1 4 . 0
b c
yc yc
yb yb b b c
t b
F R
F t R b t
≤
≤
Where:
- bb: Unreduced beam flange width.
- tb: Beam flange thickness.
- RybFyb: Probable yield stress of the beam.
- RycFyc: Probable yield stress of the column.
The requirements for continuity plates are the same as those for BUEP and BSEP connections.
Other restrictive parameters
The expected location of the plastic hinge measured from the face of the column, x, is given by:
2 a s x= +
The minimum span-to-depth ratio is seven. Also, the maximum flange thickness is 44mm; and the maximum relation be/2t is 7.3, where be is the reduced beam flange width.
Special seismic steel framing systems
Up to now, this report has been focused in reviewing the main aspects of seismic design of steel structures for framing systems and connections types that are well-known and are commonly used in the construction industry of Canada.
Requirements for these systems are extensively covered in the CISC HSC, FEMA documents, the American Institute of Steel Construction (AISC) publications, among others. However, there are also many non-conventional steel framing systems for seismic applications that are very innovative in their design and they may be implemented in the codes in the next years. New systems are continuously being developed by researchers, since many aspects of seismic steel design still remain as a challenge.
The clause 27 of the CAN/CSA S16-01 states that when special steel framing systems are used in structures, their design should be based on published research results, design guidelines,
observed performance in past earthquakes, or special investigation.
The level of safety using these systems must be similar to the one that is established in the CAN/CSA S16-01.
The last part of this report will be focused in describing two of these special systems. The first one is the special truss moment frame, which provides savings in costs and time of construction compared to conventional systems. The second one is the friction-damped steel frame. Different types of damping devices have been developed in the past years and are added to the structure to dissipate more energy during an earthquake. We will describe some of these devices.
Special truss moment frames (STMF)
The STMF is a specially designed SFRS that reduces the earthquake damage of steel structures. This design was the result of a research that was developed at the University of Michigan.
The system is designed in such a way that when it is subjected to earthquake loading, inelastic deformation is moved to some segments of the truss that are specially designed. This truss has several diagonal members in a segment at the midspan designed for this purpose, they absorb most of the energy and dissipate it by yielding. The ductile behavior of this system is similar to that of the eccentrically braced frames, since all the inelastic deformation is taken by the special segment, which acts as the link. After the earthquake, the diagonal members that were damaged can easily be repaired or replaced (USACE: 7-101). A STMF with an X-braced configuration is shown in the following figure:
Figure No.29: Special truss moment frame Source: USACE: 7-103.
This type of system must satisfy certain special design requirements that are described in a document made by the US Army Corps of Engineers (USACE), in chapter 7. These requirements are covered in the preceding paragraphs.
These trusses are limited to a span length of 18m and a depth of 8m. The truss elements outside the special segment and the columns are designed elastically. The length of the special segment ranges from 0.1 to 0.5 times the total length of the span.
The panels in the special segment should have a length-to-depth ratio that ranges from 0.67 to 1.5. They may have a Vierendeel of X-braced configuration, but not a combination of them. In the Vierendeel configuration, a weakened beam with holes in it is used for energy dissipation.
If diagonal elements are used in the special segment, they must have an X-pattern arrangement and be interconnected at the points of crossing, and must be separated by vertical elements.
They must also be made of identical cross-sections. The interconnection nodes of diagonal members must have a design strength enough to resist a force equal to 0.25 times the nominal tensile strength of the member.
The web members in the special segment must not have bolted connections. The chord members must not be spliced within the special segment and within half the panel length measured from the end of the special segment, and must have a constant cross-section. The axial forces in the web diagonal members in the special segment due to factored dead and live loads must not exceed 0.03AgFy, where Ag is the gross area of the member, to limit their strength degradation.
When yielding occurs in the system, the special segment must develop its nominal shear resistance, through the nominal flexural strength of the chord elements and the nominal axial tensile and compressive strengths of the diagonal web elements.
All these elements are proportioned in such a way that at least 25%
of the shear resistance is provided by the chord elements. The required axial strength of the chord elements must not exceed 0.45φAgFy, taking φ = 0.9. The end connections of the diagonal elements in the special segment must have a design strength of at least the nominal tension strength of the web element, given by RyFyAg.
