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Canadian Seismic Design of
Steel Structures
An Organized Overview
By: Alfredo Bohl
University of British Columbia
Department of Civil Engineering
March, 2005
Abstract
In this report, an overall overview of the seismic design of
steel structures in Canada will be given. The design philosophy,
general requirements and modeling issues of the main steel seismic
force resisting systems are presented; as well as physical testing
and design procedures for moment-resisting connections. Special
seismic steel framing systems will also be discussed.
Introduction
Seismic design provisions established in the codes are
constantly being changed and improved, for structures to have a
better performance during earthquakes. A lot of research and
development of new structural systems is continuously being
carried out. However, there are still many aspects of steel seismic
design that remain as a challenge.
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ALFREDO BOHL
The new upcoming 2005 Edition of the National Building
Code of Canada, as well as the latest 8th. Edition of the Handbook
of Steel Construction, contain significant changes compared to
their previous editions regarding seismic design. The overview
given in this report is based on the provisions contained in these
documents.
Since this is a very extensive topic, this report is intended
to cover the main aspects of steel seismic design for the most
common framing systems used in Canada. The first part of the
report will be an overview of the seismic design requirements
contained in the Handbook of Steel Construction. The clause 27 of
the Handbook of Steel Construction covers the specific seismic
design requirements for steel structures. In the last edition, new
structural systems have been introduced, like the ductile plate
walls. The force reduction factors for ductile systems have been
increased, but detailing requirements for these systems are now
more demanding. In this report, the steel seismic force resisting
systems are classified in accordance to their ductility-related force
modification factor, and each of these is explained separately.
Also, the derivation of the new overstrength-related force
modification factor for these systems, contained in the last edition
of the National Building Code of Canada, will be presented.
The second part of the report will cover the procedures to
perform physical tests of beam-to-column moment-resisting
connections for seismic applications, which are required when
connections that are not prequalified are going to be used in a
structure. Also, the design procedure for three types of prequalified
connections, which are the most commonly used in Canada, will be
presented. These procedures are contained in documents published
by the Federal Emergency Management Agency.
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R  1.0D   0.5L  1.0E  (S16-01, clause 7.2.6(b)(ii))
In the last part of the report, two special seismic steel
framing systems are introduced, the special truss moment frame
and the friction-damped steel frame.
Where:
Formatted spreadsheets have been developed to perform
calculations related to some of the design procedures exposed in
this report, including the design of links in eccentrically braced
frames, and the design of moment-resisting connections.
-
I recommend reading this term project to those who are
interested in learning a little more about on how seismic design of
steel structures is performed in Canada, and the structural systems
that are available.
Load combinations including earthquakes
The fundamental safety criteria that must be met in limit
states design is the following (CISC 2004: 2-13):
Factored resistance ≥ Effect of factored loads
For load combinations that include earthquake, the effect of
factored loads is the structural effect due to the factored load
combinations taken as (CISC 2004: 1-20):
: Resistance factor.
R: Resistance.
D: Dead loads.
L: Live loads.
E: Live loads due to earthquake.
: Importance factor, which should not be less than 1.00.
However, for structures where it can be demonstrated that
collapse will not cause injury or any other serious
consequences, it should not be less than 0.80.
New force reduction factors in the 2005
NBCC
With the introduction of the new 2005 Edition of the
National Building Code of Canada (NBCC), the expression to
determine the lateral seismic force at the base of the structure using
the quasi-static analysis has been modified significantly. This
expression in the upcoming code will be the following (Mitchell
2003: 309):
R  1.0D   1.0E  (S16-01, clause 7.2.6(a))
V
And either one of the following (the first expression is for
storage and assembly, the second expression is for all other
occupancies):
S Ta M v I EW
Rd Ro
Where:
-
R  1.0D   1.0L  1.0E  (S16-01, clause 7.2.6(b)(i))
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ALFREDO BOHL
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V: Design shear force.
S(Ta): Design spectral response acceleration.
Mv: Factor for the higher mode effects on the shear base.
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IE: Earthquake importance factor of the structure.
W: Expected weight of the structure.
Rd: Ductility-related force modification factor.
Ro: Overstrength-related force modification factor.
Comparing this expression with the one in previous codes,
the 2005 NBCC recognizes two force modification factors, Rd and
Ro. The factor Rd reflects the capability of the structure to dissipate
energy through inelastic behavior, this factor corresponds to the R
factor used in the previous 1995 edition. The factor Ro accounts for
the dependable portion of reserve strength in a structure designed
according to the NBCC provisions, it is related to the calibration
factor U used in the previous code (Mitchell 2003: 309).
The main modification in the determination of the base
shear in the new code is that the account of overstrength is
considered explicitly. In the previous code, the factor U considered
implicitly all the sources of overstrength in the structure, like the
actual strength of the material. Instead, the factor Ro takes into
account the various sources of overstrength, through the following
expression (Mitchell 2003: 310 – 311):
Ro  Rsize R R yield Rsh Rmech
Where:
-
-
Rsize: Factor accounting for overstrength arising from
restricted choices of sizes of elements and rounding up of
dimensions.
R: Factor accounting for overstrength due to the difference
between the nominal and factored resistances, equal to 1/,
where  is the material resistance factor defined in the CSA
standards.
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ALFREDO BOHL
Ryield: Ratio of the “actual” yield strength to the minimum
specified yield strength.
Rsh: Factor accounting for overstrength due to development
of strain hardening, has larger values for more ductile
systems.
Rmech: Factor accounting for overstrength arising from for
the additional resistance that can be developed before a
collapse mechanism forms in the structure. This additional
resistance in the structure can only be displayed if it is
redundant and if yielding takes place in a sequence instead
in all the elements at the same time.
Due to the experience gained in past earthquakes, the Rd
factors in steel structures have been increased for ductile and
moderately ductile systems in the new 2005 NBCC to 3.5 and 5.0,
compared to 3.0 and 4.0 in the previous code. So, the design forces
for these systems are now lower; however, the detail requirements
to ensure adequate ductility according to these factors are more
demanding (Mitchell 2003: 312).
The clause 27 of the CISC 8th. Edition of the Handbook of
Steel Construction (HSC), developed by the Canadian Institute of
Steel Construction (CISC), provides the seismic design
requirements for steel structures in Canada. It provides the force
reduction factor for several structural systems, corresponding with
the provisions in the 2005 NBCC, and gives design and detail
requirements to provide ductility consistent with the factors used,
in accordance to the Canadian Standards Association (CSA)
standard. These minimum requirements have been introduced in
this last edition in order to avoid brittle failure and to mobilize
energy dissipation properties through the structure (CISC 2004: 2105).
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Steel seismic force resisting systems
-
The 2005 NBCC recognizes different types of steel seismic
force resisting systems (SFRS), their corresponding Rd and Ro
factors, and the design and detail requirements for each of them
according to the CSA standard CSA-S16-01 (Mitchell 2003: 313 –
314). In each of these SFRS, there are certain structural elements
which are designed to dissipate energy by inelastic deformation;
these must be able to sustain various cycles of inelastic loading
with a minimum reduction of strength and stiffness. The other
elements and connections must respond elastically to loads induced
by yielding elements.
-
  C f Rd  f
U2  1 
 V h
f

