Retrofitting Methods for Spatially Expanding Old Office Buildings · Visco-elastic materialseas ily...

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Retrofitting Methods for Spatially Expanding Old Office Buildings Sadatoshi Ohno, Ph.D. 1 , Masashi Yamamoto DrEng. 1 , Yoshihiko Ohta 1 , Kiyoaki Hirakawa 2 , Haruhiko Okamoto DrEng. 1 , Hideto Tanaka DrEng. 2 , Yuuichi Iwai 2 1 Research & Development Institute, Takenaka Corporation, 1-5-1 Otsuka, Inzai, Chiba, 270-1395, Japan, [email protected] , [email protected] , [email protected] , [email protected] . 2 Design Division, Osaka Head Office, Takenaka Corporation, 4-1-13, Honmachi, Chuo-ku, Osaka, 541-0053, Japan, [email protected] , [email protected] , [email protected] Keywords: retrofit, seismic isolation, visco-elastic damper, spatially expanding, removing columns Summary This paper proposes a new approach to expanding old buildings. The main concepts are 1) obstructing structural members are removed after reinforcing the other members, and 2) the building is made earthquake resistant by installing a seismic isolation system in the middle story. This paper describes three key technologies for spatially expanding old buildings. The paper also describes experiments that confirm the validity of the technological concepts. The first technology is the displacement controlling visco-elastic damper. These dampers can suppress displacement to within 20 centimeters in the isolated layer, making them applicable to buildings in densely built-up urban areas. By incorporating seismic isolation systems and dampers inside the column heads, more interior space is opened up for other uses. Each damper consists of a viscous-elastic material that behaves stably under different temperatures. The second technology raises the ceiling by transforming a frame structure into a flat slab structure. This is accomplished by increasing the slab depth and adding column capitals. The main technical problem of this transformation method is that it transfers stress to the column-slab connection. The performance of the transformed column head has been confirmed through experiments. The connection is strong enough to meet design specifications for seismic deformation. The third technology removes the intermediate columns. The beams are strengthened with outer cables and a seismic isolation system is installed to enhance the building’s earthquake resistance. In order to confirm structural performance after an intermediate column is removed, loads were applied to two test specimens. The results indicate that outer-cable reinforced beams can easily handle design loads even after a column is removed. 1. Introduction Office buildings inevitably become functionally obsolete over time, which depreciates their value in the leasing business. Thus, most office buildings are reconstructed for reasons of economic efficiency rather than for environmental or lifecycle management concerns. In Japan, the building standard act was revised in 1971 and again in1982 in order to improve the seismic resistance of buildings. Although seismic retrofitting has been strongly recommended for buildings built before 1982, over 40% of old office buildings don’t satisfy current seismic codes. Current seismic retrofit methods, such as increasing the number of walls or braces, tend to reduce the interior space, making it difficult for many building owners to justify seismic retrofits. The authors have investigated new approaches to spatially expanding old buildings and simultaneously enhancing their seismic resistance. This paper describes three technologies that can be used to spatially expand old buildings: 1) “Distortion Control Dampers,” which are used to improve the seismic isolation of old buildings in densely built up urban areas; 2) structure transformation technology that transforms frame structures into flat slab structures in order to increase the ceiling height; and 3) column removal technology to expand interior spaces. The 2005 World Sustainable Building Conference, Tokyo, 27-29 September 2005 (SB05Tokyo) - 2683 - 09-024

Transcript of Retrofitting Methods for Spatially Expanding Old Office Buildings · Visco-elastic materialseas ily...

Page 1: Retrofitting Methods for Spatially Expanding Old Office Buildings · Visco-elastic materialseas ily assume any shape and have clearcost advantages. Moreover theyhave a smooth hysteresis

Retrofitting Methods for Spatially Expanding Old Office Buildings

Sadatoshi Ohno, Ph.D.1, Masashi Yamamoto DrEng.1, Yoshihiko Ohta1, Kiyoaki Hirakawa2, Haruhiko Okamoto DrEng.1, Hideto Tanaka DrEng.2, Yuuichi Iwai2

1 Research & Development Institute, Takenaka Corporation, 1-5-1 Otsuka, Inzai, Chiba, 270-1395, Japan,

[email protected], [email protected], [email protected], [email protected] .