Regarding the elements and connections outside the special segment, all of these must have a design strength in order to resist the factored gravity loads, plus the lateral loads necessary to develop the expected overall vertical nominal shear resistance of the special segment, which is given by:
(
P P)
Sinα- Vne: Overall vertical nominal shear strength of the special segment.
- Ry: Factor defined in clause 27 of the CAN/CSA S16-01, taken as 1.1.
- Mnc: Nominal flexural strength of the chord element of the special segment.
- Ls: 0.9 times the length of the special segment.
- EI: Flexural elastic stiffness of the chord elements of the special segment.
- L: Span length of the truss.
- Pnt: Nominal tension strength of the diagonal elements of the special segment.
- Pnc: Nominal compression strength of the diagonal elements of the special segment.
- α: Angle of the diagonal elements of the special segment, measured from the horizontal plane.
The width-to-thickness ratio of the elements of the special segment must not exceed the following limits:
- Diagonal web elements: 2.5.
- Angles: 137/ Fy .
- Flanges and webs of tee sections in chord elements:
Fy
/
137 .
The top and bottom chords of the trusses must be laterally braced at the ends of the special segment. Intermediate braces are also required.
The advantages of the STMF compared to other SFRS are the following (Emerging Construction Technologies):
- Provides substantial cost and time savings and a better level of performance.
- Its weight is about 20% less than common framing systems carrying the same gravity loads.
- Fabrication costs are reduced in about 20% compared to common framing systems.
- Welded connections can be visually inspected without the need of additional tests.
Friction-damped steel frames (FDSF)
Damping devices are used in structures to increase their energy dissipation capacity, in order to reduce oscillations, and therefore, the structural and nonstructural damage. There are different types of dampers, like viscous dampers, visco-elastic dampers, Coulomb friction dampers, metallic dampers, among others. We will describe some of the friction dampers used in steel structures.
Friction dampers are designed in such a way they have moving parts that will slide over each other during a strong earthquake. Friction is created between these sliding elements, which dissipates energy built up in the structure. There are several types of friction damping devices, like the basic sliding joint, the rotation sliding joint, the dual level joint, the Pall friction device
and the Sumitomo friction device. Friction dampers offer the following advantages (UPC: 28 – 29):
- They have high energy dissipation capacity.
- Their behavior is not seriously affected by repeated cycles of displacement.
- The friction force between surfaces can be controlled, through the prestressing (normal) force.
- They can absorb a big amount of energy and then dissipate it.
- They are not affected by fatigue.
However, they also have some disadvantages:
- Sliding surfaces tend to heat.
- They do not contribute to dissipate energy of the structure before they start slipping.
- Changes in the sticking-sliding conditions of the damper may introduce high frequencies to the structural response.
We will describe the main features of these damping devices.
Basic sliding joint (BSJ)
The BSJ consists in incorporating slots in the bolt holes between steel plates, so that friction between the surfaces of steel plates dissipates energy. This type of joint is capable of repeated cycles of displacement without losing strength, stability or energy dissipation capacity. Their performance is influenced by three factors (Butterworth 1999: 1 – 2):
- Maintenance of contact pressure between sliding surfaces.
- Maintenance of an approximately constant coefficient of friction between sliding surfaces.
- Avoiding brittle failure when the joint reaches the limit of its sliding range.
The BSJ is shown in the following figure:
Figure No.30: Basic sliding joint Source: Butterworth 1999: 2.
The friction resistance in this device requires a normal force acting at the interface. This force is applied through the bolt placed at the joint. The normal force can be modified by adjusting the tension in the bolt. The slip force between surfaces is determined by:
bµ
slip nN
N = Where:
- Nslip: Slip force.
- n: Number of bolts.
- Nb: Tension in one bolt.
- µ: Coefficient of friction.
In the case shown in figure No.30, since two plates are used, the slip force is 2Nslip. The BSJ is used in concentrically braced frames with diagonal and chevron configuration:
Figure No.31: Applications of the basic sliding joint Source: Butterworth 1999: 2.
