Abstract:
A class of bearings, each of them can be used as a connector to connect two parts in a structural system and as a supporter to transfer loads from one part to another, for examples, gravity of a superstructure to a substructure in a bridge or a building, or that of a machine to its foundation. While performing load transmission, it is able to reduce the transmission of transient vibrations between connected two structural parts and preserve the integrity of entire structural system; for examples, to protect a bridge&#39;s structural integrity when either an earthquake strikes its pier and foundation or a tsunami hits its superstructure or both occur simultaneously.

Description:
FIELD OF INVENTION 
       [0001]    The present invention discloses a class of apparatuses. A said apparatus is used as a structural component in a large-scaled civil engineering system such as a building, a bridge, or a machine and its foundation, which has at least the following three functions: being a support to bear the weight of a part of said system, connecting different parts of the system to assure structural integrity, and transferring designed force-flows other than gravity between connected parts while damping out or isolating undesired vibrations. 
         [0002]    For said engineering system like a bridge or a building, it generally can be divided into two parts: the superstructure such as a bridge&#39;s spans and deck that carries designed live loads; and the substructure that includes the bridge&#39;s piers, footing, and foundation, which supports carried superstructure. Wherein said bearing is a structural component that connects super and substructure, transferring carried superstructure&#39;s weight and live loads to substructure 
       BACKGROUND OF THE INVENTION 
       [0003]    An earthquake is a sudden tectonic-plate&#39;s movement at a spot inside earth&#39;s crust, radiating stress waves to surrounding and resulting in earth surface&#39;s vibrations. To a large-scaled civil-engineering structure, such as a building or a bridge, the lethality of an earthquake mainly comes from the two respects: ground acceleration that causes inertia forces and resonance that accumulates the energy associated with the acceleration in structure. Hence, acceleration-induced internal inertia force is the key factor to cause structural damages. 
         [0004]    Ground acceleration can be divided into vertical (parallel to gravity direction) and horizontal component, which are respectively characterized by the corresponding peak values, teamed “Peak Ground Acceleration” (PGA) for design consideration. The horizontal PGA is generally higher than the verticals according to past experiences. Currently in United States the engineering standards and codes of buildings and bridges require all designs with the seismic resistant capacity to sustain the horizontal PGA that is quantified by the earthquake hazard map provided by USGS, see  FIG. 1 . This map gives the statistic prediction of horizontal PGA at any place of the country, with the probability of 7.5% exceedance in next 75 years.  FIG. 2  is the prediction of horizontal PGA for far eastern Asia. 
         [0005]    In seismic resistant design, for example, for bridges, a generally-accepted philosophy is to isolate superstructure from substructure that directly expose to the impact of ground accelerated motion when an earthquake occurs. A bearing, when it connects sub and superstructure rigidly, often becomes the “weakest link” in entire structural system. This is because, as a pivot to carry all live loads and superstructure, a bearing is also the “neck” of inertia-induced force flow when any structural part is struck by dynamic loads. By contrast, when it is a flexible connection that is can temporally separate connected parts when one of them is struck by an external dynamic load, the corresponding high inertia force flow will not be established. 
         [0006]    However, in reality it is generally impossible to completely “isolate” inertia force flow between connected parts in a civil engineering structure; the central of seismic-isolation design actually is to provide certain flexibility at the joints between major parts of a structure, so as to reduce inertia force while be able to temporally shift intrinsic resonate frequencies of a structure for avoiding the resonance with ground motions. On the other hand, engineering practice also requires such a joint to have certain robustness because a superstructure has to be able to sustain many different kinds of live loads, for examples, the strong lateral forces caused by hurricane and tsunami. A horrible experience during the earthquake at Mar. 11, 2011 in Japan was that many bridges and buildings were survived after the high magnitude earthquake but their superstructures were washed out by the following tsunami. 
         [0007]    Hence, in contrast to conventional isolation, the concept of “integrated design”, which requires certain flexibility at joints and bearings to reduce and damp undesired vibration while be able to keep global structure as an integrated unit, is the underlying fundamental for this invention. 
       BRIEF REVIEW OF PRIOR ARTS AND PRODUCTS AVAILABLE IN MARKET 
       [0008]    Design of seismic-resistant buildings and bridges is one of the most active and innovative areas in the field of civil and structural engineering. Using a three-storage building,  FIG. 3  illustrates various arts and technologies required, proposed or already been applied in practices. The arts disclosed in this article can be used as the seismic bearing in the left-low corner of the building or in a bridge. 
         [0009]    A bearing can be considered as a joint. According to functions, bearing products can be generally divided into three categories: (i) dumper-joints that utilize traditional mechanical devices, such as piston-cylinders damper, cams-pin-friction damper, and so on, for which some modern arts are implemented with shape memory alloys and controlled by electric sensors; (ii) common structural bearings such as elastomeric that has certain enhanced lateral resistance; (iii) the bearings based on friction-pendulum mechanism that focuses on seismic isolation. 
