US 3638377 A
An earthquake-resistant multistory structure that effectively isolates the superstructure from the ground motions during a major earthquake by permitting relative displacement between the superstructure and the foundation, the structure incorporating means which effectively control both the magnitude of the base shear force required to initiate relative displacement and the magnitude of relative displacement.
Claims available in
Description (OCR text may contain errors)
United States Patent Caspe 1 Feb. 1, 1972  EARTHQUAKE-RESISTANT MULTISTORY STRUCTURE  Inventor: Marc S. Caspe, 1809 Ralston Ave.,
Belmont, Calif. 94002  Filed: Dec. 3, 1969  Appl.No.: 881,810
Related 05. Application Data  Continuation-impart of Ser. No. 767,767, Oct. 15,
 U.S.Cl. ..52/167, 52/294  Int. ..E04h9/02  FieldoiSearch ..52/167,294;188/1B  References Cited UNITED STATES PATENTS 1,572,574 2/1926 Stromborg ..52/l67 1,761,322 6/1930 Wells ..52/167 2,001,169 5/1935 Wallace. .....52/167 2,690,074 9/1954 Jones ..52/167 3,510,999 5/1970 Habacher.. .....52/167 468,186 2/1892 Beardsley ..52/167 FOREIGN PATENTS OR APPLICATIONS 1,213,573 1960 France ..52/l67 1,084,064 1967 Great Britain ..52/167 Primary Examiner-l-lenry C. Sutherland Attorney-Townsend and Townsend  ABSTRACT 24 Claims, 18 Drawing Figures PATENTED FEB H972. 35383.
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SHEET 5 OF 7 INVENTOR,
MARC S. CASPE ATTORNEYS EARTHQUAKE-RESISTANT MULTISTORY STRUCTURE RELATED APPLICATIONS This application is a continuation-in-part application of the copending patent application bearing Ser. No. 767,767, filed Oct. 15, I968 for Earthquake Resistant Multistory Structure now abandoned.
BACKGROUND OF THE INVENTION Earthquake damage is, for the most part, caused by energy waves that are emitted from deep within the earth's crust when slippage occurs along a nearby fault plane. Although many different types of energy waves are emitted during a single earthquake, it is the shear waves that cause the greatest structural damage. These waves vibrate the bedrock beneath buildings, and as the horizontal component of these vibrations is perpendicular to the main strength of the structure, it is the accelerations in this plane that are most troublesome. If the building is founded upon a soil mantle this soil will be excited into horizontal vibration which will then be transmitted to the structures supported thereon. Structures founded upon bedrock will be excited directly by the rock.
The structure responds to these excitations in a unique manner dependent upon its natural period of vibration relative to that of the ground, its ability to absorb energy by damping and its ability to absorb energy by deforming plastically (i.e., deforming beyond its elastic limit without collapse).
Prior practice in high-rise building design and construction has been to support all columns and walls upon concrete footings or walls that bear directly upon the ground. This typing of the structure to an ultimate ground support is of course necessary to resist the pull of gravity. Forces due to wind are also transmitted to the ground through these same structural members although in a somewhat different manner because horizontal rather than vertical forces (loads) are involved.
When an earthquake occurs the ground translates and accelerates in a random manner that has been recorded numerous times. Because conventional buildings are tied directly to the ground they must translate and accelerate with the ground. The ground acceleration, which can reach as high as 16 feet/second/second in major earthquake areas, causes the previously stationary building to vibrate thereby causing high horizontal inertial forces. In California, for example, these inertial forces could be many times larger than those developed by the maximum possible horizontal wind force that could be brought to bear.
Heretofore, the usual design practice permitted multistory structures to accept the excitation of the ground and to respond to it with the horizontal energy of the vibrating ground being resisted and absorbed by the structural framework. In the design of conventional structures, the intent has been to overstress the steel in the structural elements (structural steel or reinforced concrete) beyond the yield point, thereby absorbing greatly increased amounts of energy through internal work in the plastic zone. Such design philosophy is well stated in the Commentary to the 1967 Lateral Force Code of the Structural Engineers Association of California (SEAOC) as follows:
...structures designed in conformance with the provisions and principles set forth therein (SEAOC Code) should be able to:
I. Resist minor earthquakes without damage;
2. Resist moderate earthquakes without structural damage, but with some nonstructural damage;
3. Resist major earthquakes, of the intensity of severity of the strongest experiences in California, without collapse, but with some structural as well as nonstructural damage.
In most structures it is expected that structural damage,
even in a major earthquake, could be limited to repairable damage. This, however, depends upon a number of factors, including the type of construction selected for the structure.
As will be apparent from the foregoing, serious structural damage can be expected in prior multistory structures during a major earthquake and, although loss of life may be limited, some prior structures will not be repairable and will require replacement. Even those structural joints that are repairable will have questionable serviceability during a following earthquake because seismic damage is cumulative.
Another disadvantage of prior art structures is that the extra strength required for joint ductility is difficult and expensive to attain. This factor accounts for increased costs and lesser heights of multistory structures in California, for example, as opposed to multistory structures in other parts of the United States.
The members most susceptible to damage in multistory structures are the columns as they are less ductile (i.e., less capable of deforming beyond the elastic limit without rupture) due to the heavyv axial loads that they carry. As the columns are the most important members in the support of a frame structure, the inherent weakness of prior structural systems is obvious.
SUMMARY OF THE INVENTION The present invention overcomes the above as well as other shortcomings of the prior art, and in according with the present invention, an earthquake resistant multistory structure is provided which limits the horizontal inertial forces that can be transmitted from the ground to the superstructure during an earthquake, such limit being above a severe wind force that can be expected to develop in the vicinity so as to avoid relative displacement during such a windstorm. The present invention enables the construction of multistory structures whereby displacement of the foundation relative to the superstructure is achieved only at a horizontal load greater than this severe horizontal wind force that can be expected to act upon the structure. The present invention also includes means that will effectively prevent accidental relative displacement of any substantial magnitude due to unpredictable wind forces in addition to providing a self-righting feature that counters excessive displacement during an earthquake and limits permanent displacement following an earthquake.
The present invention provides apparatus for isolating the superstructure from its foundation to prevent damage to the superstructure from excessive horizontal forces caused by earthquakes, aerial blasts and the like.
In its broadest form, the invention provides a connection between the foundation and the superstructure which has a bilinear (or multilinear) force-deflection characteristic. While a horizontal force up to a predetermined maximum, relative to the design wind force, acts on the superstructure, the superstructure remains essentially stationary with respect to the foundation except for minute displacements due to elastic shear, tension or compression, or bending deformation in the connection. When the horizontal force between the superstructure and the foundation tends to exceed the predetermined maximum, the force exerted by the connection ceases to increase, at least temporarily, and remains substantially constant so that the foundation begins to move with respect to the superstructure. Generally, it is preferable that the connection between the superstructure and the foundation oppose the relative movement of the superstructure with a force which increases as a function of the total displacement from an original or zero relative position of the superstructure. The rate of increase of the motion opposing force exerted by the connection can be adjusted in accordance with the maximum permissible displacement of the superstructure, available design space, and like considerations.
Accordingly, in one form, the apparatus of the present invention comprises means for transferring the superstructure weight to the foundation which permits substantial relative horizontal movements between the superstructure and the foundation under the influence of minor horizontal forces. Control means, which are independent of the weight transferring means, transmit horizontal forces between the superstructure and the foundation. The control means have a bilinear force-deflection characteristic which substantially prevents horizontal movements between the superstructure and the foundation when subjected to a horizontal force up to a predetermined magnitude, while permitting substantial horizontal movements between the superstructure and the foundation once the horizontal force exceeds the predetermined magnitude. The force exerted by the control means during the relative movement of the superstructure is relatively constant and at least about equal to the maximum force exerted by the control means during nonmovement of the superstructure.
In the preferred embodiment of the invention, the apparatus includes stop means for limiting the displacement between the superstructure and the foundation to a predetermined maximum. The superstructure weight transferring means comprises low-friction ball bearing clusters and the control means comprise stress or control members which are constructed so that they are stressed to their yield stress when the predetermined maximum wind force acts on the superstructure. Thus, the wind force causes inconsequential displacements of the superstructure within the elastic deformation of the stress members. Forces in excess of the maximum wind forces, however, such as forces developed during earthquakes, stress the members beyond their yield stress so that permanent or inelastic deformation of the members occurs. Such a deformation permits substantial movements of the superstructure with respect to the foundation. The horizontal forces that can be transmitted from the foundation to the superstructure, and which can cause serious damage or collapse of the superstructure during an earthquake, are thereby limited. Permanent displacement of the superstructure after the earthquake is adjusted by returning the superstructure to its original position with the help of hydraulic jacks and like equipment.
