Lateral force resisting structures and connections therefor

A force resisting structure for providing lateral support to a structure includes first and second substantially vertical structural members. These structural members each have first and second ends, the first ends being secured to an exterior support or structure. A third structural member having a first end connected to the first structural member and a second end connected to the second structural member is also included. The structure also includes means for movably connecting the third structural member to the first structural member so as to provide selective predetermined relative motion between these members when a lateral load is applied to the structure. Alternatively, the structure may include primary and secondary lateral bracing members extending in parallel from the first end of the first structural member to the second end of the second structural member. The secondary lateral bracing member is movably connected to the first structural member so as to provide selective predeterined relative motion between the primary and secondary lateral bracing members when a load is applied to the structure. The movable connection means provides a structure having a reduced amplitude of response to dynamic lateral loads, such as forces induced by earthquake and winds.

BACKGROUND OF THE INVENTION 
This invention relates to lateral support systems for structures subject to 
dynamic lateral loads. More particularly, it relates to lateral support 
structures and connections therefor in which selected members are coupled 
so as to provide selective predetermined substantially frictionless 
relative motion between the members. 
Typically, buildings and other structures are designed primarily to resist 
gravity loads. That is, the arrangement and sizing of the structural 
elements is determined by considering only gravity loads. Gravity loads 
include the weight of the building itself, the weight of attachments to 
the structure such as pipes, electrical conduits, air-conditioning, 
heating ducts, lighting fixtures, coverings, roof coverings, and suspended 
ceilings (i.e., dead load) as well as the weight of human occupants, 
furniture, movable equipment, vehicles stored goods (i.e., live load). 
Structures designed to resist forces caused by dynamic lateral loads such 
as wind, earthquakes, explosions, vibrating machinery, temperature changes 
and long-term, gradual distortions due to shrinkage, creep and/or 
settlement, involve special considerations. Primarily, the principal 
application of these forces is in a horizontal direction, or, more 
precisely, in a direction perpendicular (or lateral) to the direction of 
gravity. 
For example, the application of wind force to a closed building create 
lateral pressures applied normal to the exterior surfaces of the building. 
These forces may be either inward (i.e., positive pressures) or outward 
(i.e., negative or suction pressure). The shape of the building and 
direction the wind determine the distribution of pressures on the various 
exterior surfaces of the building. The total effect on the building is 
usually determined by considering the vertical profile, or silhouette, of 
the building as a single vertical plane surface at right angles to the 
wind direction. 
During an earthquake, the ground surface moves in all directions. The most 
damaging effect on structures, however, is caused by movements in the 
direction parallel to the ground surface (i.e., horizontally). Thus, for 
design purposes, the major effect of an earthquake is usually considered 
in terms of horizontal force, similar to the effect of wind. 
Since most structures are conceived in terms of their gravity resistance, 
designing for dynamic loads such as winds or earthquakes is often dealt 
with by bracing the gravity resisting system against lateral forces. In a 
typical structure, the lateral force system is provided by bracing systems 
that include solid walls (called "shear walls"), diagonally or otherwise 
braced bays, and rigid frames. Structures that are designed primarily to 
resist gravity loads always contain such lateral bracing systems to 
provide stability against lateral forces induced by unsymmetric load 
distribution. These lateral bracing systems are usually augmented to 
provide resistance against lateral forces induced by earthquakes, winds, 
etc. 
The principal concern in structural design for earthquake forces is for the 
laterally resistant system of the building or structure. In most 
buildings, this system consists of some combination of horizontally 
distributing elements (usually roof and floor diaphragms) and vertical 
bracing elements (shear walls, rigid frames, braced frames, etc.). Failure 
of any part of this system, or of connections between the parts, can 
result in major damage to the building, including the possibility of total 
collapse. 
The primary elements of a lateral load resistive system are often braced 
frames. Post and beam systems, consisting of separate vertical and 
horizontal members, may be inherently stable for gravity loading, but they 
must be braced in some manner for lateral loads. The three basic ways of 
achieving this are through shear panels, moment resistive joints between 
the members, or by bracing. 
When shear panels are used, the panels themselves are usually limited to 
the direct shear force resistance. Thus, the lateral resistive system is 
essentially that of a box system, although a complete frame structure 
exists together with the diaphragm elements of the box. 
When moment-resistive joints are used, lateral loads induce bending and 
shear in the elements of the frame. In rigid frames with moment-resistive 
connections, both gravity and lateral loads produce interactive moments 
between the members. In most cases, rigid frames are actually the most 
flexible of the basic types of lateral resistive systems. This deformation 
character, together with ductility, make the rigid frame a structure that 
absorbs energy through deformation. 
Most moment-resistive frames consist of either steel or concrete. Steel 
frames have either welded or bolted connections between the linear members 
to develop the necessary moment transfers. Frames of concrete achieve 
moment connections through the monolithic concrete as well as through the 
continuity and anchorage of the steel reinforcing. Because concrete is 
basically brittle and not ductile, the ductile character is essentially 
produced by the ductility of the steel reinforcing. 
In braced frames, on the other hand, trussing or triangulation of the frame 
is used to achieve lateral stability. The trussing is usually achieved by 
inserting diagonal members in the rectangular bays of the frame. If single 
diagonals are used, they serve a dual function, acting in tension for the 
lateral loads in one direction and in compression when the load direction 
is in the opposite direction. Because tension members are generally more 
structurally efficient, the frame is sometimes braced with a double set of 
diagonals (called "X-bracing"). In any event, the trussing causes lateral 
loads to induce only axial force in the members of the frame, as compared 
to the behavior of the rigid frame. It also generally results in a frame 
that is stiffer, having less deformation than the rigid frame. 
Significantly, in designing a structure to resist lateral loads, it is not 
necessary to brace every individual bay of the rectangular frame system. 
Usually, sufficient bracing is achieved by bracing only a few bays, or 
even only a single bay. Trussing tends to produce a structure that has a 
overall stiffness somewhere between that of a stiff diaphragm (shear wall) 
and that of the flexible moment-resistive frame. 
Another major consideration in designing a structure subject to, for 
example, earthquakes is the detailing of construction connections so that 
the building is quite literally not shaken apart by earthquake. With 
regard to the structure, this means that the various separate elements 
must be positively secured to one another. 