         [0010]      FIG. 4  illustrates a prior art “energy absorber” (WO97/25520), whereby various zigzag-shaped interfaces, including wavy and V-shaped interface, are designed for force transmission while no sliding between the core material and the frame containing it. Obviously, it can be used as lateral bracing in  FIG. 3  to damp shear force but is incapable to carry gravity. 
         [0011]      FIG. 5  is the prior art (U.S. Pat. No. 4,187,573) that uses elastomer 5 to damp vibrations while the frame 11 to confine relative horizontal displacement between the contacted two parts, by which, obviously, no confinement of vertical displacement is provided.  FIG. 6  is another prior art (WO2008/004475), a variation of conventional elastomer bearing, by which the key components are the composite block, which is made of the laminar structure by elastomer  2   b  and reinforce plate  2   c,  and the center core  3  that is made of high plasticity material. The latter&#39;s functions are to reinforce lateral deformation resistance while improve the capacity of damping. When the core material is Lead, this kind of bearings is also termed “Lead-Rubber Bearing (LRB)”. However, when a structure is suffering strong ground motion, the friction resistance between elastomer and bearing pads may not be enough to resist inertia-induced sliding force. Once sliding occurs after the core deformed, there is no internal driving force to restore such a bearing back to its original shape. 
         [0012]      FIG. 7  is the prior art (U.S. Pat. No. 6,021,992), termed friction pendulum sliding bearing (FPS). It belongs to a group that includes dozen of US patents and tens in other countries which are based on the principal of the pendulum depicted on the right-hand side of the figure, utilizing carried superstructure&#39;s weight as a natural force to resist horizontal inertia caused by ground motion. Once the spectrum of ground motion passed, the gravity restores the bearing back to its original position. 
         [0013]    Theoretically speaking, a pendulum is a conservative system that does not dissipate energy. Therefore, if there is no friction, an actual pendulum can swing around its static position forever once the motion is triggered. Therefore, friction between the contact surface-pair is also a key-mechanism in a FPS bearing, which requires considerable large contact area to assure enough friction force and capacity for carrying heavy superstructure. On the other hand, certain height of curved surface, at least for the bottom seat of the bearing in  FIG. 7 , is required to gain enough lateral resistance. 
         [0014]    The integrity between sub and superstructure&#39;s integrity is crucial for high-rise buildings and the bridges with high structural features. This is because, except those strong external forces such as hurricane and tsunami that directly imposed to superstructure, a horizontal ground motion-induced vibration may cause turnover moment to a superstructure; the magnitude of this moment is approximately proportional to the ratio between a structure&#39;s height and the largest one in its length and width dimensions on earth surface. 
         [0015]    To gain super and substructure integrity,  FIG. 8  is another prior art (U.S. Pat. No. 5,669,189), termed antiseismic connector (ANSC). It is actually an assembly of a laminated elastomeric bearing  3  plus the cables (tendons)  6  fastened to the connected super and substructure by the rotatable fastener  21 . However, by tendons and rotatable fasteners have limited capabilities against horizontal sliding and high structure&#39;s rotation. 
       SUMMARY OF THE INVENTIONS 
       [0016]    According to the literatures search, no prior art has been found of heavy gravity-carrying bearings that has the dual properties in isolation/damping of strong vibrations and preserving structural integrity of a large-scaled civil engineering structure. The U.S. Pat. No. 5,669,189 is a solution toward this class of problems, at least, for light superstructure like family house; however, the design of the tendons and rotation-free fastener system in the art leaves the flexibility in horizontal motion for carried superstructure. This motion leads to less resistance against turnover moment and, once it occurs, the frictions among elastomeric layers become the resistance to prevent the bearing to restore its original shape. On the other hand, the layout of tendon-fasteners system requires relatively large space for the device. 
         [0017]    Therefore, in order to provide practically-applicable and effective bearing products for our habilitations and transportation means, this application disclose a new class of apparatuses that can be used as structural bearings that aim at the satisfaction of following criteria:
       (A) Robustness: a stable and reliable connection between connected structural parts, for example, super and substructure of a bridge, in regular service condition.   (B) Fuser: capable to accommodate a temporal separation between connected parts when one of them is struck by a transient accelerated motion that may be caused by earthquake, hurricane, barge or vessel&#39;s collision, or explosion, so as to minimize the damage to other parts.   (C) Integrity: always keep the connected parts as an integrated structural system although temporally localized separation for the purpose of internal isolation.   (D) Self-restoration: capable to restore original state after performing aforementioned “fuse” function.   (E) Environment-friendly: does not introduce noise or extra material hazards, nor consumes extra energy during operation.   (F) Reliability for long-term application and convenience in management.   (G) Do not introduce difficulties for manufacturing and for field erection and construction.   (H) Enable quantitative design to meet broad needs, for example, to damp and to isolate the inertia forces cause by the spectrum of ground accelerations predicted by  FIGS. 1 and 2 .       
 
