JPH11343755A - Earthquake damping structure - Google Patents

Abstract

PROBLEM TO BE SOLVED: To realize an earthquake damping structure more excellent than conventional devices from functional and economical viewpoints by forming an earthquake damping structure having higher energy absorbing efficiency in earthquake damping structure, in which the damping performance of medium-rised, high-rised and super high-rised buildings and a tower-shaped building is improved and earthquake-resistant safety performance is enhanced. SOLUTION: Sub-structures 21, 22... structurally separated from a main-body structure are installed in spite of internal damping type earthquake damping structure, in which damping devices 7 are arranged among the upper and lower layers of a mutilayer structure, in conventional earthquake damping structure, and damping devices 27 are disposed among the sub-structures and the main-body structure, thus realizing external damping type earthquake damping structure having the same effect as the damping devices 7 are arranged among a ground and each layer. Double-damping earthquake damping structure jointly having both an internal damping mechanism and an external damping mechanism by combining the damping devices 27 with the conventional damping devices 7 disposed among layers. The earthquake damping structure displays a large earthquake damping effect even in a structure, in which bending deformation diminates such as a tower-shaped structure, the tower-shaped structure on a building including a high-rised building.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

[Industrial applications] In the Great Hanshin-Awaji Earthquake of 1995 and the Northridge earthquake of the United States one year before, steel columns of steel structures, which had been considered to be highly safe until now, were subject to brittle fracture or failure. -Many cracks and fractures were found at the beam joints, and it was clarified that there was a major problem in the seismic safety of steel structures. INDUSTRIAL APPLICABILITY The present invention is capable of dramatically improving the seismic safety of middle- to high-rise building structures and tower-like structures such as towers and structures, in which steel structures that include the above problems are often employed. It proposes a configuration method of a vibration control structure. INDUSTRIAL APPLICABILITY The present invention has a great effect on improving the seismic safety of building structures having middle or higher layers, particularly high-rise / super-high-rise buildings, and various tower structures such as steel towers and towers.

[0002]

2. Description of the Related Art As a structural method for improving earthquake resistance and wind resistance of a high-rise building, various types of energy such as steel dampers and viscous dampers are used for framed structures composed of columns, beams, or diagonal members such as braces. Vibration control structures using absorbers have been developed and put into practical use. Since the Great Hanshin Earthquake, the use of high-rise buildings has been increasing.

On the other hand, as a measure for improving the seismic safety of middle- and low-rise buildings exposed to more severe acceleration response, the use of seismic isolation structures using various types of seismic isolation devices, mainly laminated rubber seismic isolation devices, has increased. It is getting.

In the seismic isolation structure, an extremely low horizontal rigidity portion (seismic isolation layer) is provided between the ground and the structure, and horizontal deformation is concentrated there, so that seismic energy input to the structure is absorbed by the seismic isolation layer. In contrast to seismic energy absorption methods, the seismic control structure is a method in which seismic energy input into a building is dispersed and absorbed by damping devices (energy absorbing devices) distributed throughout the building. It is intended to improve seismic safety by increasing the damping performance (= energy absorption performance) of objects.

[0005] Some designers adopting a vibration control structure can use the hysteresis energy absorption due to the plastic deformation of the structural members such as columns and beams in the conventional seismic design concept to a more reliable energy absorption device. Some are thinking of replacing it. The idea is to concentrate the damage site due to energy absorption on a specific member and replace the damaged energy absorption member. This is a step forward in terms of separating energy absorption from the main structural framework of columns and beams, but it is said that it is a seismic control structure that still has a major problem in that main structural members must be replaced. I have to say.

[0006]

Although the seismic control structure which has been put into practical use so far has achieved far superior seismic performance compared with the conventional seismic structure, it is used for middle and low-rise buildings. When adopted, the acceleration suppression effect is generally not as great as the seismic isolation structure. In the case of high-rise or high-rise buildings, it may be possible to achieve considerably superior performance.However, in order to achieve a large response suppression effect, naturally, many damping devices must be used. And a considerable cost burden is imposed. In addition, in the case of the above-mentioned replacement, a large economic expenditure is required when replacing the equipment.