In an alternate form of the invention, the apparatus for isolating the superstructure from a foundation to prevent damage to the former by limiting the horizontal forces acting between them comprises horizontally disposed friction interfaces which permit relative horizontal motions between the foundation and the superstructure and means for subjecting the interfaces to a predetermined transverse load. The interfaces and the load-applying means are constructed to develop friction forces which prevent relative horizontal movements of the superstructure until a horizontal force between the superstructure and the foundation exceeds the predetermined friction force. The friction force is so selected that it equals the predetermined maximum wind force expected to act upon the superstructure. After movement of the superstructure commences, the friction force opposing such movement remains nearly constant.
In another embodiment of the invention, certain ones of a plurality of structural columns which serve to support the above-grade stories of the building, preferably exterior columns of the building, are utilized as stiff control columns and are mounted on low-friction bearing means having substantially constant static and dynamic coefficients of friction permitting lateral displacement of such columns during earthquake conditions while the remaining flexible columns such as, for example, the interior columns of the building are mounted so as to have a much less horizontal stiffness thereby permitting a rigid ground floor diaphragm to transmit all base shear to the stiffer control columns until slippage occurs. Whenever the total base shear exceeds the total axial force in the control columns multiplied by the coefficient of friction of the bearing means, initial slippage can take place. This feature limits the inertial forces that an earthquake can impart to the building. Resilient restraining means is provided for limiting the lateral movement of the low-friction bearing mounted columns to complement the restraining means of the flexible columns. The restraining means are constructed to: store the energy of displacement whenever slippage occurs and at the same time build up a resistance to further slippage thereby stopping any accidental slippage with a minimum of displacement; limit the relative displacement of the ground with respect to the structure during an earthquake by acting upon the structure in the direction of the ground displacement and thereby causing the structure to accelerate in the direction of the ground displacement with a smooth motion and lesser values of acceleration than those of the ground in displacing to this same point; limiting displacement under coincident action of wind and earthquake; and acting to return the structure to near its original position with respect to the ground after the earthquake vibrations cease.
In the aforementioned embodiment of the invention each bearing means is comprised ofa plurality of Teflon or like lowfriction bearing pads which are disposed for movement relative to each other between the lower end portions of the control columns and upper end portions of the concrete footings when subjected to shear forces greater than the maximum shear forces encountered due to wind pressure. In this form of the invention the restraining means is comprised of square neoprene pads which surround the Teflon bearing pads and which act as a spring when deflected laterally.
A further embodiment of the invention accomplishes substantially the same purpose as the preceding embodiment except that the stiff control columns having low-friction bearing means are replaced with stiff control springs having a bilinear force deflection characteristic. The function of the stiff control springs is to limit the displacement of the superstructure when loaded horizontally with a base shear less than or equal to that associated with the design Windstorm. Should a major earthquake cause base shears in excess of that associated with the design Windstorm, the control springs form a plastic hinge mechanism and deform without developing additional load. The control spring continues to distort beyond the yield point without contributing additional resistance to horizontal deformation until strained to the range of strain hardening where an increase in load-carrying capacity is realized. The direction of the resisting force acts to cause the superstructure to follow the ground displacement to a greater extent than does the control column of the first embodiment in which the direction of the force was dependent upon the instantaneous direction of the relative velocity between ground and structure. This serves to spread the change in acceleration of the superstructure over a longer interval of time, which effect has an important physiological bearing upon the occupants of the structure.
This embodiment is comprised of a number of short vertical members (control linkages) that are inserted about the periphery of the structure on line with the exterior columns but at the midpoint between said columns. The control linkages are therefore not required to support any vertical load. The top of the member is pin connected to the underside of the girders that comprise the ground floor diaphragm and the bottom is fixed against rotation at the top of the basement wall pilasters. In this manner all horizontal load is distributed to these stiffer elements by the ground floor diaphragm and they are loaded in single curvature through a limit-stop bracket at the top.
The design of the control linkages permits the formation of a plastic hinge within the linkage material. The ideal material for this linkage is a mild steel pipe section because it is multidirectional and has (a) great ductility, (b) high resistance to local bucking, and (c) a well-defined yield point on a momentrotation curve. The hinge is designed to form simultaneously at the bottom of each of the control linkages when the total horizontal resistance is equal to the equivalent force of the design Windstorm. The design takes account of the horizontal elastic displacement in the control linkages that is associated with this wind force as this displacement will be reflected directly in the adjacent breakaway joint during a Windstorm.
Means comprised of control rods cooperating with limit stops may alternatively be utilized to control the magnitude of the relative displacement between the ground and the structure, and if desired the various embodiments of the present invention may be combined in a multistory structure.
It is an object of the invention to provide an improved earthquake-resistant structure incorporating improved means for limiting the horizontal inertial forces that can be transmitted from the ground to the structure during earthquake conditions.
Another object of the invention is to provide an improved earthquake resistant structure incorporating improved means that will effectively prevent accidental displacement of any substantial magnitude due to unpredictable wind forces, provide a self-righting feature that counteracts excess displacement during an earthquake, limit permanent displacement following an earthquake and provide a fail-safe mechanism should an earthquake of unusual magnitude occur.
The above as well as other objects and advantages of the present invention will become apparent from the following description, the appended claims and the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a side elevational view of a typical multistory building embodying the present invention;
FIG. 2 is an end elevational view of the structure illustrated in FIG. 1;
FIG. 3 is a typical floor plan of the structure illustrated in FIG. 1',
FIG. 4 is an enlarged, fragmentary, sectional view of the foundation of the structure illustrated in FIG. 1;
FIG. 5 is an enlarged, fragmentary, sectional view of a control column of the structure illustrated in FIG. 1, showing the same under normal conditions;
FIG. 6 is a view similar to FIG. 5 illustrating such structure at its extreme limit during earthquake conditions;
FIG. 7 is a cross-sectional view of the structure illustrated in FIG. 4, taken on the line 7-7 thereof;
FIG. 8 is a schematic view of an interior column of the structure illustrated in FIG. 4 when distorted during earthquake conditions;
FIG. 9 is a plan view of another embodiment of the inventron;
FIG. 10 is an elevational view of the structure illustrated in FIG. 9, taken on the line 1010 thereof;
FIG. 11 is an enlarged, fragmentary, sectional view of the loading bracket at the top of one of the control linkages illustrated in FIG. 10, showing the same under normal conditions;
FIG. 12 is a view of the structure illustrated in FIG. 11, showing the same at its extreme limit during earthquake conditions;
FIG. 13 is a schematic view of a control linkage when distorted during earthquake conditions;
FIG. 14 is a sectional side elevational view of a multistory building wherein the various embodiments of the inventions are combined therein;
FIG. 15 is-a sectional view of a portion of the control rod and cooperating limit stop illustrated in FIG. 14;
FIG. 16 is a fragmentary plan view illustrating a superstructure isolated from its foundation in accordance with the preferred form of the present invention;
FIG. 17 is a fragmentary elevational view of the structure illustrated in FIG. 16; and
FIG. 18 is a fragmentary, enlarged view in section of mechanically preloaded friction interfaces between the superstructure and the foundation.
DESCRIPTION OF THE PREFERRED EMBODIMENTS Referring first to FIGS. 16 and 17, a building 202 comprises a superstructure 204, foundation 206 and a connection 208 between the superstructure and the foundation. Connection 208 comprises ball bearing clusters 210 defined by opposing bearing face plates 212 between which a plurality of hard, high-strength stainless steel balls 214 are disposed. The ball bearing clusters transmit the weight of the superstructure to the foundation while permitting relative horizontal movements between the superstructure and the foundation under only minor, relatively insignificant horizontal forces. To permit such relative motions of the superstructure, clearance (best seen at 216) for lateral movements is maintained between the foundation and the superstructure.
Connection 208 further includes control or horizontal force-transmitting means 218 which are independent of the vertical load-transmitting ball bearing clusters 210 and which, in the preferred embodiment of the invention, comprise a plurality of control or stress rods 220 having their respective ends suitably connected to superstructure 204 and foundation 206. The control rods are preferably constructed of steel pipe of the like and prevent relative horizontal movements of the superstructure when the superstructure is subjected to horizontal forces such as wind forces until the horizontal forces exceed the total yield strength of the control rods in a given direction. Thereafter, if horizontal forces acting on the superstructure exceed the yield strength, as, for example, during an earthquake, the control rods are subjected to inelastic or permanent deformation (in tension or compression) which permits relative movements of the superstructure on bearing clusters 210. The maximum horizontal forces transmitted between the superstructure and the foundation is thereby controlled.
As the superstructure moves with respect to the foundation and the control rods continue to be inelastically deformed, strain-hardening of the control rods can set in to thereby increase the forces exerted by the control rods in opposition to the superstructure movement. The movement of the superstructure is thereby slowed down and the total displacement of the superstructure under such excess horizontal forces is reduced. As is more fully described hereinafter, such relative displacement of the superstructure can further be controlled with the help of additional stress members, springs, stop means, and the like.
