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Numerical and experimental study of hysteretic behavior of cylindrical friction dampers
Engineering Structures 33 (2011) 3647–3656
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Numerical and experimental study of hysteretic behavior of cylindrical friction dampers Masoud Mirtaheri ∗ , Amir Peyman Zandi, Sahand Sharifi Samadi, Hamid Rahmani Samani K.N. Toosi University of Technology, Department of Civil Engineering, Tehran, Iran
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Article history: Received 6 December 2010 Received in revised form 26 July 2011 Accepted 28 July 2011 Available online 26 August 2011 Keywords: Friction damper Energy dissipation Hysteretic loading Passive control
abstract Frictional dampers utilize the mechanism of friction for absorbing and dissipating the energy imparted to the dynamic systems. Frictional dampers are widely used in mechanical systems in various industries in order to mitigate the impact and vibration effects. Frictional dampers are also utilized in structures as means of passive control to improve the seismic behavior of structures. In this investigation, an innovative type of frictional damper called cylindrical friction damper (CFD) is proposed. This damper consists of two main parts, the inner shaft and the outer cylinder. Dimensions and properties of the main parts are defined based on seismic demand of structures. These two parts are assembled such that one is shrink fitted inside the other. Upon application of proper axial loading to both ends of the CFD, the shaft will move inside the cylinder by overcoming the friction. This in turn leads to considerable dissipation of mechanical energy. In contrast to other frictional dampers, the CFDs do not use high-strength bolts to induce friction between contact surfaces. This reduces construction costs, simplifies design computations and increases reliability in comparison with other types of frictional dampers. The hysteretic behavior of CFD is studied by experimental and numerical methods. The results show that the proposed damper has great energy absorption by stable hysteretic loops, which significantly improves the performance of structures subjected to earthquake loads. Also, a close agreement between the experimental and numerical results is observed. © 2011 Elsevier Ltd. All rights reserved.
1. Introduction Many different types of energy dissipation devices have been developed and tested for seismic applications in recent years, and more are still being investigated. Frictional devices dissipate energy through friction caused by two solid bodies sliding relative to each other. Pall and Marsh [1] proposed frictional dampers installed at the crossing joint of the X-brace. Tension in one of the braces forces the joint to slip thus activating four links, which in turn force the joint in the other brace to slip. This device is usually called the Pall frictional damper (PFD). Wu et al. [2] introduced improved Pall frictional damper (IPFD), which replicates the mechanical properties of the PFD, but offers some advantages in terms of ease of manufacture and assembly. Sumitomo friction damper [3] utilizes a more complicated design. The pre-compressed internal spring exerts a force that is converted through the action of inner and outer wedges into a normal force on the friction pads. Fluor
∗ Corresponding address: K.N. Toosi University of Technology, Department of Civil Engineering, No. 1346, Valiasr St., Mirdamad intersection 19967, P.O. Box 15875-4416, Tehran, Iran. Tel.: +98 0912 1050129; fax: +98 21 8877 9476. E-mail addresses: [email protected] (M. Mirtaheri), [email protected] (A.P. Zandi), [email protected] (H.R. Samani). 0141-0296/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2011.07.029
Daniel Inc. has developed and tested another type of friction device which is called Energy Dissipating Restraint (EDR) [4]. The design of this friction damper is similar to Sumitomo friction damper since this device also includes an internal spring and wedges encased in a steel cylinder. The EDR utilizes steel and bronze friction wedges to convert the axial spring force into normal pressure on the cylinder. A full description of the EDR mechanical is given in [5]. Constantine et al. [6] proposed frictional dampers composed of a sliding steel shaft and two frictional pads clamped by high strength bolts. Li and Reinhorn [7] verified the seismic performance of a reinforced concrete building with frictional dampers through a combined experimental and analytical study. Grigorian et al. [8] studied the energy dissipation effect of a joint with slotted holes both analytically and experimentally. Mualla and Belev [9] proposed a friction damping device and carried out tests for assessing the friction pad material. Cho and Kwon [10] proposed a walltype friction damper in order to improve the seismic performance of the reinforced concrete structures. Numerical models of friction dampers for multi degree of freedom structures were proposed by Bhaskararao and Jangid [11]. The results were validated with those obtained from an analytical model. Park et al. [12] proposed a new equivalent linearization technique for a friction damper–brace system based on the probability distribution of the extreme displacement. Lee et al. [13] proposed a design methodology of friction
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Fig. 1. Main parts of the CFD: (a) solid shaft; (b) tubular cylinder; (c) manufactured shaft and cylinder.
Fig. 2. The CFD: (a) Longitudinal section of CFD; (b) Assembled CFD.
damper–brace systems, to determine the quantity and slip load of the frictional damper and the brace stiffness systematically for an elastic multistory building structure based on the story shear forces. Min et al. [14] proposed a design process to determine a desired control force of a friction damper to satisfy a given target performance of a structure subjected to an earthquake ground excitation. Colajanni and Papia [15] analyzed and compared the dynamic response of braced frames with and without friction dampers. Most of the frictional dampers are made of a set of steel plates, with a certain friction coefficient, that are forced by bolt pretention in order to induce the friction between them. Using pretensioned bolts to induce friction makes the behavior of frictional dampers unpredictable. The purpose of this study is to propose an innovative type of frictional dampers called Cylindrical Friction Damper (CFD), which does not need mechanical means for inducing contact pressure resulting in frictional damping. Both experimental and numerical models of the CFD are examined and effectiveness of the dampers in seismic protection is evaluated. 2. Components and mechanism of cylindrical friction damper CFD consists of two main parts, the shaft (Fig. 1(a)) and the cylinder (Fig. 1(b)). Suitable end-plate or eye bar connections are provided at two ends of the damper (Fig. 1(c)). A longitudinal section of the CFD is shown in Fig. 2(a). The inner diameter of the cylindrical element is slightly smaller than the diameter of the shaft at a predefined length L0 . When the cylindrical part is heated,
Fig. 3. Schematic load–deformation curve for CFD.
its diameter will increase due to thermal expansion and the shaft can be easily placed into the cylinder (Fig. 2(b)). Reaching thermal equilibrium, the design pressure will be developed between the contact surfaces (i.e. outer surface of the shaft and inner surface of the cylinder), which results in friction between these surfaces. If the damper’s axial force overcomes the static friction load, the shaft inside the cylinder will move, thereby resulting in considerable mechanical energy absorption. Since the main parts are in contact at a certain constant length (i.e. L0 ), the slippage load remains constant during the motion. A schematic load–deformation curve for the CFD is shown in Fig. 3.
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Fig. 4. Normal pressure developed by reaching thermal equilibrium between contact surfaces.