In the diagonal bracing system, the braces require that the compression capacity is greater than the slip load of the SBJ to have and adequate seismic performance. In the chevron bracing system, the braces must be designed for compression, to resist the reversible sliding in the SBJ, but their cross-sections are smaller than in a typical chevron system (Butterworth 1999: 2 – 3).
Rotating sliding joint (RSJ)
The RSJ is used in moment-resisting frames. The energy dissipation is achieved by friction between the surfaces of steel plates through a rotational action. It was developed by Tang and Popov (Butterworth 1999: 4). The RSJ is shown in the following figure:
Figure No.32: Rotating sliding joint Source: Butterworth 1999: 4.
When the joint is subjected to a moment, it behaves elastically until the beam flange reaches the slip level of the sliding connections. The beam will then start to rotate around the central pivot, shown in figure No.32, until the bolts reach the end of their slots. The maximum moment is given approximately by:
D nN Mslip = bµ Where:
- Mslip: Slip moment.
- D: Beam depth.
In the case shown in figure No.32, since two friction interfaces are used in both flanges, the slip moment is 2Mslip.
Dual level joint (DLJ)
The DLJ is also used in moment-resisting frames, and also dissipates energy by friction between the surfaces of steel plates through a rotational action. However, it differs from the RSJ because it has a dual slip level capacity. This is achieved by making the slip force of the top flange of the beam higher than that
of the bottom flange, using higher tension at the interface or more bolts. The centre of rotation is closer to the top flange; this is convenient, for example, to avoid damage in concrete floor slabs (Butterworth 1999: 5). The DLJ is shown in the following figure:
Figure No.33: Dual level joint Source: Butterworth 1999: 5.
Under the action of an increasing moment, the joint responds elastically until the bottom flange starts to slip once its threshold or slip moment has been reached. This causes plastic rotation around a centre of rotation in the top flange until the bolts in the bottom flange reach the end of the slots. The joint starts rotating elastically again, without any slipping, until the slip moment at the top flange is reached. The top flange then starts slipping, while the bottom flange rotates plastically around a centre of rotation. When the bolts in the top flange reach the end of the
slots, the joint rotates elastically again until it reaches the yield point.
This dual action has the following advantages in the design:
- The lower threshold level provides sufficient strength for loads arising from the design earthquake.
- The upper threshold level provides a strength reserve for extreme events.
- If the bottom flange fails to slip, energy can still be dissipated by the top flange when it reaches its slip moment.
- If the top flange fails to slip, all the slip will eventually occur in the bottom flange.
The required length of the slots is determined by (Butterworth 1999: 6):
d D L= θ + Where:
- L: Length of the slot.
- θ: Inelastic rotation of the joint.
- d: Bolt diameter.
Pall friction device
The Pall friction device is used in concentrically braced frames with cross-bracing configuration. This type of damper was developed by Dr. Avtar Pall during his doctoral studies. It consists of rigid diagonal brace elements, with slotted holes in them, that have a friction interface (friction hinges) at their intersection. They
are interconnected by horizontal and vertical link members using bolts. These links assure that when the forces acting on the device, through the braces, are high enough to initiate slip on the tension diagonal, the compression diagonal also slips an equal amount in the opposite direction; resulting in frictional sliding occurring at the interface (Aiken 1993: 11). This device is shown in the following figure:
Figure No.34: Pall friction device Source: Aiken 1993: 12.
The friction resistance in the device requires a normal force acting at the interface. This force is applied through a bolt placed at the intersection of the diagonals, and it can be modified by adjusting the tension in the bolt, as in the BSJ (Aiken 1993: 12).
The following figure shows how this friction device works:
Figure No.35: Installation of Pall dampers in cross-bracing systems Source: UPC: 33.
A patented version of this device is now available in the market and has been used in many new and retrofitted buildings in
Canada (Butterworth 1999: 3). One of the most famous cases is the Concordia University’s Webster Library building in downtown Montreal, which has 150 Pall friction dampers installed. Other buildings that have this damping device are the Casino on lle Ste.
Helene in Montreal, and the Space Agency in St. Hubert, Quebec.