Where:
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
 (S16-01, clause 27.1.8)


U2: Amplification factor that takes into account secondorder effects due to gravity loads, it must not exceed 1.4.
Cf: Factored axial force.
f: First-order lateral displacement.
Vf: Factored shear force.
h: Storey height.
Ductile behavior of steel frames
Steel frames are classified in three types, depending on
their ductility. The more ductile systems have the highest force
reduction factors (CISC 2004: 2-105):
In order to ensure that yielding in some elements will occur
before others, relative strengths between the dissipating and nondissipating elements must be known, so we must know the
probable yield stress. For non-dissipating elements, the minimum
yield stress given in the material standard and specifications must
be used. In energy dissipating elements, the probable yield stress
should be used, being taken as RyFy, where Ry = 1.1. The product
RyFy must be at least 385 MPa, and the yield strength Fy should not
be less than 350 MPa. Width-thickness limits are calculated using
this Fy value (CISC 2004: 2-107).
The amplification factor that takes into account the P-delta
effects for structural elements in SFRS is calculated differently
compared to conventional design:
ALFREDO BOHL
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Ductile or Type D: These frames are designed so that they
can have severe inelastic deformations. They have a force
reduction factor between 4.0 and 5.0.
Moderately ductile or Type MD: Inelastic deformations are
more limited than in type D frames, members are designed
to resist greater loads. They have a force reduction factor
between 3.0 and 3.5.
Limited ductile or Type LD: These are new types of frames
introduced in the 8th. Edition of HSC. Inelastic
deformations are even more limited and design loads are
greater than in type MD frames. They have a force
reduction factor of 2.0.
The connections in type D and MD frames must be tested
physically to ensure that they satisfy certain deformation criteria
under cyclic loads. In type LD frames, physical test are not
necessary, and can be detailed as traditional connections.
In the following part of this report, we will expose the
design and detail requirements for the different types of SFRS
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defined in the CAN/CSA S16-01, classified according to their Rd
factors.
SFRS with Rd = 5.0
Ductile SFRS defined in CAN/CSA S16-01 with a force
reduction factor of 5.0 are the ductile moment-resisting frames and
the ductile plate walls. We will expose the design philosophy and
general requirements of these systems according to the CAN/CSA
S16-01.
ALFREDO BOHL
weakening the beam at the point where the plastic hinges are
expected to form. Plastic hinges can also be formed in columns
only at the base of the structure for multi-storey buildings, since if
they develop at different locations, a storey may have very large
inelastic deformations compared to the ones expected in the
design. For single storey buildings, this is not a problem and
plastic hinges can be formed at the top of the column. In these
cases, columns must be class 1 sections.
Ductile moment-resisting frames
In ductile moment-resisting frames, the energy dissipating
elements are the beams, so they must be able to undergo inelastic
response without stability failures. The columns must be stronger
than the beams. So, beams must be class 1 sections and columns
must be class 2. The failure mode of the different types of class
sections are shown in the following table:
Class
1
2
3
4
Failure mode
Plastic design, permits attainment of the plastic moment and subsequent
redistribution of the bending moment (plastic deformation).
Compact, permits attainment of the plastic moment but need not allow
for subsequent moment redistribution (plastic-elastic deformation).
Non-compact, permits attainment of the elastic yield moment (elastic
deformation).
Slender section, strength of section is governed by local buckling of
elements in compression.
Table No.1: Failure modes for different class sections
Source: Chu 2003: 5.
Figure No.1: Failure mechanisms: (a) desired (b) undesired
Source: CISC 2004: 2-108.
The main advantages of this type of system is that they
absorb less shear forces due to their flexibility and have high
energy dissipation capacity. However, they are subjected to large
inter-storey drifts (Schubak 2005: 6-2).
At plastic hinge locations, beams must be braced to resist
lateral and torsional displacement. It is not necessary to brace the
last hinge to be formed which will lead to a failure mechanism.
The maximum unbraced length between plastic hinges is:
Lcr 17250  15500

(S16-01, clause 13.7(b))
ry
Fy
Beams are designed so that plastic hinges form at a short
distance from the columns, without failure of the connections. This
is done by strengthening the beams near the columns or by
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Where:
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Lcr: Unbraced length.
ry: Radius of gyration about the weak axis.
: Ratio of the smaller factored moment to larger factored
moment at opposite ends of the unbraced length, positive
for double curvature and negative for single curvature.
Fy: Yield strength.
For plastic analysis, the distribution of moments due to
seismic loads may be taken as varying linearly with zero at one end
and the plastic moment at the other, in order to determine .
Formation of plastic hinges in beams induces forces in
elements and connections adjacent to them. This force is calculated
as 1.1Ry times the nominal resistance of the beam, ZFy, where Z is
the plastic modulus of the steel section.
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Columns must be able to resist the accumulated forces due
to yielding of elements and gravity loads. In order to assure that
the plastic hinges will form in the beams before the columns
(except in single-storey buildings), the following equation must be
satisfied at each beam-column intersection:
M
rc

d

'   1.1R y M pb  Vh  x  c
2



  (S16-01, clause 27.2.3.2)

Where:
M
Non-dissipating elements adjacent to columns must be able
to resist forces induce by formation of plastic hinges. This force is
calculated as 1.1Ry times the nominal resistance of the column,
which is given by:
rc

Cf
'  1.18M pc 1 
 C
y


  M pc (S16-01, clause 27.2.3.2)


Where:
-

  M pc (S16-01, clause 27.2.3.1)


-
Where:
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Mpc: Nominal plastic moment resistance of the column.
Cf: Axial force resulting from summing Vh acting at the
level considered and above.
Vh: Shear force acting at the plastic hinge location when
1.1RyMpb is reached at beam hinge location.
Mpb: Nominal plastic moment resistance of the beam.
: Resistance factor, equal to 0.9 for this case.
Cy: Axial compression force at yield stress.
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In the case of columns, the maximum unbraced length
between plastic hinges is determined the same way as in beams,
taking  = 0. In high seismic areas, the maximum axial load shall
be 0.3AFy for all load combinations, because the flexural
resistance of the column deteriorates fast when high axial loads are
applied, limiting the ductility.