         [0026]    In order to reduce and ultimately prevent possible damages to buildings and bridges caused by broad spectrum of natural disasters, multiple apparatuses with respective independent embodiments or combination of them are disclosed in this article. 
         [0027]    The first key-embodiment is the V-shape contact surface-pair, as the core of a class of the disclosed bearings, see  FIG. 9 ; wherein said bearing is an apparatus to connect different parts of a structural system while transfer designated service-loads, for example, weight, along the direction vertical to said surface-pair between connected parts; wherein a said V-shape contact surface comprises at least two facets and fillet at the intersection between adjacent facets; wherein said “vertical” refers to the direction of a straight line that is perpendicular to the intersection line between said two adjacent facets and that has equal declinate angles to its respective projections onto the two facets. A said service-load introduces lateral force component on a facet with declined angle. When said two V-shape surfaces in a contact surface-pair are completely attached, the service-load introduced lateral forces from all contact facet-pair conceal each other. A sliding along one or multiple said facet-pairs in said V-shape surface-pair means loss of contact between the rest facet-pairs in said surface-pair; the un-balanced lateral forces tend to push said V-shape surface-pair back to fully-contacted position. Therefore, the lateral forces on a said V-shape surface assures the bearing to be a solid connector in regular service condition and works as a resistance against lateral sliding when the structural system is suffering an external impact-induced acceleration, see  FIG. 10 . The bearings with the design of disclosed V-shape contact surface-pair are able to meet all the aforementioned criteria except the criterion (C). 
         [0028]    There can be multiple or single or no mate sheet between the top and bottom pads of the bearing in  FIG. 9 . The functions of the mate sheets are to lubricate the sliding surfaces and to damp the vibrations along vertical direction. However, when the amplitude for this kind of vibrations is high, an additional novel design of a sliding-pin becomes necessary. This embodiment is described in  FIG. 11 , which makes the device satisfying the criterion (C). 
         [0029]    When multiple mate sheets are desired, it leads to another key-embodiment, i.e. vertically embedded pins, which includes two subclasses: (i) the pin that enhances to the V-shape mate sheets and is made of the material with the yield strength lower than the sheet material but has the capacity for large plastic deformation; (ii) the pin that is made of the material with the yield strength higher than mate sheet material while the two ends of each pin are respectively fastened to top and bottom pads without the flexibility to rotation. The former, termed vertically-laid dissipation pin (VDP) with the major function to dissipate vibration energy. The latter, the high strength pin, does not deal with dissipation but provide additional lateral resistance against vibration and restoration driving force, termed vertical reinforcement pin (VRP).  FIG. 12(   a ) is the prototype that combines with the embodiment in  FIG. 11  with VDP.  FIG. 12(   b ) is a prototype of V-shape Elastic Bearing with multiple V-shapes in a contact surface-pair and with additional VRPs. 
         [0030]    An advantage for the embodiment of the vertically-reinforced pin (VRP) is that ties connected parts, for example, super and substructure of a bridge, together, whereas the bearing still plays the function for damping. Obviously, the apparatus with VRP satisfies all aforementioned criteria. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0031]      FIG. 1 : Earthquake hazard map provided by USGS (United States Geological Survey); the iso-contour lines in the map indicate the values of the predicted horizontal “peak-ground-acceleration (PGA) with 7.5% probability of exceedance in the next 75 years. This map is used by US bridges and buildings design standard. 
           [0032]      FIG. 2 : Predicted horizontal “peak-ground-acceleration (PGA) with 10% probability of exceedance in the next 50 years. in Continent of Far-Eastern Asia (excluding Pacific-Rim seismic area such as Japan), source: Global Seismic Hazard Assessment Program (see www.usgs.gov). 
           [0033]      FIG. 3 : Technologies currently applied for a seismic-resistant designed three-storage building; the art disclosed in this article is a class of new seismic isolation bearings showing in the left-low corner. 
           [0034]      FIG. 4 : Prior art: an energy absorber to damp lateral vibration forces through the deformation of its core  28 , made of absorptive material such as lead, after pressure is imposed from vertical direction. To assure no-sliding between the core material and the frame such as top pad  10  or bottom pad  12  or the middle pad  20 , various designs of the interface geometry  11  are introduced by the drawings on the right. 