2 Design Division, Osaka Head Office, Takenaka Corporation, 4-1-13, Honmachi, Chuo-ku, Osaka, 541-0053, Japan, [email protected], [email protected], [email protected]

Keywords: retrofit, seismic isolation, visco-elastic damper, spatially expanding, removing columns

Summary This paper proposes a new approach to expanding old buildings. The main concepts are 1) obstructing structural members are removed after reinforcing the other members, and 2) the building is made earthquake resistant by installing a seismic isolation system in the middle story. This paper describes three key technologies for spatially expanding old buildings. The paper also describes experiments that confirm the validity of the technological concepts. The first technology is the displacement controlling visco-elastic damper. These dampers can suppress displacement to within 20 centimeters in the isolated layer, making them applicable to buildings in densely built-up urban areas. By incorporating seismic isolation systems and dampers inside the column heads, more interior space is opened up for other uses. Each damper consists of a viscous-elastic material that behaves stably under different temperatures.

The second technology raises the ceiling by transforming a frame structure into a flat slab structure. This is accomplished by increasing the slab depth and adding column capitals. The main technical problem of this transformation method is that it transfers stress to the column-slab connection. The performance of the transformed column head has been confirmed through experiments. The connection is strong enough to meet design specifications for seismic deformation.

The third technology removes the intermediate columns. The beams are strengthened with outer cables and a seismic isolation system is installed to enhance the building’s earthquake resistance. In order to confirm structural performance after an intermediate column is removed, loads were applied to two test specimens. The results indicate that outer-cable reinforced beams can easily handle design loads even after a column is removed.

1. Introduction Office buildings inevitably become functionally obsolete over time, which depreciates their value in the leasing business. Thus, most office buildings are reconstructed for reasons of economic efficiency rather than for environmental or lifecycle management concerns. In Japan, the building standard act was revised in 1971 and again in1982 in order to improve the seismic resistance of buildings. Although seismic retrofitting has been strongly recommended for buildings built before 1982, over 40% of old office buildings don’t satisfy current seismic codes. Current seismic retrofit methods, such as increasing the number of walls or braces, tend to reduce the interior space, making it difficult for many building owners to justify seismic retrofits. The authors have investigated new approaches to spatially expanding old buildings and simultaneously enhancing their seismic resistance. This paper describes three technologies that can be used to spatially expand old buildings: 1) “Distortion Control Dampers,” which are used to improve the seismic isolation of old buildings in densely built up urban areas; 2) structure transformation technology that transforms frame structures into flat slab structures in order to increase the ceiling height; and 3) column removal technology to expand interior spaces.

The 2005 World Sustainable Building Conference,Tokyo, 27-29 September 2005 (SB05Tokyo)

- 2683 -

09-024

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2. Concept for spatially expanding office buildings

Structural changes to expand a building’s space generally reduce the seismic resistance of the buildings because members are removed. Thus, the seismic resistance lost by the removal of members must be replaced by adding other types of members.

The transformed structures of retrofitted old buildings must satisfy current Japanese codes for seismic safety. This is not easy to do in old buildings with reduced seismic resistance. Therefore, the authors propose installing a seismic isolation system in the middle story of these buildings, (normally on the first floor or the lower ground floor), as shown in Figure 1. Since the input force acting on the above stories is drastically reduced by the seismic isolation system, it is easy to implement various structural changes to expand a building’s interior space. During actual design, a non-linear time history analysis of the structural changes is performed, and the modified members are adjusted according to the various limitations of the design.

2.1 Dampers provide seismic isolation for buildings in urban areas

Buildings built before 1982, which are often the targets of spatial enhancements, are commonly located in densely built up urban areas. However, the worry is that, because there is no space between the buildings in these areas, they may strike neighboring buildings if seismic isolation systems are installed. Even in such cases, seismic isolation can be achieved by controlling the displacement of the isolated layer with a “displacement controlled seismic isolation system.“ This chapter introduces the visco-elastic damper, which makes possible this “displacement controlled seismic isolation system.“

2.2 Visco-elastic damper

Visco-elastic materials easily assume any shape and have clear cost advantages. Moreover they have a smooth hysteresis loop and good vibration properties, such as providing a damping effect even under small amplitudes of vibration. However, the problem is that these properties tend to change as their temperature rises due to the internal heat generated while damping vibrations. To date, a few trials have been conducted with the aim of developing materials that are more stable at varying temperatures(5) or controlling the surrounding temperature of the devices(6), but these materials are not yet practical.