[0007] The present invention is intended to improve the seismic control structure, which has been left with problems in terms of both performance and cost, in order to further improve the seismic safety performance, thereby making it more economical. The practical application of a vibration control structure that can be realized in Therefore, it is a main object of the present invention to dramatically increase the energy absorption efficiency of the vibration control structure as compared with the conventional vibration control structure.

[0008]

In a conventional vibration control structure, an energy absorbing member (attenuator) is arranged on each layer of the multilayer structure. Therefore, in the hysteretic energy absorption type damping device, a resistance is generated with respect to a relative displacement (interlayer displacement) between the upper and lower layers, and energy is absorbed. Further, a viscous or viscoelastic damping device generates a resistance to the relative speed between the upper and lower layers (interlayer speed difference) and absorbs energy. These damping devices produce an effect on the difference in relative motion between the upper and lower layers, and this kind of damping mechanism is called an internal (viscous) damping mechanism.

The present invention aims at realizing a damping mechanism of an external (viscous) damping mechanism, while all the conventional vibration damping structures are based on the basic principle of internal (viscous) damping. It is. That is, while the internal damping has an effect on the interlayer speed difference and the interlayer displacement, the external damping has an effect on the relative displacement or the relative speed difference between the foundation or the ground surface and each layer. . Therefore, in the external damping mechanism, the effect of the first layer is the same, but the relative displacement and the relative speed difference from the foundation (ground surface) increase with the second floor and higher, so that the higher the floor, the lower the damping The effect will increase dramatically.

[0010] In the internal damping mechanism, the efficiency of damping is affected by the deformation mode of the structure. As the structure becomes higher, the ratio of the total bending deformation to the horizontal deformation increases, and the ratio of the shear deformation decreases. For this reason, it has been considered that a general damping device that can only exert an effect on the shear deformation component has a lower effect as it becomes a high-rise building. However, since the external viscous mechanism exerts an effect on the total horizontal displacement or horizontal velocity difference with respect to the base surface, it is much higher regardless of the ratio of the bending deformation component and the shear deformation component to the deformation in the building. The resistance of the damping device is exerted.

If the external damping mechanism is realized, the resistance generated in each damping device becomes much larger than that of the conventional internal damping type. In comparison, much less damping device is required, so that large damping performance is realized at low cost.

In order to realize the external damping mechanism, it is necessary to connect the damping device to the ground or the foundation and each floor. This is inevitably realized on the first layer, but usually not easily realized on the second and higher layers. Therefore, the conventional damping structures have considered the internal damping mechanism as a natural condition.

The present invention introduces the concept of a substructure separate from the main structure in order to realize this external damping mechanism. That is, although it is extremely difficult to arrange the damping device between the second floor or higher floor and the ground, a substructure that moves in the same way as the ground is formed and the pseudo ground surface is set at the same height as each floor. Is provided. The substructure needs to be separated from the building structure and provided with rigidity and strength that does not cause significant deformation due to the resistance transmitted from the damping device. Because of this, the substructure is separated from the building main body, and the seismic inertial force generated by the weight of the building main body is not transmitted, so that the rigidity and strength can be easily provided.

If the external damping mechanism can be realized, it is possible to provide a conventional internal damping mechanism inside the building and to use the external damping mechanism in combination with the lower part of the building, so that both functions of the internal damping mechanism and the external damping mechanism can be realized. A completely new vibration control structure with This is claim 5, and this invention relates to
Double damping mechanism = named "double damping system" or "double damping mechanism".

The external damping mechanism and the double damping system of the present invention can be easily applied to tower-like structures such as steel towers and towers, as well as middle-, high-rise, and super-high-rise building structures. The present invention can be applied to a tower-like structure installed on a building as described in claim 7, and a great effect can be exhibited.

[0016]

Embodiments of the present invention will be described below with reference to the drawings.

FIG. 1 is a conceptual view of a conventional middle-to-high-rise building having an earthquake-resistant structure. (1) is a framed structure in which columns and beams are rigidly connected, which is the most common structure called a pure ramen structure in Japan. Format. (3) combines this with a brace (diagonal material) as an earthquake-resistant element. By combining the brace and the earthquake-resistant wall, the horizontal rigidity and horizontal strength of the whole building can be increased. (2) expresses the vibration characteristics of these conventional seismic structures in a simple manner by expressing the weight of each floor of the building as a mass at the floor position and the rigidity of each frame as a spring connecting each mass. It is a general expression example of a vibration analysis model called a mass spring model of a mass point system.