Referring briefly to FIGS. 16 through 18, control rods 220 illustrated in FIGS. 16 and 17 can be replaced with other members exerting a force in opposition to the horizontal force acting on the superstructure and having a bilinear forcedeflection characteristic. A presently preferred alternative to the control rods is the provision of preloaded friction bearings 222 illustrated in FIG. 18. The friction bearing comprises a U- shaped bearing housing 224 having spaced-apart soleplates 226 secured to each other with a stiffener 228. The housing is secured to foundation 206 with pretensioned steel rods. A diaphragm plate 231 is rigidly attached to the superstructure (not fully shown in FIG. 18) and extends between soleplates 226. The adjacent sides of the soleplates 226 and diaphragm plate 231 are provided with low-friction facings 230 such as Teflon layers which have a relatively constant static and dynamic coefficient of friction.
Diaphragm plate 231 includes an oversize bore 234 through which an anchor bolt 236 extends, the bolt is tightened against the soleplates of housing 224 prior to making the weld 238 between stiffeners 228 and soleplates 226, and preloads the interfaces defined by bearing facings 230 so that a predetermined horizontal force is required to overcome the friction developed between the facings and thereby permit movements of the superstructure with respect to the foundation on bearing clusters 210 (not shown in FIG. 18). The preload is set so that the friction force developed between the facings is about equal to the design wind force of the building.
Another embodiment of the invention is illustrated in FIGS. 1 through 8 incorporated in a typical multistory frame structure, generally designated 10. The structure 10 is shown in the drawings, by way of example, as having 24 stories and the structure is comprised of 24 interior columns 12, four exterior corner columns 14, and 20 additional exterior columns 16 which are disposed between the four exterior corner columns 14.
In this embodiment ofthe invention, the portions 17 of all of the columns, beams and girders above the first floor 18 of the structure 10 are made of any common structural material while the portions of the first floor and the columns, beams and girders below the first floor are preferably made of structural steel. It will be understood, however, that other suitable materials having sufficient strength and ductility to withstand the forces and motions exerted thereon may be utilized in the construction of all or portions of the columns.
In this embodiment of the invention, the 20 exterior columns 16 between the corner columns are selected as shear control columns, and as illustrated in the drawings, are mounted on support means generally designated 20 which permit lateral movement of the control columns 16 under earthquake conditions. As shown in the drawings, each of the control columns 16 is in the form ofa tube substantially circular in cross section, and the lower end of each of the columns 16 is fixed, as by welding, to a baseplate 22 which is preferably square in plan view and which is provided with a chamber 24 around the periphery thereof. A square pad 26 constructed of a low-friction material such as Teflon having a relatively constant static and dynamic coefficient of friction is bonded to the lower surface of the baseplate 22 by a suitable adhesive, the pad 26 in turn bearing directly upon a pad 28 which is also preferably made of Teflon. The pad 18 is bonded to a soleplate 30 and the soleplate is fixed to a pilaster 32 forming part of the concrete foundation 34 of the structure 10. In the drawings the soleplate is illustrated as being fixed to the pilaster 32 by bolts 36 and nuts 38 which are spaced circumferentially around the periphery of the soleplate 30. A square guide plate 40 is provided which is disposed in upwardly spaced, parallel relationship with respect to the soleplate 30, the guide plate 40 being welded or otherwise fixed to the exterior surfaces of the column 16, A plurality of angularly spaced, generally triangular stiffener plates 42 are provided to stiffen the connection between the guide plate 40 and the column 16.
An annular resilient restraining member or sleeve 44 is provided, the upper surface of which is bonded to the lower surface of the guide plate 40 adjacent the periphery thereof while the lower surface of the restraining member 44 is fixed to the soleplate 30 in spaced relationship with respect to the baseplate 22. The restraining member 44 is preferably made of neoprene or other suitable resilient material having sufficient strength to withstand the forces exerted thereof and having the upper and lower surfaces of the restraining member bonded to the guide plate 40 and the soleplate 30, respectively, by a suitable adhesive. An annular neoprene pad having a height of 6 inches and a wall thickness of4 inches and which had a O-durometer hardness was found to be-well suited for use in the design of a 30-story building. The pad does not support any portion of the building weight but serves as a shear spring to provide a restoring force during an earthquake. The pad has a very low stiffness and does not restore the building to its original position on the foundation, it merely aids the return motion of the building during earthquake oscillations. The actual restoration of the building to its original position is accomplished with hydraulic jacks and the like after the earthquake occurred.
A stop' member 46 is provided which surrounds the resilient restraining member 44 and which is provided with a beveled surface 48 around the interior thereof, the stop member 46 being retained by the bolts 36 and acting as a positive stop for the restraining member 44 when the restraining member 44 is forced against the stop member by the baseplate 22 under earthquake conditions, as will be described hereinafter in greater detail.
The first floor 18 is a conventional orthotropic steel plate floor which functions as a vertical floor slab supporting the live loads of the structure and as a horizontal diaphragm transferring high-point applied horizontal shear loads to the control columns. The orthotropic plate floor being supported upon girders 50 which in turn are supported by the columns l2, l4 and 16. The upper end portions ofeach of the control columns 16 are fixed to the girders 50 by plates 52 reinforced by stiffeners 54. The upper end portionsof the corner columns 14 and the interior columns 12 are also fixed to the girders 50 by plates 56 reinforced by stiffeners 58. As shown in FIG. 4, the portions of the corner column 14 and the interior columns 12 below the first floor 18 are substantially longer than the control columns 16 and have minimum shear-resisting capabilities, as will be described hereinafter in greater detail. The columns 12 and 14 pass through the intermediate basement floor 60 in spaced relationship in respect thereto and the lower end portions of the columns 12 and 14 are fixed to the basement floor 62 by plates 64 reinforced by stiffeners 66. The portions of the interior columns 12 and the corner columns 14 below the floor 18 are preferably in the form of solid steel shafts as shown in FIG. 7. The interior portions of the floor 60 and the corner portions thereof are supported by tubular members 68 which surround the columns 12 and 14 while the peripheral portions of the floor 60 between the corner columns 14 are supported vertically by the foundation wall 34 while in turn providing horizontal support for the wall pilasters 32. With such a construction, the tubular members 68 separate the floor 60 from the columns 12 and 14 and prevent the floor 60 from transmitting earthquake forces through the floor 60 to the intermediate portions of the columns 12 and 14.
As shown in FIG. 4, the curtain wall 70 of the structure 10 is separated from the top of the basement wall 34 by an expansion joint 72 which is preferably made of a relatively flexible material retained by an unbonded elastomeric sealant which will break away upon relative translational movement between the floor 18 and the top of the basement wall 34. Such a construction is easily repairable and prevents damage to the curtain wall and windows during an earthquake.
In the design of a multistory building, such as the structure 10, so as to embody the present invention, those skilled in the art should commence the design procedure with the establishment ofa design criteria for the external forces that can be expected to act upon the structure. The design Windstorm should be that having the maximum velocity that could be expected in the vicinity with a selected frequency of recurrence (say the 50year storm). Similarly, the design earthquake should be characterized by a strong motion occurrence normalized to a peak magnitude that is estimated very conservatively from such conditions as the proximity to the fault zone and the soil conditions on the site.
The design of the superstructure can then proceed as though the building were to be built in a conventional fashion. in an area of nonseismicity. The analysis and design for dead and live vertical load combined with the wind pressures to be countered is standard practice well known in that art and need not be described herein in detail.
After the design of the superstructure is completed, the dead load that is to be carried by each column within the structure should be calculated in the conventional manner. An estimate can then be made as to the magnitude of semipermanent live loads, such as partitions and office furniture, together with an estimate of expected live loads due to useage, With the foregoing data, the present invention can then be embodied in the structure.
In the embodiment of the invention illustrated in FIGS. 1 through 8, the columns 16 were selected as control columns. These control columns 16 should be short and stiff in comparison with the other columns 12 and 14, thereby causing the ground floor slab 18 to act as a diaphragm that distributes substantially all horizontal shearing forces to the control columns 16. It is preferred that the selected control columns 16 support a minimum total vertical load equal to the desired initial sliding force previously determined, divided by the minimum value of the coefficient of friction between the Teflon pads 26 and 28.
As previously mentioned, it is preferred that the pads 26 and 28 be made of polytetraflouroethylene (Teflon), such material exhibiting the unique property of having a slightly lower coefficient of friction under static conditions than under sliding conditions. This very small difference permits smooth motion, without the highly objectionable start and stop jolting that would occur with many other materials. Glass-reinforced Teflon pads have a very low coefficient of friction of between 0.06 to 0.08 under well protected atmospheric conditions, when loaded to less than 2,000 psi (on thin sheets of about 100 mils) and experiencing a relative velocity of less than 10 feet per minute. This coefficient can be expected to double when relative velocities reach 100 feet per minute. The material is easily bondable to steel and is highly resistant to decay, having a negligible change in characteristics with age.