According to the prior art, for example, when using trussed structures, it 
was necessary to ensure that the structure itself is "tight." That is, 
connections should be made in a manner to assure that they will not be 
initially free of slack and will not loosen under load reversals or 
repeated loadings. This meant avoiding connections that are loose or which 
allow movement between the structural members. Avoiding loose connections 
is particularly important in systems subject to dynamic loading since 
relative movement between the structural members leads to increased wear 
and deterioration of the connection. 
As is well known in the art, a zero resistance rotation may be introduced 
into a structure during the erection of rigidly braced frames. 
Specifically, certain initial column-girder connections may be constructed 
to permit rotation at the girder support during the application of a 
superimposed dead load. After the initial load application, however, a 
final fixed connection of the columns is installed to prevent free 
rotation under any additional loading. 
Movement in connections or slip response has also been proposed in seismic 
base isolation systems. In such systems, rigid body motion of the entire 
structure due to sliding of the foundation provides a constant frictional 
resistance. 
In some other cases it is desirable to allow for some degree of independent 
motion of selected parts of a structure. In particular, it is desirable to 
use separation joints to secure various nonstructural elements, such as 
window glazing, to the structure. These joints permit some degree of 
independent movement of the nonstructural elements to prevent undesired 
transfer of force to these elements. 
Another type of earthquake resistant system involves "active control". In 
these systems, a motion sensor detects motion of the structure and 
activates active controls, such as actuators or other mechanical devices, 
which counteract the motion. Active control systems are expensive and 
require maintenance for the electro-mechanical components. 
SUMMARY OF THE INVENTION 
I have devised new structural connections for interconnecting structural 
components in lateral force resisting systems. These connections may be 
used to either improve the response of an overall structure to dynamic 
loads or drastically reduce the amount of material required to resist 
dynamic loads. Specifically, I have devised new structural connections for 
interconnecting structural members in a lateral force resisting system 
which provide for substantially frictionless relative motion between 
interconnected members, in response to lateral loads. As such, certain 
structural members connected according to my invention become "active" 
(i.e., resist force or moments) only after a predetermined amount of 
relative motion (displacement and/or rotation) has taken place. 
In accordance with the present invention, structural connections are 
disclosed for interconnecting the structural members of a lateral force 
resisting system. The structural connections provides for substantially 
frictionless relative motion, such as translation or rotation, between 
structural members attached thereby. These connections comprise means for 
providing predetermined displacement and/or rotation between the members 
attached thereby and means for resisting relative motion once the 
predetermined displacement and/or rotation has occurred. For example, the 
connection may include connecting openings or holes in one member of a 
lateral force resisting system which are slotted or elongated in the 
direction of the desired relative motion. 
Advantageously, connections in accordance with my invention may be used 
with structural members of steel, wood, reinforced concrete, prestressed 
concrete and the like. Also, these connections may be used in all types of 
lateral bracing systems, including shear walls, rigid frames and braced 
frames. 
This type of connection, hereinafter referred to as sequential connection, 
has the advantages of: 
(a) Reducing the stiffness of the overall structure as compared to 
structures of equal strength and constructed of an equal amount of 
material, but which use traditional connections. It is well known in the 
art that a suitable reduction in the stiffness of the structure results in 
the lowering of its frequency of response and evokes a reduction of the 
amplitude of seismic excitation. Furthermore, when the excitation is 
caused by thermal effects, settlement of foundations, and similar 
situations which impose deformation or displacement, the reduced stiffness 
results in a lower amplitude of the forces in the bracing system. 
(b) Increasing the energy absorption of the structure when the applied 
lateral loads produce forces in the lateral force resisting system which 
exceeds the elastic limit of the individual components of the system, 
since the response of the structure is affected by a complex force 
deformation path dictated by the sequential connection. 
(c) Providing simple connection details and requiring a minimum amount of 
field connections. 
All of the above properties are desirable and beneficial for the design of 
structures that are subject to time dependent excitation. 
Furthermore, structures in which sequential connections are used: 
(1) may use an amount of material equal to that of a standard lateral force 
resisting system but exhibit a reduced peak deformation response, 
resulting in increased safety of the structure; 
(2) exhibit a significant reduction in permanent deformations, which 
reduces or eliminates maintenance and repair costs; and 
(3) may be designed to exhibit a response that is identical to that of a 
structure using standard connections but which requires significantly less 
material, leading to cost savings. 
Also in accordance with the present invention, I have devised lateral force 
resisting structures for a structure subject to lateral loads. In 
particular, I have devised lateral force resisting structures in which 
certain members are sequentially connected so as to provide for 
substantially frictionless relative motion of the members connected 
thereby, in response to lateral loading. For example, the lateral force 
resisting structure may comprise a frame which includes first and second 
substantially vertical structural members. Both of these members are 
provided with first and second ends, the first ends being secured to an 
exterior support structure. 
The lateral force resisting structure also includes a third structural 
member which extends from the second end of the first structural member to 
the second end of the second structural member, thereby forming a frame. 
This frame may be used in a variety of structures, such as buildings or 
bridges, for providing lateral support thereto. 
In accordance with my invention, the lateral force resisting structure 
further includes means for connecting the second end of the third 
structural member to the second end of the second structural member so as 
to provide for substantially frictionless relative motion between the 
third structural member and the second structural member when a lateral 
load is applied to the planar frame. 
Also in accordance with my invention, I have devised methods for 
retrofitting an existing structure to improve the response of the 
structure to dynamic lateral loads. In one such method, increased lateral 
force resistance is provided to an existing structure by sequentially 
connecting additional structural members to the lateral force resisting 
system of the structure. For example, in an existing structure having a 
lateral force resisting structure comprising a plurality of braced bays, 
additional structural members, such as plates, may be sequentially 
connected to the existing bracing members. 
In an alternate method, increased lateral force resistance is provided to 
an existing structure by replacing selected connections of the existing 
lateral force resisting system with sequential connections. 