Cf
1.18M pc 1 
 C
y

ALFREDO BOHL
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3/14/2016
Mrc’: Sum of column factored flexural resistances at the
intersection of beam and column centrelines.
x: Distance from the plastic hinge location to the column
face, it is determined by physical testing of the joints.
Procedures on how to determine this distance for
prequalified connections will be exposed later.
dc: Depth of column.
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The following free-body diagrams help to understand how
these calculations are performed:
ALFREDO BOHL
elements. If the plastic hinges are expected to form in the beams,
the panel zone must resist forces arising from beam moments of:

 1.1R M

y
pb
d

 Vh  x  c
2


  (S16-01, clause 27.2.4.1)

For single-storey buildings, if plastic hinges are expected to
form near the top of the columns, the panel zone shall resist forces
due to the plastic hinge moments of as 1.1Ry times the nominal
resistance of the column.
For high seismic areas, the sum of the panel zone depth and
width, divided by the thickness, must be less than 90. In this case,
the shear resistance of the panel zone is given by:
2

3bc t c 

 (S16-01, clause 27.2.4.2(a))
Vr  0.55d c w' Fyc 1 

d
d
w
'
c b


Where:
Figure No.2: Free-body diagram showing forces necessary for beam and
column design
Source: CISC 2004: 2-110.
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Special consideration must be taken in column splices
having partial-joint-penetration-groove welds if the axial force in
the column is tensile, since they are not ductile under tension
loads. In this case, splices are designed more conservatively, they
must resist twice this tensile force.
In relation to the column joint panel zone, limited inelastic
deformations are permitted if they are properly detailed. The entire
perimeter of doubler plates must be welded to the contiguous
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Vr: Shear resistance.
w’: Sum of thickness of column web plus the doubler
plates.
Fyc: Yield strength of the column.
bc: Width of column flange.
tc: Thickness of column flange.
db: Depth of beam.
If this does not apply, the width-to-thickness limit of the
panel zone should satisfy:
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k
h
 439 v (S16-01, clause 13.4.1.1(a))
w
Fy
Where:
-
h: Clear depth of the web between flanges.
w: Width of plate.
kv: Shear buckling coefficient.
ALFREDO BOHL
The beams, columns and joints must be braced. Lateral
bracing at joints must be provided at least at one beam flange when
the plastic hinges form in the beam, and at both beam flanges when
they form near the top of the columns. In case no lateral support
can be provided at a certain level, the slenderness ratio of the
column shall not exceed 60.
Most of the requirements described previously are
summarized in the following figure. This figure also shows details
for type MD and LD systems, which will be described later:
In this case, the shear resistance of the panel zone is given
by:
Vr  0.55d c w' Fyc (S16-01, clause 27.2.4.2(b))
The beam-to-column joints and connections must be
capable to develop an inter-storey drift angle of 0.04 rad under
cyclic loading, this has to be demonstrated by physical testing. The
strength at the column face must be at least Mpb, or 0.8Mpb when
reduced beam sections are used. The factored resistance of the
connection must be at least enough to resist gravity loads and
shears induced by moments of 1.1RyZFy at the plastic hinge
location.
As it is mentioned in clause 27, the appendix J of the
CAN/CSA S16-01 contain references to documents which show
the procedures to perform physical test of connections in momentresisting frames. Except the fact that joints must be capable to
develop an inter-storey drift angle of 0.04 rad under cyclic loading,
all other requirements described regarding panel zones, joints and
connections do not need to be satisfied if these procedures are
used. Design requirements for connections contained in some of
these documents will be shown later in this report.
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Figure No.3: Summary of design requirements for moment-resisting frames
Source: Mitchell 2003: 314.
Modeling moment-resisting frames to perform structural
analysis is usually a simple task, using beam elements to represent
the longitudinal axis of the beams and columns, while joints are
represented as simple points (nodes) where these elements
intersect. However, when we have very deep beams and columns,
the joints will be very large, and cannot be accurately modeled
using nodes. If we have large joints, the deformations in these are
smaller than in adjacent beams and columns, and the frame
stiffness is increased. Therefore, we need to model the joint in
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ALFREDO BOHL
these cases (Schubak 2005: 6-4). This can be done by overlapping
segments of the beams and columns with rigid elements, as shown
in the following figure:
Figure No.5: Failure mechanism of ductile plate walls
Source: Mitchell 2003: 311.
Figure No.4: Model of a joint in moment-resisting frames for deep beam
and column sections
Source: Schubak 2005: 6-4.
Ductile plate walls
Plate walls are transversely stiffened vertical plate girders
constituting web plates designed to resist lateral loads. Ductile
plate walls are framed by columns and beams connected with
moment-resisting connections. In this system, the main energy
dissipating element is the web plate; framing elements also
dissipate energy once the plate has yielded. Plate walls can develop
large inelastic deformations by yielding of the web and formation
of plastic hinges in the framing elements. The main advantage of
this SFRS compared to other systems is their large stiffness, which
reduces the displacements and, therefore, the amount of nonstructural damage during an earthquake.
The web plate carries the shear forces by tension fields that
develop in the web plates parallel to the direction of the stress
principal axis. This tension field and the shear force and bending
moment of the storey produce axial forces and moments to the
beams and columns. The overall behavior of the plate wall can be
modeled by equivalent diagonal braces:
Figure No.6: Plate diagonal tension brace model
Source: CISC 2004: 2-91.
When using this model, the area of the equivalent diagonal
brace can be estimated by the following expression:
The general requirements for beams, columns, panel zones,
joints and connections are the same as in moment-resisting frames;
except that columns must always be class 1. Columns splices must
develop full flexural resistance of the smaller column section.
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A
wLSin 2 (2 )
(S16-01, clause 20.2)
2Sin Sin 2
Where:
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1
Tan 4 
wL
2 Ac
 1
h3 

1  wh

A
360
I
L
c 
 b
ALFREDO BOHL
(S16-01, clause 20.3.1)
Where:
-
A: Area of the equivalent diagonal brace.
w: Web plate thickness.
L: Distance between column centerlines.
: Angle of inclination of the principal stresses measured
from the vertical axis, it must be between 38º and 45º.
: Angle of inclination of the equivalent diagonal brace
measured from the vertical axis.
Ac: Cross-sectional area of the column.
h: Storey height.
Ab: Cross-sectional area of the beam.
Ic: Moment of inertia of the column.
This model allows to find moments in beams and columns,
but not the tension fields. In order to determine these, a more
sophisticated model with a series of inclined pin-ended strips can
be used to model the plate wall:
Figure No.7: Strip model for a plate wall
Source: CISC 2004: 2-92.
However, since there are limitations for the angle of
inclination of the principal stress, this model does not work well
for tall and short plate walls.
In order for yielding to occur first in the web plate, the
beams and columns must be stronger. This is the principle for the
capacity design of a plate wall. The ultimate loads in the beams
and columns are increased by an amplification factor, equal to:
B
Vre
 Rd (S16-01, clause 27.8.2.4)
Vf
Where:
Vre  0.5R y Fy wLSin 2 (S16-01, clause 27.8.2.4)
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ALFREDO BOHL
Where:
-
B: Overstrength factor for ductile plate walls.
Vre: Probable shear resistance at the base of the wall.
Vf: Factored lateral seismic force at the base of the column.
Rd: Force modification factor.
To calculate the design moments at each storey, the
following procedure must be followed:
-
Calculate the design moment at the base as BMf, where Mf
is the factored seismic moment at the base of the wall.
Extend this moment to a length L, but not less than two
storeys from the base.
Calculate the design moment at the top of the building as B
times the moment in the level below the top.
Calculate the design moments in the storeys above L,
assuming they have a linear variation from the level above
L to the top. The design moment at each level does not
need to exceed Rd times the moment at that level.
With these moments, we can calculate the axial forces in
the columns. This procedure is illustrated in the following figure:
Figure No.8: Capacity design of ductile plate walls
Source: CISC 2004: 2-123.
The top and bottom web plates must also be anchored to
stiff elements, so that the plates can develop full tension fields. At
the top panel, the web plate must be attached to the beam. At the
bottom panel, the web must be attached to the substructure, or
alternatively, to a very rigid beam. This is to anchor the vertical
components of the tension fields. The horizontal components must
also be transferred to the substructure.
The columns must also be stiffened at the base, so that the
plastic hinges form at a distance at least 1.5 the column depth
above the base plate. These stiffeners must resist 1.1Ry the nominal
flexural resistance of the column or the tensile load in the column,
the one that is greater.
Most of the requirements described previously are
summarized in the following figure. This figure also shows details
for type LD systems, which will be described later:
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ALFREDO BOHL
Figure No.10: Configuration of eccentrically braced frames
Source: Schubak 2005: 6-15.
Figure No.9: Summary of design requirements for ductile plate walls
Source: Mitchell 2003: 315.
SFRS with Rd = 4.0
The link beams must be class 1. The web must have a
uniform depth, have no penetration or any type of reinforcement,
except stiffeners. The resistance of the link is given by the lower
value between Vp’ and 2Mp’e, which are defined as:
Ductile SFRS defined in CAN/CSA S16-01 with a force
reduction factor of 4.0 are the eccentrically braced frames. We will
expose the design philosophy and general requirements of this
system according to the CAN/CSA S16-01.
Vp ' Vp