Sumitomo friction device
The Sumitomo friction device is used in concentrically braced frames with chevron configuration. It consists of a cylindrical steel casing device with friction copper pads, with pieces of granite inside, that slide directly on the inner surface of the case. They are typically installed on the underside of the beams of the frames. This device was designed and developed by Sumitomo Metal Industries, Ltd, Japan; and was originally used for railway cars (Aiken 1993: 4). They have the following configuration:
Figure No.36: Longitudinal section of the Sumitomo friction device Source: UPC: 38.
The way this type of damper is implemented in steel buildings is shown in the following figure:
Figure No.37: Installation of Sumitomo dampers in chevron systems Source: Aiken 1993: 6.
Design procedure for friction-damped steel frames Structures that have dampers installed in them are usually designed using dynamic analysis, time-history analysis or performance based design. There are no standard procedures for the design of dampers in the present codes, so their design is based on results obtained in previous research projects.
A code design procedure for friction-damped steel frames has been developed and proposed by Yaomin Fu and Sheldon Cherry, and has been published in the Journal of Structural Engineering in 1998. The name of this article is “Simplified Seismic Code Design Procedure for Friction-Damped Steel Frames”. These authors have developed a method to establish a ductility-related force modification factor for friction-damped steel frames. This allows to use the quasi-static analysis approach established in the code to analyze this type of structures, it may be applied to steel structures having any of the friction dampers
described previously. We will show how the Rd factor is determined using this method.
This method was developed by analyzing a single-degree-of-freedom viscous damped system, which has also a friction damper installed in it. This model may represent a storey segment of a friction-damped frame or an equivalent single-degree-of-freedom system of a multi-storey building subjected to a ground motion.
Figure No.38: Single-degree-of-freedom model of a friction-damped system Source: Fu and Cherry 1998: 56.
The concept this method is based on is that the friction damper installed in the system will add stiffness to it. Considering an elasto-plastic behavior, when the system is subjected to a ground motion, the total stiffness of the system is the sum of the stiffness of the primary system (system without the friction damper) and the stiffness provided by the damper. When the threshold level of the damper is reached, it starts slipping and stiffness is only provided by the primary linear system. Then, when the system reaches its yield point, it can no longer sustain increasing forces. This type of system is called a trilinear system, its nonlinear behavior is shown in the following figure:
Figure No.39: Force-displacement relation of a trilinear system Source: Fu and Cherry 1998: 57.
This system is characterized by three parameters, the added stiffness ratio, the slip ratio and the yield ductility. These parameters are defined as:
y y
s s
f a a
u u
u u
K K
max max
=
=
=
µ µ α
Where:
- αa: Added stiffness ratio.
- Ka: Added stiffness provided by the friction damper.
- Kf: Stiffness of the primary system.
- µs: Slip ratio.
- umax: Maximum displacement of the system.
- us: Displacement at which the friction damper starts to slip.
- µy: Yield ductility. In building codes, the common assumption is that it is equal to the Rd factor.
- uy: Yield displacement.
The friction damper will increase the period and energy dissipation capacity of the primary linear system. The trilinear system is usually analyzed using an equivalent linear system, whose stiffness and viscous damping ratio can be determined from the parameters of the nonlinear system. The equivalent normalized stiffness, normalized energy dissipated and damping ratio of this linear system can be determined by:
( ) ( )
- Keo: Equivalent normalized stiffness.
- Edo: Equivalent normalized energy dissipated.
- ξe: Equivalent viscous damping ratio.
- ξo: Viscous damping ratio of the primary system, usually equal to 2% for steel structures.
The normalized displacement of a friction-damped system is defined as the ratio between the spectral displacement of the equivalent linear system and the primary system. It can be obtained using the following expression:
( )
- Rsd: Normalized displacement of the friction-damped system.
- B: Constant whose values vary between 18 and 65, leading to the upper and lower bounds of damping reduction factors. The authors have considered a value of 30, to have an average reduction factor.
The normalized restoring force of a friction-damped system, Rf, is defined as the ratio between the restoring force of the
The normalized restoring force of a friction-damped system, Rf, is defined as the ratio between the restoring force of the