According to another important aspect of my invention, I have devised a 
method of designing a lateral force resisting structure for complex and 
multistory structures. This method generally follows the steps used by an 
engineer in designing a lateral force resisting structure. According to my 
method, however, the engineer selectively replaces certain connections of 
the lateral force resisting structures with sequential connections. For 
example, the method may include the steps of: determining the lateral 
loads on the structure; selecting a lateral support system for the 
structure, such as braced frames, rigid frames, shear walls or come 
combination thereof; and sequentially connecting certain members in the 
selected lateral support system.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
FIG. 1 illustrates, in front elevation view, a planar frame 1, which 
includes a pair of substantially vertical structural members 10. The lower 
ends of vertical members 10 may be secured to a foundation or a lower 
structural member via a suitable connection or connecting member. 
A substantially horizontal structural member 20 extends from the upper end 
of one vertical member 10 to the upper end of the second vertical member 
10. Planar frame 1 may be inherently stable for gravity loading, but it 
must be braced in some fashion to resist lateral loads. FIGS. 2-6 
illustrate, in front elevation view, typical lateral force resisting 
structures used to support a structure under lateral loads. Specifically, 
FIGS. 2-4 illustrate internally braced frames. In particular, FIG. 2 
illustrates a "knee-braced" frame in which a pair of short "knee-braces" 
25 connect the upper portions of vertical members 10 to horizonal member 
20. 
FIG. 3 illustrates an internally braced frame having a single diagonal 
member 30 which extends diagonally from the lower end of one vertical 
member 10 to the upper end of the second vertical member 10. When a 
lateral load is applied to frame 1 in the direction indicated by arrow A, 
diagonal member 30 resists the lateral load in tension. When the lateral 
load is applied to frame 1 in the direction indicted by arrow B, diagonal 
member 30 resists the lateral load in compression. 
FIG. 4 illustrated an "X-braced" frame in which a pair of diagonal members 
31, 32 are provided. A first diagonal member 31 extends from the lower end 
of one vertical member 10 to the upper end of the second vertical member 
10. Conversely, the second diagonal member 32 extends from the lower end 
of the second vertical member 10 to the upper end of the first vertical 
member 10. When a lateral load is applied to frame 1 in the direction 
indicated by arrow A, diagonal member 31 resists the load in tension. 
When, however, the lateral load is applied in the direction indicated by 
arrow B, diagonal member 32 resists the load in tension. 
FIG. 5 illustrates a frame in which lateral support is provided by 
moment-resistive connections 15 which rigidly connect horizontal member 20 
to the upper ends of vertical members 10, forming a rigid frame 2. Such 
movement-resistive connections are typically welded or bolted connections 
between horizontal member 20 and vertical members 10 which develop the 
necessary movement transfers. As such, lateral loads applied to rigid 
frame 2 produce bending in vertical members 10 and horizontal member 20. 
FIG. 6 illustrates a shear wall 40. Shear wall 40 may comprise a frame, 
such as frame 1 illustrated in FIG. 1, having some surfacing elements, 
such as plywood, plaster or drywall, or may comprise masonry. Preferably, 
however, shear wall 40 comprises reinforced concrete. In a shear wall 40 
comprising reinforced concrete, resistance to lateral loads is provided by 
the steel reinforcing bars (not shown) which carry the lateral load in 
compression or tension. 
The various lateral resisting structures described above in connection with 
FIGS. 2-6 are illustrative of the basic types of lateral force resisting 
systems available to a structural engineer in designing a structure 
subject to dynamic lateral loads such as earthquakes or forces caused by 
wind. 
Significantly, in a structure comprising a number of frames 1, it is not 
necessary to provide lateral support in the form of bracing, rigid 
motive-resistive connections or shear walls in each frame. Accordingly, as 
illustrated in FIGS. 7 and 8, a single story structure 50 comprising four 
frames 1, each formed by a pair of vertical members 10 and horizontal 
member 20, may be provided with sufficient lateral support by "partial 
trussing". For example, in FIG. 7, single story structure 50 is braced to 
resist lateral load, such as a load applied in the direction indicated by 
arrow C, by adding a first diagonal member 33 to a first frame 1, diagonal 
member 33 extending from the upper end of one vertical member 10 to the 
lower end of the second vertical member 10. A second diagonal member 34 is 
added to another frame 1 so that it extends from the lower end of one 
vertical member 10 to the upper end of the second vertical member 10. 
Accordingly, structure 50 resists lateral loads by tension in either 
member 34 (when the load is applied in the direction of arrow C) or member 
33 (when the load is applied in the direction opposite to the direction 
indicated by arrow C) much like the X-braced frame described in FIG. 4. 
FIG. 8 illustrates an alternative bracing system for structure 52 in which 
a single frame is X-braced by diagonal members 33 and 34. 
Similarly, multistory structures, such as those illustrated in FIGS. 9 and 
10, require lateral support in only certain frames. FIG. 9 illustrates a 
multistory structure 60 in which a first frame 1 on each story is braced 
with a diagonal member 33 and a second frame 1 on each story is braced 
with a diagonal member 34, similar to the single story structure 50 
described above in connection with FIG. 7. FIG. 10, on the other hand, 
illustrates a multistory structure 62 in which a single frame 1 on each 
story is X-braced with diagonal members 33 and 34, similar to single story 
structure 50 described above in connection with FIG. 8. 
The bracing schemes described above are merely illustrative of an endless 
variety of available schemes. As is apparent to one of ordinary skills in 
the art, a lateral support system for single story structure 50, 52 and 
multistory structure 60, 62 may comprise laterally supporting preselected 
frames in the structures by providing the preselected frames with rigid 
movement-resistive connections, shear walls or diagonal bracing members. 
Turning now to FIGS. 11 and 12, there is illustrated a preferred embodiment 
of the present invention, designated by the numeral 100, in which one end 
of horizontal member 20 is connected to the upper end of a vertical member 
10 in a manner to provide selective predetermined relative motion between 
horizontal member 20 and vertical member 10. 
Specifically, FIGS. 11 and 12 illustrate sequential connection 100 for a 
rigid frame, such as that described in connection with FIG. 5. Connection 
100 includes means for connecting horizontal member 20 to the upper end of 
one vertical member 10 so as to permit horizontal member 20 to displace a 
predetermined amount in response to a lateral load. 