           [0035]      FIG. 5 : A prior art (U.S. Pat. No. 4,187,573): a structural bearing that uses elastomer to damp lateral and vertical vibration while carry the weight of the superstructure. 
           [0036]      FIG. 6 : A prior art, WO2008/004475, which can be considered as the further development of the art in  FIG. 5 , whereby the key component is the composite block that is made of the laminar structure by elastomer  2   b  and reinforce plate  2   c.  The block contains a center core  3 , made of high plasticity material, e.g. Lead, to reinforce lateral deformation resistance while improve the capacity of damping. 
           [0037]      FIG. 7 : prior art (U.S. Pat. No. 6,021,992), termed friction pendulum sliding bearing (FPS), which belongs a group of dozen US patents and tens in other countries which are based on the principal of the pendulum depicted on the right-hand side of the figure, utilizing the carried superstructure&#39;s weight as a natural force to resist horizontal inertia caused by ground motion. Once such a spectrum of ground motion passed, the gravity restores the bearing back to its original position. 
           [0038]      FIG. 8 : A prior art (U.S. Pat. No. 5,669,189), termed anti-seismic connector (ANSC). It is actually an assembly of a laminated elastomeric bearing  3  plus the tie-bars (or ropes)  6  that are fastened to the connected super and substructure by the rotate-able fastener  21 . 
           [0039]      FIG. 9 : The embodiment of the V-shaped contact surface-pair base bearing for seismic isolation. 
           [0040]      FIG. 10 : How gravity is utilized to resist horizontal ground acceleration-induced vibration by the V-shape contact surface-pair; for simplification, it is assumed friction coefficient vanishing in the figure. 
           [0041]      FIG. 11 : The embodiment of the V-shaped contact surface-pair base bearing with sliding-pin. 
           [0042]      FIG. 12 : (a) prototype of V-shape Elastic Bearing with sliding-pin in  FIG. 11  with vertically-laid dissipation pin (VDP); (b) a prototype of V-shape Elastic Bearing in  FIG. 10  but with multiple V-shapes in a contact surface-pair and with additional vertical reinforcement pin (VRP). 
           [0043]      FIG. 13 : (a) A prototype of VEB with double orthogonally overlaid V-shape contact surface-pairs to accommodate the vibrations along any direction within a horizontal plane. (b) A prototype of VEB with U-shape contact surface-pair overlaid above V-shape contact surface-pairs to accommodate superstructure&#39;s rotation 
           [0044]      FIG. 14 : Top: a design example of UVEB, by which the mate sheets  2  and  4  have specially designed contact areas to control the friction coefficient. The two sliding positions in lower part of the figure show how the longitudal stopper works. 
           [0045]      FIG. 15 : A prototype of MVEB, a sub-class of the invented apparatuses, by which the V-shaped contact surface compromises more than three facets. Between the top or bottom pot contact surfaces is an elastomeric mate block that contains at least one metal or high-strength composite mate plates. 
           [0046]      FIG. 16 : Design examples of 360° VEB: (a)3-fold; (b)4-fold; (c)4-fold UV and the mate sheets with designed contact-surface areas. 
           [0047]      FIG. 17 : Design example of a “one-way VEBSP”, which is able to accommodate vibration-induced lateral relative-separation within the plane of the V-geometry while the sliding along the direction perpendicular to the V-shape is restrained by the cover-plates fixed to top pad. 
           [0048]      FIG. 18 : Design example of a 360° VEBSP that is able to accommodate vibration-induced lateral relative-separations along all horizontal directions while keep the connected super and substructure&#39;s integrity. 
           [0049]      FIG. 19 : Design examples of sliding pins and side stoppers for VEBSP. 
           [0050]      FIG. 20 : Two prototypes of VEBSP with damping mechanisms. 
           [0051]      FIG. 21 : An illustration how the damping mechanism works for the prototype given by  FIG. 20(   a ), in top; and design of the device. 
           [0052]      FIG. 22 : The embodiment of “vertical reinforced elastomeric bearing (VREB)” with reinforce-pins, chart of problem-solution. 
           [0053]      FIG. 23 : Two design examples of V-shape base VREB: (a) without post tension; (b) with post tension. 
           [0054]      FIG. 24 : Two design examples of flat contact-surface VREB: (a) without post tension; (b) with post tension. 
           [0055]      FIG. 25 : Two design examples of VREB with damping core: (a) V-shape contact-surface design; (b) flat contact-surface design. 
       