The authors have developed a practical visco-elastic damper with less than half the temperature dependence of other materials. Consisting of visco-elastic materials sandwiched between two steel plates, the damper resists shear deformation. The damper’s shear face is positioned laterally, making it effective in two directions. Detailed sizes and an example of a setup are shown in Figure 2. For a designed ultimate displacement of 200 mm, the visco-elastic materials are 66 mm thick (33 mm x 2 layers). In the case shown in Figure 2(a), the dampers can compactly surround the isolation system (Figure 3). The properties of the damper were evaluated during a test using a full-scale test specimen. Figure 4 shows the results of the test.

Spatially expanding and increasing seismic resistance

Lower ground floor

2nd floor

1st floor

Seismic isolation

Spatially expanding and increasing seismic resistance

Lower ground floor

2nd floor

1st floor

Seismic isolation Figure 1 Seismic Isolation in the middle story

Figure 2 Set-up image of the dampers Figure 3 Set-up at the column periphery

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2.3 Design confirmation

The analytical model of the damper was a normal tri-linear model (Figure 4). The initial stiffness was 490kN/cm, and the strength at the first and the second folding points were 49kN and 98kN, respectively. The ratios of stiffness to the initial stiffness at the second and third folding points were 0.025 and 0.012, respectively. In this paper, the analytical model was a building consisting of 10 stories, each 1000 tons in weight. A modified degrading tri-linear model based on the behavior of an actual RC building was used to model the hysteresis characteristics (see Figure 5 for the characteristics of each story.) For the initial stiffness, the first natural period was 0.8 seconds. This period received 2% damping, which was proportional to the stiffness.

The design was evaluated as a case of seismic isolation using only rubber bearings with lead plugs on which the acting pressure was 10MPa. The analytical model was a normal bilinear model, and the following were assumed. Initial stiffness: 2156kN/cm; yield load: 4900kN; stiffness ratio at the second folding point :0.153; and no damper at the isolated layer. In the analytical model, the number of dampers was taken into account as a parameter. Figure 5 shows the results of the seismic response analysis when the artificial seismic wave (level 2) proposed by the Building Center of Japan was adopted as the input data. Figure 5 lists the ratios of response and displacement with and without isolation. These are applied as a parameter of the number of dampers. The results show that increasing the number of dampers decreases the displacement at the isolation layer and increases both the maximum relative story displacement and the acceleration at the top of the building. When 80 dampers are installed, the displacement at the isolation layer is within 20 cm, which is corresponding to 56% of the displacement when no dampers are installed. Figure 6 shows the response values of each story plotted on a graph of the shear force, and the relative story displacement relationship.

(a) short span direction (b) long span direction Figure 4 Load-displacement relationship of the visco-elastic damper in the full-scale tests

Figure 5 Response ratio with the number of dampers Figure 6 Response values at the different story

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Although the relative story displacement doubles for each story when 80 dampers are installed, the maximum displacement is within about 3x10-3. This implies that displacement control seismic isolation using dampers can be installed so long as structural safety is ensured by properly determining the safe maximum relative story displacement and the maximum allowable displacement of the dampers.

3. Structural conversion to raise the ceiling height

Various factors such as the beam depth or separate ducts for air conditioning and electrical systems make it difficult to raise the ceiling height. Normally, ceilings can be raised a few centimeters without changing the structure or remodeling the members. Although a different approach can also be applied, this paper investigated the transformation of a frame structure into a flat slab structure. As shown in Figure 7, the slabs are made thicker by casting concrete. Column capitals are then installed to strengthen the slab-column connections. Finally, the beams are removed.

For this structural change, it is important to ensure that stress is transferred between the column and the slab, since the arrangement of the reinforcement around the slab-column connection on the newly constructed flat slab structure is inevitably altered. This chapter reports on the results of experiments using a structural model to confirm the stress transfer capacity of the connection.

3.1 Experiment

The he test was designed to evaluate the different stress transfer mechanisms at the connection between the slab and the column. Specimen No. 1’s stress transfer mechanism is shear cotter, which is created by removing the cover concrete from the column. Specimen No. 2’s stress transfer mechanism is the transfer of frictional stress from the pre-stressed steel frame cotter to the column. The test specimens are one-third scale models consisting of only the capital head and column. Therefore, the slab depth of the specimen is the same at any location. The reinforcement was arranged by estimating the pre-dominant flexural failure. Figure 8 shows the test specimens. Figure 9 describes the stress transfer connection in the specimens. The properties of the materials are shown in Table 1.