2

Pf 
Mp
M p '  1.18M p 1 


AF
y


Ductile eccentrically braced frames
(S16-01, clause 27.7.2)
Where:
In eccentrically braced frames, the energy dissipating
elements are the links, which are the beam segments between the
brace connections and the beam. The link is designed to fail either
in flexure or shear. Therefore, the columns, braces, beam segments
outside the link and connections must be stronger than the link
itself and behave elastically. These SFRS have the advantage that
they combine the ductile behavior of the moment-resisting frames
and the stiffness of the concentrically braced frames, which will be
described later (Schubak 2005: 6-15). They can have the following
configurations:
Document1
 Pf
1 
 AF
y

V p  0.55wdFy
M p  ZFy
(S16-01, clause 27.7.2)
Where:
-
3/14/2016
Vp: Plastic shear resistance.
Pf: Factored axial force in the link (compression or
tension).
PAGE 12 OF 50
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-
CANADIAN SEISMIC DESIGN OF STEEL STRUCTURES
A: Gross area of the beam link.
Mp: Plastic moment resistance.
e: Length of the beam link.
w: Web thickness of the beam link.
d: Depth of the beam link.
The length of the link should not be less than its depth. In
case Pf/(AFy) > 0.15, the length of the link is determined by:

Pf Aw  1.6M p

e  1.15  0.5

 V
V
A
f
p


1.6M p
Vf
A
e
; if w  0.3
Vp
A
Pf
 Aw
Vf
; if
 0.3

A
Pf

Figure No.11: Forces acting on the beam link
Source: Schubak 2005: 6-16.
Short links have a better performance than long links, due
to the following reasons:
(S16-01, clause 27.7.3)
-
Where:
Aw  wd  2t  (S16-01, clause 27.7.3)
Where:
-
Vf: Factored shear force.
Aw: Area of web.
Short links (e < 1.6Mp/Vp): Yield in shear.
Long links (e > 2.6Mp/Vp): Yield in flexure.
Intermediate links: Yield in both shear and flexure.
Document1
The shear force is constant along the length of the link, so
shear strains are uniformly distributed, meaning there are
no local strains.
All the link contributes to dissipate energy, not only the
ends.
The maximum allowed rotation of the link depends on the
behavior of the link. This rotation is calculated given the drift of
the frame. The drift of the frame is obtained multiplying the drift
from the analysis by Rd, to get the maximum inelastic deformation
expected in a severe earthquake. The link rotation limits are the
following:
-
The behavior of the link is related to its length (Schubak
2005: 6-16):
-
ALFREDO BOHL
0.09 rad for shear yielding.
0.03 rad for flexure yielding.
Use linear interpolation to obtain the limits when 1.6Mp/Vp
< e < 2.6Mp/Vp.
The relations between the drift and the link rotation are
given in the following figure:
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-
-
ALFREDO BOHL
If 1.6Mp/Vp < e < 2.6Mp/Vp, the stiffeners must be placed
at 1.5bf from each end of the beam link, and intermediate
links are placed according to the spacing criteria previously
explained.
If e ≥ 5Mp/Vp, the link does not require intermediate
stiffeners.
Links with a depth of less than 650mm only need
intermediate stiffeners at one side. These must have a width of at
least 0.5(bf – 2w), where bf is the width of the flange; and a
thickness not less than w or 10mm, take the larger.
Figure No.12: Relations between drift and link rotation
Source: Schubak 2005: 6-16.
The link must have full-depth web stiffeners at both ends of
it, in order to clearly define the length of the link, transfer shear
forces over the whole depth, and prevent buckling at the plastic
hinges. Both stiffeners must have a combined width of at least (bf –
2w), where bf is the width of the flange; and a thickness not less
than 0.75w or 10mm, taking the larger. Both ends of the link must
also be braced at both flanges.
If the link is directly connected to the column, the link
beam-to-column connection must be able to develop anticipated
plastic deformation. In this case, physical test are required to show
that the connection is able to develop a rotation of 1.2 times the
rotation obtained by multiplying the drifts by Ry. The same
standard procedures for physical tests mentioned previously apply
for this. However, this requirement may be avoided if all of the
following conditions are satisfied:
-
Full-depth intermediate stiffeners are also required to make
sure that the link will have a ductile behavior. The spacing between
them is determined in the following way:
-
-
If e < 1.6Mp/Vp, the maximum spacing is (30w – 0.2d) if
the rotation of the link is 0.09 rad, and (52w – 0.2d) if the
rotation of the link is 0.03 rad or less. Spacing for
intermediate angles is obtained by interpolation.
If 2.6Mp/Vp < e < 5Mp/Vp, the stiffeners must be placed at
1.5bf from each end of the beam link.
Document1
-
The link is separated from the column at a short distance,
and the beam in this distance is reinforced so that the
connection behaves elastically.
If e < 1.6Mp/Vp.
Full-depth stiffeners are provided at the end of the
reinforced location.
As we mentioned previously, the portion of the beam
outside the link must behave elastically. The link inelastic straining
will induce forces to the beam. So, the beam outside the link is
designed for a larger force than the link. This force is equal to
1.3Ry the nominal strength of the link, and the factored resistance
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is equal to the link factored resistance multiplied by Ry/. Lateral
bracing also needs to be provided at both flanges. If a plastic hinge
is expected to form at the link end, then the maximum unbraced
length is given by:
ALFREDO BOHL
column, where hs is the storey height. At the base of the top
columns, this factor is 0.5/hs.
Most of the requirements described previously are
summarized in the following figure:
Lcr 25000  15000