Preferably, the connecting means include at least one plate member 110 
which connects horizontal member 20 to the upper end of vertical member 
10. Plate member 110 includes a plurality of elongated slots 112 for 
receiving fasteners 114. Elongated slots 112 preferably extend along the 
longitudinal axis 113 of horizontal member 20. As shown in FIGS. 11 and 
12, plate member 110 is rigidly secured to the upper end of one vertical 
member 10. 
Horizontal member 20, which is shown as a flat plate member, preferably 
includes a plurality of mounting holes 22 at the end sequentially 
connected to plate 110, for receiving fasteners 114. Mounting holes 22 
align with elongated slots 112 in plate member 110 when horizontal member 
20 is coupled to plate members 110. The connecting means also include a 
plurality of fasteners 114, such as rivets or bolts, which extend through 
mounting holes 22 in horizontal member 20 and elongated slots 112 in plate 
members 110. As shown in FIG. 11, a gap "g" is formed between fastener 114 
and each end portions 112A, 112B of elongated slots 112. Gap g provides 
for relative motion between horizontal member 20 and plate member 110. 
Horizontal member 20, may be constructed from steel, reinforced concrete, 
composite materials, plastic, wood or the like. In addition, horizontal 
member 20 may comprise a number of structural shapes, such as I-shapes, 
T-shapes, angles, channels, flat plates, structural tubing or pipe and the 
like. 
FIG. 13 illustrates one alternative embodiment of the rigid frame having 
sequential connection 100 illustrated in FIGS. 11 and 12. In this 
embodiment, horizontal member 20 includes upper and lower flanges 24 and 
26, respectively, and a web 25. Accordingly, mounting holes 22 may be 
formed through upper and lower flanges 24 and 26. Preferably upper and 
lower plate members 110 are provided at the upper end of vertical member 
10 for connecting upper and lower flanges 24 and 26, respectively, to 
vertical member 10. Accordingly, upper and lower plate members 110 are 
rigidly secured to the upper end of member 10, and a plurality of 
fasteners 114 extend through elongated slots 112 in upper plate member 110 
and mounting holes 22 in upper flange 24 of horizontal member 20. 
Similarly, a plurality of fasteners 114 extend through elongated slots 112 
in lower plate member 110 and mounting holes 22 in lower flange 26 of 
horizontal member 20. 
Alternatively, as shown in FIG. 14, at least one plate member 110 is 
sequentially connected to web 25 of horizontal member 20. In this 
embodiment, mounting holes 22 are formed through web 25. Preferably, two 
plate members 110 having elongated slots 112 are provided. In this 
embodiment, one plate member 110 is sequentially connected to one side of 
web 25 and a second plate member 110 is sequentially connected to the 
other side of web 25. 
As an alternative to embodiments described above, mounting holes 22 may be 
formed through plate member 110, while elongated slots 112 are formed 
through horizontal member 20. 
Turning now to FIG. 15, there is illustrated a selective angular change (or 
rotation) between horizontal member 20 and vertical member 10 provided by 
sequential connection 100 of FIG. 13. In particular, horizontal member 20 
undergoes a slight angular change when upper flange 24 and lower flange 26 
move in opposite directions. As a result, fastener 114 through upper 
flange 24 and upper plate member 110 abuts a first end portion 112A of 
elongated slot 112 while fastener 114 through lower flange 26 and lower 
plate member 110 abuts a second end portion 112B of elongated slot 112. 
Turning now to FIG. 16 there is illustrated the selected substantially 
frictionless relative motion between horizontal member 20 and plate member 
110 (as well as vertical member 10) provided by sequential connection 100. 
In particular, FIG. 16 illustrates a selective predetermined displacement, 
equal to gap g, of horizontal member 20 relative to plate member 110. 
Thus, as described in detail below, when a lateral load is applied to a 
structure having a planar frame 1 in which sequential connection 100 
movably connects horizontal member 20 to a vertical member 10, horizontal 
member 20 rotates and/or displaces a predetermined amount relative to 
vertical member 10 before it carries load and/or moment. The advantages of 
a force resisting structure using sequential connections will be 
illustrated below in connection with FIGS. 28-41. 
FIGS. 17 and 18 illustrate another alternative embodiment 200 of sequential 
connection 100. In this embodiment, one end of horizontal member 20 is 
provided with a necked portion 28. Necked portion 28 includes at least one 
elongated opening 29 having end portions 29A and 29B. Plate 110 in this 
embodiment is provided with at least one protruding portion 116 which 
engages slot 29. A gap "g" for providing selective substantially 
frictionless relative motion between horizontal member 20 and plate 110 is 
provided between protruding portion 116 and end portions 29A, 29B of 
elongated slot 29. Accordingly, horizontal member 20 is free to rotate 
and/or displace a predetermined amount when a load is applied to a 
structure having sequential connection 200. 
In a preferred embodiment, necked portion 28 includes a pair of elongated 
openings 29 which extend longitudinally along horizontal member 20. 
Elongated openings 29 may be positioned in a parallel arrangement as shown 
in FIG. 18, staggered or arranged consecutively along the length of neck 
portion 28. Also, in the preferred embodiment, elongated slots 29 are 
positioned along the longitudinal edges of necked portion 28. 
Significantly, the size and placement of protruding portions 116 of plate 
member 110 are coordinated with the size and placement of elongated slots 
29 to ensure that protruding portions 116 engage elongated slots 29, so as 
to leave a gap g on either side of protruding portions 116. 
FIG. 19 illustrates another preferred embodiment of the present invention, 
designated by the numeral 300, designed to improve the dynamic response of 
a braced frame, such as those described in connection with FIGS. 2-4, to 
lateral loads. 
The lateral support system of FIG. 19 includes a diagonal member 30 which 
provides lateral support to frame 1. As shown in FIG. 19, diagonal member 
30 preferably comprises a primary lateral bracing member 30A and a 
secondary lateral bracing member 30B. Primary and secondary lateral 
bracing members 30A, 30B are secured to the lower end of one vertical 
member 10 and the upper end of the second vertical member 10, as 
illustrated in FIG. 3. 