    
    
     DESCRIPTION OF EMBODIMENTS 
       [0056]    The first embodiment is based on the concept of “V-sliding” in  FIG. 9 , which employs at least one pair of V-shape sliding-contact surfaces to establish the connection between super- and sub-structure of a large-scaled civil engineering structural system, allowing a temporally relative sliding when one of sub or superstructure is struck by single or a spectrum of external impacts, so as to protect another part from the inertia force flow induced by the impacts. Once such a contacted surface-pair tends to slide, the weight of carried superstructure introduces lateral force toward the opposite direction of the sliding, which, in conjunction with friction, assures the bearing is solid connection during regular services or when inertia-induced lateral force is lower than the resultant of static friction and superstructure&#39;s weight-induced lateral resistance. The latter is determined by the slope angle of the V that is designed according to  FIG. 1  or  2 , which is also the driving force to restore its original connection after the temporal sliding. The apparatuses based on this embodiment forms a subclass of the disclosed art, termed VEB that stands for “V-shape Elastic Bearing”. An innovative sliding-pin&#39;s design, see  FIG. 11 , in conjunction with VEB, defines the second sub-class of said apparatuses that satisfies the criterion C, termed “VEBSP”, standing for “V-shape Elastic Bearing with Sliding-Pin”. 
         [0057]    Obviously, the angle α of the V-shape is the key design parameter, which determines the threshold of the lateral force that causes sliding-separation. This force, denoted as Q, results in corresponding stress distribution over both super and substructure, by which the peak value of the stress ratio, 
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         [0000]    should be limited to an allowable level that will not cause damage, i.e. 
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         [0000]    where σ Y  is the yielding strength of the material element with the stress σ peak (Q) under the lateral force Q and designed live and dead load; n Q  is safety factor and n Q &gt;1. The condition (1) actually assures entire structure without yielding, so the angle α of the V-shape surface-pair is designed by the threshold of allowable impact force, denoted as “Q TH ”, which is the upper bound of Q to satisfy (1), i.e.: 
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         [0058]    Now consider an example: a bridge that has four bearings and the total mass of its superstructure and designed live load is represented by the quantity “4M”. Then, Q R , the lateral resistance against onset of sliding, is (see  FIG. 17 ): 
         [0000]        Q   R   =M·g [tan(α)+ f   r ]  (3)
 
         [0000]    where f r  is friction coefficient between V-contact surface and mate sheet. According to (2): 
         [0000]      Q R ≦Q th    (4)
 
         [0000]    By substituting (3) into (4) and taking equal-sign, the maximum allowable angle α that satisfies (2) yields: 
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         [0000]    For the invented V-shape bearings family, the second key design-parameter is the maximum allowable sliding distance l, which is quantitatively determined by applying the second Newton&#39;s law. When the bearings are primarily applied to seismic isolation,  FIGS. 1 and 2  provide the prediction of horizontal PGA (peak ground acceleration) at any location where a building or a bridge is built. An actual earthquake generally includes a spectrum of ground motions with various frequencies κ i , i=1, 2, . . . n, but its amplitudes are bounded by PGA. Therefore, one can define a “characteristic frequency”, for example, the average: 
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         [0000]    to represent the ground motion spectrum in the form of following sinusoidal wave: 
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         [0000]    So the corresponding inertia-induced lateral force to each bearing of the bridge at the time t is: 
         [0000]    
       
         
           
             
               
                 
                   