(S16-01, clause 13.7(a))
ry
Fy
Where:
-
-
Lcr: Unbraced length.
ry: Radius of gyration about the weak axis.
: Ratio of the smaller factored moment to larger factored
moment at opposite ends of the unbraced length, positive
for double curvature and negative for single curvature.
Fy: Yield strength.
The diagonal braces of the frame, although are expected to
behave elastically, must be class 1 or 2, since they can carry more
load than expected. Sometimes, the brace and link are connected
with moment-resisting connections, so that the brace can take some
of the loads produce by the straining of the link, and this way,
relief the segments of the beam outside the link. Also, the brace-tobeam connection must not extend into the link.
The columns and their splices must be designed for
secondary moment effects due to the frame drift, and to resist
forces due to yielding of the links. Forces due to yielding in the
columns are equal to 1.15Ry times the nominal strength of the
beam; in the case of multi-storey buildings, this force is taken as
1.3Ry for the top two storeys. The column splices must resist shear
forces equal to 0.3/hs times the nominal flexural resistance of the
Document1
Figure No.13: Summary of design requirements for eccentrically braced
frames
Source: Mitchell 2003: 315.
When modeling eccentrically braced frames, the difficulties
arise when we have to model the link. The other elements of the
frame can be represented by beam elements. The model we use for
the link will depend on its behavior. To model a link which fails in
flexure is not a problem, we just have to place plastic hinges at the
ends of the link. However, when the link fails in shear, it is
difficult to represent it in the model. An approach used in pushover
analysis is to replace the link’s plastic moment Mp with an
equivalent moment that corresponds to the shear force at which the
link reaches its yield point in shear, given by (Schubak 2005: 617):
M p  0.5V p e
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SFRS with Rd = 3.5
Moderately ductile SFRS defined in CAN/CSA S16-01
with a force reduction factor of 3.5 are the moderately ductile
moment-resisting frames. We will expose the design philosophy
and general requirements of this system according to the
CAN/CSA S16-01.
Moderately ductile moment-resisting frames
In moderately ductile moment-resisting frames, as in
ductile moment-resisting frames, the energy dissipating elements
are the beams, so they must be able to undergo inelastic response
without stability failures. This type of SFRS can develop a
moderately amount of inelastic deformation by formation of plastic
hinges in the beams at a short distance from the columns.
Since the elements for this type of frames are designed to
resist higher forces, they will have larger sections, and most of the
general requirements are the same as for the ductile momentresisting frames. However, a few of these requirements are
different, and are explained in the preceding paragraphs.
The beams must be class 1 or 2 sections. The maximum
unbraced length between plastic hinges for beams and columns is
given in this case by the same expression used to determine the
maximum unbraced length of the portion of the beam outside the
link for eccentrically braced frames, repeated here for
convenience:
Lcr 25000  15000