CFDs need not move during mild winds and earthquake events with high probability of occurrence. However, during a major earthquake, the shaft starts to move in the cylinder and prevents yielding of structural members.
Fig. 5. Connection of the CFD to a reaction block.
3. CFD design computations In the design of the frictional dampers, it is important to determine the slip load. The CFD can be simply set for different slip loads by selecting the appropriate geometric parameters. For simplicity, all parameters except L0 can be considered to be constant, and the slip load can be set by changing L0 . Fig. 4 shows the pressure between cylindrical contact surfaces reaching thermal equilibrium. The radial displacement at the inner face of a thick-walled cylinder under internal pressure is [16]
∆c =
P .ri
ro2 + ri2 ro2 − ri2
E
+ν
(1)
where P is the internal pressure, ri and ro are the inside and outside radii of the cylinder respectively, E is the modulus of elasticity and finally, ν is Poisson’s ratio. Note that Eq. (1) corresponds to a plane stress condition. The radial strain in the shaft and the corresponding radial displacement due to normal pressure are P
εs =
E
∆s =
(1 − ν)
P .ri
(2)
∆c + ∆s =
Step 4. Compute normal pressure, P, by Eq. (5). Step 5. Compute contact length, L0 , by means of Eq. (6).
δ
(3) 4.1. Test setup
(4)
2 where δ is the difference in the diameters of the shaft and the cylinder along L0 (Fig. 1(b)). Substituting Eqs. (1) and (3) into Eq. (4) yields E .δ ro2 − ri2 4ro2
ri
.
(5)
Equilibrium along the axial direction of damper requires L0 =
Fig. 7. Experimental setup.
4. Experimental study of hysteretic behavior of the CFD
(1 − ν).
E The compatibility of deformations requires
P =
Fig. 6. Schematic view of the test setup.
Fs P .π .D.µ
(6)
in which Fs is the slip load, µ is the friction coefficient, D is the diameter of the shaft and L0 is the contact length. Step by step procedure for designing the CFD can be summarized as follows. Step 1. Determine slip load and maximum displacement of dampers by structural analysis of the model including proposed dampers. Step 2. Select proper material for damper, specifying ν, µ and E. Step 3. Fix geometric dimensions, i.e., t , δ and D.
The axial force–displacement curve of the CFD can be determined by a test. Uniaxial tests are performed by means of a 300 kN hydraulic actuator which is attached to a reaction block. The actuator can apply reciprocal motion to the CFD with predetermined amplitudes. One side of the CFD is attached to the reaction block and the other side is attached to the actuator as shown in Fig. 5. Both reaction blocks are fixed to a strong strip by heavy bolts. Fig. 6 shows the test setup which consists of a hydraulic actuator, reaction blocks at two ends and a test specimen. To measure relative slip of the CFD, a Linear Variable Differential Transformer (LVDT) is installed on each of the specimens, as shown in Fig. 7. The distance between the reaction blocks is variable, and the CFD with various lengths can be tested. When properly connected and fixed, the internal parts of the CFD move relative to each other. Each test includes twenty full displacement cycles applied to the specimen. The frequency of loading and stroke of the CFD are determined for a particular application (e.g. story drift). 4.2. Specifications of manufacture of the CFD Two types of CFD with different slip loads are designed based on the step by step method presented in the previous section.
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Table 1 Specifications of studied CFDs. Name
Design slip load (kN)
D (mm)
t (mm)
δ (µm)
L0 (mm)
displacement (mm)
Energy dissipation per cycle (kJ)
Total length (mm)
Type A Type B
130 250
100 100
10 10
100 100
49.4 95
±50 ±50
26 50
300 400
Fig. 8. Experimental axial force–displacement curve of the CFD (Type A).
Fig. 9. Experimental axial force–displacement curve of the CFD (Type B).
All geometric parameters, except L0 , are the same for both types. Table 1 gives the specifications of these dampers. For each type, two specimens are produced. Shafts are made of CK45 steel (according to DIN steel grades) with chrome lining and cylinders are made of CK15 steel. The shaft needs no machining; only the cylinder is machined to exact dimensions. The coefficients of static and dynamic frictions (µs , µk ) are obtained based on several tests. The value of µs is 0.286 and the value of µk is 0.224. To improve the damper’s function, special techniques are utilized to coat contact surfaces in order to make µs , µk closer. 4.3. Test results 4.3.1. Slip load The axial force–displacement curve for Type A and Type B dampers are presented in Figs. 8 and 9 respectively. As seen in these figures, the CFD behavior can be described in two following stages.
Fig. 10. Slip load versus cycle number (Type A).
1. Non slip stage: there is no relative displacement between the CFD components and the CFD behaves as an elastic spring. 2. Slip stage: applied axial force overcomes the design slippage load and the shaft inside the cylinder will move. According to ASCE/SEI 41-06 [17], the slip load due to one cycle of each test for the specimen considered must not differ by more than ±15% from the average slip load as calculated from all cycles in that test. Tables 2 and 3 compare the slip load of each cycle with the average slip load for Type A and Type B, respectively. Neglecting the first cycle for the second specimen of Type A, the maximum difference is 10% in the case of Type A and 15% for Type B. Figs. 10 and 11 present slip load versus cycle number for Type A and Type B, respectively. As can be seen, slip load is increased over the cycles. This is because the roughness of contact surfaces increases, which subsequently results in the incensement of the slip load. 4.3.2. Hysteresis of CFD Hysteretic curves of the specimens are shown in Figs. 12–15. As one could expect, the CFD exhibits rigid plastic rectangular hysteresis loops. Furthermore, the CFD has almost the same performance in tension and compression. Dissipated energy of the CFD over a vibration cycle is expressed as
∫ Edi =
Fsi |y| dt
(7)
Fig. 11. Slip load versus cycle number (Type B).
in which Edi is the dissipated energy in the ith load cycle, Fsi is the slip load of the ith cycle and y is the displacement of the CFD. The above integral is equal to the net area of the region bounded by the load–displacement loop. Assuming the slip load to be constant over a cycle, Eq. (7) can be simplified as:
∫ Edi =
∫ Fsi |y| dt = Fsi
|y| dt = 4Fsi × ∆max .
(8)
According to ASCE/SEI 41-06, within each test, the dissipated energy of an energy dissipation device for any one cycle should not differ by more than plus or minus 15% from the average dissipated energy as calculated from all cycles in that test.
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Table 2 Slip load for each cycle of loading (Type A). Cycle no.
