13th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 2004 Paper No. 1986
PERFORMANCE DETERIORATION OF SLOTTED-BOLTED CONNECTION DUE TO BOLT IMPACT AND REMEDY BY RESTRAINERS Panitan LUKKUNAPRASIT1, Assawin WANITKORKUL2 and Andre FILIATRAULT3
SUMMARY The behaviour of slotted-bolted connections when the maximum slip travel exceed the available slot length is presented. The drastic degradation behaviour of slotted-bolted connections under bolt impact is demonstrated. Remedy by means of the concept of restrainers is proposed, which is also advantageous in suppressing the build-up of resonance motion by virtue of the change in system stiffness at different stages. Nonlinear dynamic analyses were performed on a prototype 6-storey steel building equipped with friction dampers with and without restrainers. Three historical earthquake records from California, i.e. the 1989 Loma Prieta, the 1966 Parkfield, and the 1940 El Centro records, were considered in the analyses. In the worst loading case, dampers with restrainers are superior to that without restrainers, resulting in reduction of the peak inter-storey drift by 16% and the peak slip travel by 15%. The shorter slip travel obviously provides extra safety to the system. Increasing the maximum restraining force is generally beneficial in reducing the peak inter-storey drift. However for steel bracings, the restraining force limit should be kept sufficiently below the buckling capacity to avoid buckling of the bracings. Furthermore, a higher restraining force would induce higher storey base shear. Hence, the adequacy of the foundation has to be properly addressed as well in retrofitting of buildings. INTRODUCTION The slotted-bolted connection (SBC) has been recognized as a low-cost passive friction-damping system for reduction of damages caused by strong motions, e.g. FitzGerald et al. [1], Grigorian et al. [2], Tremblay and Stiemer [3]. Most studies, except the one by Roik et al. [4], do not address the situation when the slip travel of the SBC reaches the provided slip length. However, Roik et al. [4] did not investigate the effect of stiffening due to the restraining action. Since earthquake characteristics are unpredictable, it cannot be 1
Professor, Dept. of Civil Engineering, Chulalongkorn University, Bangkok 10330, Thailand. Email:
[email protected] 2 Research Assistant, Dept. of Civil Engineering, Chulalongkorn University, Bangkok 10330, Thailand. Email:
[email protected] 3 Professor, Dept. of Civil, Structural, and Environmental Engineering, SUNY, Buffalo, NY 14260, USA. Email:
[email protected]
guaranteed that in the most severe case the bolts would slide freely in the “finite length” slot available. Furthermore, it is not practical, or even impossible in some cases, to provide long slots. It is thus significant to investigate the behavior of such a damping system in the event of bolt impact and the restraining effect thereafter. CONVENTIONAL SBC UNDER BOLT IMPACT Wanitkorkul [5] performed a series of displacement controlled, cyclic tests on slotted-bolted connections, with and without impact on high-strength bolts. The damper specimen consisted of three A36 steel plates, i.e. one central plate and two cover plates each with a thickness of 11 mm. Brass plates were inserted between the central plate and the cover plates to create steel-on-brass contacting surfaces. The damper was designed to have two slots symmetrically placed on the central plate. This aimed to minimize accidental eccentricity. To avoid shear failure in the bolts after the provided slot length was reached, the thickness of the central plate at the friction surface was reduced to 6 mm with a clean mill scale surface condition. All plates were clamped together using two 12-mm-diameter A325 high-strength bolts with “Belleville washers”. The total clamping force on each sliding surface was 108 kN (70% of bolt tensile strength). The test assembly was subjected to 30 displacement cycles without bolt impact, followed by 10 displacement cycles with impact on high-strength bolts, in general. Testing frequencies of 0.1, 0.5, and 1 Hz were used in the cyclic tests.