On each floor of such a conventional multilayer framed structure, various types of energy absorbing devices called dampers are incorporated to improve the damping performance of the building. This is a structural method called a vibration damping structure, and a typical example is shown in FIG.
(1) is an example in which a wall-shaped viscous damping device “vibration damper” is employed, and (3) is an example in which a hysteretic damper such as a steel damper or a friction damper is installed via a mounting wall plate. In addition to this, several installation methods have been put to practical use, such as one in which a damper is attached using a brace material. (2)
It shows the concept of the vibration model. It shows that the energy absorption element (dashpot) expressing the damper is placed between each mass point in the vibration model of the seismic structure, and shows that it is a vibration control structure of the internal damping mechanism. I have.

FIG. 3 to FIG. 5 show how to implement claim 1. In FIG. 3A, a substructure whose rigidity is increased by a brace or the like is formed in a plane of a lower part of the building, and a damping device is arranged between the substructure and the main building structure.
(3) shows the case where the substructure is formed outside the building plane, and (2) shows the concept of the vibration analysis model of both. The substructure has a relatively small mass and high rigidity as compared to the main structure, and a dashpot representing a damping device is disposed between the mass points of the substructures. Because the sub-structure moves almost the same as the ground surface due to its high rigidity, the damping device connecting them has the same effect as being connected to the ground surface, thus realizing an external damping mechanism.

FIGS. 4A and 4B show a case where sub-structures are provided both inside and outside a building plane. FIG. 4A is a sectional view and FIG. 4B is a vibration analysis model.

FIG. 5 shows an example in which the sub-structure is formed inside the building plane, and shows a method of providing the columns of the sub-structure at the same plane position as the columns of the main structure. (1)
Is a sectional view thereof. Relative displacement occurs at the joint between the two structures of the pillars arranged at the same plane position, so that the vertical load of the pillar is transmitted to the joint and horizontal displacement is allowed while laminated rubber, sliding bearing, roller bearing, etc. Is interposed. (2) is the vibration analysis model. 3 to 5 have the same concept in terms of vibration dynamics.

FIGS. 6 and 7 show a method of applying the present invention to a building structure having a core according to the second aspect. FIG. 6 shows a case of a building of a both side core type, and (1) shows a conventional general structure method in which the entire building plane is integrally formed. On the other hand, (2) shows the gist of the present invention, in which the core part and the other main body framing part are separated and constructed, and a damping device is incorporated in a joint between the two parts, thereby achieving a high energy absorption efficiency control. It realizes a seismic structure.

FIG. 7 shows a configuration method in the case of a center core type, where (1) is a conventional general configuration method, and (2)
Is the present invention in which the core portion and other portions are separated from each other. The interposition of the damping device at the junction between the two parts is the same as in FIG.

FIG. 8 shows a third embodiment. This is a more efficient development of the method of separating the core part and the other main part according to claim 2, wherein the core part separated from the main part is limited to a plurality of lower layers, and Is formed integrally without separating the core and other parts. Since a relative displacement occurs between the separated lower core part and the upper core part, a laminated rubber / slide bearing that can tolerate horizontal displacement while transmitting the vertical load of the column is connected to the joint.・ Use roller bearings. An attenuating device is disposed between the core and the body of the lower layer at a portion where the core and the body are separated.

[0025] With this configuration, the separated core portion moves almost the same as the ground surface due to its high rigidity, and the same effect as when the ground surface is raised to the height of each layer is produced.
The lower part of the building main body becomes a pure ramen structure, and the lower part having low rigidity can be easily formed. Further, since the upper layer portion that is not separated is integrated with the core portion, the rigidity is high, and the deformation can be concentrated on the lower rigid layer of the lower layer portion. Due to these three synergistic effects, the vibration control structure can achieve extremely high energy absorption efficiency.

FIG. 9 shows a fourth embodiment in which a substructure is formed near a column where a large vertical axial force is generated by a horizontal load, and a viscoelastic body, a viscous damping device, or the like is provided between the two columns. A friction damper or the like is provided to exert a damping resistance against vertical displacement or vertical relative velocity. (1) shows an application example in the case of a building with both side cores, and (2) shows an application example in the case of a center core type building.