1st specimen
2nd specimen
Experimental slip load (kN)
Deviation from average (%)
Experimental slip load (kN)
Deviation from average (%)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
137.9 122.4 121.9 122.4 123.5 123.9 122.4 123 123.9 125.3 124 125.3 126.2 128.7 130.3 131.9 133.8 135.8 137.4 139.6
8.35 3.85 4.26 3.87 2.97 2.70 3.84 3.37 2.69 1.59 2.61 1.56 0.86 1.10 2.34 3.59 5.10 6.64 7.90 9.69
153.3 132.2 130 125.6 125.6 124.4 125.4 126 126.5 127 126.4 127.7 126.8 127.3 125.9 126 126.8 127.5 128 128.4
19.45 3.01 1.29 2.13 2.13 3.07 2.29 1.82 1.43 1.04 1.51 0.50 1.20 0.81 1.90 1.82 1.20 0.65 0.26 0.05
Average
127.9
128.34
Table 3 Slip load for each cycle of loading (Type B). Cycle no.
1st specimen
2nd specimen
Experimental slip load (kN)
Deviation from average (%)
Experimental slip load (kN)
Deviation from average (%)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
201 182.8 178.9 179 182.3 185.1 185.7 189.8 192.2 197.8 201.4 202.3 206.9 207 217.7 219 223.3 224.5 227.6 231.4
0.39 9.41 11.34 11.29 9.66 8.27 7.97 5.94 4.75 1.97 0.19 0.26 2.53 2.58 7.89 8.53 10.66 11.26 12.79 14.68
244 229.4 231.4 235.7 242.3 244 251.1 256.4 247.3 254.3 252.7 251.6 259 256 254 254 252.3 255.1 252.5 254
1.95 7.82 7.01 5.29 2.63 1.95 0.90 3.03 0.62 2.19 1.55 1.10 4.08 2.87 2.07 2.07 1.38 2.51 1.46 2.07
Average
201.78
Fig. 12. Experimental force–displacement curve for the first specimen of type A.
Tables 4 and 5 compare the dissipated energy of each cycle and the average dissipated energy for Type A and Type B, respectively. Due
248.855
Fig. 13. type A.
Experimental force–displacement curve for the second specimen of
to a manufacturing problem (specifically in the second specimen of Type A), the deviation from average in the first cycle of specimens
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M. Mirtaheri et al. / Engineering Structures 33 (2011) 3647–3656 Table 4 Dissipated energy for each cycle of loading (Type A). Cycle no.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Average
1st specimen
2nd specimen
Dissipated energy (kJ)
Deviation from average (%)
Dissipated energy (kJ)
Deviation from average (%)
25.341 24.227 24.196 24.359 24.643 24.753 24.516 24.648 24.868 24.89 24.888 25.156 25.334 25.835 26.153 26.473 26.857 27.251 27.574 28.029 25.5
0.62 4.99 5.11 4.47 3.36 2.93 3.86 3.34 2.48 2.39 2.40 1.35 0.65 1.31 2.56 3.82 5.32 6.87 8.13 9.92
31.027 26.251 23.892 25.573 24.108 23.693 22.786 22.553 23.738 23.552 23.118 22.875 24.637 23.571 22.135 20.821 23.185 22.157 23.153 22.517 23.767
30.55 10.45 0.53 7.60 1.43 0.31 4.13 5.11 0.12 0.91 2.73 3.75 3.66 0.83 6.87 12.40 2.45 6.77 2.58 5.26
Table 5 Dissipated energy for each cycle of loading (Type B). Cycle no.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Average
1st specimen
2nd specimen
Dissipated energy (kJ)
Deviation from average (%)
Dissipated energy (kJ)
Deviation from average (%)
35.162 34.345 33.153 33.983 34.263 35.409 35.709 35.213 36.541 37.167 38.251 38.614 39.325 39.738 40.436 41.068 41.689 42.178 43.221 43.565 37.952
7.39 9.54 12.68 10.49 9.76 6.74 5.95 7.25 3.76 2.11 0.75 1.70 3.58 4.66 6.50 8.17 9.80 11.09 13.84 14.74
43.211 45.434 43.525 44.271 46.313 45.591 47.721 48.151 47.623 47.656 48.211 49.13 49.825 48.188 48.776 49.027 48.201 47.998 51.46762 51.96248 47.614
9.25 4.58 8.59 7.02 2.73 4.25 0.22 1.13 0.02 0.09 1.25 3.18 4.64 1.21 2.44 2.97 1.23 0.81 8.09 9.13
Fig. 14. Experimental force–displacement curve for the first specimen of type B.
is greater than that of other cycles. Neglecting the first cycles, the maximum difference is 10% in the case of Type A and 15% in the case of Type B.
Fig. 15. type B.
Experimental force–displacement curve for the second specimen of
4.3.3. Performance of the CFD in the long run As CFD is designed for seismic applications, the working demand of this damper is certainly occasional and infrequent.
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Fig. 18. The contact pressure developed after thermal analysis for Type A (MPa). Fig. 16. Slip load versus cycle number (first specimen of Type A).
Fig. 19. The contact pressure developed after thermal analysis for Type B (MPa).
5.2. Analysis
Fig. 17. Finite element model of CFD.
However, in order to investigate the performance of the CFD in the long run, fifty full displacement cycles are applied to the first specimen of Type A. The results show that there is no noticeable sign of wear on the contact surfaces. Moreover, the temperature of the device after the last cycle is measured to be about 70 °C. Because of the massive nature of the device, this kind of heat is quickly dissipated. Furthermore, Fig. 16 shows that there is no sign of degradation of the slip load after fifty cycles. 5. Numerical analysis of hysteretic behavior of the CFD
As mentioned earlier, appropriate temperature difference between the shaft and the cylindrical element should be created in order to place the solid shaft into the cylinder. Hence, the first step of analysis consists of thermal loading. The second step of the analysis is cyclic loading which begins as the solid shaft is placed into the cylinder and contact pressure is developed. 5.3. Numerical results Figs. 18 and 19 show the contact pressure developed after thermal analysis, for Type A and Type B respectively. 5.4. Comparison between numerical and experimental results
The analytical computations to estimate the capacity of the CFD are based on some simplifying assumptions. For example, the normal pressure, P, is assumed to be uniformly distributed along the contact length. In order to assess the accuracy of the analytical results, numerical models are developed and the results from the two approaches are compared.
Figs. 20 and 21 show a comparison between experimental and numerical results of load–displacement curves. As can be seen, there is a good agreement between the numerical results and those obtained from experiments. In the case of Type A, the difference between numerical and experimental slip loads is about 3.2% for the first specimen and 6% for the second specimen. In the case of Type B, this difference is about 20% for the first specimen and 6% for the second specimen.