(S16-01, clause 13.7(a))
ry
Fy
Document1
ALFREDO BOHL
For plastic analysis, the distribution for seismic loads may
be taken as varying linearly with zero at one end and the plastic
moment at the other, in order to determine .
Also for the columns, in high seismic areas, the maximum
axial load shall be 0.5AFy for all load combinations, because the
flexural resistance of the column deteriorates fast when high axial
loads are applied, limiting the ductility.
The beam-to-column joints and connections must be
capable to develop an inter-storey drift angle of 0.03 rad under
cyclic loading, this has to be demonstrated by physical testing.
Except the fact that joints must be capable to develop this interstorey drift angle, all other requirements described regarding panel
zones, joints and connections (which are the same as for ductile
moment-resisting frames) do not need to be satisfied if the
procedures from appendix J of the CAN/CSA S16-01 are used.
Some of these requirements are summarized in figure No.3,
shown previously.
Modeling issues are the same that those for ductile
moment-resisting frames.
SFRS with Rd = 3.0
Moderately ductile SFRS defined in CAN/CSA S16-01
with a force reduction factor of 3.0 are the moderately ductile
concentrically braced frames. We will expose the design
philosophy and general requirements of this system according to
the CAN/CSA S16-01.
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ALFREDO BOHL
Moderately ductile concentrically braced frames
In moderately ductile concentrically braced frames, the
energy dissipating elements are the diagonal braces, which carry
the lateral loads by axial forces and dissipate energy through
inelastic straining. Therefore, columns, beams and connections
must be stronger than the braces and have an elastic behavior. In
this system, the braces intersect the beams at one point. There are
three types of bracing configurations accepted by the CAN/CSA
S16-01:
-
Tension-compression bracing systems.
Chevron braced systems.
Tension-only bracing systems.
Alternatively, other systems that can respond inelastically
without losing their stability are also permitted. Some common
configurations are shown in the following figure:
Figure No.14: Common configurations of concentrically braced frames
Source: Schubak 2005: 6-7.
Some bracing systems, like K-bracing, are not allowed,
because in this type of systems, the tension brace imposes bending
to the column, and plastic hinges tends to form in the clear length
of the columns, causing instability of the structure.
Document1
Figure No.15: Non-permitted configuration of concentrically braced frames
Source: Schubak 2005: 6-7.
Systems with concentrically braced frames tend to have a
soft-storey response, especially in tall buildings, because inelastic
demands tend to concentrate in the lower levels, since they are the
first ones to be affected by ground motions; and in the upper
levels, due to higher mode effects. That is why height restrictions
are imposed for buildings with these systems.
Because ground motions may occur in any direction, the
structural configuration of these frames must be as symmetric as
possible. The dimensions of the diagonal braces must be such that
the shear resistance in each storey provided by the tension forces
developed in these elements is similar for storey shears acting in
opposite directions. For this, the ratio between of the sum of the
horizontal components of the factored tensile resistances in
opposite directions must be between 0.75 to 1.33.
For tension-compression bracing systems, the building can
have no more than eight storeys. In these, the brace in compression
will buckle after certain amount of cycles, due to deterioration of
its strength. So, class 2 sections with low slenderness ratios are
required for these braces, the maximum value is 200 (Mitchell
2003: 312). Also, its cross-sectional area should be small so that
they yield before the other elements of the frame. So, finding an
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optimum section for the compression braces is not possible
sometimes, since it is difficult to obtain low areas and low
slenderness ratios. This is still a matter of research (Schubak 2005:
6-9).
Figure No.16: Failure mechanism of tension-compression bracing systems
Source: Mitchell 2003: 311.
For chevron bracing systems, the building also can have no
more than eight storeys. The beams can also respond inelastically
in this kind of system, they must be continuous between columns
and across braces, and both flanges must be braced at the brace
connection. The problem with this kind of bracing system is that
when the compression braces buckles, severe bending in the beam
from the tension brace occurs. So, the beams must be strong
enough to resist yielding and buckling forces from the braces
together with gravity loads, without considering the support from
the braces.
ALFREDO BOHL
The force induced due to yielding of the tension brace to
the beam is equal to AgRyFy, where Ag is the gross area of the
brace, and from the compression brace equal to 0.2AgRyFy. When
the brace is connected to the beam from above, the compression
force is 1.2 times the compressive resistance of the brace, which is
equal to Cr/, where Cr is the factored compressive resistance
which depends on RyFy. In the case of buildings with four storeys
or lower, limited inelastic deformations are allowed in the beams,
since this does not affect negatively the response of the structure,
as long the beams are class 1 and their connections can resist loads
due to formation of plastic hinges in the beam. In this case, the
tension force induced to the beam is taken as 0.6AgRyFy.
The beam-to-column connections must be able to resist
gravity forces along with forces induced by the probable nominal
flexural resistance of the beam at the brace connection, in case the
tension brace force is less than AgRyFy. Brace connections must be
laterally braced.
For tension-only bracing systems, the building can have no
more than four storeys. The energy dissipation capacity in this kind
of frames is limited. The braces are connected the beam-tocolumns connections and must be able to carry all the seismic
loads, in tension. The columns must be continuous and of constant
cross-section, and its splices must have the moment resistance of
the cross-section and a shear resistance of 2ZFy/hs.
In relation to the diagonal braces of the three bracing
systems, because post-buckling resistance of these elements is
required to maintain the stability of the structure and they may
fracture prematurely, the limit to its slenderness ratio is:
Figure No.17: Failure of chevron concentrically braced frames
Source: Schubak 2005: 6-10.
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kL
 200 (S16-01, clause 27.5.3.1)
r
Where:
-
k: Effective length factor that depends on the boundary
conditions of the element.
L: Length between the points where formation of plastic
hinges is expected.
r: Radius of gyration.
When kL/r ≤ 100, the width-to-thickness ratio of the braces
must not exceed the following limits:
-
For rectangular and square HSS: 300 / Fy .
-
For circular HSS: 1000/Fy.
For legs of angles and flanges of channels: 145 / Fy .
-
For other elements: Class 1 cross-sections.
When kL/r = 200, the width-to-thickness ratio of the braces
must not exceed the following limits:
-
For HSS members: Class 1 cross-sections.
For legs of angles: 170 / Fy .
-
For other elements: Class 2 cross-sections.
Linear interpolation is used when 100 < kL/r < 200. In low
seismic areas, sections may be class 1 or 2; except for HSS
sections, that must be class 1.
Document1
ALFREDO BOHL
Regarding the effective length factor, for cross-bracing, it
can be taken as 0.4 for in-plane buckling and 0.5 for out-of-plane
buckling. For other types of bracing, it can be taken as 0.5 for inplane buckling and 1.0 for out-of-plane buckling.
In brace connections, eccentricities between the brace and
supporting elements must be minimized. These connections must
be able to resist axial loads due to buckling of the compression
brace and tensile yielding of the tension brace. So, the factored
resistance must be at least AgRyFy in tension and 1.2 the probable
compressive resistance in compression.
Buckling of the compression brace will redistribute forces
along the elements, and they need to be considered to determine
the connection resistance. The post-buckling resistance of the
braces can be taken as the lower value between 0.2AgRyFy and the
probable nominal compressive resistance. Since the magnitude of
ground motions is uncertain, a value of Rd = 1 is used for this
calculation. However, the tensile force in the brace does not need
to be greater than combined effect of gravity loads and seismic
loads corresponding to Rd = 1; this tensile force should be resisted
by the net section, and the resistance of it may be multiplied by a
factor of Ry/.
The brace connections must also be detailed to have a
ductile rotational performance if high inelastic response is
expected, in or out of the plane of the frame, depending on the
governing effective slenderness ratio. When plastic hinges are
expected to form in the braces, the factored flexural resistance of
the brace connection must be at least 1.1ZRyFy, this resistance may
also be multiplied by a factor of Ry/.
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ALFREDO BOHL
If plastic hinges are allowed to be formed in beams in
chevron braced systems, the tensile force in the connection can be
reduced. In this case, it can be taken as the maximum value
between the tensile force due to yielding of the beam or 1.2 the
probable compressive resistance of the brace.
The beams, columns, and connections excepting brace
connections, must be able to resist loads due to yielding of the
braces and redistribution of forces due to buckling. The columns
and their splices must be designed for secondary moment effects
due to the frame drift. Columns in multi-storey buildings,
including those that do not form part of the SFRS, must be
continuous and have a constant cross-sectional area over a
minimum of two storeys, except for tension-only bracing systems,
to prevent soft-storey response. Class 4 sections are not allowed
for columns, and columns in brace bays must be class 1 or 2,
because they play a major role in resisting lateral loads and are
subjected to large axial forces during an earthquake. Columns in
brace bays must be designed for a flexural resistance of 0.2ZFy,
and considering single curvature ( = -1). The columns splices
must have a shear resistance equal to 0.4/hs times the nominal
flexural resistance of the columns.
Most of the requirements described previously are
summarized in the following figure. This figure also shows details
for type LD systems, which will be described later:
Figure No.18: Summary of design requirements for concentrically braced
frames
Source: Mitchell 2003: 315.
Modeling concentrically braced frames is fairly simple,
using beam elements to represent the longitudinal axis of the
beams, columns and braces. We must just take into account that
the braces in compression are expected to buckle. If we use a linear
model, these braces must be omitted or have a limited carrying
capacity corresponding to post-yielding. If we use a nonlinear
model, the elements that represent the compression braces should
reflect their hysteretic behavior (Schubak 2005: 6-11).
SFRS with Rd = 2.0
Limited ductile SFRS defined in CAN/CSA S16-01 with a
force reduction factor of 2.0 are the moment-resisting frames with
Document1
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limited ductility, the limited ductility concentrically braced frames
and the limited ductility plate walls. We will expose the design
philosophy and general requirements of these systems according to
the CAN/CSA S16-01.
Moment-resisting frames with limited ductility
In moment-resisting frames with limited ductility, as in
ductile and moderately ductile moment-resisting frames, the
energy dissipating elements are the beams, so they must be able to
undergo inelastic response without stability failures. This type of
SFRS can develop a limited amount of inelastic deformation by
formation of plastic hinges in the beams at a short distance from
the columns.
Since the elements for this type of frames are designed to
resist higher forces, they will have even larger sections than the
moderately ductile moment-resisting frames, and most of the
general requirements are the same as for this system. However, a
few of these requirements are different, and are explained in the
preceding paragraphs.
This type of systems cannot be used in high seismic areas
and may be used in buildings not exceeding 12 storeys. The beams
must be class 1 or 2 sections. Columns must be class 1 and be Ishaped.
The beam-to-column joints and connections must have a
moment resistance equal to the lower value between 1.1RyMpb, or
the effect of combined gravity and seismic loads multiplied by
two. The shear resistance of the connection must be enough to
resist shears due to gravity loads and due to moments applied at
each end equal to the moment resistance of the connection. The
Document1
ALFREDO BOHL
beam flanges are to be directly welded to the columns flanges.
Partial-joint-penetration-groove welds and fillet welds must not be
used to resist tensile forces in the connections.
Alternatively, the beam-to-column joints and connections