In selecting control columns it is desirable to select the exterior columns for a number of reasons. Exterior columns are less heavily loaded than those on the interior and therefore require a greater number of columns to achieve the same total force upon the sliding surfaces. The greater number of columns requires lesser shear transfer at each column thereby simplifying the details and improving the reliability of the diaphragm 18. It is important that the control columns be placed symmetrically about both axes of the structure. In this manner the overturning moment can be made to induce an increase in the compressive force on one side of the structure that is equal in magnitude to the decrease on the other side, thereby resulting in a total vertical force on the control columns that is relatively constant at every instant of time. The exterior columns 16 also provide greater resistance to torsional rotations than do the interior columns 12 and can be founded directly upon the top of the exterior basement retaining wall thereby permitting a complete break between the superstructure and the substructure.
The interior and corner columns 12 and 14 are long and flexible in comparison with the control columns 16 so that the floor diaphragm 18 transfers all horizontal shear to the stiffer control columns prior to slippage, the control columns 16 being short and supported directly upon the top of the basement wall pilasters 32, while the longer and more flexible columns 12 and 14 are maintained clear of the walls and wall support systems and are founded at or near the lowest level of the basement.
The control columns 16 are proportioned to slip at a horizontal load approximately equal to that associated with the design Windstorm. With such a construction, no slippage will occur during a Windstorm and the superstructure will function in precisely the same manner as any other building until a major earthquake or a most unusual Windstorm occurs.
Structures embodying the present invention will slip during an earthquake as soon as the ground acceleration induces an inertial base shear in excess of that associated with the maximum Windstorm (i.e., that permitted by the control columns). Beyond this point vibratory slippage of the ground continues beneath the structure. The Teflon pads act as Coulomb (friction) dampers, and no additional accelerationcan be induced into the structure through these pads until the ground acceleration and velocity again fall below the magnitude associated with initial slippage. The structure will then behave, once again, in a manner similar to that of any other building.
It should be noted that velocity is equally as important as acceleration in determining the point at which shear reversal occurs between the Teflon pads 26 and 28. Although acceleration alone controls the inertial forces causing initial slippage of the structure, the simultaneous occurrence of low velocity and low acceleration is required to permit slippage to stop. When the ground is translating at high velocity and zero acceleration, the relative velocity between the ground and structure is high, thereby requiring a very large acceleration of the structure for it to catch up" with the ground velocity. Slippage will therefore continue until the simultaneous occurrence of low velocity and low acceleration, which condition will occur infrequently during the duration of the earthquake. For these few instances it is important that the low-friction bearing material have a constant coefficient of friction for both static and low-velocity sliding conditions.
The shear force upon the base of the structure always acts in the same direction as the relative velocity of the ground with respect to the structure. While sliding at low velocity, the base experiences minor variations in shear force due to vertical accelerations. These variations are self-compensating and do not affect the calculated motions between ground and structure.
The present invention provides continuous control of the structures behavior during an earthquake by storing strain energy in direct proportion to the relative displacement between the ground and the structure. The potential energy is stored in spring-type mechanisms with magnitude continually increasing as the ground translates away from the structure. This stored energy is then released as kinetic energy that smoothly translates the structure in the direction of the ground motion but at much lesser values of acceleration than that ofthe ground in moving to this same point.
In accordance with the present invention, means is provided for storing strain energy during an earthquake, such means includes the long flexible columns 12 and 14 and the restraining member 44. The columns 12 and 14 are fixed at both top and bottom, and such columns will be distorted in double curvature as illustrated in FIG. 8 by the relative motion of the ground and structure during an earthquake. This distortion induced by the translation of the ground causes strain energy to be stored in the springs which act to restore the structure towards its original position with respect to the ground.
Flexibility is required in these column springs to prevent the transfer of the ground motions directly into the structure. Inherent in this flexibility is a lack of bending strength as both parameters are a function of the moment of inertia and length of the columns 12 and 14. The distortion of these columns together with the heavy axial load that they carry will cause high stresses and the simultaneous formation of plastic hinges at both the top and bottom of the columns 12 and 14. Once such hinges are formed the columns 12 and 14 are no longer capable of storing recoverable strain energy and any energy that is absorbed by the material beyond this point is in the form of internal friction attributable to hysteretic effects. It is therefore apparent that the columns will not serve as reliable capacitors for the storage of recoverable strain energy throughout the entire range of displacement and the restraining member 44 is required to supplement the columns 12 and 14 in storing the strain energy.
By correlating the transverse dimensions, height and hardness of the neoprene restraining member 44, the desired shear stiffness can be obtained that is necessary to supplement that of the flexible columns 12 and 14 in storing the strain energy of displacement during an earthquake.
If during an earthquake of greater magnitude than that foreseen in the design, the baseplate 22 should contact the base of the restraining member 44 at the limit of expected displacement, the restraining member 44 would be locked between the baseplate 22 and the bolted stop plate 46, thereby confining the restraining member 44 for a finite length and causing it to act in compression as a very stiff spring. The restraining member 44 also serves as a hermetic seal to prevent the entry of dust and grit to the mating surfaces of the Teflon pads 26 and 28 thereby maintaining the coefficient of friction at a relatively constant value. Further, the restraining member 44 functions as a highly effective fireproof insulation for the Teflon pads 26 and 28 in the event of a high-intensity fire, the restraining member 44 being easily replaceable if damaged by fire, whereas the Teflon pads 26 and 28 are not.
An understanding of the mode of operation of structures embodying the present invention is facilitated by a review of the relationships between the time-dependent parameters of an earthquake. In an earthquake, the variation of accelerations, velocities and displacements are not harmonic, the periods of each parameter being different. The variation in amplitude of the acceleration curve is not symmetrical about the base axis of time. Instead it is weighted towards one direction and then the other in a long period, small amplitude cycle that is comprised of a series of short period, high-amplitude cycles superimposed directly thereon. Since the velocity at any time is the cumulative area under the acceleration curve, the maximum velocity occurs whenever the long period cycle of acceleration crosses the time axis and begins changing the velocity into the opposite direction. Isolated spikes that are not representative of the direction of weighting do not necessarily cause a reversal in the direction of the ground velocity even though they do cross the time axis. It is for this reason that the period of the velocity component is much longer than that of the acceleration spikes. Similarly the displacement is an accumulation of the area under the velocity curve. The earthquake ground motion is therefore that of a short period (0.2 seconds) excitation that causes long period (2 to 6 seconds) displacements. That is to say that the ground vibrates slowly off in one direction and then vibrates back and into the other direction. The final position of the ground being somewhat displaced from the initial position.
Comprehension of the above facilitates an understanding of the force balance that exists upon the foundation of the structure 10 during an earthquake. The columns 12 and 14 and the restraining members 44 which function as springs to store strain energy at the base of the structure 10 have a stiffness that causes a resistance to relative displacement whose magnitude is directly proportional to said displacement. Hence, whenever the ground moves in one direction relative to the structure the columns 12 and I4 and the restraining members 44 act as self-righting mechanisms that accelerate the structure slowly in the direction of the ground displacement. Since the ground displacement has a much longer period than does the ground acceleration, the columns 12 and 14 and the restraining members 44 have sufficient time to force the structure back towards its original position with respect to the ground with a lesser acceleration than that of the vibrating ground in displacing to this same point. In essence, the columns 12 and 14 and the restraining members 44 act to smooth out the sharp vibratory acceleration of the ground to produce a gentler motion upon the structure that is a function of the spring stiffness, thereby providing a vibration barrier that effectively limits the magnitude of the dynamic forces acting upon the structure.
The interrelationships between the components of a structure embodying the present invention can best be demonstrated with a typical design example, the 24-story frame structure 10 being utilized as an example for analysis. It is assumed that the structure 10 is 310 feet high and has 24 interior and 24 exterior columns as shown in FIGS. 1, 2, and 3, the fundamental period of vibration of the superstructure being 1.91 seconds. The probable base shear computed by superposition from an elastic modal analysis of the response to the El Centro earthquake motions which occurred in California in 1940 is 12,000 kips on the basis of the square root of the sum of the squares of the first five modes of vibration and 17,000 kips on the basis of the fundamental mode plus the square root of the sum of the squares of the succeeding four modes. The base shear contribution of the fundamental mode is 10,000 kips.
Assume that the total permanent dead weight including that of the ground floor is 92,000 kips, based upon a 190 p.s.f. permanent dead load and a 10 p.s.f. curtain wall load, and is assigned to each column as follows:
8 Interior Cols.
l6 Isl Inter. Col's.