                     
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         [0000]    Assuming the superstructure starts to slide at the time t 0  when Q pred (t)&gt;Q th , at the instance t&gt;t 0  its sliding speed is V(t) and the distance traveled is S(t), so 
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         [0000]    according to the second Newton&#39;s law. 
         [0059]    Hence, in a VEBSP the superstructure is able to slide its maximum allowable sliding distance I VEBSP  along lower V-contact surface within a duration t s -t 0  and, then, will be stopped by side stopper that has an equivalent mass M side  and stiffness K side  corresponding to the superstructure&#39;s impact induced information. Applying momentum conservation law, F side , the impact force to the stopper, can be approximately estimated by: 
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                       - 
                       
                         
                           
                             Q 
                             th 
                           
                           
                             2 
                              
                             M 
                           
                         
                          
                         
                           t 
                           S 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The time t S  can be solved by the first equation of (9) when F side  is known, which should be determined based on the allowable stress of the bearing; then using the second equation to determine I VEBSP  or verse versa. 
         [0060]    Similarly, for a VEB, the requirements to the sliding distance l VEB , which assures that the sliding of a carried superstructure will stop within V-shape contact surface at the time t E , yields: 
         [0000]        V ( t   E )=0 and  S ( t   E )≦ l   VEB    (10)
 
         [0000]    Substituting the first relation of (10) into (8) determines t E , then, substituting the t E  into the second relation of (8) to solve l VEB , which finalizes the basic parameters in a VEB designs. 
       Design Examples with Additional Embodiments 
       [0061]      FIG. 13  illustrates two design prototypes of VEB: the one on left has orthogonally overlaid double V-shape contact surface-pairs that is able to damp vibrations along any direction within a horizontal plane, which is termed “V-VEB”. The one on right utilizes U-shape contact surface-pair overlaid above V-shape contact surface-pairs to accommodate superstructure&#39;s rotation, which can be termed “U-VEB”.  FIG. 14  is the design example of an U-VEB design, which includes another embodiment that is to adjust the friction coefficient between mate sheet and bearing pads through adjusting contact area. 
         [0062]    In order to utilize the advantages of elastomer or elastomer-like material for damping and for environmental-friend purpose, for example, reduced noise, a problem to be solved in practice is to minimize the risk of tension instability for this class of materials. This leads to the invention of another sub-class VEB, termed “Multi-V Elastomeric Bearing (M-VEB)”. A design of MVEB is given in  FIG. 20 . For a V-shape contact surface-pair, when relative sliding occurs between a facet-pair while separations take place between other pairs of facets, such a separation stretches contained elastomer layer and may cause tension instability. Therefore, in the design of  FIG. 15  the waive-like, multi-facet, V-contact geometry redistributes the single space caused by the separation between non-sliding side single facet-pair into the cavities of multi-V facet-pairs, by which the key-embodiment of VEB and associated beneficial properties remain. This benefit, in conjunction with the favorable properties of elastomer material, make this class of bearing to be a candidate to the structures in the region with moderate seismic risk. 
         [0063]    As compared to the VVEB illustrated in  FIG. 13(   a ),  FIG. 16  introduces the design examples with the embodiment to utilize single prism-shape contact surface-pair to damp the vibrations along any direction within a horizontal plane based on the concept of VEB, by which a prism contact surface comprises N facets where N is an integer that is greater than 2; there facets may have the same or different inclined angles to horizontal plane. When a vibration-induced sliding-separation takes place, the sliding may either occur within one contact facet-pair that has the inclined angle α F  or along two adjacent facet-pairs with the motion along the edge between the two adjacent facets. For the latter, the edge has an inclined angle α E  to horizontal plane, determined by the following equation: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       sin 
                        
                       
                           
                       
                        
                       
                         α 
                         E 
                       
                     
                     
                       sin 
                        
                       
                           
                       
                        
                       
                         α 
                         F 
                       
                     
                   