must be capable to develop an inter-storey drift angle of 0.02 rad
under cyclic loading, this has to be demonstrated by physical
testing.
Some of these requirements are summarized in figure No.3,
shown previously.
Modeling issues are the same that those for moderately
ductile moment-resisting frames.
Limited ductility concentrically braced frames
In limited ductility concentrically braced frames, as in
moderately ductile concentrically braced frames, the energy
dissipating elements are the diagonal braces, which carry the
lateral loads by axial forces and dissipate energy through inelastic
straining.
Since the elements for this type of frames are designed to
resist higher forces, they will have larger sections than the
moderately ductile concentrically braced frames, and most of the
general requirements are the same as for this system. However, a
few of these requirements are different, and are explained in the
preceding paragraphs.
For both tension-compression and chevron bracing
systems, the maximum height is 12 storeys. This is because, since
the sections are bigger, the frames have a greater lateral resistance,
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and it is more unlikely that they will have a soft-storey response.
For chevron systems, in case they have four storeys or less, the
beams do not need to be designed for forces due to buckling and
yielding of the braces as long as they are class 1, and as long as the
braces and beam-to-column connections can resist the forces due
to buckling of the braces. Also, the beam must be able to support
gravity loads without considering the support provided by the
braces.
Tension-only bracing systems cannot have more than eight
storeys, and the columns must be continuous and of constant crosssection over a minimum of two storeys. The diagonal braces for
this system, in case of single-storey or two-storey buildings, can
have a maximum slenderness ratio of 300.
Diagonal braces also do not have limits in their width-tothickness ratios if their slenderness ratio is greater than 200, since
very little inelastic straining is expected in these cases. In low
seismic areas, the braces can be class 2 or less compact, and the
width-to-thickness ratio of the legs of the angles should not exceed
170 / Fy .
In low seismic areas, ductile rotational behavior of the
bracing connections is not required if the slenderness ratio of the
braces is greater than 100, and columns splices in columns that do
not form part of the SFRS do not need to have shear resistance for
loads due to yielding of the braces and redistribution of forces due
to buckling.
Some of these requirements are summarized in figure
No.18, shown previously.
Document1
ALFREDO BOHL
Modeling issues are the same that those for moderately
ductile moment-resisting frames.
Limited ductility plate walls
In limited ductility plate walls, the energy dissipating
element is the web plate; not the framing elements as in ductile
plate walls. The web plate dissipates a limited amount of energy by
yielding.
Since the elements for this type of systems are designed to
resist higher forces, they will have even larger sections than the
ductile plate walls. Plate webs must still satisfy minimum
requirements, and must have a factored shear and flexural
resistance greater or equal to the corresponding factored loads.
Because the beams and columns are not expected to yield, they do
not have any special requirements. Also, there is no need for
moment-resisting connections, and these can be designed
conventionally. Buildings with this type of system cannot exceed
12 storeys.
Some of these requirements are summarized in figure No.9,
shown previously.
Modeling issues are the same that those for ductile plate
walls.
SFRS with Rd < 2.0
SFRS defined in CAN/CSA S16-01 with a force reduction
factor lower than 2.0 are the cantilever column structures and
conventional construction. It is the first time that the CAN/CSA
S16-01 considers requirements for these types of systems.
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Cantilever column structures
This type of structures consists of beam-column systems
with little redundancy, which is fixed at the base and free at the
upper end. They are assigned an Rd = 1; except when the elements
have class 1 cross-sections, an Rd = 1.5 is assigned in this case.
As general requirements, the base connections must resist a
moment of 1.1Ry times the nominal flexural resistance of the
column. The amplification factor that takes into account P-delta
effects should not be greater than 1.25.
Conventional construction
This type of structures can dissipate some energy through
yielding and friction, available if conventional construction
requirements are satisfied. They are assigned an Rd = 1.5.
As general requirements, the SFRS of these structures must
have ductile failure modes or be designed for greater loads in high
seismic areas; these design loads are equal to the combined effects
of gravity and seismic loads multiplied by two in very high seismic
areas, and by 1.5 in other cases. The elements and connections
must have factored resistances corresponding to the factored load
effects, but design loads for connections can be limited to Ry times
the nominal strength of the joined elements. Connections for
moment resisting-frames or braced frames should be used.
Deduction of the Ro factors for SFRS
We have covered so far the main aspects related to the
ductility-related force modification factor, Rd. We will now expose
briefly the most relevant aspects of the overstrength-related force
Document1
ALFREDO BOHL
modification factor, Ro. As we mentioned previously, the new
NBCC takes into account in a more explicit way the overstrength
in structures, by identifying the sources of it and assigning factors
that consider each of these sources. The product of all these factors
is the Ro factor. We will explain how these factors have been
derived for the SFRS described (Mitchell 2003: 314 – 316).
The Rsize factor accounts for overstrength arising from
restricted choices of sizes of elements and rounding up of
dimensions. It is taken as 1.05 for steel structural shapes. For web
plates, it is taken as 1.10 considering that its thickness is rounded
up to the next plate thickness available.
The R factor accounts for overstrength due to the
difference between the nominal and factored resistances, equal to
1/. Since  is equal to 0.9 for ductile failure in steel structures,
this factor is equal to 1.11.
The Ryield factor is the ratio of the “actual” yield strength to
the minimum specified yield strength. It is taken as 1.10, which is
the mean ratio of the actual and minimum specified yield strength
for W shapes.
The Rsh factor accounts for overstrength due to
development of strain hardening. It depends on the yielding and
the level of inelastic deformations. For eccentrically braced frames,
it is approximately 1.30 when the link yields in shear and 1.15
when it fails in flexure; it has been considered as 1.15 to be more
conservative. For plastic hinges in beams, this factor is
approximately 1.15, so this is the value assigned for ductile and
moderately ductile moment-resisting frames. For moment-resisting
frames with limited ductility, this factor is 1.05, since lower
inelastic deformations are expected. In tension elements, this factor
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is approximately 1.05; this is the value assigned to concentrically
braced frames, because only braces in tension develop strain
hardening. For plate walls, the web plates develop strain hardening
due to the tension fields; it has been assigned a value of 1.05.
The Rmech factor accounts for overstrength arising from for
the additional resistance that can be developed before a collapse
mechanism forms in the structure. For moment-resisting frames,
this factor is greater than 1.00 when plastic hinges form in the
columns after the beams, it is taken conservatively as 1.00.
Overstrength in concentrically braced frames arises when the
compression brace buckles and an additional force is required so
that the tension brace yields; but Rmech is taken also conservatively
as 1.00, due to deterioration of compressive resistance under cyclic
loading. For eccentrically braced frames, the collapse mechanism
forms once the link has yielded, so this factor is 1.00. For ductile
plate walls, overstrength arises due to the fact that the collapse
mechanism occurs once the web plate has first yielded and then the
framing system, and because the compression that develops in
these elements provides an additional resistance. So, Rmech is taken
as 1.10. For limited ductility plate walls, it is taken as 1.05.
The values of the Ro factors in the 2005 NBCC for SFRS
are summarized in this table:
Table No.2: Summary of Ro factors for SFRS in the 2005 NBCC
Source: Mitchell 2003: 316.
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ALFREDO BOHL
Structures with combined SFRS
We have exposed the Rd and Ro factors that are used for
different types of SFRS. However, when we have structures with
combined SFRS, some special considerations need to be taken into
account (NBCC 2005 Part 4: 22):
-
-
-
If a particular value of Rd is used, then the corresponding
Ro must be used.
For combinations of different types of SFRS in the same
direction in the same storey, the product RdRo shall be
taken as the lowest value of RdRo of all of these.
For vertical variations of RdRo, not including penthouses
whose weight is less than 10% of the level below, the value
of RdRo in a particular direction must be less or equal than
the lowest value of RdRo used for the storeys above.
If it can be demonstrated by physical testing or analysis that
the seismic response of a structure is equivalent to one
particular SFRS, then this SFRS qualifies as a good
representation of the structural system, and the
corresponding Rd and Ro can be used.
Physical tests to evaluate the behavior of
connections in moment-resisting frames
As we mentioned previously, connections in type D and
MD frames must be tested physically to ensure that they satisfy
certain deformation criteria under cyclic loads. When performing
these tests, the test assemblies must represent the prototype
characteristics, and the test loading the deformation magnitude and
cyclic nature. These design procedures are specified in the
appendix J of the CAN/CSA S16-01, which provides a list of
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ALFREDO BOHL
references with guidelines. The inelastic cyclic behavior of a
connection is a function of the size of the elements, bracing
arrangements, and welding details and procedures.
The Federal Emergency Management Agency (FEMA)
conducted a project in which they tested several types of momentresisting connections after the Nortridge earthquake, in order to
investigate their performance. This project ended with the
publication of four engineering practice guidelines documents
(FEMA 2000 a, b, c, d) for design and evaluation of momentresisting frames (CISC 2004: vii). In these documents, they specify
prequalified connections that may be used if the prototype
connection size and details are similar to those tested. In case these
prequalified connections are used and satisfy these conditions,
physical tests are not necessary. Some of these prequalified
connections will be mentioned later.
Table No.3: Inter-storey drift angle limits for various performance levels
Source: FEMA 350 2000: 3-75.
The drift angle capacity is measured according to the
following figure:
The procedures that will be described to perform the
physical tests are the ones described in the FEMA 350 document,
in chapter 3. These tests are for connections that do not form part
of those that are prequalified, or for a qualified connection that is
used outside its parametric limits.
Figure No.19: Angular rotation of test assembly
Source: FEMA 350 2000: 3-75.
Testing procedure
For each given combination of beam and column size, tests
of at least two specimens must be performed. The results obtained
must be able to predict the mean value of the drift angle capacity,
, of the connection, given the following performance levels:
Document1
The test specimens must satisfy certain conditions. The size
of the beam used in the specimen must be at least the largest depth
and heaviest weight used in the structure. The column must
represent the expected inelastic action of the column in the real
structure for the beam selected, and must provide a flexural
strength consistent with the requirements of strong-column-weakbeam connections. Also, the tested column must have a height
similar to the real column, so that the drift angles obtained are
representative of the real structure.
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ALFREDO BOHL
In relation to the loading history, it is divided into steps,
and the peak deformation at each step j is given by j, a
predetermined value of the drift angle. The number of cycles to be
performed at the load step j is denoted as nj. The loading history is
shown in the following table:
Table No.5: Minimum qualifying total inter-storey drift angle capacities for
OMF and SMF systems
Source: FEMA 350 2000: 3-77.
In the case that the clear-span-to-depth ratio of the beam in
the real steel frame is less than eight, it is expected that it will have
larger strains in the flanges, so the drift angle capacities indicated
can be increased using the following expressions:
8d 
L  L' 
1 
 SD (FEMA 350, equation 3-70)
L 
L 
L  L' 