Preferably, one end of secondary lateral bracing member 30B is sequentially 
connected to a vertical member 10. Illustratively, FIG. 19 shows the upper 
end of secondary lateral bracing member 30B sequentially connected to the 
upper end of vertical member 10. In this embodiment, sequential connection 
300 comprises a plate member 310 for securing primary and secondary 
lateral bracing members 30A, 30B to the upper end of vertical member 10. 
Plate member 310 may be provided with mounting holes 312 for firmly 
securing primary lateral member 30A thereto. Plate member 310 also 
includes a plurality of elongated slots 314, having end portions 314A and 
314B. Elongated slots 314 preferably extend axially along the longitudinal 
axis 315 of secondary lateral bracing member 30B. Mounting holes 36 are 
provided in the end of secondary lateral bracing member 30B which is 
sequentially connected to plate member 310. Mounting holes 36 align with 
elongated slots 314 of plate member 310 when secondary lateral bracing 
member 30B is sequentially connected thereto. 
Sequential connection 300 further includes a plurality of fasteners 316 
which extend through mounting holes 36 of secondary lateral bracing member 
30B and elongated slots 314 of plate member 310. As described above in 
connection with FIGS. 11 and 16, a gap g is provided between fastener 316 
and end portions 314A, 314B of elongated slot 314. Gap g provides for 
selective predetermined substantially frictionless relative motion between 
secondary lateral bracing member 30B and plate member 310 when a lateral 
load is applied to a structure having a sequential connection 300. As a 
result, when a lateral load is applied to the structure, primary lateral 
bracing member 30A carries the entire load in either tension or 
compression as previously described, until member 30A undergoes a 
deformation (either elongating or shortening, accordingly) equal to gap g. 
At that point, fastener 316 will abut either end portion 314A or 314B of 
elongated slots 314 in plate member 310, causing secondary lateral bracing 
member 30B to carry load (i.e., become active). 
As previously described in connection with FIGS. 11-18, secondary lateral 
bracing member may comprise any number of a wide variety of shapes and 
materials. Also, elongated slots 314 may be formed in secondary lateral 
bracing member 30B while mounting holes 36 are formed in plate member 310. 
FIGS. 20-22 illustrate an alternative embodiment 301 of sequential 
connection 300. As shown in FIG. 20, diagonal member 30 again preferably 
comprises a primary lateral bracing member 30A, such as a plate or 
I-section, and at least one secondary lateral bracing member 30B. Primary 
lateral bracing member 30A is secured to the lower end of one vertical 
member 10 and the upper end of the second vertical member 10, as 
illustrated in FIG. 3. Secondary lateral bracing member 30B is 
sequentially connected, in this illustration, at its upper end to primary 
lateral bracing member 30A. 
Sequential connection 301 also includes means for movably connecting at 
least one secondary bracing member 30B to primary bracing member 30A so as 
to provide selective substantially frictionless longitudinal motion of 
secondary lateral bracing member 30B relative to primary lateral bracing 
member 30A, and means for resisting relative motion once the selective 
longitudinal motion has taken place. 
As shown in FIG. 21, primary lateral bracing member 30A preferably 
comprises a section, such as a channel or I-section, having upper and 
lower flanges and a web. A plurality of mounting holes 38 are provided at 
a predetermined distance from one end portion of primary lateral bracing 
member 30A, for receiving fasteners 318, which sequentially connect 
secondary lateral bracing member 30B thereto. Mounting holes 38 may be 
provided in the web or, preferably, in the upper and lower flanges of 
primary lateral bracing member 30A. 
In this embodiment, the means for movably connecting at least one secondary 
lateral bracing member 30B to primary lateral bracing member 30A further 
comprises a plurality of elongated slots 36 provided through one end of 
secondary lateral bracing member 30B. The other end of secondary lateral 
bracing member 30B is preferably securely fixed to primary lateral bracing 
member 30A by standard bolted connections, welds, adhesives, or the like. 
Slots 36 preferably extend axially along the longitudinal axis 315 of 
secondary lateral bracing member 30B and align with mounting holes 38 in 
primary lateral bracing member 30A. A plurality of fasteners 318 extend 
through mounting holes 38 in primary lateral bracing member 30A and 
elongated slots 36 in secondary lateral bracing member 30B. As described 
above in connection with FIG. 16, a gap g is provided between fasteners 
318 and send portions 36A and 36B of elongated slots 36. Gap g provides 
for substantially frictionless relative movement between primary lateral 
bracing member 30A and secondary lateral bracing member 30B as will be 
described below. 
As is readily apparent, secondary lateral bracing member 30B is movable in 
a longitudinal direction relative to primary lateral bracing member 30A 
when a lateral load is applied to a structure having a sequential 
connection 301. In particular, secondary lateral bracing member 30B is 
movable relative to primary lateral bracing member 30A from a first 
position in which fasteners 318 are located a predetermined distance g 
from end portions 36A and 36B of elongated slots 36, to a second position 
in which fasteners 318 abut either end portion 36A or 36B of slot 36, 
depending on the direction of the applied force. This movement is similar 
to the movement illustrated in FIG. 16, and is similarly without 
significant friction between moving parts. 
Significantly, when a lateral load is applied to a frame having a secondary 
lateral bracing member 30B which is connected to a primary lateral bracing 
member 30A by sequential connection 301, primary lateral bracing member 
30A deforms axially, either by elongating or shortening depending upon the 
direction of the load, while secondary lateral bracing member 30B moves 
relative to primary lateral bracing member 30A without carrying load. 
Accordingly, primary lateral bracing member 30A carries the total lateral 
load applied to the frame until secondary lateral bracing member 30B moves 
to the second position. As described above, at this second position, 
fasteners 318 abut end portions 36A or 36B and thus secondary lateral 
bracing member begins to carry load, which is transferred to it by 
fasteners 318. At this position, secondary lateral bracing member 30B is 
considered "active". 
In an alternative embodiment illustrated in FIG. 22, mounting holes 38 are 
formed through the web of primary lateral bracing member 30A and at least 
one secondary lateral bracing member 30B having elongated slots 36 is 
sequentially connected thereto. Preferably, a pair of secondary lateral 
bracing members 30B are used, whereby one secondary lateral bracing member 
30B is sequentially connected to one side of the web and a second 
secondary lateral bracing member 30B is sequentially connected to the 
other side of the web. 