12 Exterior Col's.
Long Side) 26(20)(2S)(0.l90)=2490 each 26( 21 25 0. l 90)=2590"' each =1380" each 8 Exterior Cols. 25( l3)(20)(0.l90)+310120)(0.()l
(Short Side) =l300 each 4 Cornet Col's 25( 14 l2 )(0. l)+290(26)(0.0l)
=870" each and Bernoulli's equation of flow: 7
/2mv /2(0.076/32 )v (5,20/3,6O0) =0.00256v, the force acting per foot of building width is:
300 300 f ap z= 1.2(.00256) (65) /gg mosz where C,, is the sum of the windward (0.8) and the leeward (0.4) drag coefficients. The maximum total wind force is therefore 8.5(179) or 1,520 kips if the full component of the design Windstorm is assumed to impinge horizontally upon the broadest face of the structure. The total force for yaw angles other than zero will be slightly less than 1,520 kips. Lesser values of C, could be used on the leeward side if verified by wind tunnel tests.
The 20 exterior control columns I6 provide a resistance to slippage of at least 20(0.06)( 1,370) or 1,650 kips. As this is a lower limit, an added safety factor against slippage in a windstorm is provided by the semipermanent weight of office furniture (partition weight has already been included in the dead load), any live load that is present as well as any increase in the friction factor of the Teflon pads 26 and 28 above their minimum.
Assuming further that the maximum ground displacement is 8 inches (El Centro, Calif. occurrence of 1940), it is reasona ble to assume that the combination of Teflon pads 26 and 28, the columns 14 and I6 and the restraining members 44 can effectively limit the structure to a maximum relative displacement of6 inches with respect to the ground.
In this design example the control column details shown on FIGS. 5, 6 and 7 are considered as existing beneath each of the 20 exterior control columns 16. The bearing stress in the Teflon pads when supporting the total dead load is 1,970 psi.
The neoprene restraining members 44 are unloaded in compression due to their lesser stiffness. The rib stiffeners 42 on the guide plate 46 prevent distortion ofthe plate 40 and assure the transfer of pure shear to the annular restraining members 44 so long as the width to thickness ratio is greater than onehalf. The chamfered edges of both the limit-stop plate 46 and the column baseplate 22 provide a surface contact with the restraining members 44 at the limit-stop position of 6 inches relative displacement.
Since the column bearing plates 30 are supported upon the pilasters 32 set off from the main basement wall 34, the
elimination of the pilasters 32 allow the exterior columns 14 that are not control columns to extend down past the wall 34 to achieve the length required for flexibility. In this example a flexible column length of 30 feet is selected as giving a good balance between stiffness and the formation of plastic hinges. It should be understood that the length of the columns need not necessarily correspond to the height of the basement levels but can be built up above or drilled down below the bottommost basement floor.
The interior flexible columns 12 are assumed to be 16-inch diameter solid steel shafts and fixed against rotation at both the top and bottom, the circular steel section providing the cross-sectional area necessary to support the vertical load with a minimum of moment of inertia or stiffness. The circular section is also multidirectional and exhibits satisfactory resistance to failure in the bucking mode.
The axial stress in a typical l6-inch diameter interior steel column is:
The allowable stress in a 30 foot long unbraced column under static loading conditions is:
and under dynamic loading conditions is:
The column acts as a spring, when deflected as shown on FIG. 8, having spring stiffness:
A u/A 12EI/L 12(30 )322O/30 (1728) 25.0 thereby developing moment at a rate of:
The column will experience an initial yield in compression when:
it has a plastic moment capacity of:
where Z is the plastic modulus of the column reduced for axial load. As the central part of the column can be assumed to resist the axial load, the compression area required when stressed to yield is:
.4,,,.,,,,=P/o-y=2,750/35.0=78 in. or an approximate rectangular area of /2 inches by 5 inches. The section modulus of the remaining area is the first moment of that area about the axis of rotation. This can be calculated as the modulus of the full circle minus that of the central rectangle hence:
Therefore the plastic moment capacity of the section is:
M,,=0,,Z=35(583)/12=1,700"" and V,,=2M,,/L=2(1,700)/30=ll3 Thus, initial yielding occurs at a relative displacement of: A,,=M,,/(M/A)=715/375=1.9 in. and full plasticity occurs when:
if the stiffness is taken as the average over the transition from an elastic to a fully plastic section. The curvature related to the yield moment is:
The curvature related to the moment at the 6-inch limit-stop can be derived with certain simplifying assumptions. After initial yield at 1.9-inch displacement further end rotation continues as:
However this rotation does not occur at one section but is distributed along the plastic zone of length L extending to a point ofinitial yielding where:
To be conservative, assume that the maximum curvature is twice the average curvature along the plastic zone, hence:
5 =2l9/L'=2(.0057)/7.7(l2)=l2.3 lfl inf and the ductility ratio at 6 inch displacement is:
The effect of secondary bending upon the column moments is to create an increase in stress of approximately 5 percent with a corresponding increase in the ductility ratio. It is also 1 important to note that the axial load increases the displace ment associated with inertial distortion thereby reducing the shear stiffness of the column. This is equivalent to a reduction in the horizontal shearing force (FIG. 8) associated with a given displacement and a corresponding reduction in the elastic spring stiffness ofthe column an amount:
A=V/A=P/l,=2,750/30120 (12)=7.7 resulting in a net elastic stiffness of:
prior to initial yield. As the stiffness due to elastic deformation decreases beyond the yield point, the elastic shear at maximum relative displacement should be checked to assure that it is well in excess of the shear associated with secondary bending. 1f the column is so flexible that this is not the case, the resultant shear will tend to increase rather than limit the relative displacement between ground and structure before the limit-stop is reached.
The neoprene restraining members 44 have a constant stiffness regardless of the displacement. This value is calculated for each control column as 0.l90[2(4)50+2(4)42/l.l8]/7% or 17.5 kips per inch of displacement for a 65 hard material. The factor 1.18 is a reduction in the effective area of the narrow band of the restraining members due to bending deformation and is calculated by assuming that the neoprene has an elastic modulus of 20 times the shearing modulus.
Assuming further that the flexible corner columns 14 are 14-inch solid steel shafts having a net elastic stiffness of 10 kips per inch and that the first interior columns are 18-inch solid steel shafts having a net elastic stiffness of 20 kips per inch, the overall spring stiffness of the foundation can be evaluated in stages ofincreasing relative displacement as follows: Stage 1 Prior to the initiation of slippage all shear is transmitted directly through the shear control columns 16 and Teflon bearing pads 26 and 28 to the concrete foundation 32. The fundamental period of vibration of the structure is calculated to be 1.9 seconds.
Stage 2 After initial slippage and prior to the start of column yielding, the shear force is maintained constant between the Teflon bearing pads 26 and 28 and the remainder of the shear developed by displacement is distributed between the flexible columns 12 and 14 and the neoprene restraining members 44 in accordance with the elastic spring stiffness of these elements. The magnitude of this shear is linearly proportional to the instantaneous relative displacement between the ground and the structure. The fundamental period of vibration of the structure is calculated to be 3.8 seconds once the structure starts to slide.
Stage 3 After the start of column yielding at a displacement of 1.9
inches and up to the formation of a full plastic hinge at a displacement of 7.2 inches the shear is distributed in the same manner as defined above, except that column stiffness continually decreases with increasing displacement. The fundamental period of vibration of the structure is in transition within this stage.
Stage 4 After the formation of a fully plastic hinge the columns 12 and 14 cease to absorb recoverable strain energy and only the restraining members 44 can accept additional shear forces. The fundamental period of vibration of the structure is calculated to be 5.5 seconds once the plastic hinge is formed. Stage 5 After reaching the limit-stop the restraining members 44 act in compression as a very stiff spring to limit further displacement. The chamfered backup plate 46 then functions to provide a locked-in, well-confined section of neoprene which does not depend upon the epoxy bonding material for support.
These relationships can be stated in terms of the design example by summing up the horizontal forces transmitted through each column for every inch of relative displacement up to the limit-stop at 6 inches. The assumption is made that the decrease in column stiffness is linear between the limits of L9 inches and 7.2 inches relative displacement. The shear force acting upon the structure is positive in the direction of the relative ground displacement hence, the negative shear values in the Teflon pads 26 and 28 occur whenever the relative velocity between the ground and structure is counter to the direction of this displacement:
This tabulation shows clearly that the resultant force acting upon the structure during an interval of time is always unbalanced in the direction of the ground translation. It is this action that causes the structure to follow the ground displacement at accelerations which are considerably below those of the oscillating ground. The maximum base shear that could possibly develop is only 5,750 kips and this is highly improbable as it requires that the relative velocity be in the direction of additional displacement when the relative displacement between the ground and structure is already 6 inches. Although this maximum base shear is substantially more than the 1,520-kip wind force previously used in the elastic design of the elements of the superstructure, the difference is resisted by the superstructure in a number of manners; the summation of which indicates that the superstructure as designed for wind force is adequate to absorb the energy transferred to it during a major earthquake. A general discussion of each such manner of absorbing or reducing the energy transferred to the superstructure follows immediately below.