5.1. Finite element modeling
6. A numerical example
Two three-dimensional finite element models have been developed for Type A and Type B dampers, using the commercial finite element software package ANSYS. Taking advantage of symmetry, only 1/4 of the total damper is modeled. Moreover, the outer cylinder is only modeled at contact length. 20-node solid elements are used to model the solid shaft and the outer cylinder is modeled using eight-node shell elements with constant thickness. Surface to surface contact is utilized to simulate the friction. The finite element model of the damper is shown in Fig. 17.
6.1. Description of models To investigate the effectiveness of CFDs in a real building, two analytical models are made and studied comparatively. First, the two-dimensional model of Fig. 22 is modeled using OpenSees software. Beams and columns are modeled using force-based nonlinear fiber beam–column elements with five integration points along their length. The element cross-section is discretized into uni-axial fibers. Column bases have been fully fixed. Gravity
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Fig. 20. Comparison between numerical and experimental force–displacement curves of the CFD (Type A).
Fig. 23. Maximum displacement at the top of the frame versus slipload. Table 6 Earthquake records for nonlinear analysis. Earthquake Coalinga 1983 Northridge 1994 Loma Prieta 1989 Kocaeli, Turkey 1999
Fig. 21. Comparison between numerical and experimental force–displacement curves of the CFD (Type B).
Station and direction 0
Parkfield—Cholame 8W-0 LA HABRA—BRIARCLIFF-00 SF Intern. Airport-00 Ambarli-00
Magnitude
Scale
6.4 6.7 6.9 7.4
4.11 5.87 2.87 2
specified as 240 MPa. A 1% post-yield stiffness is used to account for the hardening of steel beyond yield strength. The periods of vibrations of the first two modes of the structure are 0.77 and 0.23 s, respectively. 6.2. Optimum slip load In order to find the optimum slip-load, various slip loads must be examined. As the first trial load, 80% of the buckling load of the brace member is selected as the CFD slip load. Subsequently, a parametric study is conducted and the slip load is bracketed until the minimum displacement of the top of the frame is reached. The result of parametric study for Coalinga earthquake is shown in Fig. 23. As it can be seem from the Fig. 23, the optimum slip load is 90 kN. 6.3. Nonlinear time history analysis
Fig. 22. Elevation of the frame.
loads are supposed to be similar to common residential buildings in the region. CFD dampers are added to the model subsequently. Nonlinear zero-length elements, with elastic–perfectly plastic behavior are used to model the CFD at the middle of bracing members. The framing members are designed according to AISC seismic provisions for seismic zone 2 with a response factor of 6. The Giuffre–Menegotto–Pinto model with isotropic strain hardening is used for framing material, in which a transition curve is defined to avoid the unsmooth response of bilinear kinematic hardening behavior in the yielding point, and consequently, the path-dependent nature of the material can be traced effectively. Furthermore, the Bauschinger effect is intrinsically defined in the material stress–strain curve so that the deterioration of strength in the element behavior is modeled. The yield strength of the steel is
Four earthquake records are used to compare the results of the frame with and without dampers. The earthquakes are scaled to produce a first mode spectral acceleration of 1 g. The description of each of the earthquake records is shown in Table 6. The comparative plots of displacement and acceleration responses at the top of the frame for Coalinga earthquake are shown in Figs. 24 and 25 respectively. By using the CFD with a slip load of 90 kN, maximum displacement of the roof is reduced by 44.5% and maximum acceleration of the roof is reduced by 48%. Fig. 26 shows the cumulative dissipation of friction energy in the CFDs. The peak responses of the frame for all earthquake records are shown in Table 7. 6.4. Incremental Dynamic Analysis (IDA) For more investigation, Incremental Dynamic Analysis (IDA) [18,19] is applied on the frame. IDA involves subjecting a structural model to one (or more) ground motion record(s), each scaled to multiple levels. The result is a curve that shows the Engineering Demand Parameter (EDP) plotted against the Intensity Measure (IM) used to control the increment of the ground motion. The IM of a scaled accelerogram is a non-negative scalar or a vector
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Table 7 Peak responses of the frame. Earthquake
Coalinga 1983 Northridge 1994 Loma Prieta 1989 Kocaeli, Turkey 1999
Maximum displacement
Maximum acceleration
Without damper (m)
With damper (m)
Reduction (%)
Without damper (m/s2 )
With damper (m/s2 )
Reduction (%)
0.138 0.1356 0.195 0.1373
0.0767 0.08937 0.156 0.1212
44.5 34 20 11.7
10.24 17.396 15.57 11.06
5.3 10.798 10.38 9.89
48 37.9 34 10
Fig. 27. IDA curve of the frame. Fig. 24. Displacement response at the top of the frame for Coalinga earthquake.
loading. In this study, EDP and IM have been selected to be the maximum displacement at the top of the frame and PGA (Peak Ground Acceleration), respectively. The IDA curve of the Coalinga earthquake is shown in Fig. 27. As shown in Fig. 27, in case of the frame without damper, the global collapse of the frame occurs at PGA = 0.8 g while in case of the frame with damper, the global collapse of the frame occurs at PGA = 1.4 g, which is 75% improvement. However, results may change to some degree from record to record. 7. Conclusion
Fig. 25. Acceleration response at the top of the frame for Coalinga earthquake.
An innovating type of friction damper which is called cylindrical friction damper (CFD) was introduced. Unlike other kinds of friction dampers, CFDs do not need mechanical means such as high-strength bolts to create friction between contact surfaces. This reduces construction costs and increases their reliability in comparison with other types of friction dampers. Experimental and numerical studies of CFD show that its performance is predictable and reliable while highly effective to reduce earthquake damages on structure. A three dimensional finite element model was also developed which shows that there is good agreement between the experimental results and those obtained from numerical analyses. Moreover, time history and IDA analyses are applied to a frame with CFD and the same frame without CFD, and the results are compared. It was shown that by using CFD, seismic performance is extremely improved. References
Fig. 26. Cumulative dissipation of friction energy in the CFDs (Coalinga earthquake).
that has been proposed to characterize the intensity of a ground motion. The EDP is a non-negative scalar that characterizes the response of the structural model due to prescribed seismic
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[13] Lee SH, Park JH, Lee SK, Min KW. Allocation and slip load of friction dampers for a seismically excited building structure based on storey shear force distribution. Eng Struct 2008;30:930–40. [14] Min Kyung-Won, Seong Ji-Young, Kim Jinkoo. Simple design procedure of a friction damper for reducing seismic responses of a single-story structure. Eng Struct 2010;32:3539–47. [15] Colajanni Piero, Papia Maurizio. Seismic response of braced frames with and without friction dampers. Eng Struct 1995;17:129–40. [16] Popov EgorP. Mechanics of material. 2nd ed. Prentice Hall; 1976. [17] ASCE/SEI 41-06 . Seismic rehabilitation of existing buildings. Reston (VA): American Society of Civil Engineers (ASCE); 2006. [18] Vamvatsikos D, Cornell CA. Seismic performance, capacity and reliability of structures as seen through incremental dynamic analysis. Report no. RMS-55. Stanford (CA): RMS Program, Stanford University; 2000. [19] Asgarian Behrouz, Yahyai Mahmood, Mirtaheri M, Samani Hamid Rahmani, Alanjari Pejman. Incremental dynamic analysis of high-rise towers. 2009. doi:10.1002/tal.518.