                   = 
                   
                     cos 
                      
                     
                       ( 
                       
                         π 
                         N 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
         [0000]    α E  is generally smaller than the angles of adjacent facets. This subclass of VEB is termed “360° VEB”. The design examples in  FIG. 16  are, respectively, 3-fold, 4-fold, and 4-fold UV type 360° VEB. 
         [0064]      FIG. 17  is a design example of VEB with sliding-pin, which is able to accommodate vibration-induced lateral relative-separation within the plane of the V-geometry, guided by the sliding-pins that preserve super and substructure as an integrated structure through mounted top and bottom pads. Along the direction perpendicular to the V-shape the sliding is restrained by the cover-plates that are fixed onto top pad. This subclass of V-sliding concept base bearing is termed “one-way VEBSP”. By contrast,  FIG. 18  is a design example of “360° VEBSP” that is able to accommodate vibration-induced lateral relative-separations along all horizontal directions while keep the connected super and substructure&#39;s integrity. In the design examples of  FIGS. 17 and 18  the sliding-pins can slide freely within the grooves on top pad but guided by the slits on the sider stoppers that are screwed onto bottom pad. There is no essential difference if sider stoppers are fixed to top pad while the sliding-pin grooves are cut from bottom pad. 
         [0065]      FIG. 19  presents various design-examples of sliding pins and sider stoppers of VEBSP. The cylinder rod-pin has lower contact friction but strict requirements to material&#39;s strength and wear-resistance. The sider stopper with straight slot provides tied vertical constraint to the relative movement between top and bottom pads but needs more careful maintenance for the contact surfaces on the pins and on the stoppers&#39; slits to avoid friction-locking; it also requires certain distance between the pins&#39; groove and the V-shape contact surface. 
         [0066]    For a VEB (or VEBSP) bearing, for example, that in  FIG. 11 , during the transition of the sliding between one pair of facets to another facet-pair that was separated, the sliding movement changes direction. To reduce the impact caused by this sliding-kick, designs with respective damping mechanisms are given in  FIG. 20 , in addition to the VDP in  FIG. 12(   a ). The device in (b) employs a deformable ring containing a damping core. The ring is fixed onto the ends of two opposite sliding-pins, stretched and compressed when sliding occurs, which results in the core&#39;s plastic deformation. The core is made of deformation-inert material, for example, Lead. A design of this device is given in  FIG. 21 . The device in  FIG. 20(   b ) is similar to that in (a) but with two deformable rings and contained cores. 
         [0067]    For both VEB and VEBSP, appropriated materials should be chosen to manufacture each piece of corresponding apparatus to satisfy the requirements of (i) strength; (ii) fatigue resistance; (iii) friction properties that include specified friction coefficient and wear-resistance; (iv) stiffness, (v) capacity for energy absorption and damping, (vi) corrosion resistance. 
         [0068]    Elastomer, the traditional material for bridges&#39; and building&#39;s bearings, can also be used as the mate sheet material between the V-shape contact surface-pair, for examples, the prototype in  FIG. 15 . Due to its high friction coefficient, the sliding-separation mechanism in other material-mated VEB or VEBSP may not happen when elastomer mate sheet is employed. Generally speaking, elastomer is often attached to metal surface in bearings&#39; application; sliding between metal surface and elastomer may cause local tension instability that will cause the latter&#39;s failure. Obviously, the lateral resistance provided by elastomer&#39;s shear modulus is limited. Therefore, this class of bearing lacks sufficient driving force for self-restoration when struck by strong ground motions. Also, when environmental temperature drops below frozen point, elastomer becomes brittle with lower friction resistance. 
         [0069]    To avoid the aforementioned drawbacks for this kind of materials while to utilize its beneficial properties, another key-embodiment of this invention is the concept of “vertical reinforcement”, as presented by the bearing prototypes in  FIG. 22 , termed “vertically-reinforced elastomeric bearing”, in short, VREB. The key-feature of VREB is to perpendicularly embed an array of pins, made of high-strength elastic material, into an elastomeric block, which is termed VRP (vertical reinforcement pin) previously; the two ends of each pin are respectively fastened by upper and bottom pads without the freedom of rotation while tie the two pads together. Because the top pad is mounted onto superstructure while the bottom pad is mounted onto substructure, so these vertically-laid pins essentially hold the two parts as integrated structure. When the both ends of such a pin are respectively fastened tightly by upper and bottom pads, no free rotation is allowed for the pin around its tied ends, which introduce addition resistance against horizontally dislocated motion between the pads while provide intrinsic elasticity force to drive the system back to original position after the dislocations. The simplicity in its geometry implies the convenience for manufacturing with enhanced cost-effectiveness. Similar to structural concrete, the embedded vertical pins and horizontal metal sheet make the elastomeric like a rubber-composite with desired stiffness and damping capacity. The embedded pins may also provide additional structural functions such as to process post-tension. 
         [0070]    As illustrated in  FIG. 22 , the embodiment of VREB is lighted by the superior properties of human&#39;s hair. Such a hair&#39;s strength is actually higher than mild steel. Its super tenderness and flexibility is due to the small diameter, which inspires the idea to employ multiple high-strength, small diameter, reinforce bars into elastomeric blocks for the desired dual (isolation and reinforcement) properties. 6 Design examples of VREB are given in  FIGS. 23-25   
       INDUSTRIAL APPLICABILITY 
       [0071]    The applicability of the disclosed art has been explained by  FIG. 3  and associated text. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
           