Firstly, a large reserve strength of at least 150 percent and more nearly 200 percent of the design lateral wind force (L650 kips) remains before the elements of the structure begin to approach initial yield. Additional reserve strength is of course available beyond this point both in the form of plastic deformation at the first hinges to form and elastic deformation throughout the remainder of the superstructure.
The differences between the manner in which seismic excitation ofthe foundation and external wind forces are applied to the superstructure, will serve to reduce still further the comparable stresses within the load-carrying elements. Wind is an external force that must be transmitted directly to the ground, whereas seismic vibrations can only induce damage when resonant periods are established causing magnification of the ground motions within the superstructure.
The fundamental period of vibration prior to slippage is 1.9 seconds. After slippage this value is increased to about 3.8 seconds, thereby eliminating the possibility of major resonance in the fundamental mode during an earth quake. The elastic response spectrum for a simple oscillator subject to the earthquake motions such as those encountered in the El Centro earthquake, and having a fundamental period of 3.8 seconds would show a maximum acceleration of 0. 10 g. with 2 percent damping and 0.07 g. with 10 percent damping. As the superstructure is not expected to enter the plastic range to any major extent, it is appropriate and conservative to assume a completely elastic response spectrum with a damping factor of about 5 percent of critical damping. However, this damping value will be increased considerably by the Coulomb damping associated with slippage of the Teflon pads 26 and 28 and the visco-elastic damping of the restraining members 44.
The 3.8-second period of vibration for stage 2 was calculated using a Raleigh analysis which, when compared to the 3.5-second period of an equivalent simple oscillator having the mass of the total structure and the stiffness of the flexible columns 12 and 14 combined with the restraining members 44, indicates that the soft base spring controls the vibration of the structure in the fundamental mode. The effective weight was calculated as 98 percent of the true weight. The stage 4 period of vibration was found to be controlled entirely by the soft base spring. This demonstrates conclusively that the long natural period of vibration of the structure after slippage effectively prevents resonance with the ground in the higher modes of vibration.
From the foregoing it will be apparent that the combination of elastic and plastic reserve strength in the structure together with the Coulomb damping of the Teflon pads 26 and 28, the viscous damping of the neoprene restraining members 44 and the improbability of resonance due to the long fundamental period of vibration after slippage, permits the initial design of the superstructure to be based upon wind loading without regard for seismic action. Local strengthening for added ductili ty can of course be accomplished at joints within the superstructure that are found to be critical.
The foregoing analysis indicates that the structure should be permitted to displace to a maximum of 6 inches with respect to the ground, this upper limit being selected arbitrarily for the example illustrated and being based upon a maximum ground motion of 8 inches for the design earthquake. Once the maximum relative displacement is established, all structural and architectural details at the ground floor level can readily be designed to accommodate these motions which include a conservative factor of safety. For example, all high-speed elevators should stop at the first basement level and other units, such as heavy-duty hydraulic units, used to service the subbasement levels. In this manner no elevator would pass through any floor that could experience relative displacement with respect to the unit. Stairwells at the ground floor landing and the landing immediately below should allow for expansion and contraction in addition to rotation due to motions perpendicular to the run of the stair. Pipes and vent ducts should be designed with universal joints placed immediately below the ground floor level. These joints should be designed for the maximum relative displacement and as such merely represent an extension of existing technology well known in the art. Provision is made to permit jacking of the superstructure with respect to the foundation should residual relative displacement be present after an earthquake.
Another embodiment of the invention is illustrated in FIGS. 9 through 13, this embodiment of the invention accomplishing substantially the same purpose as the embodiment illustrated in FIGS. 1 through 8. The stiff control columns 16 having lowfriction bearing means are replaced with stiff control springs or rigid posts 116 having a bilinear force deflection charac teristic. The function of the stiff control springs 116 is to limit the displacement of the superstructure when loaded horizontally with a base shear less than or equal to that associated with the design Windstorm. Rigid posts 116, also referred to as control springs 116 or control linkages 116. The prefix control" indicates that the particular member has a bilinear forcedeflection characteristic obtained by employing the welldefined elastic limit characteristic of mild steel and like materials or the stick-slip characteristic of a precompressed friction surface. Mild steel pipe and reinforced Teflon, respectively, appear to be the most suitable materials for achieving reliability and control over the bilinear force-deflection characteristic. Other materials and shapes can of course be substituted where desired. Should a major earthquake cause base shears in excess of that associated with the design windstorm the control springs 116 form a plastic hinge mechanism and deform without developing additional load. The control spring continues to distort beyond the yield point without contributing additional resistance to horizontal deformation, until strained to the range of strain hardening where an increase in load-carrying capacity is realized. The direction of the resisting force at every instant of time serves to cause the superstructure to follow the ground displacement to a greater extent than does the control column 16 of the first embodiment in which the direction of the force was dependent upon the instantaneous direction of the relative velocity between ground and structure. This serves to spread the change in acceleration of the superstructure over a longer interval of time, which effect has an important physiological bearing upon the occupants of the structure.
This embodiment is comprised of a number of short vertical members (control linkages) that are inserted about the periphery of the structure on line with the exterior columns 112 and 114 but at the midpoint between the columns 1 12 and 114. The control linkages 116 are therefore not required to support any vertical load. The tops of the members 116 are pin connected to the underside of the girders 150 that comprise the ground floor diaphragm 118 and the bottom of each of the members 116 is fixed against rotation at the top of the basement wall pilasters 132. In this manner all horizontal load is distributed to these stiffer elements by the ground floor diaphragm 118 and they are loaded in single curvature through a limit-stop bracket 120 as will be described hereinafter in greater detail.
The design of the control linkages 116 permits the formation of a plastic hinge at the base of the linkage material. The ideal material for this linkage is a mild steel pipe section because it has (a) multidirectional strength characteristics, (1)) great ductility, (c) high resistance to local buckling, and (d) a well-defined yield point on a momentrotation curve. The hinge is designed to form at the bottom of each of the control linkages 116 simultaneously when the total horizontal resistance is equal to the equivalent force of the design windstorm. The design takes account of the horizontal elastic displacement in the control linkages that is associated with this wind force because this displacement will be reflected directly in an adjacent breakway joint during a Windstorm.
A design example using the 24-story structure previously analyzed is typical of the design procedure in this embodi ment. The total shear force associated with any displacement within the elastic range is:
and the moment at the base of each control linkage 1 16 is:
M=3ElA/L resulting in a stress in the outer fiber of the pipe section of:
If it is desired to limit the ultimate shear force to 1,650 kips, the shear force that will cause initial yield at the outer fiber of the control linkages is 1,650/(Z/S) or 1,270 kips if the shape factor of the pipe section is 1.3. Using 24 control linkages 116 to reduce the shear transfer at each linkage, and permitting a deflection of approximately 0.20 inch at initial yielding, the equations on lines 6 and 10 above can be written for a pipe having a l-inch thick wall and composed of steel having a yield point of 35 k.s.i. as follows:
a' avg/L l ,270/20.5(0.50)(0.20)24=25.9 inP/ft." and (d.,,-,,+0.50)/L 35/3 l2(0.20)=0.556 in./ft. Solving by trial and error L is equal to 5.5 feet and d, is 16.8 inches. Using a 16-inch extra long steel pipe that is 5 ft. 6 inch long:
M,,==35( l6.0l 5.0)(0.098)/l6.0( l2)=226" and M,,=35( l6.0"l 5.0)/6( l2)=355. The corresponding values of total shear are: V,,=266( 24 )/5.5=l l 60" and m I ,,=35 5 (2 4 /5.5=l ,550"
As the 28 flexible columns 12 and 14 of the previous embodiment had a stiffness of 500 kips per inch, it is reasonable to approximate the added stiffness of the 20 exterior flexible columns 112 of this embodiment as 300 kips per inch for a total stiffness of 800 kips per inch of relative displacement. The deflection at initial yield is:
Ay=0',,L /3o Ec=35(5.5) 144/3(30,OOO)8.O=0.21l inch. Therefore the contribution of the flexible columns 112 and 114 to base shear is 800(0.21 1) or kips at initial yield of the outer fiber and 170( l6.0/15.0) or kips at initial yield of the inner fiber. The combined resistance of 1,550-1-180) or 1,730 kips is slightly in excess of the desired wind resistance of 1,650 kips. The rotation at initial yield on the outer fiber is:
,,,,=2a,,/Ed,=2( 35 )/30,000( l6.0)=0.000146 radians/in. and on the inner fiber is:
=0.000146(15.0/15.0)=0.000155 radians/inch. The rotation at the base when the limit stop is engaged at 6 inches relative displacement is:
(PA LM 6.0.21 5.5(144)(355266) and assuming that the maximum curvature is 20 percent greater than the average curvature for a pipe section:
The ductibility ratio at 6 inches displacement is then:
This value is beyond the limit of the strain-hardening range (u=l 2developed at displacements greater than:
Ash. A,,+ 6 .0%,
= 1.75 inches.