FIG. 10 shows claim 5.
By combining both the external damping mechanism realized by claims 1 to 4 and the conventional internal damping mechanism inside the building, a completely new vibration control structure having both functions of the internal damping mechanism and the external damping mechanism is realized. it can. According to the present invention,
The heavy damping mechanism is named "double damping system" or "double damping mechanism", and an extremely high performance damping structure is born. (1) is an example of a cross-sectional view showing the configuration, and (2) shows the concept of the vibration analysis model.

FIG. 11 (1) shows the lower part of the vibration model of the double damping system, and FIG. 11 (2) explains its effect. Since the core part separated from the building main body has high horizontal rigidity, the relative displacement with the ground is extremely small, so the external damping device connecting the core part and the building main body has a relative displacement or relative speed difference from the ground. Resistance occurs. This figure also shows the interlayer displacement or interlayer speed difference at each floor of the building that generates the resistance of the conventional internal damping mechanism. From the comparison between the two, it is obvious at first glance how effective and effective the external damping mechanism is.

The external damping mechanism and double damping system of the present invention can be easily applied not only to building structures such as middle-rise, high-rise, and super-high-rise buildings but also to tower-like structures such as steel towers and towers. FIG. 12 shows an application example of the sixth aspect to a tower-like structure. (1) is a method in which a damping device is attached to a boarding structure in an internal damping type, which is a method of applying a conventional vibration damping structure, and (2) shows a vibration analysis model thereof. On the other hand, in (3), a substructure separated from the tower body is formed in the lower layer of the tower body, and an attenuation device is arranged between the tower body and the substructure. (4) is the same, but shows a case where the tower body is a cylindrical tower-like structure, and (5) shows the concept of a vibration analysis model of both.

Further, the present invention can be applied to a tower-like structure installed on a building as described in claim 7. FIG.
(1) shows a conventional method of forming a general structure, and (2) shows a vibration analysis model thereof. To apply the present invention to a tower on such a building, as shown in (3), a substructure separated from the tower is provided near the lower part of the tower, and an attenuation device is provided between the substructure and the tower. Is installed. In these tower-like structures, since the ratio of the entire bending deformation is generally large, it has been found that the conventional internal damping type damping device arrangement is not so effective. However, if the damping device arrangement of the external damping method of the present invention is adopted, a large vibration damping effect can be exerted because it is not affected by the components of the bending deformation component and the shear deformation component.
(4) shows the concept of the vibration analysis model.

Claim 8 defines the type of damping device to be used in the vibration control structure of the present invention, and employs a viscous type and a viscoelastic type damping device as the device most effective in exhibiting performance. Shows the case.

In addition, although the effect is slightly degraded from the appearance of performance, the use of a history damper or a friction damper made of a metal material using steel or lead is also considered due to practical conditions such as economy and a large number of equipment manufacturers. Conceivable. Claim 9 shows this condition.

[0033]

According to the present invention, the damping structure which has been realized so far has been an internal damping type damping structure in which damping resistance is generated with respect to the interlayer displacement or the interlayer speed difference. An external damping type damping structure and a double damping damping structure having both external damping and internal damping are realized. As a result, in the new vibration control structure, a completely new excellent vibration control effect (response suppression effect by damping performance) can be expected from the conventional vibration control structure in the following points.

Effect: The external damping greatly increases the efficiency of the generation of the damping resistance, thereby exhibiting a large response suppressing effect, and a large effect can be obtained with a smaller number of damping devices. A much more economical system.

Effect: Because of the external damping type, the effect is not affected by the horizontal deformation mode of the structure main body, and it can be reliably applied to a structure having a large bending deformation component, which is considered to be ineffective in the conventional vibration control structure. The effect is exhibited. Therefore, the present invention exerts a great effect not only on high-rise / high-rise buildings but also on various tower-like structures such as steel towers and towers.

Effect: In the double damping system,
Since it has both the external damping mechanism and the internal damping mechanism, an extremely large damping effect is exhibited, and the reliability of the manifestation of the effect is extremely high.