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Numerical and experimental study of hysteretic behavior of cylindrical friction dampers Masoud Mirtaheri ∗ , Amir Peyman Zandi, Sahand Sharifi Samadi, Hamid Rahmani Samani K.N. Toosi University of Technology, Department of Civil Engineering, Tehran, Iran
article
info
Article history: Received 6 December 2010 Received in revised form 26 July 2011 Accepted 28 July 2011 Available online 26 August 2011 Keywords: Friction damper Energy dissipation Hysteretic loading Passive control
abstract Frictional dampers utilize the mechanism of friction for absorbing and dissipating the energy imparted to the dynamic systems. Frictional dampers are widely used in mechanical systems in various industries in order to mitigate the impact and vibration effects. Frictional dampers are also utilized in structures as means of passive control to improve the seismic behavior of structures. In this investigation, an innovative type of frictional damper called cylindrical friction damper (CFD) is proposed. This damper consists of two main parts, the inner shaft and the outer cylinder. Dimensions and properties of the main parts are defined based on seismic demand of structures. These two parts are assembled such that one is shrink fitted inside the other. Upon application of proper axial loading to both ends of the CFD, the shaft will move inside the cylinder by overcoming the friction. This in turn leads to considerable dissipation of mechanical energy. In contrast to other frictional dampers, the CFDs do not use high-strength bolts to induce friction between contact surfaces. This reduces construction costs, simplifies design computations and increases reliability in comparison with other types of frictional dampers. The hysteretic behavior of CFD is studied by experimental and numerical methods. The results show that the proposed damper has great energy absorption by stable hysteretic loops, which significantly improves the performance of structures subjected to earthquake loads. Also, a close agreement between the experimental and numerical results is observed. © 2011 Elsevier Ltd. All rights reserved.
1. Introduction Many different types of energy dissipation devices have been developed and tested for seismic applications in recent years, and more are still being investigated. Frictional devices dissipate energy through friction caused by two solid bodies sliding relative to each other. Pall and Marsh [1] proposed frictional dampers installed at the crossing joint of the X-brace. Tension in one of the braces forces the joint to slip thus activating four links, which in turn force the joint in the other brace to slip. This device is usually called the Pall frictional damper (PFD). Wu et al. [2] introduced improved Pall frictional damper (IPFD), which replicates the mechanical properties of the PFD, but offers some advantages in terms of ease of manufacture and assembly. Sumitomo friction damper [3] utilizes a more complicated design. The pre-compressed internal spring exerts a force that is converted through the action of inner and outer wedges into a normal force on the friction pads. Fluor
∗ Corresponding address: K.N. Toosi University of Technology, Department of Civil Engineering, No. 1346, Valiasr St., Mirdamad intersection 19967, P.O. Box 15875-4416, Tehran, Iran. Tel.: +98 0912 1050129; fax: +98 21 8877 9476. E-mail addresses: [email protected] (M. Mirtaheri), [email protected] (A.P. Zandi), [email protected] (H.R. Samani). 0141-0296/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2011.07.029
Daniel Inc. has developed and tested another type of friction device which is called Energy Dissipating Restraint (EDR) [4]. The design of this friction damper is similar to Sumitomo friction damper since this device also includes an internal spring and wedges encased in a steel cylinder. The EDR utilizes steel and bronze friction wedges to convert the axial spring force into normal pressure on the cylinder. A full description of the EDR mechanical is given in [5]. Constantine et al. [6] proposed frictional dampers composed of a sliding steel shaft and two frictional pads clamped by high strength bolts. Li and Reinhorn [7] verified the seismic performance of a reinforced concrete building with frictional dampers through a combined experimental and analytical study. Grigorian et al. [8] studied the energy dissipation effect of a joint with slotted holes both analytically and experimentally. Mualla and Belev [9] proposed a friction damping device and carried out tests for assessing the friction pad material. Cho and Kwon [10] proposed a walltype friction damper in order to improve the seismic performance of the reinforced concrete structures. Numerical models of friction dampers for multi degree of freedom structures were proposed by Bhaskararao and Jangid [11]. The results were validated with those obtained from an analytical model. Park et al. [12] proposed a new equivalent linearization technique for a friction damper–brace system based on the probability distribution of the extreme displacement. Lee et al. [13] proposed a design methodology of friction
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Fig. 1. Main parts of the CFD: (a) solid shaft; (b) tubular cylinder; (c) manufactured shaft and cylinder.
Fig. 2. The CFD: (a) Longitudinal section of CFD; (b) Assembled CFD.
damper–brace systems, to determine the quantity and slip load of the frictional damper and the brace stiffness systematically for an elastic multistory building structure based on the story shear forces. Min et al. [14] proposed a design process to determine a desired control force of a friction damper to satisfy a given target performance of a structure subjected to an earthquake ground excitation. Colajanni and Papia [15] analyzed and compared the dynamic response of braced frames with and without friction dampers. Most of the frictional dampers are made of a set of steel plates, with a certain friction coefficient, that are forced by bolt pretention in order to induce the friction between them. Using pretensioned bolts to induce friction makes the behavior of frictional dampers unpredictable. The purpose of this study is to propose an innovative type of frictional dampers called Cylindrical Friction Damper (CFD), which does not need mechanical means for inducing contact pressure resulting in frictional damping. Both experimental and numerical models of the CFD are examined and effectiveness of the dampers in seismic protection is evaluated. 2. Components and mechanism of cylindrical friction damper CFD consists of two main parts, the shaft (Fig. 1(a)) and the cylinder (Fig. 1(b)). Suitable end-plate or eye bar connections are provided at two ends of the damper (Fig. 1(c)). A longitudinal section of the CFD is shown in Fig. 2(a). The inner diameter of the cylindrical element is slightly smaller than the diameter of the shaft at a predefined length L0 . When the cylindrical part is heated,
Fig. 3. Schematic load–deformation curve for CFD.
its diameter will increase due to thermal expansion and the shaft can be easily placed into the cylinder (Fig. 2(b)). Reaching thermal equilibrium, the design pressure will be developed between the contact surfaces (i.e. outer surface of the shaft and inner surface of the cylinder), which results in friction between these surfaces. If the damper’s axial force overcomes the static friction load, the shaft inside the cylinder will move, thereby resulting in considerable mechanical energy absorption. Since the main parts are in contact at a certain constant length (i.e. L0 ), the slippage load remains constant during the motion. A schematic load–deformation curve for the CFD is shown in Fig. 3.