This is not critical in that it does not approach a collapse condition. The control linkage 116 does not support axial load and steel has the capacity to continue rotation to an ultimate ductility of over 150. A safety factor of greater than 150/43 or 3.5 is still present prior to failure of the linkage and even were failure to occur, it would present no danger to the superstructure and could be easily repaired following the earthquake.
The fail-safe feature in this embodiment of the invention is located at the top of the control linkages 116 where the limitstop brackets 120 act to load each control linkage 116. The limit-stop brackets are preferably circular in plan view and en- Opposite ends of an 18-inch diameter top plate 121 move up It is preferred that the top plate 121 be made with rounded edges that are bonded with Teflon and fit to the walls of the limit-stop bracket 120 with a very close tolerance so that it acts as a loading plate that is free to rotate. By positioning the top plate 121 as shown in FIG. 11 it is made to engage the flange portion 123 and the top wall 124 of the limit-stop bracket 120 in the manner shown in FIG. 12 at the moment when the predetermined limit of relative displacement is reached. In this manner the control linkage 116 is restrained at the top and further rotation is prevented. The control linkage 116 is now capable of developing an additional 1,650 kips with a minor additional displacement of approximately 0.20 inch. As this, in combination with the shear resistance of the flexible columns 112 and 114, and that previously developed by each control linkage 116, is undoubtedly in excess of the mechanism capacity of the superstructure, failure cannot occur within the isolation device. Adjustment of the location of the top plate 121 within the limit-stop bracket 120 can be provided by numerous means to permit repositioning in the event of a differential settlement. For example, a simple flange coupling (not shown) at the three-quarter height of the control linkage, having shim plates inserted between the bolted flanges, is one such means. Other means could be developed to limit the plastic hinge rotation at the ends of the control linkage by engaging a locking mechanism at a predetermined displacement. A stub column having an outside diameter slightly smaller than the inside diameter of the control linkage and fastened to the end plate within the control linkage is one such means of providing a locking mechanism and thereby providing additional control upon the limit-stop behavior.
Another control means is illustrated in FIGS. 14 and 15 wherein a control member 126 is provided which extends between and is secured to the pilasters 132 and the girders 150, the control member 126 having sufficient length to give the desired stiffness prior to yield and the desired ductility after yield. The length required to limit the relative displacement at initial yielding of the member to 0.20 inch would be:
and the total cross-sectional area required would be:
A=P/o' =l ,650/40=41 inF. The ductility ratio at 6 inches displacement would be 6.0/0.2 or 30. The cross-sectional area should be developed with thinwall pipe sections of sufficient diameter to prevent compression buckling of both the member and the pipe shell.
The control member 126 represents an extremely simple means of achieving the desired bilinear control characteristic. However, certain design problems must be recognized when incorporating such members into an actual structure. Consideration must be given to the multidirectional motions to be resisted by the orthogonal grid of rods and the design must account for the disparity between resistance to motions in the orthogonal and diagonal directions. The anchorage of the control members must be capable of rotation to prevent the development of bending moments due to motions perpendicular to the length of the rod. Also, the design must incorporate a fail-safe device which feature requires that means be provided to engage a limit-stop at a predetermined elongation or shortening of the control member. This may be built into the control member by inserting a solid steel rod 128 within the pipe member 130 and having a locking mechanism as shown on FIG. 15.
As shown in FIGS. 14 and 15, one end of the pipe member 130 is secured to a thrust block 131, fixed to the pilaster 132 while the opposite end of the pipe member is fixed to an end block 134, the end block 134 in turn being secured by a pin connection 136 fixed to a thrust block 138 secured to the girder 150. The rod 128 extends coaxially with the pipe member 130 and one end of the rod 128 is fixed to the thrust block 131. The rod 128 extends through bracing spiders 140 which prevent buckling of the rod. A generally tubular limitstop member 142 is provided which projects into the pipe member 130 in coaxial relationship therewith. One end of the limit stop 142 is fixed to the end block 134 while the opposite end of the limit-stop 142 is provided with inwardly projecting flanges 144. A collar 146 is fixed to the adjacent end of the rod 128, the collar 146 having resilient pads 148 and 149 which, for example, may be made of neoprene and which are adapted to engage the flanges 144 and the end block 134, respectfully, at its extreme limit under earthquake conditions. The limit-stop 142 is sized to permit free movement of collar 146 without restraint (unlike a dash pot) for shortening or elongation of the pipe member 130 to a predetermined limit beyond which the rod 128 is engaged in tension or compression through the engagement of the collar by flanges 144 of limit-stop 142 or end block 134. The total resistance of the pipe member 130 and the rod 128 must exceed the base shear associated with a failure mechanism in the superstructure.
To this point the various embodiments of the invention for controlling the force required to initiate relative displacement have been described separately. If desired the various embodiments of the invention may be combined in a single structure as illustrated in FIG. 14, to incorporate the more advantageous features of each embodiment. The elastic motions inherent in both the control linkage 116 and the control rod devices 126 prior to yield can be eliminated by employing control columns 16 that are sufficient to resist approximately 25 percent of the initial sliding force. As the control columns can be made much stiffer than the control linkages 116 they will serve to attract all horizontal shear prior to slippage, thereby eliminating all relative motions during minor windstorms.
The control linkage 116 and/or control rods 126 which are designed to resist the remaining 75 percent of the initial sliding force, are considerably more accurate than the control columns 16 in establishing the base shear at which initial rela tive displacement occurs. These devices are not subject to variations in either the axial load acting upon a column or the coefficient of friction of a low-friction material. The range between the upper and lower bound solutions is substantially reduced by these devices which in turn increases both the reliability of the design and the overall safety of the structure.
The sliding and elastic control devices shown and described herein are seen to be complimentary, in that their combination effectively enhances the advantages of each. A further extension of this compatibility can be achieved if the maximum wind force acting upon the building is known to come from a given direction, as is usually the case with prevailing winds. In such an instance it would prove useful to jack an initial slippage into the structure in such a manner that the control linkages 116 were preloaded against the control columns 16 thereby acting to aid in the resistance of wind forces from that direction.
The following table is provided for the convenience of those skilled in the art.
Notations a Area (inf) C, Drag Coefficient Distance to Outer Fiber (in.) D Diameter (in.)
do Outer Diameter (in.)
tli Inner Diameter (in.)
davg Average Diameter (in.)
E Modulus of Elasticity (K/in?) I Moment of Inertia (in!) K Dimensionless factors 1. Length I. Length of Plastic Zone (ft.)
m Mass Rate of Flow (#S /F") M Bending Moment (FK) N Number of Control Linkages p Pressure (psf) I Axial Load (kips) r Radius ofGyration (in.)
S Elastic Section Modulus (in?) v Velocity (m.p.h.)
V Shear (kips) 2 Height of Flow Above Grade (ft.) Z Plastic Section Modulus (in?) A or 6 Displacement (in.)
6 Angle of Rotation (radians) A Horizontal Stiffness in Bending (K/in.) A Horizontal Stiffness Due to Axial Load (K/in.) u Ductility Ratio t; Radius of Curvature (in.)
0- Stress (k.s.i.)
42 Curvature (UL-1) Subscripts p- Full Plasticity u Ultimate y Yield Point 6 Six Inch Displacement s.h. Strain Hardening b Bottom t Top While preferred embodiments of the invention have been shown and described, it will be understood that various changes and modifications may be made without departing from the spirit of the invention.
1. Apparatus for isolating a superstructure from its foundation to prevent damage to the superstructure from horizontal forces acting between the superstructure and the foundation comprising: means for transferring the superstructure weight to the foundation, the weight transferring means permitting substantial relative horizontal movements between the superstructure and the foundation under the influence of minor horizontal forces, and control means independent of the weight-transferring means for the transmission of horizontal forces between the superstructure and the foundation, the control means having a bilinear force-deflection characteristic substantially preventing horizontal movements between the superstructure and the foundation when subjected to a horizontal force of up to a predetermined magnitude and permitting substantial horizontal movements between the superstructure and the foundation when the horizontal force exceeds the predetermined magnitude so that the force exerted by the control means during substantial relative movement of the superstructure is at least about equal to the maximum force exerted by the control means during nonmovement of the superstructure.
2. Apparatus according to claim 1 wherein the control means comprises a plurality of upright members, and means for subjecting the members to horizontal forces, the members and the last-mentioned means being secured to the superstructure and the foundation,'the members being formed to have a strength so that the horizontal force of predetermined magnitude acting on the superstructure subjects the members to inelastic deformation.