[Brief description of the drawings]

Fig. 1 Construction method of building structure using conventional seismic structure (1) Frame structure of pure ramen (2) Conceptual diagram of vibration analysis model (3) Frame structure of ramen structure with braces

Fig. 2 Configuration method of conventional vibration control structure building (1) Configuration example of vibration control structure using viscous damping wall (2) Schematic diagram of vibration analysis model of conventional vibration control structure (3) Control structure using hysteretic damper Configuration example

FIG. 3 is a diagram illustrating a configuration method of an external damping type vibration damping structure according to the present invention (1) (1) a case where a substructure is provided in a lower part in a plane of a building body (2) a vibration analysis model of the external damping type vibration damping structure Conceptual diagram (3) When the sub-structure is installed in the lower part outside the building body plane

FIG. 4 is a diagram illustrating a method of configuring an external damping type vibration damping structure according to the present invention (2) (1) A case where sub-structures are provided in a lower portion of a building body in a plane and outside a plane (2) Conceptual diagram of a vibration analysis model

FIG. 5 is a diagram illustrating a method of constructing an external damping type vibration damping structure according to the present invention (3) (1) When a substructure is provided in a lower layer portion of a plane of a building body by utilizing a pillar position of the building body (2) ) Schematic diagram of the vibration analysis model

FIG. 6 shows a method of applying the present invention to a side-core type building (Claim 2). (1) Configuration of a conventional building (2) The present invention is applied by separating a core part and other building main parts. Case.

[FIG. 7] A method of applying the present invention to a center-core type building (Claim 2) (1) Configuration of a conventional building (2) Applying the present invention by separating a core part and other building main parts if you did this.

FIG. 8 A method of applying the present invention to a lower part of a building having a core (Claim 3) (1) In the case of a side-core type building (2) In the case of a center-core type building

[Fig. 9] Method of exerting damping effect on vertical displacement (Claim 4) (1) In case of side core type building (2) In case of center core type building

FIG. 10 is a double damping control structure having both an external damping mechanism and an internal damping mechanism. (Claim 5) (1) Cross-sectional configuration diagram of a double damping building (2) Conceptual diagram of its vibration analysis model

FIG. 11 is a diagram illustrating the effects of double damping and an external damping mechanism. (1) Enlarged view of a vibration analysis model of a double damping building. (2) Description of a relative displacement and a relative velocity difference that cause the appearance of an external damping mechanism and an internal damping mechanism. Figure

FIG. 12 shows a method of applying the present invention to a tower-like structure (Claim 6). (1) A conventional method of constructing a vibration control structure of a tower-like structure. The method of constructing a vibration control structure of a tower-like structure according to the present invention (4) The method of constructing a vibration control structure of a tower-like structure according to the present invention (in the case of a cylinder type tower) (5) Schematic diagram of its vibration analysis model

FIG. 13 shows a method of applying the present invention to a tower-like structure installed on a building (Claim 7). (1) Configuration of a conventional tower-like structure on a building (2) Schematic diagram of its vibration analysis model ( 3) A method of constructing a vibration control structure of a tower-like structure on a building according to the present invention (4) Schematic diagram of its vibration analysis model

[Explanation of symbols]

1: pillars of a conventional building 2: floors and beams of a conventional building 3: braces of a conventional building 4: mass points of a conventional building model 5: springs of a conventional building model (models of horizontal stiffness of each floor by a structural framework) 6: Internal damping type dashpot modeling damping device 7: Damping device (viscous damping wall) 8: Damping device (history damper) 11: Pillar of main body structure 12: Floor and beam of main body structure 14: Main body Mass point of structure model 15: Spring of main body structure model 20: Core separated as sub-structure 21: Column of sub-structure 22: Floor and beam of sub-structure 23: Brace of sub-structure 24: Sub-structure Mass point of body model 25: Spring of substructure model 26: External damping dashpot that models a damping device connecting between main body structure and substructure 27: Damping arranged between main body structure and substructure Equipment (external damping (Type) 28: seismic isolation device placed between pillars of main structure and substructures 30: core of conventional building 31: earthquake-resistant wall constituting core 47: between main structure and substructure Vertical damping device to be arranged 51: Displacement of each mass point of main structure 52: Displacement of each mass point of substructure 53: Inter-layer displacement or inter-layer speed difference that generates conventional internal damping type damping resistance 54: The present invention Relative displacement or relative velocity difference causing an external damping type damping resistance force 61: Column of tower-like structure 62: Beam of tower-like structure 63: Brace of tower-like structure 64: Material point of tower-like structure model 65: Spring of a tower-like structure model 66: Dashpot (internal attenuation type) modeling a conventional damping device of a tower-like structure 67: Example of arrangement of conventional attenuation device of a tower-like structure (internal attenuation type) 71 : Pillar of substructure for tower-like structure 72: Beam of sub-structure for tower-like structure 73: Brace of sub-structure for tower-like structure 74: Mass point of sub-structure model 75: Spring of sub-structure model 76: Damping connecting tower-like structure and sub-structure Dashpot (External damping type) that models the device 77: Damping device (external damping type) arranged between tower-like structure and substructure 81: Wall plate for mounting damping device 90: Main body structure and core portion Separation zone 100: Integrated zone of main body structure and core