200 150
Force (kN)
100 50 0 -20
-15
-10
-5
-50
0
5
10
15
20
-100 -150 -200 Displacement (mm) Fig. 1 Force-displacement relationship of SBC: 30 cycles, 0.1 Hz, without bolt impact Figure1 shows the force-displacement hysteresis of a SBC specimen under the first thirty displacement cycles without bolt impact. Generally, the hysteresis under each testing frequency is similar, hence only the results from the testing frequency of 0.1 Hz are demonstrated. The resulting force-displacement relationships were nearly rectangular in shape, which was consistent with the results obtained from many past investigations. The initial friction forces were around 45 kN, and they became stable around 95 kN after approximately 20 displacement cycles. Despite the fluctuation of the friction forces, steel-on-brass friction type specimens were accepted because the variation of frictions was in the initial stage, therefore
it would not affect the behaviour of damper when the specified slip travel was reached upon bolt impact. The stiffness increased sharply as can be seen in Figure 2 which illustrates the portion of the hysteresis of a SBC specimen during bolt impact. From the figure, the first plateau indicates the level of friction, while the second one shows the yield strength of the connection. During cycling of bolt impact, degradation of
200 150
Force (kN)
100 50 0 -15
-10
-5
-50
0
5
10
15
-100 -150 -200 Displacement (mm) Fig. 2 Force-displacement relationship of SBC: 10 cycles, 0.1 Hz, with bolt impact
(a)
(b)
Fig. 3 SBC specimen after tests: (a) central plate and bolts; (b) cover plates and brass plates the friction force is evident. More than 50% of friction force was lost after only 4-mm of displacement was imposed beyond the provided slot length. Bearing caused permanent deformations in the clamping bolts,
with the consequence of the friction loss. Figure 3 shows each component of the specimen after test. Damage to the clamping bolts can be clearly seen in the figure. More experimental results can be found in the original document by Wanitkorkul [5]. THE FRICTION-GRIP CONNECTION WITH RESTRAINERS With unacceptable behaviour of SBC under bolt impact illustrated, it is obvious that remedy is needed to prevent bolt impact. The restraining concept proposed by Roik et al. [4] to prevent undesirable bolt impact is adopted in this study, with slight modification. The device with restrainers will slip at the predetermined slip load Fs. The restrainers will be activated when the slip travel is larger than the Fmax Kr
Fs
∆g
Fig. 4 Force-slip travel relationship of friction-grip connection with restrainers provided slip distance ∆g, which results in increasing of the resisting force of the device at a stiffness Kr. This restraining force is further limited to a threshold value Fmax which remains constant at the second yield plateau. Figure 4 shows the force-slip travel relationship of friction-grip connection with restrainers. In this study, the restraining stiffness Kr of the device on each floor is assigned a value equal to an axial stiffness of the corresponding bracing element. NONLINEAR DYNAMIC ANALYSES Building, retrofit scheme, and model assumptions We first take the case study of the steel structure considered by Filiatrault et al. [6]. The building is a 6storey steel structure, rectangular in plan, and is braced by two exterior moment-resisting frames. Gravity loads acting on the frame during the earthquake are assumed equal to 3.8 kPa from roof dead load, 4.5 kPa from floor dead load, 0.7 kPa from floor live load, and 1.7 kPa from weight of the exterior cladding. Steel grade A36 is used for all members. The building, designed for seismic zone 4 in the United States, would not survive strong earthquakes when weld fractures occur in the welded beam-to-column connections. For retrofit, chevron-brace members are introduced in the central bay of the two exterior moment-resisting frames as shown in Figure 5. The steel section HSS 300 mm x 300 mm x 15 mm is used for all chevronbrace elements. Slotted-bolted connections are incorporated at one end of all bracing members. Both conventional SBC and slotted-bolted connections with restrainers (SBC-R) are considered. The fundamental vibration period of the original building was 1.30 sec and was reduced to 0.67 sec after retrofitted with the proposed system. Because of symmetry, only one exterior moment-resisting frame was modeled as a two-dimensional structure. Floor slabs and architectural elements were excluded. The panel zones of the beam-column
joints were assumed to have no panel shear deformation and yielding during strong excitations. Large displacement effect was also considered in the analyses. P-∆ effect from interior columns is included by introducing a pin-ended gravity column into the building model, which represents all interior columns. Total gravity loads acting on the interior columns are applied to the gravity columns. Both the exterior frames and the gravity columns are constrained to undergo the same lateral displacement at each floor, which represents a rigid floor diaphragm assumption. Bilinear moment-curvature relation with a curvature-hardening ratio of 2% is assigned to all columns.
N
DAMPING
Fig. 5 Building model and retrofit scheme The flexural strength degradation model [6] shown in Figure 6 was introduced at both ends of all beams to account for the brittle behaviour of welded beam-to-column connections. It was assumed that the strength degradation was independent in positive and negative bending. Only fractures at the beam-to-column
% of Initial Strength
interfaces were considered. An elasto-plastic moment-curvature relation was specified for all beam elements to prevent an increase in the flexural strength after fractures occur. The connections were assumed to have no loss in shear capacity when weld fractures occur. More details on the building model can be found in the original paper.
