacement (mm)

7 special phenomenon that brace force of IPVFD increases when the damper force is decreasing is related to the geometry nonlinearity of the damper, which will be addressed in Section 4. The tested maximum damper force is 4 kn (case 6) [], while the damper force of the original PVFDs with the similar dimension was only 4 kn. Apparently, the capacity of IPVFDs is much higher than that of original PVFDs Comparison with T shaped core plates dampers(tfds) If the T plates of IPVFD are replaced by the T plates with equal thickness, i.e., with flat parts instead of wedge parts, IPVFDs will become ordinary friction dampers with T shaped core plates (TFDs). TFDs have the same hysteretic behavior as Pall dampers []. The hysteretic behavior of a TFD with the same dimension of the above IPVDFs is also tested. The hysteretic loops of the TFD of one case is shown in Figure 9. From the comparison of Figures 8 and 9, it is seen that with approximately the same prescribed initial friction force, the brace force of the IPVFD and TFD are 6.9kN and 6.36kN, respectively. The former is 38% of the latter. The significantly reduced tensile brace force may result in the increase of moment and ductility capacity of the adjacent columns. Force(kN) Displacement(mm) (a)damper (b)brace Figure 9 Experimental hysteretic loops of TFDs 4. NUMERICAL ANALYSIS OF HYSTERETIC BEHAVIOR OF IPVFDS 4.. Computation method The computation schematic of IPVFD is shown in Figure, from which we see that the damper-brace structural system is incompletely rigid. The configuration of the damper-brace structural system is actually of the so called critical form [6]. The stiffness matrix of the damped structure will be singular according to the conventional method of structural mechanics, if the influence of damper position on its mechanical behavior is not considered. Then the structural analysis cannot be carried out. Therefore, the geometric nonlinearity induced by large deformation of the damper has to be considered as in the following analyses. Force(kN) - Displacement(mm)

8 brace A A l Ad' B Δ B' brace H Ad φ Cd' θ Dd Bd Bd' C (C' ) Cd L Dd' D(D') Figure Computation schematic of IPVFD When horizontal displacement of the frame,, occurs, the damper will move and/or deform, pushed or dragged by the braces. If the actions of the braces exerted on the damper are not large enough to make the damper overcome the friction force, the damper will just displace and will not change its shape. At this stage, movement of the damper consists of horizontal movement and rotational around its center. If the damper overcomes the frictional force and slides, its shape will be changed, as well as it moving and rotating. To simplify the analysis, the center of the IPVFD is selected as the origin of the coordinate system. The coordinates of the upper corners of the frame and the damper before and after the displacement of the frame are: L H L H l h l h A : (, ), B : (, ), Ad : (, ), Bd : (, ) L + H L + H A': (, ), B': (, ) l hsinφ hcosφ sinθ l hsinφ hcosφ cosθ Ad ': ( + ) cosθ +, ( )sinθ + l hsinφ hcosφ sinθ l hsinφ hcosφ cosθ Bd ': ( + ) cosθ +, ( + )sinθ + The coordinates of the lower ones can be obtained according to symmetry. With the coordinates shown above, the original length of braces and, l and l, and their length after deformation, l ' and l ', can be calculated. It is seen from coordinates expressions that l ' and l ' will be nonlinear functions of θ and φ. Let l '(θ, φ) and l '(θ, φ) denote l ' and l ', respectively. Using Hooke s law, the forces of the braces may be written as EA( l i '( θ, φ) li ) F = i ( θ, φ) max, Fcr, i=, () li where E is the elastic modulus of steel, A is the area of braces, F and F are brace forces which are positive when stretched and negative when compressed, and F cr is the buckling force of braces which takes negative value. Note that the Equation is valid only when the braces are not yielded. The yielding of the braces will significantly reduce their energy dissipation capacity, thus, this case should be avoided in the design, and it is not considered in this paper. Now we consider the forces acting on the damper, which are shown in Figure. Taking moments about the center of the damper, we get F θ, φ) d ( θ, φ) + F ( θ, φ) d ( θ, φ) () ( =