Another alternative embodiment is shown in FIGS. 23-26. In particular FIG. 
23 illustrates a multistory structure having a plurality of frames 5. Each 
frame 5 comprises a pair of vertical members 10 and a horizontal member 20 
which extends from one vertical member 10 to the second vertical member 
10. Frame 5 also includes a diagonal member 30 which extends from a lower 
portion of the second vertical member 10 to an upper portion of the first 
vertical member 10. Diagonal member 30 provides lateral support to frame 
5. 
Preferably, diagonal member 30 comprises a primary lateral bracing member 
30A which is secured to a gusset plate 410 at each end, and at least one 
secondary lateral bracing member 30B. In the embodiment shown in FIGS. 25 
and 26, primary lateral bracing member comprises an I-section. 
Alternatively, member 30A may comprise a variety of shaped sections or may 
comprise a flat plate. 
Secondary lateral bracing member 30B is movably connected to primary 
lateral bracing member 30A by sequential connection 400. Illustratively, 
secondary lateral bracing member 30B comprises a flat plate. As is 
apparent, however, other structural shapes may be used. 
Sequential connection 400 comprises a plurality of C-shaped straps 402, a 
pair of guide plates 403, a flat strap 404 and a stop 405. As illustrated 
in FIG. 26, C-shaped straps 402 each enclose a portion of secondary 
lateral bracing member 30B, which are shown as a pair of plates movably 
connected to the upper and lower flanges, respectively, of primary lateral 
bracing member 30A. Alternatively, secondary lateral bracing member 30B 
may comprise a pair of plates which are sequentially connected to the web 
of primary lateral bracing member 30A as shown in FIG. 22. C-shaped straps 
402, which may comprise steel, plastic, aluminum and the like, are secured 
to the upper and lower flanges of primary lateral bracing members 30A. 
As shown in FIG. 24, at one end of secondary lateral bracing member 30B, a 
pair of guide plates 403 are secured to primary lateral bracing member 
30A, on either longitudinal side of secondary lateral bracing member 30B. 
As shown in FIG. 25, guide plates 403 have a thickness that is slightly 
greater than the thickness of secondary lateral bracing member 30B. Flat 
strap 404 extends from one guide plate 403 to the second guide plate 403, 
thereby enclosing a portion of secondary lateral bracing member 30B. 
Secondary lateral bracing member 30B is provided at one end with a necked 
portion 39 which is positioned a predetermined distance away from guide 
plates 403. This predetermined distance forms a gap g. 
As is best seen in FIG. 24, stop 405 is secured to primary lateral bracing 
member 30A by adhesive, welding, fastening or the like, at a predetermined 
distance from one end of secondary lateral bracing member 30B when member 
30B is movably connected thereto. The predetermined distance also defines 
a gap g which corresponds to substantially frictionless selective axial 
movement of secondary lateral bracing member 30B relative to primary 
lateral bracing member 30A. 
Accordingly, secondary lateral bracing member 30B is movably connected to 
primary lateral bracing member 30A. When a lateral force is applied to the 
multistory structure, primary lateral bracing member 30A carries the 
entire load, causing member 30A to elongate or shorten accordingly. 
Secondary lateral bracing member 30B, on the other hand, does not carry 
load initially. Instead, secondary lateral bracing member 30B moves 
relative to primary lateral bracing member 30A and is guided by C-shaped 
straps 402 and guide plates 403. Once secondary lateral bracing member 30B 
moves a distance g in either longitudinal direction, necked portion 39 of 
secondary lateral bracing member 30B will abut either stop 405 or guide 
plates 403 which thereafter limits relative movement of secondary lateral 
bracing member 30B. Thereafter, secondary lateral bracing member 30B 
carries the lateral load applied to frame 5 along with primary lateral 
bracing member 30A. 
As will be readily apparent from the above description to one of ordinary 
skill in the art, the embodiments described above in connection with a 
single braced frame are also applicable to X-braced frames wherein one end 
of each X-brace is sequentially connected by any of the previously 
disclosed sequential connections. 
Another embodiment of the present invention (not shown) involves 
sequentially connecting structural X-bracing cables to vertical members 
10. In this embodiment, one end of each X-braced cable may be connected to 
a vertical member 10 using a connecting member which provides a 
predetermined substantially frictionless relative motion between the cable 
and vertical member 10 in response to a lateral load. Accordingly, 
X-bracing cables which are sequentially connected to a vertical member 10 
will not carry load (via tension) until the predetermined relative motion 
has occurred. 
FIG. 27 illustrates another embodiment of the present invention. In this 
embodiment, sequential connection 500 is illustrated for use in a 
structure comprising reinforced concrete members, such as a rigid frame 2 
shown in FIG. 5 or shear wall 40 shown in FIG. 6. 
In one such embodiment, the structural member sequentially connected 
according to my invention comprises a plurality of reinforcing bars which 
extend from one vertical member 10 to the second vertical member 10. To 
ensure structural continuity, anchor members are provided which tie the 
sequentially connected member to an adjacent vertical member 10. 
Alternatively, anchor members are provided in a reinforced concrete member 
so as to provide substantially frictionless selective predetermined 
relative motion between adjoining reinforcing members. 
Sequential connection 500 comprises means for movably connecting a second 
end of a reinforcing bar 41 with a first end of an adjacent anchor member 
42. Preferably, the connecting means comprise a sleeve 501 having an inner 
cavity 502. Cavity 502 further includes a first end 503 for receiving the 
second end of reinforcing bar 41 and a second end 504 for receiving the 
first end of anchor member 42. Preferably the second end of reinforcing 
bar 41 is secured to sleeve 501 by any suitable means, such as welding, 
adhesive and the like. In the preferred embodiment, the second end of 
reinforcing bar 41 is welded to sleeve 501 by weld 505. 