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Fig. 4. Normal pressure developed by reaching thermal equilibrium between contact surfaces.
CFDs need not move during mild winds and earthquake events with high probability of occurrence. However, during a major earthquake, the shaft starts to move in the cylinder and prevents yielding of structural members.
Fig. 5. Connection of the CFD to a reaction block.
3. CFD design computations In the design of the frictional dampers, it is important to determine the slip load. The CFD can be simply set for different slip loads by selecting the appropriate geometric parameters. For simplicity, all parameters except L0 can be considered to be constant, and the slip load can be set by changing L0 . Fig. 4 shows the pressure between cylindrical contact surfaces reaching thermal equilibrium. The radial displacement at the inner face of a thick-walled cylinder under internal pressure is [16]
∆c =
P .ri
ro2 + ri2 ro2 − ri2
E
+ν
(1)
where P is the internal pressure, ri and ro are the inside and outside radii of the cylinder respectively, E is the modulus of elasticity and finally, ν is Poisson’s ratio. Note that Eq. (1) corresponds to a plane stress condition. The radial strain in the shaft and the corresponding radial displacement due to normal pressure are P
εs =
E
∆s =
(1 − ν)
P .ri
(2)
∆c + ∆s =
Step 4. Compute normal pressure, P, by Eq. (5). Step 5. Compute contact length, L0 , by means of Eq. (6).
δ
(3) 4.1. Test setup
(4)
2 where δ is the difference in the diameters of the shaft and the cylinder along L0 (Fig. 1(b)). Substituting Eqs. (1) and (3) into Eq. (4) yields E .δ ro2 − ri2 4ro2
ri
.
(5)
Equilibrium along the axial direction of damper requires L0 =
Fig. 7. Experimental setup.
4. Experimental study of hysteretic behavior of the CFD
(1 − ν).
E The compatibility of deformations requires
P =
Fig. 6. Schematic view of the test setup.
Fs P .π .D.µ
(6)
in which Fs is the slip load, µ is the friction coefficient, D is the diameter of the shaft and L0 is the contact length. Step by step procedure for designing the CFD can be summarized as follows. Step 1. Determine slip load and maximum displacement of dampers by structural analysis of the model including proposed dampers. Step 2. Select proper material for damper, specifying ν, µ and E. Step 3. Fix geometric dimensions, i.e., t , δ and D.
The axial force–displacement curve of the CFD can be determined by a test. Uniaxial tests are performed by means of a 300 kN hydraulic actuator which is attached to a reaction block. The actuator can apply reciprocal motion to the CFD with predetermined amplitudes. One side of the CFD is attached to the reaction block and the other side is attached to the actuator as shown in Fig. 5. Both reaction blocks are fixed to a strong strip by heavy bolts. Fig. 6 shows the test setup which consists of a hydraulic actuator, reaction blocks at two ends and a test specimen. To measure relative slip of the CFD, a Linear Variable Differential Transformer (LVDT) is installed on each of the specimens, as shown in Fig. 7. The distance between the reaction blocks is variable, and the CFD with various lengths can be tested. When properly connected and fixed, the internal parts of the CFD move relative to each other. Each test includes twenty full displacement cycles applied to the specimen. The frequency of loading and stroke of the CFD are determined for a particular application (e.g. story drift). 4.2. Specifications of manufacture of the CFD Two types of CFD with different slip loads are designed based on the step by step method presented in the previous section.
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Table 1 Specifications of studied CFDs. Name
Design slip load (kN)
D (mm)
t (mm)
δ (µm)
L0 (mm)
displacement (mm)
Energy dissipation per cycle (kJ)
Total length (mm)
Type A Type B
130 250
100 100
10 10
100 100
49.4 95
±50 ±50
26 50
300 400
Fig. 8. Experimental axial force–displacement curve of the CFD (Type A).
Fig. 9. Experimental axial force–displacement curve of the CFD (Type B).
All geometric parameters, except L0 , are the same for both types. Table 1 gives the specifications of these dampers. For each type, two specimens are produced. Shafts are made of CK45 steel (according to DIN steel grades) with chrome lining and cylinders are made of CK15 steel. The shaft needs no machining; only the cylinder is machined to exact dimensions. The coefficients of static and dynamic frictions (µs , µk ) are obtained based on several tests. The value of µs is 0.286 and the value of µk is 0.224. To improve the damper’s function, special techniques are utilized to coat contact surfaces in order to make µs , µk closer. 4.3. Test results 4.3.1. Slip load The axial force–displacement curve for Type A and Type B dampers are presented in Figs. 8 and 9 respectively. As seen in these figures, the CFD behavior can be described in two following stages.
Fig. 10. Slip load versus cycle number (Type A).
1. Non slip stage: there is no relative displacement between the CFD components and the CFD behaves as an elastic spring. 2. Slip stage: applied axial force overcomes the design slippage load and the shaft inside the cylinder will move. According to ASCE/SEI 41-06 [17], the slip load due to one cycle of each test for the specimen considered must not differ by more than ±15% from the average slip load as calculated from all cycles in that test. Tables 2 and 3 compare the slip load of each cycle with the average slip load for Type A and Type B, respectively. Neglecting the first cycle for the second specimen of Type A, the maximum difference is 10% in the case of Type A and 15% for Type B. Figs. 10 and 11 present slip load versus cycle number for Type A and Type B, respectively. As can be seen, slip load is increased over the cycles. This is because the roughness of contact surfaces increases, which subsequently results in the incensement of the slip load. 4.3.2. Hysteresis of CFD Hysteretic curves of the specimens are shown in Figs. 12–15. As one could expect, the CFD exhibits rigid plastic rectangular hysteresis loops. Furthermore, the CFD has almost the same performance in tension and compression. Dissipated energy of the CFD over a vibration cycle is expressed as
∫ Edi =
Fsi |y| dt
(7)
Fig. 11. Slip load versus cycle number (Type B).
in which Edi is the dissipated energy in the ith load cycle, Fsi is the slip load of the ith cycle and y is the displacement of the CFD. The above integral is equal to the net area of the region bounded by the load–displacement loop. Assuming the slip load to be constant over a cycle, Eq. (7) can be simplified as:
∫ Edi =
∫ Fsi |y| dt = Fsi
|y| dt = 4Fsi × ∆max .