9 For the force equilibrium along the horizontal link, A d 'B d ', the following equation exists. F ( θ, φ)cos( α + θ + φ) + F cos( α θ φ) = F () In Equations and, α and α are elevation angles of brace and brace, respectively, which can be determined according to coordinates of the damper and the frame; F is friction force; d (θ, φ) and d (θ, φ) are moment arms about the center of the damper, which are also determined according to coordinates of the damper and the frame. When the friction pad slides, F in Equation takes the value of F I in Equation 8.Then θ and φ can be evaluated from Equations and. When the action of the braces on the damper is not strong enough to activate the damper, φ equals before the initial slip, or φ takes the value at the end of last slip. Then θ can be calculated from Equation. With θ and φ solved, the brace forces are evaluated from Equations. Obviously, Equations and are a pair of nonlinear equations in θ and φ. The Newton-Raphson iterative method (e.g. Zwillinger []) is used to solve Equations and. 4.. Numerical result The parameters in the following analysis are chosen according to the testing setup and testing results described in section and 3. Let frame span L= 8mm, story height H=94mm, damper length l= mm, and damper height h= mm. The measured section stiffness of the brace, EA, is.6 4 kn, as mentioned in last section, and the calculated buckling force is 43. kn. The tested damper forces at the onset of sliding, i.e.,.kn, is chosen as the initial friction force. The numerical results with friction force of kn are shown in Figure. From the hysteretic curves shown in Figure, we see that the general shape of hysteretic loops of the damper and brace is quite similar to the testing results, and especially that the brace force increases when the damper force is decreasing is verified by the testing results (Figure 8). The special feature of IPVFD that brace force increases with large displacement is related to the geometry nonlinearity of the damper. Actually, this feature is undesirable when we consider the safety of the adjacent columns at large displacement. One possible way to solve the problem is to abandon the current friction mechanism and incorporate the damper with single diagonal brace or V brace. Force (KN) Force (KN) Displacement (mm) Displacement (mm) (a)damper (b)brace Figure Numerical hysteretic loops of IPVFD (case) -. CONCLUSIONS From the above experimental and numerical studies, the following remarks are concluded.

10 () With the development of IPVFDs, local stress concentration existing in the friction surface of the previous version of PVFDs is eliminated. Compared to previous version of PVFDs, IPVFDs possess much higher capacity and much better fatigue property. ()Compared to TFDs, a Pall type dampers, the brace force of IPVFDs at large frame displacement is reduced significantly, which may increase the moment and ductility capacity of adjacent columns. (3)The numerical results reasonably agree with experimental results, which shows the validity of the computation method considering geometric nonlinearity. ACKNOWLEDGEMENTS This work was supported by Grant 998 from the National Science Foundation of China. REFERENCES. Pall A.S., Marsh C., Response of friction damped braced frames, J. Struct. Div. ASCE 98; 8: Aiken I., Kelly J., Earthquake simulator testing and analytical studies of two energy absorbing systems for multi-storey structures, Report No. UCB/EERC-9/3, EERC, Berkeley, Grigorian C.E., Popov E.P., Slotted bolted connection energy dissipaters, Earthquake Spectra, EERI 993;9(3): Nims D.K., Richter P.J., Bachman R.E., The use of the energy dissipation restraint for seismic hazard mitigation, Earthquake Spectra, EERI 993; 9(3): Wu, Bin, Zhang J., Williams M., Testing and numerical analysis of the brace forces of pall frictional dampers, Proceedings of 6th ASCE Engineering Mechanics Conference (CD), Seattle, 3 6. Wu, Bin and Ou, J.P., The Pseudo-Viscous Frictional Energy Dissipator : a New Device for Mitigating Seismic Effects, Earthquake Engineering and Structural Dynamics, 3, 3(), Balazic, J., et al., Seismic rehabilitation of justice headquarters building Ottawa, Canada. Paper, WCEE, New Zealand,. 8. Soong, T.T., Spencer Jr, B.F. Supplemental energy dissipation: state-of-the-art and state-of-thepractice, Engineering Structures,,4: Ou, J.P., Zou X.Y., Long, X., Wu, Bin, et al., Seismic Analysis and Design for Refectory Structure of Yunnan Zhenrong Middle School with Energy Dissipators, The International Workshop on Structural Control and Health Monitoring, Shenzhen, China, December -,. Zou, X.Y., Experiment, Analysis and Application of Energy Dissipation Structures with Viscoelastic and Pseudo-Viscous dampers, PhD Dissertation, Harbin Institute of Technology,. Wu, Bo, Li, H., Lin, L.Y. and Shan, M., Strengthening the Earthquake Resistance of a Building Using Friction Dampers, Journal of Building Structures, 998, 9(): Ou, J., Wu, Bo, Soong, T.T., Recent advances in research and applications of passive energy dissipation system, Earthquake Engineering and Engineering Vibration 996; 6(3):_ Hanson, R.D., et al., State-of the Art and State-of-the-Practice in Seismic Energy Dissipation, Seminar on Seismic Isolation, Passive Energy Dissipation, ATC -, Vol, pp

11 4. Pall, A.S., Pall, R., 993, "Friction-Damper Used for Seismic Control of New and Existing Buildings in Canada", Seminar on Seismic Isolation, Passive Energy Dissipation, ATC -, Vol, pp Wu, Bin, Zhang, J. and Ou, J., Testing and numerical analysis of an improved pseudo-viscous frictional damper, Chinese Journal of Civil Engineering, 3, 3(): Timoshenko, S.P. and Young D.H., Theory of Structures. McGraw-Hill, London, 96. Zwillinger, D., Ed., Standard Mathematical Tables and Formulae (3th Edition), CRC Press, Boca Raton, 996.

Special edition paper

Special edition paper Development of New Aseismatic Structure Using Escalators Kazunori Sasaki* Atsushi Hayashi* Hajime Yoshida** Toru Masuda* Aseismatic reinforcement work is often carried out in parallel with improvement