100
35 1 4.3
8.5
10.5
Curvature Ductility Fig. 6 Flexural strength degradation model Parameters for slotted-bolted connection with restrainers (SBC-R) model For SBC, a slip load value (Fs1) of 1524-kN was assigned for the device on the first floor, which was equal to 40% of the buckling strength (Pb1) of the corresponding bracing element. In the case of SBC with restrainers, the maximum restraining force (Fmax) was limited to 60% of bracing buckling load to avoid damage to the bracing members, Based on the design procedure proposed by Filiatrault and Cherry [7], slip loads of the connections on the second to the sixth floor were assigned a value equal to 80% of slip load on the first floor. Similarly, limits on restraining forces on the other floors were also assigned to be 80% of the maximum restraining force of the device on the first floor. The restraining stiffness was set equal to the corresponding bracing stiffness on each floor. A limit on slip travel was selected based on the maximum slip required in the most severe case, which will be discussed later. Axial springs with an elasto-plastic axial force-displacement relationship were used for all bracing members. 0.60
Loma Prieta
0.30
Acceleration (g)
Acceleration (g)
0.60
0.00
-0.30
0.00
-0.30
-0.60
-0.60 0
10
20 30 Time (sec)
40
0
0.60
10
20 30 Time (sec)
40
1.8 Loma Prieta Parkfield El Centro
El Centro
0.30
Sa (g)
Acceleration (g)
Parkfield
0.30
0.00
-0.30 -0.60
1.2 0.6 0.0
0
10
20 30 Time (sec)
40
0
1
2 3 Period (sec)
4
5
Fig. 7 Accelerograms and pseudo-acceleration response spectra with 5% damping: Earthquake ground motions Three historical earthquake ground motions from California were considered in the nonlinear dynamic analyses, i.e. the 1989 Loma Prieta and the 1966 Parkfield earthquakes, which have the same peak ground
acceleration of 0.48g, and the 1940 El Centro record with PGA’s of 0.32g. Figure 7 depicts the accelerograms and the pseudo-acceleration response spectra with 5% damping associated with these earthquakes. NUMERICAL RESULTS This section presents results from nonlinear dynamic analyses of the case study building under all ground motions. Inter-storey drifts are selected as performance indices of the retrofitted building. Comparisons between hystereses of the SBC with and without restrainers are presented. The effects of limited slip travels and maximum restraining forces are also demonstrated.
6
6
5
5
4
4
Level
Floor
Unretrofitted building VS Braced building (without dampers) The unretrofitted building considering the weld fracture effect collapses under all earthquakes considered with the peak inter-storey drift greater than 5% which indicates that retrofit is required for this structure. Before consider the performance of the building with friction dampers, performance of the building with bracings only was investigated. Note that an elasto-plastic, axial force-displacement relationship was assumed for the bracing members, the buckling phenomenon was neglected. Figure 8 depicts the peak floor displacements and the peak inter-storey drifts of the building with bracings only. With the presence of bracing system, the braced building survives all earthquakes considered. However, for the case of nearfield ground motions, the compression forces of bracings reach the buckling strength of the member. Hence, utilization of the friction-grip connection would be beneficial to prevent buckling of the bracings.
3 2
Loma Prieta Parkfield El Centro
3 2
Loma Prieta Parkfield El Centro
1
1
0
0 0
50
100 Floor displacement (mm)
150
200
0.0
0.5
1.0
1.5
2.0
2.5
Inter-storey drift (%)
Fig. 8 Peak floor displacements and peak inter-storey drifts of building with bracings only Retrofitted building with conventional slotted-bolted connections (SBC) Figure 9 shows the peak floor displacements and the peak inter-storey drifts of the retrofitted building with the conventional SBC. The most severe scenario results from the Parkfield earthquake, which results in the peak inter-storey drift of about 1.2% on the ground floor and the maximum curvature ductility of 3.8 in the ground floor columns. Damage is concentrated only on the first two floors with no yielding taking place on other floors. The Loma Prieta earthquake having the second highest spectral value results in the maximum inter-storey drift of 0.8% and a peak curvature ductility of 2.7 in the ground floor columns. Less damage compared to Parkfield, yielding concentrates only in beams and columns on the first floor. The El Centro motion, it causes the least damage, which is consistent with its lowest spectral value compared with other near-field records. Only one column on the ground floor yields with the maximum curvature ductility of 1.3. Figure 10 illustrates the peak slip travels of the device obtained from analyses. The maximum slips of the devices on the first and second floors are 35 and 20 mm, respectively, which result from the case of Parkfield earthquake. These slip values are used for calculation of slip limits as discussed in the next section.