(8)
According to ASCE/SEI 41-06, within each test, the dissipated energy of an energy dissipation device for any one cycle should not differ by more than plus or minus 15% from the average dissipated energy as calculated from all cycles in that test.
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Table 2 Slip load for each cycle of loading (Type A). Cycle no.
1st specimen
2nd specimen
Experimental slip load (kN)
Deviation from average (%)
Experimental slip load (kN)
Deviation from average (%)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
137.9 122.4 121.9 122.4 123.5 123.9 122.4 123 123.9 125.3 124 125.3 126.2 128.7 130.3 131.9 133.8 135.8 137.4 139.6
8.35 3.85 4.26 3.87 2.97 2.70 3.84 3.37 2.69 1.59 2.61 1.56 0.86 1.10 2.34 3.59 5.10 6.64 7.90 9.69
153.3 132.2 130 125.6 125.6 124.4 125.4 126 126.5 127 126.4 127.7 126.8 127.3 125.9 126 126.8 127.5 128 128.4
19.45 3.01 1.29 2.13 2.13 3.07 2.29 1.82 1.43 1.04 1.51 0.50 1.20 0.81 1.90 1.82 1.20 0.65 0.26 0.05
Average
127.9
128.34
Table 3 Slip load for each cycle of loading (Type B). Cycle no.
1st specimen
2nd specimen
Experimental slip load (kN)
Deviation from average (%)
Experimental slip load (kN)
Deviation from average (%)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
201 182.8 178.9 179 182.3 185.1 185.7 189.8 192.2 197.8 201.4 202.3 206.9 207 217.7 219 223.3 224.5 227.6 231.4
0.39 9.41 11.34 11.29 9.66 8.27 7.97 5.94 4.75 1.97 0.19 0.26 2.53 2.58 7.89 8.53 10.66 11.26 12.79 14.68
244 229.4 231.4 235.7 242.3 244 251.1 256.4 247.3 254.3 252.7 251.6 259 256 254 254 252.3 255.1 252.5 254
1.95 7.82 7.01 5.29 2.63 1.95 0.90 3.03 0.62 2.19 1.55 1.10 4.08 2.87 2.07 2.07 1.38 2.51 1.46 2.07
Average
201.78
Fig. 12. Experimental force–displacement curve for the first specimen of type A.
Tables 4 and 5 compare the dissipated energy of each cycle and the average dissipated energy for Type A and Type B, respectively. Due
248.855
Fig. 13. type A.
Experimental force–displacement curve for the second specimen of
to a manufacturing problem (specifically in the second specimen of Type A), the deviation from average in the first cycle of specimens
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M. Mirtaheri et al. / Engineering Structures 33 (2011) 3647–3656 Table 4 Dissipated energy for each cycle of loading (Type A). Cycle no.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Average
1st specimen
2nd specimen
Dissipated energy (kJ)
Deviation from average (%)
Dissipated energy (kJ)
Deviation from average (%)
25.341 24.227 24.196 24.359 24.643 24.753 24.516 24.648 24.868 24.89 24.888 25.156 25.334 25.835 26.153 26.473 26.857 27.251 27.574 28.029 25.5
0.62 4.99 5.11 4.47 3.36 2.93 3.86 3.34 2.48 2.39 2.40 1.35 0.65 1.31 2.56 3.82 5.32 6.87 8.13 9.92
31.027 26.251 23.892 25.573 24.108 23.693 22.786 22.553 23.738 23.552 23.118 22.875 24.637 23.571 22.135 20.821 23.185 22.157 23.153 22.517 23.767
30.55 10.45 0.53 7.60 1.43 0.31 4.13 5.11 0.12 0.91 2.73 3.75 3.66 0.83 6.87 12.40 2.45 6.77 2.58 5.26
Table 5 Dissipated energy for each cycle of loading (Type B). Cycle no.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Average
1st specimen
2nd specimen
Dissipated energy (kJ)
Deviation from average (%)
Dissipated energy (kJ)
Deviation from average (%)
35.162 34.345 33.153 33.983 34.263 35.409 35.709 35.213 36.541 37.167 38.251 38.614 39.325 39.738 40.436 41.068 41.689 42.178 43.221 43.565 37.952
7.39 9.54 12.68 10.49 9.76 6.74 5.95 7.25 3.76 2.11 0.75 1.70 3.58 4.66 6.50 8.17 9.80 11.09 13.84 14.74
43.211 45.434 43.525 44.271 46.313 45.591 47.721 48.151 47.623 47.656 48.211 49.13 49.825 48.188 48.776 49.027 48.201 47.998 51.46762 51.96248 47.614
9.25 4.58 8.59 7.02 2.73 4.25 0.22 1.13 0.02 0.09 1.25 3.18 4.64 1.21 2.44 2.97 1.23 0.81 8.09 9.13
Fig. 14. Experimental force–displacement curve for the first specimen of type B.
is greater than that of other cycles. Neglecting the first cycles, the maximum difference is 10% in the case of Type A and 15% in the case of Type B.
Fig. 15. type B.
Experimental force–displacement curve for the second specimen of
4.3.3. Performance of the CFD in the long run As CFD is designed for seismic applications, the working demand of this damper is certainly occasional and infrequent.
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Fig. 18. The contact pressure developed after thermal analysis for Type A (MPa). Fig. 16. Slip load versus cycle number (first specimen of Type A).
Fig. 19. The contact pressure developed after thermal analysis for Type B (MPa).
5.2. Analysis
Fig. 17. Finite element model of CFD.
However, in order to investigate the performance of the CFD in the long run, fifty full displacement cycles are applied to the first specimen of Type A. The results show that there is no noticeable sign of wear on the contact surfaces. Moreover, the temperature of the device after the last cycle is measured to be about 70 °C. Because of the massive nature of the device, this kind of heat is quickly dissipated. Furthermore, Fig. 16 shows that there is no sign of degradation of the slip load after fifty cycles. 5. Numerical analysis of hysteretic behavior of the CFD
As mentioned earlier, appropriate temperature difference between the shaft and the cylindrical element should be created in order to place the solid shaft into the cylinder. Hence, the first step of analysis consists of thermal loading. The second step of the analysis is cyclic loading which begins as the solid shaft is placed into the cylinder and contact pressure is developed. 5.3. Numerical results Figs. 18 and 19 show the contact pressure developed after thermal analysis, for Type A and Type B respectively. 5.4. Comparison between numerical and experimental results
The analytical computations to estimate the capacity of the CFD are based on some simplifying assumptions. For example, the normal pressure, P, is assumed to be uniformly distributed along the contact length. In order to assess the accuracy of the analytical results, numerical models are developed and the results from the two approaches are compared.