The specimens were manufactured by initially casting concrete to the half-depth level of the slab and the column. The surface of the slab was roughened with a wire brush, reinforcements were placed, and concrete was cast on the pre-made slab. In both test specimens,

Columncapital

Newlythickened slab

Old slab

New ceiling

Air conditioningequipment

Raising ceiling height

Old ceilingRemovingebeam

Columncapital

Newlythickened slab

Old slab

New ceiling

Air conditioningequipment

Raising ceiling height

Old ceilingRemovingebeam

Figure 7 Conversion from frame to flat slab structure for raising ceiling height

Figure 8 Test specimen

a) shear cotter after b) steel frame attached removing cover concrete via prestressing

Figure 9 Stress transfer connection between column and slab-capital

Table 1. Material properties Materials Location Yong’s modulus Comp. Strength x104N/mm2 N/mm2 Concrete column & 2.69 23.4 beam new slab 3.05 32.1 Steel Location Yong’s Yield Tensile Elong- modulus strength strength ation type x105N/mm2 N/mm2 N/mm2 (%) φ3.2 old slab 2.03 621 678 5.7 D6 new slab 1.73 328 481 19.5 φ9.2 PC rods 2.06 1122 1345 7.8

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the newly placed reinforcements were cut at the surface end of the column but were not anchored in the column. However, the ends of the reinforcements in specimen No.2 were welded to the steel frame, which was attached to the column via pre-stressing. The average pre-stressing force of the steel frame was 3.1N/mm2.

Loading tests were carried out on the two test specimens using the set-up shown in Figure 10, where a lateral load is repeatedly applied to the top of the column under a settled vertical load corresponding to sustained loading.

3.2 Experimental results and discussion

The relationship between the shear force of the column and the relative story displacement is shown in Figure 11. The cracking pattern of the slab in the ultimate condition is illustrated in Figure 12. In test specimen No. 1, flexural cracking was observed on the top surface of the slab at the vertical load corresponding to the permanent load. At the bottom surface (newly added side) of the slab, flexural cracks started to occur at a story deformation angle of 1.3x10-3rad. As the story deformation angle increased, the cracks radiated outwards at the top surface and perpendicular to the loading direction at the bottom face. Loading reached the maximum value at a story deformation angle of 15 x10-3rad., then the load gradually decreased with compressive failure of the slab concrete in the vicinity of the column. The lateral loading capacity decreased drastically during repeating loading at a story deformation angle of 50x10-3rad. After the loading test, cotter failure was confirmed by observing the inside of the slab.

In test specimen No.2, flexural cracking was observed on the top surface at a story deformation angle of 0.5x10-3rad., and on the bottom face at a story deformation angle of 2.0x10-3rad. The cracks spread in the same manner as in specimen No.1 when the story deformation angle was increased. The maximum load occurred at a story deformation angle of 15 x10-3rad. Subsequently, the load gradually decreased with compressive failure of the slab concrete in the vicinity of the column. The lateral loading capacity decreased drastically at a story deformation angle of 30x10-3rad., with the form of the failure zone similar to that produced by punching failure. After the loading test, the vertical slip between the steel plate and the column surface was confirmed by observing the inside of the slab.

In the design of flat slab structures, the limiting values for the story deformation angle under seismic conditions are considered to be 2.5x10-3rad. in rare earthquakes (once in 50-year return period) and 5.0x10-3rad. in very rare earthquakes (less than once in 100-year return period). Since neither test specimen showed a drastic decrease in load until 10.0x10-3rad. under repeated loading, this test indicates that a frame structure can be transformed into a flat slab structure by simultaneously installing seismic isolation systems.