In the preferred embodiment, anchor member 42 is preferably provided with a 
bar-like body 44 having a head portion 43 which is positioned inside 
cavity 502 of sleeve 501, and a tail portion 45. Tail portion 45 may be 
connected to vertical member 10. Head portion 43 is slightly smaller than 
the inner dimensions of cavity 502 so that head portion 43 can move freely 
therewithin. Preferably, when a reinforced concrete member is provided 
with a sequential connection 500, head portion 43 is positioned a 
predetermined distance g from both the second end of reinforcing bar 41 
and second end 504 of cavity 502. As such, anchor member 42 is freely 
movable relative to reinforcing bar 41, in the direction marked by arrow D 
a distance g in either direction. Accordingly, when a lateral load is 
applied to a structure having a reinforced concrete member sequentially 
connected by sequential connection 500, reinforcing bar 41 carries the 
entire load until reinforcing bar 41 deforms a distance g. Thereafter, 
head portion 43 of anchor member 42 will abut either the second end of 
reinforcing bar 41 or second end 504 of sleeve 501. At this point, anchor 
member 42 carries load along with reinforcing bar 41. 
As is readily apparent to one of ordinary skill in the art, any of the 
above-described sequential connections or combination of sequential 
connections may be used in designing a lateral support structure for a 
structure subject to dynamic lateral loads. For example, in a multistory 
structure having a plurality of bays, it is possible to provide lateral 
support to some bays by sequentially connecting certain predetermined 
horizontal members 20 to certain vertical members 10 by sequential 
connections 100, 200 or 500. Meanwhile, other bays may be diagonally or 
X-braced using sequential connections, such as connections 300, 301 or 
400. 
FIG. 28 is a graphical representation of a single loading/unloading cycle 
of amplitude .+-.2 R. This graph compares the response of two equivalent 
structural systems having a lateral support system comprising a standard 
diagonally braced frame, such as those illustrated in FIGS. 3, 7 and 9. In 
the first system (hereinafter called System 1) diagonal member 30 
comprises a primary lateral bracing member 30A and a secondary lateral 
bracing member 30B, each having a stiffness k, which are connected using 
standard connections. Accordingly, System 1 has a total stiffness of 2 k. 
In the second system (hereinafter System 2), also comprising a primary 
lateral bracing member 30A and a secondary lateral bracing member 30B each 
having a stiffness k, each secondary lateral bracing member 30B is 
sequentially connected using sequential connection 300 of FIG. 19. In both 
systems, the primary and secondary lateral bracing members have a yield 
resistance R. 
Dashed line A--A represents the elastic load resistance path of amplitude 
.+-.2 R of System 1. The solid lines illustrate the complex load 
resistance path of System 2, which uses a sequential connection. In 
particular, this load resistance path includes several segments, described 
below in which the numbered paragraphs corresponds to the numbers on the 
graph. 
(1) linear elastic response occurs in primary lateral bracing member 30A 
for stress levels below the yield resistance R of member 30A. When the 
stress level is equal to or more than R, primary lateral bracing member 
30A deforms (either elongating or shortening), thereby causing the system 
to absorb energy. At a predetermined point of deformation, u.sub.0 (=g), 
fastener 316 will abut end portion 314A of elongated slot 314 thereby 
causing secondary lateral bracing member 30B to carry load (i.e., become 
active). The system then carries load, at a stiffness k, to +2 R with the 
system undergoing a total deformation of 2 u.sub.0. 
(2) Since secondary lateral bracing member 30B is active, it acts together 
with primary lateral bracing member 30A during unloading. Thus, the system 
unloads at a stiffness 2 k. In addition, because of deformation u.sub.0 in 
primary lateral bracing member 30A, the systems stores energy during 
unloading. 
(3) As the unloading cycle continues, fastener 316 moves away from a 
position abutting end portion 314A of elongated slot 314, again forming a 
gap. Thus, secondary lateral bracing member 30B becomes inactive. 
Therefore, unloading continues at a stiffness k, provided only by primary 
lateral bracing member 30A. 
(4) Because of deformation u.sub.0 in primary lateral bracing member 30A, 
the system experience a low amplitude (-R) yield plateau in which lateral 
bracing member 30A undergoes a second deformation -u.sub.0 which is in the 
opposite direction of the initial deformation. Energy dissipation is 
enhanced by the presence of this low amplitude yield plateau, which is 
similar to the well-known Bauschinger effect. In addition, the low 
amplitude yield plateau reduces residual permanent deformation in the 
system under dynamic excitation. 
(5) Since primary lateral bracing member 30A has undergone deformation 
-u.sub.0, fastener 316 now abuts end portion 314B of elongated slot 314. 
The System then carries load, at stiffness k, to -2 R with the System 
undergoing a total deformation of -2 u.sub.0. 
(6) as in segment (2), primary lateral bracing member 30A and secondary 
lateral bracing member 30B act together during unloading to provide a 
stiffness 2 k. The System again absorbs energy during unloading due to the 
deformation -u.sub.0 in primary lateral bracing member 30A. 
As can be seen from FIG. 28, the reduced loading stiffness, indicated by 
(1) above, which results from the sequential connection of secondary 
lateral bracing member 30B, implies a lower frequency of the sequentially 
connected system. 
To highlight the dramatic improvement to a structure's dynamic response, 
the following comparison of System 1 and System 2 is also provided. The 
load resistance path for System 1 is illustrated in FIG. 29, while the 
load resistance path for System 2 is illustrated in FIG. 30. 
In this illustration, diagonal member 30 of both systems is constructed of 
a material having a standard elasto-plastic manner and a yield resistance 
R. Accordingly, diagonal member 30 comprises a primary lateral bracing 
member 30A and a secondary lateral bracing member 30B such that R=R.sub.A 
+R.sub.B, where R.sub.A equals the yield resistance of primary lateral 
bracing member 30A and R.sub.B equals the yield resistance of secondary 
lateral bracing member 30B. 
FIG. 40 represents a parametric optimization of the ratio .alpha. of 
material used in lateral bracing members 30A and 30B to resist the 
loading. In an optimum solution (i.e., where the response of the System is 
at a minimum) where secondary lateral bracing member 30B of System 2 is 
provided with elongated slots 314 such that g=2 u.sub.0, .alpha.=0.50. 
Accordingly, the resulting yield resistances of the lateral bracing 
members will be R.sub.A =0.67 R and R.sub.B =0.33 R, respectively. 