Figs. 20 and 21 show a comparison between experimental and numerical results of load–displacement curves. As can be seen, there is a good agreement between the numerical results and those obtained from experiments. In the case of Type A, the difference between numerical and experimental slip loads is about 3.2% for the first specimen and 6% for the second specimen. In the case of Type B, this difference is about 20% for the first specimen and 6% for the second specimen.
5.1. Finite element modeling
6. A numerical example
Two three-dimensional finite element models have been developed for Type A and Type B dampers, using the commercial finite element software package ANSYS. Taking advantage of symmetry, only 1/4 of the total damper is modeled. Moreover, the outer cylinder is only modeled at contact length. 20-node solid elements are used to model the solid shaft and the outer cylinder is modeled using eight-node shell elements with constant thickness. Surface to surface contact is utilized to simulate the friction. The finite element model of the damper is shown in Fig. 17.
6.1. Description of models To investigate the effectiveness of CFDs in a real building, two analytical models are made and studied comparatively. First, the two-dimensional model of Fig. 22 is modeled using OpenSees software. Beams and columns are modeled using force-based nonlinear fiber beam–column elements with five integration points along their length. The element cross-section is discretized into uni-axial fibers. Column bases have been fully fixed. Gravity
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Fig. 20. Comparison between numerical and experimental force–displacement curves of the CFD (Type A).
Fig. 23. Maximum displacement at the top of the frame versus slipload. Table 6 Earthquake records for nonlinear analysis. Earthquake Coalinga 1983 Northridge 1994 Loma Prieta 1989 Kocaeli, Turkey 1999
Fig. 21. Comparison between numerical and experimental force–displacement curves of the CFD (Type B).
Station and direction 0
Parkfield—Cholame 8W-0 LA HABRA—BRIARCLIFF-00 SF Intern. Airport-00 Ambarli-00
Magnitude
Scale
6.4 6.7 6.9 7.4
4.11 5.87 2.87 2
specified as 240 MPa. A 1% post-yield stiffness is used to account for the hardening of steel beyond yield strength. The periods of vibrations of the first two modes of the structure are 0.77 and 0.23 s, respectively. 6.2. Optimum slip load In order to find the optimum slip-load, various slip loads must be examined. As the first trial load, 80% of the buckling load of the brace member is selected as the CFD slip load. Subsequently, a parametric study is conducted and the slip load is bracketed until the minimum displacement of the top of the frame is reached. The result of parametric study for Coalinga earthquake is shown in Fig. 23. As it can be seem from the Fig. 23, the optimum slip load is 90 kN. 6.3. Nonlinear time history analysis
Fig. 22. Elevation of the frame.
loads are supposed to be similar to common residential buildings in the region. CFD dampers are added to the model subsequently. Nonlinear zero-length elements, with elastic–perfectly plastic behavior are used to model the CFD at the middle of bracing members. The framing members are designed according to AISC seismic provisions for seismic zone 2 with a response factor of 6. The Giuffre–Menegotto–Pinto model with isotropic strain hardening is used for framing material, in which a transition curve is defined to avoid the unsmooth response of bilinear kinematic hardening behavior in the yielding point, and consequently, the path-dependent nature of the material can be traced effectively. Furthermore, the Bauschinger effect is intrinsically defined in the material stress–strain curve so that the deterioration of strength in the element behavior is modeled. The yield strength of the steel is
Four earthquake records are used to compare the results of the frame with and without dampers. The earthquakes are scaled to produce a first mode spectral acceleration of 1 g. The description of each of the earthquake records is shown in Table 6. The comparative plots of displacement and acceleration responses at the top of the frame for Coalinga earthquake are shown in Figs. 24 and 25 respectively. By using the CFD with a slip load of 90 kN, maximum displacement of the roof is reduced by 44.5% and maximum acceleration of the roof is reduced by 48%. Fig. 26 shows the cumulative dissipation of friction energy in the CFDs. The peak responses of the frame for all earthquake records are shown in Table 7. 6.4. Incremental Dynamic Analysis (IDA) For more investigation, Incremental Dynamic Analysis (IDA) [18,19] is applied on the frame. IDA involves subjecting a structural model to one (or more) ground motion record(s), each scaled to multiple levels. The result is a curve that shows the Engineering Demand Parameter (EDP) plotted against the Intensity Measure (IM) used to control the increment of the ground motion. The IM of a scaled accelerogram is a non-negative scalar or a vector
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Table 7 Peak responses of the frame. Earthquake
Coalinga 1983 Northridge 1994 Loma Prieta 1989 Kocaeli, Turkey 1999
Maximum displacement
Maximum acceleration
Without damper (m)
With damper (m)
Reduction (%)
Without damper (m/s2 )
With damper (m/s2 )
Reduction (%)
0.138 0.1356 0.195 0.1373
0.0767 0.08937 0.156 0.1212
44.5 34 20 11.7
10.24 17.396 15.57 11.06
5.3 10.798 10.38 9.89
48 37.9 34 10
Fig. 27. IDA curve of the frame. Fig. 24. Displacement response at the top of the frame for Coalinga earthquake.
loading. In this study, EDP and IM have been selected to be the maximum displacement at the top of the frame and PGA (Peak Ground Acceleration), respectively. The IDA curve of the Coalinga earthquake is shown in Fig. 27. As shown in Fig. 27, in case of the frame without damper, the global collapse of the frame occurs at PGA = 0.8 g while in case of the frame with damper, the global collapse of the frame occurs at PGA = 1.4 g, which is 75% improvement. However, results may change to some degree from record to record. 7. Conclusion
Fig. 25. Acceleration response at the top of the frame for Coalinga earthquake.
An innovating type of friction damper which is called cylindrical friction damper (CFD) was introduced. Unlike other kinds of friction dampers, CFDs do not need mechanical means such as high-strength bolts to create friction between contact surfaces. This reduces construction costs and increases their reliability in comparison with other types of friction dampers. Experimental and numerical studies of CFD show that its performance is predictable and reliable while highly effective to reduce earthquake damages on structure. A three dimensional finite element model was also developed which shows that there is good agreement between the experimental results and those obtained from numerical analyses. Moreover, time history and IDA analyses are applied to a frame with CFD and the same frame without CFD, and the results are compared. It was shown that by using CFD, seismic performance is extremely improved. References
Fig. 26. Cumulative dissipation of friction energy in the CFDs (Coalinga earthquake).
that has been proposed to characterize the intensity of a ground motion. The EDP is a non-negative scalar that characterizes the response of the structural model due to prescribed seismic
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