4. Removal of intermediate columns One approach to spatially expanding a building is to remove the obstructing columns, but this has some limitations. Only the column between two columns can be removed, and only those in certain locations can be removed. The procedure for removing columns in SRC buildings is described in Figure 13. In order to remove the intermediate columns, the beams in the span lengthened by the removal of the columns must be

Figure 10 Loading test set-up

Hydraulic jack lateral direction

Hydraulic jack Vertical direction

Load cell

Test specimen Slab supports

Figure 11 Relationship between shear force and story displacement angle

Loading direction

(a) top surface of slab (b) bottom face of slab Figure 12 Cracking at the final stage (No.1)

Maximum load:82.8kN Maximum load: 90.11kN

Max. load:83.2kN

Max. load:86.9kN

No.1 No.2

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reinforced to support the vertical load. On the other hand, after the columns are removed, the building should also be able to withstand earthquakes. This can be achieved by installing a seismic isolation system in the middle story of the building. This chapter introduces the results of experiments on a structural model with removed columns and the beam of the lengthened span reinforced by pre-stressed outer cables.

4.1 Experiment

Figure 14 shows the test specimen, which was a 1/2-scale model of a structure with the intermediate column removed. The beam was equal in length to two spans and was reinforced on both sides with outer cables. The cable anchorages were pre-cast concrete blocks measuring 300 x 450 x 180 mm (BxWxH). They were attached to both ends of the beam with stressed PC strands. In order to simulate actual conditions, the cables were stressed while subjected to a vertical floor load of 35.3kN. During the stressing, supports were placed under the cable anchorages in the vertical direction in order to avoid flexural stress at the beam ends and extra compressive stress in the columns. The supports were removed after the pre-stressing work was completed.

As shown in Table 2 of the test program, the OCL test specimen was used to evaluate the permanent load capacity under vertical loading, while the OCE test specimen was used to evaluate seismic resistance under repeated lateral loading. In the case of the OCL specimen, vertical loading was applied at four loading points, and the shear span and the flexural span are same 1950mm. The loading set-up for the OCE specimen is shown in Figure 15. Lateral loading was applied to the OCE specimen under a sustained vertical load of 52.9kN at the vertical loading points. Table 3 shows the properties of materials used in the tests. Figure 16 shows the loading program.

outer cablescable anchorage

1) Support the beam center2) Cut the column top3) Cut the beam ends 4) Place the outer cables5) Stressing the cables6) Cast concrete at the beam ends7) Remove column and support

supports

removing column

outer cablescable anchorage

1) Support the beam center2) Cut the column top3) Cut the beam ends 4) Place the outer cables5) Stressing the cables6) Cast concrete at the beam ends7) Remove column and support

supports

removing column

Figure 13 Removing procedure of the column

Figure 14 Details of the test specimen

Figure 15 Loading set-up (for OCE specimen)

Table 2. Test program Specimens Loading Evaluation OCL vertically one direction permanent load capacity OCE laterally cyclic loading seismic load capacity

Table 3. Material properties Materials Location Yong’s modulus Comp. Strength x104N/mm2 N/mm2 Concrete column & 2.39 17.0 beam anchor block 3.23 35.9 Steel Location Yield Tensile strength strength type N/mm2 N/mm2 D10 column & beam 369 621 D10 anchor block 375 567 φ6, φ9 stirrup, beam 300 491 φ12.7 PC strand 1795 (0.2%) 1870

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4.2 Results of experiments and discussion

The load-deformation relationships and the changes in cable stresses are shown in Figures 17(a) and 17(b), respectively. The test results are shown in Table 4. To evaluate the experimental results, the ultimate moment at the beam ends of the specimen was calculated using the equations in AIJ Standards for Structural Calculation of Steel Reinforced Concrete Structures, 1991.

The ultimate moment at the center of the beam was calculated from the following equation.

Mu= (dp – k2 xn )Ap σpu + ( dr - k2 xn ) Ar σru + ( ds – k2 xn) As σsu (eq-1)

where, Ap: cross sectional area of PC cables, Ar: cross sectional area of steel bar As: cross sectional area of steel frame in tension, b: beam width, D: beam depth, dp,dr: depth from of PC cables to compression fiber of beam, Fc: nominal compressive strength xn: length from compression fiber to neutral axis of beam, calculated as xn={qsp / (k1k3)} D qsp=(Apσpu+Arσru+ Asσsu) / (b D Fc) σpu: stress in PC cables at the ultimate state is calculated as 0.75σpe+0.25σpy σpe: effective initial stress during prestressing, σpy: yield stress of PC cables σry: yield stress of steel bar, σsy: yield stress of steel frame, k1,k2,k3: stress block modulus (k1 k3=0.83, k2=0.42)