3. Apparatus according to claim 1 wherein the control meanscomprises axially loaded control rods connected to the superstructure and the foundation, the control rods being con- LII structed so that the horizontal force of predetermined magnitude acting on the superstructure subjects the control rods to inelastic deformation.
4. Apparatus according to claim 1 wherein the control means comprises: tension and compression members connected to the superstructure and the foundation, relatively rigid upright posts having free ends, means for transmitting horizontal forces to the free ends and permitting relative vertical movement between the last-mentioned means and the posts, the posts and the horizontal forcetransmitting means being connected to the superstructure and the foundation, the members and the posts being constructed to have a combined strength so that the members and the posts are subjected to inelastic deformation when the horizontal force of predetermined magnitude acts on the superstructure and to thereby permit a substantial relative displacement between the superstructure and the foundation.
5. A building comprising a foundation, a superstructure isolated from the foundation to prevent damage to the superstructure from horizontal forces acting between the superstructure and the foundation, means for transferring the superstructure weight to the foundation, the weight-transferring means including means permitting substantial horizontal movements between the superstructure and the foundation under the influence of minor horizontal forces, control means independent of the weight-transferring means for the transmission of a first horizontally acting force only between the superstructure and the foundation, the control means being constructed to prevent substantial horizontal movements between the superstructure and the foundation when the first horizontal force is below a predetermined magnitude, the control means being further constructed to permit substantial horizontal movement between the superstructure and the foundation when the first horizontal force tends to exceed the predetermined magnitude while continuing to exert a horizontal force which is at least about equal to the predetermined magnitude of the first force, means permitting relative horizontal motion between the superstructure and the foundation and exerting a second horizontal force, the magnitude of which is a function of the relative displacement between the superstructure and the foundation, and stop means for limiting the possible displacement between the superstructure and the foundation.
6. A building according to claim 5 wherein the control means comprises a plurality of relatively rigid posts connected to one of the foundation and thesuperstructure, horizontal force transmission means connected to the other one of the foundation and the superstructure and vertically movable engaging free ends of the posts for the transmission of horizontal forces between the superstructure and the foundation and through the posts, the posts having a strength so that the application of a horizontal force of the predetermined magnitude stresses the posts to their yield strength, whereby the application of horizontal forces in excess of the predetermined magnitude causes the inelastic deformation of the posts and relative horizontal displacement of the superstructure.
7. A building according to claim 6 wherein the free post ends include disks projecting past the periphery of the posts, and wherein the stop means comprises a pair of vertically spaced-apart surfaces disposed on opposite sides of the disks for engagement of the disks after a predetermined angular deflection of the disks.
8. A building in accordance with claim 6 wherein the means exerting the second horizontal force comprises elongate, flexible spring means connected to the superstructure and the foundation.
9. A building according to claim 5 wherein the control means comprises: substantially horizontally disposed stress rods having ends connected to the superstructure and the foundation, rigid upright posts, means for transmitting posts having a combined strength in the horizontal direction so that the stress rods and the posts begin to deform inelastically when the horizontal force of predetermined magnitude acts on the superstructure to thereby permit a substantial relative displacement between the superstructure and the foundation.
10. A building in accordance with claim wherein the control means comprises stress rods connected to the superstructure and the foundation and substantially immovably interconnecting the two, the stress rods having a combined effective strength so that the application of the horizontal force of predetermined magnitude subjects the rods to their yield stress, whereby a horizontal force in excess of the predetermined magnitude cannot be transferred and causes inelastic deformation of the rods and a relative horizontal displacement between the superstructure and the foundation.
11. A building according to claim wherein means exerting the second horizontal force comprises elongate, flexible upright column means supporting at least a portion of the superstructure weight and connected to the superstructure and the foundation so that relative horizontal movements between the superstructure and the foundation causes a horizontal deflection of the column means.
12. A building according to claim 10 wherein the means exerting the second horizontal force comprises a flexible member constructed of a resilient material engaging the superstructure and the foundation.
13. A building in accordance with claim 10 wherein the stop means comprises interengageable, substantially rigid members connected to the superstructure and the foundation.
14. A building according to claim 10 wherein the stop means comprises a sleeve connected to one of the superstructure and the foundation, a bar in substantial axial alignment with the sleeve extending into the sleeve and connected to the other one of the superstructure and the foundation, and means mounted to the sleeve and the bar for limiting relative axial motions between the sleeve and the bar to a predetermined maximum.
15. A building having a foundation and a superstructure iso lated from the foundation to prevent damage to the superstructure by limiting the horizontal forces acting between the superstructure and the foundation comprising: first means including horizontally disposed friction interfaces permitting relative horizontal motions between the foundation and the superstructure, means independent of the weight of the superstructure for subjecting the interfaces to a predetermined transverse load that is less than the full weight of the structure, the interfaces and the last-mentioned means being constructed to develop a horizontal friction force of a predetermined magnitude preventing relative horizontal motions of the superstructure until a horizontal force between the superstructure and the foundation exceeds the predetermined horizontal friction force, and second means connected to the superstructure and the foundation and exerting a horizontal force in opposition to horizontal movements of the superstructure which are a function of the magnitude of the relative displacement of the superstructure with respect to the foundation, whereby relative horizontal movements of the superstructure take place only after a horizontal force between the superstructure and the foundation exceeds the predetermined horizontal friction force and under horizontal forces opposing such movements and increasing in magnitude as a function of the relative displacement of the superstructure.
16. A building comprising a foundation, a superstructure, means supporting the weight of the superstructure and isolating the superstructure from all but minor horizontal forces acting between the superstructure and the foundation and having a maximum magnitude insufficient to significantly damage the superstructure, first means including horizontally disposed friction interfaces permitting relative horizontal motions between the foundation and the superstructure, and means independent ofthe superstructure weight for subjecting the interfaces to a predetermined transverse load, the interfaces and the last-mentioned means being constructed to develop predetermined friction forces preventing relative horizontal movements of the superstructure until a horizontal force between the superstructure and the foundation exceeds the predetermined value and, thereafter, permitting relative motion of the superstructure to take place under relatively constant horizontal forces opposing such movements.
17. a building according to claim 16 and including stop means for limiting the relative movement of the superstructure.
18. A building according to claim 16 wherein the means for subjecting the interfaces to a predetermined transverse load comprises: plate means defining the interfaces and means independent of the weight of the superstructure for engaging the plate means and biasing the interfaces with a predetermined force into mutual engagement and wherein the building further includes means permitting relative horizontal movements of the superstructure under the influence of minor horizontal forces for supporting the superstructure weight.
19. A building comprising: a foundation, a superstructure isolated from the foundation to prevent damage to the superstructure by limiting the horizontal forces acting between the superstructure and the foundation, a first friction surface connected to the superstructure, a second friction surface connected to the foundation, means for biasing the first and second friction surfaces into mutual engagement with a predetermined force that is independent of the superstructure weight and control means connected to the superstructure and the foundation for opposing relative horizontal movements of the superstructure thereby preventing a horizontal force above a predetermined magnitude from acting on the superstructure and overcoming the combined maximum friction force developed between the friction surfaces and a maximum elastic force developed by the control means, and means independent of the biasing means for supporting the superstructure weight and permitting relative movenients of the superstructure under the influence of minor horizontal forces, the control means permitting substantial horizontal movements between the superstructure and the foundation when a horizontal force therebetween exceeds the maximum friction and elastic forces so that a combined force continues to be exerted by the control means and the friction surfaces in opposition to such movements of the superstructure is at least about equal to the predetermined horizontal force.
20. A building according to claim 19 wherein the control means comprises axially loaded control rods connected to the superstructure and the foundation.
21. A building having a foundation and a superstructure isolated from the foundation to prevent damage to the superstructure by limiting the horizontal forces acting between the superstructure and the foundation comprising: means for transferring the superstructure weight to the foundation, the weight-transferring means including means permitting substantial horizontal movements between the superstructure and the foundation under the influence of minor horizontal forces, first means for exerting a horizontal friction force preventing horizontal movements of the superstructure with respect to the foundation until an external horizontal force between the superstructure and the foundation reaches a predetermined magnitude, the first means including horizontally disposed friction interfaces and means for continuously preloading the interfaces independently of the superstructure weight whereby relative horizontal movements of the superstructure take place only after the horizontal force between the superstructure and the foundation exceeds the preset horizontal friction force and whereby the preset horizontal friction force continues to be applied to the superstructure when relative movements between the superstructure and the foundation occur.
22. A building according to claim 21 wherein the weighttransferring means include a plurality of relatively flexible elongate column means supporting at least a portion of the weight of the superstructure and having their respective ends attached to the superstructure and the foundation so that relative horizontal movement between the superstructure and the foundation causes the column means to deflect in a horizontal