6
5
5
4
4
Level
Floor
6
3 2
3 2
Loma Prieta Parkfield El Centro
1
Loma Prieta Parkfield El Centro
1
0
0 0
50
100
150
200
0.0
Floor displacement (mm)
0.5
1.0
1.5
2.0
Inter-storey drift (%)
Fig. 9 Peak floor displacements and peak inter-storey drifts of building with SBC: Fs1/Pb1 = 0.40 40 35
1st Floor 2nd Floor
Slip travel (mm)
35 30 25
22 20
20 15
12
10
10
7
5 0 Loma Prieta
Parkfield
El Centro
Earthquake
Fig. 10 Maximum slip travel of SBC: Fs1/Pb1 = 0.40 Performance of slotted-bolted connection with restrainers (SBC-R) Half of the maximum slip travel resulted from the case of Parkfield earthquake was applied to the SBC-R model as the slip threshold for activating the restrainer in the SBC-R model. Hence, the slip travel of the SBC-R on the first floor was limited to 17.5 mm when restraining effect takes place. However, rather than using different slip limits on each floor, the slip limit assigned to all devices on the other floors was 10 mm which was half of the maximum slip occurred on the second floor. Note that, in analyzing a building with slip limit on SBC, only the cases of building subjected to the Loma Prieta and the Parkfield ground motions are needed because the maximum slips resulted from the other excitations are lower than the slip limits assigned to the device. Figure 11 presents the peak inter-storey drifts of the structure subjected to Loma Prieta and Parkfield earthquakes. For the case of Loma Prieta, the maximum slip travel is close to the limit value; hence, responses from the system without and with limited slip are similar. For Parkfield excitation, with limited slip, peak floor displacement is reduced by 11%. The inter-storey drifts on the first and the second floors are reduced by 9 and 16%, respectively, while those on the other floors increases by 6-33% because wedge actions stiffen the lower floors compared to other floors. Although the inter-storey drifts in those upper floors increase, the maximum value is still less than 0.7% which is acceptable for “immediate occupancy” performance level specified by the NEHRP seismic rehabilitation guidelines [8]. The maximum curvature ductility in the ground floor column is reduced to 3.5 which amounts to 8% reduction while there are no yielding of columns on the other floors.
6
6 No slip limit 50% limited slip
5
4
Level
4
Level
No slip limit 50% limited slip
5
3 2
3 2
1
1
Loma Prieta
0
Parkfield
0 0.0
0.5
1.0
1.5
2.0
0.0
0.5
Inter-storey drift (%)
1.0
1.5
2.0
Inter-storey drift (%)
Fig. 11 Peak inter-storey drifts of building equipped with SBC-R: Fs1/Pb1 = 0.40, Fmax/Pb1 = 0.60 It seems that the advantage of restrainers in terms of response reduction is not promising. However, it is worth noting that, without restrainers, bolt impact may occur should the intended slip travel be accidentally reduced by, for instance, error in workmanship. Significant degradation of the friction force of the device would result as mentioned earlier, which can result in much worse performance or even collapse of the structure. The advantage of the restraining action is evident from the damper force-slip travel plot shown in Figure 12. With the maximum normalized restraining force (Fmax/Pb1) of 0.60, the maximum slip travel is reduced by 15% from the case without restrainers. The shorter travel obviously provides extra safety against the undesirable bolt impact. Hence, utilization of restrainers in slotted-bolted connections is desirable and beneficial. 4000
4000 No slip limit 50% limited slip
2000
2000
1000
1000
0 -40
-30
-20
-10
-1000
0
10
20
30
-2000 -3000 -4000 Slip travel (mm)
No slip limit 50% limited slip
3000
40
Force (kN)
Force (kN)
3000
0 -40
-30
-20
-10
-1000
0
10
20
30
40
-2000
Loma Prieta
-3000
Parkfield
-4000 Slip travel (mm)