Claims (9)

[Claims] 1. A multi-layer main body structure having two or more layers, such as a building, a civil engineering structure, and a work including a column, a beam, a brace, and an earthquake-resistant wall. A damping device that constitutes a sub-structure structurally separated from the main structure over a plane, outside a plane, or inside and outside a plane, and absorbs energy with respect to the horizontal relative displacement or horizontal relative speed between the two. A damping structure characterized by having a structure disposed between the two structures. 2. A double-sided or center-core building structure comprising a column, a beam, a brace, a seismic wall, and the like, and having a rigid core on both sides of the plane or near the center of the plane. In the product, the structure of the core part and the structure of the other part are separated, and a damping device that absorbs energy with respect to the horizontal relative displacement or horizontal relative speed between them is arranged between the two structures. A vibration control structure characterized by the following. 3. A building structure comprising columns, beams, braces, earthquake-resistant walls, and the like, and a double-side core type or center core type building structure having a highly rigid core on both sides of the plane or near the center of the plane. In a product, a member with low horizontal rigidity such as laminated rubber, a sliding bearing, a roller bearing, etc. is inserted into the middle layer of the pillar that constitutes the core to separate the horizontal rigidity of the core in the vertical direction, and then the discontinuous part The following core structure is separated from the structure skeleton of the other part, and the structure above the discontinuous part is integrally formed with the structure skeleton other than the core, and the lower separated core and the core are separated. A damping structure characterized by disposing a damping device for absorbing energy with respect to a horizontal relative displacement or a horizontal relative velocity between structural frames other than a part. 4. A multi-layer main body structure having two or more layers, such as a building, a civil engineering structure, or a work including a column, a beam, a brace, and an earthquake-resistant wall. A damping device that forms a sub-structure structurally separated from the main structure over the plane, outside the plane, or inside and outside the plane, and absorbs energy with respect to the vertical relative displacement or vertical relative velocity between the two. A damping structure characterized by having a structure disposed between the two structures. 5. A multi-layer main body structure having two or more layers, such as a building, a civil engineering structure, or a work including a pillar, a beam, a brace, and an earthquake-resistant wall, is used as a main body structure. A sub-structure structurally separated from the main structure over the plane, outside the plane, or inside and outside the plane constitutes a sub-structure, and a damping device connecting the upper and lower layers of the main structure is arranged in the main structure. And a damping device for absorbing energy with respect to a horizontal or vertical relative displacement or relative speed between the main structure and the substructure. 6. A tower-like structure including columns, beams, braces, and the like, forms a sub-structure structurally separated from the main body of the tower structure, and includes the main body of the tower structure and the sub-structure. And a damping device for absorbing energy with respect to horizontal or vertical relative displacement or relative velocity between the two. 7. A composite structure in which a tower-like structure is mounted on a main supporting structure such as a building, a civil structure, or a work including a column, a beam, a brace, and an earthquake-resistant wall. The substructure is structurally separated from the superstructure on the structure, and the horizontal or vertical relative displacement or relative velocity between the superstructure and the substructure is between the substructure and the substructure. A vibration control structure characterized by the provision of a damping device for absorbing energy. 8. A damping device disposed on the structure according to claim 1 or 2, a viscous damping device such as a viscous damping wall, a viscous damping floor, a rotary viscous damping device, an oil damper, or a high damping rubber, A vibration control structure characterized by employing a viscoelastic damping device mainly composed of a viscoelastic material composed of a molecular material. 9. A damper made of low yield point steel or another steel material as a main component, a lead damper using lead as a main energy absorbing material, A seismic control structure characterized by employing a friction damper utilizing friction.