Accordingly, diagonal member 30 of both System 1 and System 2 have a total 
equivalent yield resistance R, so that displacement at yield u.sub.0 is 
identical. In System 1, however, yielding occurs simultaneously in both 
diagonal bracing members and has a value .mu..sub.1. In System 2, on the 
other hand, yielding occurs in primary lateral bracing member 30A only, 
until secondary lateral bracing member 30B becomes active. As a result, 
System 2 will have maximum and minimum values of ductility, as illustrated 
in FIG. 30. 
The response of these two systems can be evaluated by the ratios 
EQU .mu..sub.max =.mu..sub.2max /.mu..sub.1 
EQU .mu..sub.min =.mu..sub.2min /.mu..sub.1 
where .mu..sub.2max and .mu..sub.2min are defined in FIGS. 29 and 30. The 
responses may also be evaluated by the ratio of average residual permanent 
deformation .mu..sub.p, where 
EQU .mu..sub.1p =.mu..sub.1p /.mu..sub.2p 
and where .mu..sub.1p and .mu..sub.2p are the ductilities of the average 
permanent deformations of the two systems at the end of a seismic 
excitation. 
Using the single degree of freedom mass-resistance models shown in FIGS. 31 
and 32 for Systems 1 and 2, respectively, the Systems can be evaluated. 
Assuming a fundamental period of the systems 
EQU T=0.64 seconds 
which is typical value for a seven-story building, and the following values 
TABLE 1.sup.1 
______________________________________ 
System 1 System 2 
______________________________________ 
R = R.sub.A + R.sub.B = 62.sub.k 
R.sub.A = 41.3.sup.k 
R.sub.B = 20.7.sup.k 
u.sub.o = 1.30 in. u.sub.o = 1.3 in. 
m = 0.84 ksec.sup.2 /inc. 
m = 0.84 ksec.sup.2 /in. 
g = 2.6 in. 
______________________________________ 
.sup.1 The equivalent mass of the system is assumed to be 0.12 sec.sup.2 
/in/floor. The resistance R is taken at twice that of the design base 
shear force (Uniform Building Code90). 
If both systems are subjected to an acceleration time history of 50 second 
duration, corresponding to the N-S component of the 1940 El Centro 
earthquake (FIG. 33), the following seismic response of the Systems, in 
terms of ductility, are given below: 
TABLE 2 
______________________________________ 
Ratio: System 1 
System 1 System 2 System 2 
______________________________________ 
.mu..sub.1max = 4.88 
.mu..sub.1max = 3.17 
.mu..sub.max = 0.65 
.mu..sub.2min = 1.17 
.mu..sub.min = 0.24 
.mu..sub.p1 = 1.55 
.mu..sub.p2 = 0.26 
.mu..sub.p = 0.17 
______________________________________ 
The resulting displacement time histories of the systems are given in FIGS. 
34 and 35, respectively. 
As can be seen from Table 2, the peak response of System 2 is significantly 
lower. The reason for the decrease of the peak response of System 2 is 
clarified by examining the load resistance path of the two systems. In the 
sequentially connected System 2, the initial phase of the excitation 
induces a higher energy dissipation, followed by excursions around the 
second lower yield plateau. This results in a continuous decrease of the 
amplitude of the displacement response time history, shown in FIG. 35. 
System 1 shows the standard elasto-plastic loading-path (FIG. 36), and the 
displacement time history (FIG. 34) demonstrates a characteristic steady 
state response centered on the value of the peak permanent deformation. 
Such differences in the response between standard and sequentially 
connected systems have also been observed when the exciting function is 
periodic. FIGS. 38 and 39 show the displacement time histories for the two 
systems in response to a sinusoidal input. 
As illustrated by FIGS. 34-39, lateral support systems having sequential 
connections exhibit drastically improved responses to dynamic lateral 
loads. Accordingly, sequential connections offers an entirely new and 
until now unexplored avenue in the design of structures that are subject 
to dynamic excitation. The introduction of this innovation provides 
additional "degrees of freedom" to the designer to achieve optimal 
solutions to resist seismic or periodic excitation. An example of such 
optimization is shown in FIG. 40 which explores the effect of 
"partitioning" the total resistance "R" of System 1 into 
EQU R.sub.A +R.sub.B =R 
where 
EQU R.sub.B /R.sub.A =.alpha. 
In the numerical example, I used the optimal value of .alpha.=0.50 which is 
the value of .alpha. corresponding to the minimum response of System 2. 
In the design of multistory structures, there is a further opportunity to 
combine a large number of sequential components and to select appropriate 
values for the partition parameter .alpha. for each unit. Optimization can 
also be performed with respect to the dimension of the initial gap. These 
variations also offer an opportunity to influence the initial elastic 
response by affecting the elastic period and the mode shape of the 
response, in addition to the ductile response. 
The numerical example above shows a considerable difference in the peak 
response of the two systems, composed of identical structural elements. 
Sequential connections may also be used, however, to reduce the quantity 
of structural material required to achieve an acceptable response to 
lateral loading. 
The quantity of steel used in a lateral support structure is directly 
proportional to the value of 
EQU AL=(A.sub.A +A.sub.B)L 
where A.sub.A and A.sub.B are the cross sectional areas of the diagonal 
bracing members and L is their length. FIG. 41 is a parametric exploration 
of the ratio of the peak deformation responses (.mu.) of System 1 and a 
modified System 2a, where the amount of material used is a fraction .eta. 
of System 2, i.e., 
EQU System 1 material=AL 
EQU System 2a material=.eta. AL. 
FIG. 41 illustrates that the value .eta.=0.67 corresponds to .mu..sub.max 
=1, i.e., the peak deformation response of Systems 1 and 2a are identical. 
Accordingly, if the performance of the standard System 1 is acceptable, 
then the identical performance of a sequentially connected System 2a is 
obtained where the amount of lateral force resisting material is reduced 
by 33%. 
Attached hereto as Appendix A is a paper I have written entitled Sequential 
Coupling--A New Structural Connection For Seismic Control. The disclosure 
of Appendix A is incorporated herein by reference to supplement an 
understanding of a sequential system's response to lateral loads and an 
appreciation of the additional design parameters available to a structural 
designer as a result of the invention disclosed in the instant 
application. 
While the invention has been described in conjunction with specific 
embodiments, it is evident that numerous alternatives, modifications, and 
variations will be apparent to those skilled in the art in light of the 
foregoing descriptions.