               
                   
               
               
                 Citation List 
               
               
                 Related US Patent Literatures: 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 4,033,005 
                 4,187,573 
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                 4,644,714 
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                 6,178,706 B1 
               
               
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                 6,631,593 B2 
                 6,474,030 
                 6,481,894 
               
               
                 6,688,051 B2 
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                 6,951,083 B2 
                 6,971,795 B2 
                 7,398,964 B2 
               
               
                 7,419,145 B2 
                 7,547,142 B2 
                 2004/123530 
                 2005/0205749 A1 
                 2006/0024453 A1 
                 2006/0174555 A1 
               
               
                 2007/0283635 A1 
                 2008/0222975 A1 
                 2008/0136071 A1 
                 2009/0126288 A1 
                 2009/0188179 A1 
                 2009/0205273 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
           
               
                   
               
               
                 Related WO Patent Literatures: 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 82/02930 
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                 99/02287 
                 05/095819 
                 07/114072 
               
               
                 08/004475 
                 09/001807 
                 09/033213 
                 09/054533 
                 09/139645A1 
                 11/043242 
               
               
                   
               
             
          
         
       
     
       NON PATENT LITERATURES 
       [0000]    
       
         [1] Federal Emergency Management Agency (FEMA), Reports 350-353, 2000 
         [2] USGS(United State Geological Survey) website: www.usgs.gov 
         [3] California Department of Transportation (Caltran), “The Continuing Challenge: The Northridge Earthquake of Jan. 17, 1994”. 
         [4] TRB NCHRP 12-68, Final Report: Rotational Limits for Elastomeric Bearings, 2004. 
         [5] AASHTO Guide Specifications for LRFD Seismic Bridges&#39; Design, 2 nd  Ed., 2011-2012 
         [6] Amendment to AASHTO LRFD Bridge Design Specification-4 th  Ed., Section 14: Joints and Bearings, Caltran, 2010. 
         [7] Touaillon J., “Improvement in Buildings”, United States Patents Office, U.S. Pat. No. 99,973, Feb. 15, 1870. 
         [8] “Guide Specifications for Seismic Isolation Design”, AASHTO, Third Edition, July, 2010 
         [9] “Guide Specifications for Seismic Bridges&#39; Design”, AASHTO, Second Edition, 2011 
         [10] “LRFD Bridge Design Specifications”, AASHTO, 5th Edition 2011 revision. 
         [11] “California Amendment to AASHTO LRFD Bridge Design Specifications—Fourth Edition (Section 14)”, 
         [12] “Experimental Investigation on the Seismic Response of Bridge Bearings”, Univ. of California, Berkeley, EERC-2008-02, 2008. 
         [13] Kelly, J. M., 1997, “Earthquake-resistant design with rubber”, 2nd Ed., Springer, London. 
         [14] “Rotation Limits for Elastomeric Bearings”, Report 12-68, University of Washington, 2006 (published as report NCHRP 596, 2008). Civil, Structural &amp; Environmental Eng. , University at Buffalo 
         [15] Buckle, I., Nagarajaiah, S., and Ferrell, K. 2002. “Stability of elastomericisolation bearings: Experimental study.” J. Struct. Eng., 128(1), pp 3-11. 
         [16] Constantinou M. C., and Kneifati, M. C., “Dynamics of soil-base isolated structure system”, Journal of Structural Engineering, ASCE, Vol. 114, No. 1, 1988, pp. 211-221 
         [17] Jerry, B. J. and Yuen, W. P. “Seismic Performance and Design of Bridges With Curve and Skew”, FHWA Report, Accession Number: 01080786, 2006 
         [18] Cooper J., Friedland I. M., Buckle I. G., Nimis R. B., Bobb N. M., 2009, “The Northridge earthquake: progress made and learned from seismic-resistance design”, FHWA. 
         [19] Bazant, B. “Stability of Structures: Elastic, Inelastic, Fracture, and Damage Theories”, Mineola, Dover Pub. 2001 
         [20] Galambos V. Theodore, “Structural Stability of Steel Concepts and Applications for Structural Engineers”, John, Willies &amp; Son, 2008