In the OCL test specimen, flexural cracking occurred on the top surface at the ends, on the bottom at the center of the beam, and at the end of the column. Thereafter, the steel bar and upper flange of the steel frame yielded at the critical section of the beam. Under increasing vertical loading, the cracks lengthened and the maximum load was reached when compressive failure occurred in the compression zones at the center and both ends of the beam. The ultimate strength in the experiment was 1.18 times larger than the value calculated using the simplified equation (eq-1). On the other hand, the cable stress increased as the load increased, but the maximum value was 1.22 times larger than the initial pre-stressing value as shown in Figure 18(a). In other words, it didn’t reach the yield value.

Figure 17 Load-deflection curves

Figure 18 Stress of outer-cables

Figure 16 Loading program

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In the OCE test specimen for seismic resistance, flexural cracking start to occur in the beam at a story deformation angle of 1.0x10-3rad. and in the column at 2.5 x10-3rad. Shear cracks subsequently appeared at the column-beam connection just before reaching a story deformation angle of 7.5 x10-3rad. When the steel frame and the steel bar started to yield at the beam ends, compressive failure occurred at the beam ends. Thereafter, compressive failure extended rapidly at the beam ends and reached the maximum load. On the other hand, the stress acting in the cables didn’t change even during maximum deformation (see Figure 18(b)) and there was no harmful cracking in the vicinity of the anchorages and the deviators as shown in Figure 19.

The results of these experiments confirmed that the specimen has sufficient strength even after the intermediate column is removed.

5. Conclusion This paper describes some results of tests on structural conversions for spatially expanding old buildings. The authors propose converting old structures or removing obstructing structural members, installing seismic isolation systems in the middle story to enhance earthquake resistance, and strengthening some structural members. For these purposes, three technologies have been developed. The first technology is visco-elastic dampers. Experiments show that the material properties are stable under temperature changes, and that displacement can be controlled to within 20 cm under the design seismic wave. Moreover, displacement at the isolated layer can be controlled and seismic isolation achieved by installing these dampers in old buildings in urban areas. The second technology converts a frame structure into a flat slab structure by increasing the slab depth and adding column capitals. Experiments confirm that stress is transferred at the column-slab connection in the converted structure. The results show that the connection has sufficient strength for the design seismic deformation. The third technology relates to removing intermediate columns. Experiments confirm that pre-stressed outer cables strengthen the beam under vertical loads. The test results indicate that reinforced beams with outer cables have sufficient capacity to handle the design permanent load and the seismic load even after the intermediate columns are removed.

References

1) Kelly, J.M., 1993, Earthquake-Resistant Design with Rubber, Springer-Verlag, ISBN 3-540-1987-7 2) Kasai, K., et. al., 1993, Viscoelastic damper hysteretic model : theory, experiment, and application, ATC

17-1 Seminar on Seismic Isolation, Passive Energy Dissipation, and Active Control, SanFransisco, March, 1993

3) Nielsen,E.J. et.al, 1996, Viscoelastic damper overview for seismic and wind applications, Proc. SPIE Vol. 2720, Smart Structures and Materials : Passive Damping and Isolation, p. 138-144,

4) Kuo-Chun Chang and Yu-Yuan Lin, (2004), Seismic Response of Full-Scale Structure with Added Viscoelastic Dampers, J. Struct. Engrg., Volume 130, Issue 4, pp. 600-608

5) Sone, Y., et. al., 2002, Development of Visco-Elastic Damper with Styrene Elastomer, Summaries of Technical Papers of Annual Meeting Architectural Institute of Japan, B2, Structure II, pp.815-810

6) Soda, S., et. al., 2002, Method for temperature control of viscoelastic damper, Part 1 experimental study on temperature control of double-shear damper by sheet heater with ptc function, Journal of Struct Constr.Engng. , No.560 , p.59

Figure 19 Cracking at the final stage

anchors

deviators

Table 4 Test results OCL OCE Q(kN) Loading Direction Q(kN) R(%)

Yield point of 150.5 positive 98.8 1.20 steel frame, bar negative -107.0 -1.30 Compressive failure 195.2 positive 119.9 1.65 at the beam ends negative -125.3 -2.05 Maximum shear force 198.6 positive 135.0 3.00 negative -130.3 -2.70

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