Fig. 12 Force-slip travel of SBC and SBC-R: Fs1/Pb1 = 0.40, Fmax/Pb1 = 0.60 Effect of slip load and maximum restraining force To investigate the effects of slip load level and maximum restraining force of SBC-R on the performance of the structure, additional parametric studies using the normalized slip load value (Fs1/Pb1) and the normalized restraining force (Fmax/Pb1) equal to 20% and 90%, respectively, were conducted. Impact stiffness and limit on slip travel were kept unchanged. Figure 13 shows the resulting peak inter-storey drifts for building with SBC (no restrainers). With a smaller slip load, the structure’s braces are disengaged sooner, resulting in the structure’s natural frequency shifting toward the low spectral value of the spectra, which causes reduction in responses compared with a slip load of 40% of bracing buckling strength. Figure 14 illustrates the variation of peak inter-storey drifts with different slip loads and maximum restraining forces for the case of the Parkfield excitation. Generally, increasing the maximum restraining force reduces the inter-storey drifts of the structure on the first two floors, while the responses on the other floors increase slightly. For Loma Prieta ground motion, responses from the case with slip limit are similar
to the case without slip limit because the maximum slip travel is close to the slip limit value (refer to Figure 10). On the other hand, the advantage of high restraining force is more pronounced in the case of the Parkfield earthquake. With the normalized restraining force increased from 60% to 90%, the peak inter-storey drifts on the first and second floor reduce by about 5-10% for the case of 40% normalized slip load and 4% for 20% normalized slip load. The peak inter-storey drifts on the other floors increase by 126%; however, the inter-storey drift values are still below the immediate occupancy limit of 0.7%. However, for the 20% normalized slip load, further increase of the normalized restraining force from 60% to 90% practically does not yield extra benefit. 6 Loma Prieta Parkfield El Centro
5
Level
4 3 2 1 0 0.0
0.5
1.0
1.5
2.0
Inter-storey drift (%)
Fig. 13 Peak inter-storey drifts of building equipped with SBC: Fs1/Pb1 = 0.20 6
6 Fs1/Pb1 = 0.2, No slip limit
5
Fs1/Pb1 = 0.2, Fmax/Pb1 = 0.9
Fs1/Pb1 = 0.4, Fmax/Pb1 = 0.6 Fs1/Pb1 = 0.4, Fmax/Pb1 = 0.9
4
Level
4
Level
Fs1/Pb1 = 0.4, No slip limit 5
Fs1/Pb1 = 0.2, Fmax/Pb1 = 0.6
3
3
2
2
1
1
0
0 0.0
0.5
1.0 Inter-storey drift (%)
1.5
2.0
0.0
0.5
1.0
1.5
2.0
Inter-storey drift (%)
Fig. 14 Peak inter-storey drifts: Parkfield earthquake Figure 15 depicts the force-slip travel relationships of SBC-R on the ground floor with different levels of slip loads and restraining force limits for the case of Parkfield record. Figure 16 illustrates the peak slip travel of SBC and SBC-R in the ground floor. It is clearly seen that larger force limit also helps in reduction of peak slip travel of the device. With the normalized restraining force increased from 60% to 90%, the peak slip travel of the device reduces by 17% and 20% for the case of 20% and 40% normalized slip loads, respectively. Hence, higher force limit is beneficial in providing extra safety to the system. However, the maximum restraining force of 100% of buckling capacity must be avoided to protect the bracings from buckling which can lead to adverse effects.
4000
4000
Fs1/Pb1 = 0.4
3000
2000
1000
1000
0 -40
-30
-20
-10
3000
2000
Force (kN)
Force (kN)
Fs1/Pb1 = 0.2
-1000
0
10
20
30
40
0 -40
-30
-20
-2000
-10
-1000
0
10
20
30
40
-2000 Fmax/Pb1 = 0.6 Fmax/Pb1 = 0.9
-3000
Fmax/Pb1 = 0.6 Fmax/Pb1 = 0.9
-3000
-4000
-4000
Slip travel (mm)
Slip travel (mm)
Fig. 15 Force-slip travel of SBC-R: Parkfield earthquake No slip limit
Fmax/Pb = 0.6
Fmax/Pb = 0.9
40 35
Slip travel (mm)
35
31
30
30 26
25
24
22
20 15 10 5 0 Parkfield (Fs1/Pb1 = 0.2)
Parkfield (Fs1/Pb1 = 0.4) Earthquake
Fig. 16 Peak slip travel of SBC and SBC-R: Parkfield earthquake Although the benefits of SBC-R are evident, the device also induces larger base shear to the system. Figure 17 shows the peak base shear with different slip loads and restraining force limits. With restrainers, the total base shear of the retrofitted structure increases, which directly affects the foundation system. The magnitude of the additional base shear induced by SBC-R depends on the level of slip load and restraining-force limit, and the earthquake considered. For the case of the Parkfield earthquake with a 40% 8000
8000 Fs1/Pb1 = 0.2, No slip limit
Fs1/Pb1 = 0.2, Fmax/Pb1 = 0.6
Fs1/Pb1 = 0.4, No slip limit
157
6000
4000
141% 103% 100%
Fs1/Pb1 = 0.4, Fmax/Pb1 = 0.6
Fs1/Pb1 = 0.4, Fmax/Pb1 = 0.9
Total base shear (kN)
Total base shear (kN)
Fs1/Pb1 = 0.2, Fmax/Pb1 = 0.9
100%
2000
0
6000
115% 100%
139%
115% 100%
4000
2000
0 Loma Prieta
Parkfield Earthquake
El Centro
Loma Prieta
Parkfield
El Centro
Earthquake
Fig. 17 Total base shear of retrofitted building normalized slip load, the total base shear increases by 15% and 39% with the normalized force limit of 60% and 90%, respectively, while the corresponding increase for the case of Loma Prieta excitation is
about 15% only. Similarly, for 20% normalized slip load, the total base shear increases by 41% and 57% for the case of Parkfield earthquake with 60% and 90% normalized restraining force, respectively. This effect is of importance when retrofitting existing structures with a scheme that induces additional base shear to the existing foundations. It should be noted that the selected parameters, e.g. slip load, maximum restraining force, etc., are for demonstration purposes. To determine the optimum values, more parametric studies are required. This is out of scope of this study. CONCLUSIONS This study focused on the behaviour of the slotted-bolted connections (SBC) when the slip travel exceeded the provided slot length. Nonlinear dynamic analyses on a prototype building equipped with SBC and SBC-R were performed to evaluate the performance of the SBC-R as a seismic protection device. The following conclusions can be drawn from this study: 1. Bolt impact causes severe damage to the clamping bolts which significantly deteriorates the friction force of the device. Loss of friction can be more than 60%. Therefore, accidental impact of bolts in an unforeseen event can lead to disastrous result. 2. In the worst loading case, the SBC-R is superior to the conventional SBC, resulting in reduction of the peak inter-storey drift by 16% and the peak slip travel by 15%. This reduction of the peak slip travel (about 5 mm) obviously provides extra safety to the damper against bolt impact. 3. The peak inter-storey drift and the peak slip travel of the device decrease with increasing in the restraining force limit. However, the extra gain has to be balanced with the potential of buckling at the high restraining force. 4. Higher restraining force induces higher base shear; hence the adequacy of the foundations has to be properly addressed as well in retrofitting of buildings. 5. More parametric studies are required to determine the optimum parameters of friction-grip connection with restrainers. ACKNOWLEDGMENTS The writers are grateful to the Thailand Research Fund (TRF) for the support for this project. REFERENCES 1. FitzGerald, TF, Anagnos, T, Goodson, M, Zsutty, T “Slotted bolted connections in aseismic design for concentrically braced connections.” Earthquake Spectra 1989; 5(2): 383-391. 2. Grigorian, CE, Yang, TS, Popov, EP “Slotted bolted connection energy dissipators.” Earthquake Spectra 1993; 9(3): 491-504. 3. Tremblay, R, Stiemer, SF “Energy dissipation through friction bolted connections in concentrically braced steel frames.” ATC17-1, Proceedings of Seminar on Seismic Isolation, Passive Energy Dissipation, and Active Control, Vol. 2, San Francisco, CA. Applied Technology Council, 1993: 557568. 4. Roik, K, Dorka, U, Dechent, P “Vibration control of structures under earthquake loading by threestage friction-grip elements.” Earthquake. Engineering and Structural Dynamics 1988; 16: 501-521. 5. Wanitkorkul, A “Seismic response of braced frames with slotted-bolted friction dampers considering limited slip.” Doctoral Dissertation, Department of Civil Engineering, Chulalongkorn University, Bangkok, Thailand, 2003.
6. Filiatrault, A, Tremblay, R, Wanitkorkul, A “Performance evaluation of passive damping systems for the seismic retrofit of steel moment resisting frames subjected to near field ground motions.” Earthquake Spectra 2001; 17(3): 427-456. 7. Filiatrault, A, Cherry, S “Seismic design spectra for friction-damped structures.” ASCE, Journal of Structural Engineering 1990; 116(5): 1334-1355. 8. Applied Technology Council (ATC) “NEHRP guidelines for the seismic rehabilitation of buildings.” Federal Emergency Management Agency (FEMA 354), 2000.