 'U  1 
 U (FEMA 350, equation 3-71)
L 

 ' SD 
Table No.4: Numerical values of j and nj
Source: FEMA 350 2000: 3-76.
Where:
Acceptance criteria
-
For the connection to have an acceptable performance, the
mean value of the drift angle capacity at strength degradation and
at connection failure must not be less than the values shown in the
following table, for ordinary moment frames (OMF) and special
moment frames (SMF):
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’SD: Increased qualifying strength degradation drift angle
capacity.
SD: Basic qualifying strength degradation drift angle
capacity.
’U: Increased qualifying ultimate drift angle capacity.
U: Basic qualifying ultimate drift angle capacity.
L: Distance between the longitudinal axis of the columns.
L’: Distance between plastic hinges in the beam.
d: Depth of the beam.
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ALFREDO BOHL
These limits in the drift angles capacities where determined
after extensive probabilistic evaluations of several structural
systems. If these requirements are met, then there is a 90% chance
that the frames will be protected against global collapse of the
structure, and a 50% chance that local collapse will not occur.
Analytical prediction of structural behavior
The connection tests results must be supported with the
development of analytical design procedures, so that the same
connections with different sizes can be used for design. These
analytical models should be able to identify the strength and
deformation demands, as well as limit states, of the elements that
are part of the connection.
Figure No.20: Physical test of a beam-to-column connection
Source: Chen, Yeh and Chu 1996: 1295.
Example of a physical test of a beam-to-column
connection
The following figure shows an example of a full-scale
beam-to-column connection assembly used in a physical test. It is a
reduced beam section connection, a special moment-resisting
connection that will be explained later. The beam section is Htype, with section H600×300×12×20; and the column section is a
box type, with section HSS500×500×20×20. In this case, this test
was carried to investigate the performance of this connection when
it is subjected to a large shear and bending moment. A force is
being applied at the end of the beam to simulate this situation. Five
different specimens were tested.
Design of moment-resisting connections
for seismic applications
We have seen how physical tests are conducted to evaluate
the performance of moment-resisting connections. Understanding
the structural behavior of connections is not easy, since it is
affected by several factors, like geometric alterations, hole drilling
for bolts, welding, among others. A connection is considered
adequate when it has enough rotational capacity, since this affects
strongly the energy dissipation capacity of the frame. The
connection must be properly detailed in order to achieve this.
Some types of connections, which are commonly used in
standard practice, do not have enough rotational capacity to
withstand strong earthquakes. One of these is the typical welded
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flange-bolted web moment connection, in which the beam is
connected to the columns by bolting the beam web to the shear tab
of the column plate, and then welding the beam flange to the
column plate. This arrangement is shown in the following figure.
Its lack of rotational capacity has been demonstrated in a research
project held in Taiwan, in which 37 prototypes of this type of
connection were tested. Eight of these specimens had a brittle
failure (Chen, Yeh and Chu 1996: 1292).
ALFREDO BOHL
publication, which cover most of the practical applications in
Canada.
These prequalified connections must satisfy certain criteria
and size limitations so that they can be used in design, since they
must have similar sizes and details to those that were tested to
predict their performance. They apply to frames with wide-flange
beams and columns subjected to strong axis bending only, and
column cross-sections must be within the depth of W360 sections.
The three types of connections described in this document are:
-
Bolted unstiffened end plate connection.
Bolted stiffened end plate connection.
Reduced beam section connection.
The general design procedure of these connections is as
follows:
Figure No.21: Welded flange-bolted web moment connection
Source: Chen, Yeh and Chu 1996: 1292.
That is why ductile moment-resisting connections for
seismic applications must satisfy more rigorous design and detail
requirements. The appendix J of the CAN/CSA S16-01 contains a
list of references with guidelines of the design procedures for
different types of these connections used in type D and MD
frames; that were prequalified by FEMA after they conducted a
project in which they tested several prototypes of connections. One
of these publications is “Moment Connections for Seismic
Applications”, developed by the CISC, which contains design
procedures of three types of prequalified beam-to-column momentresisting connections that were provided in the FEMA 350.
Prototype testing will not always be possible for new designs, so
these connections may be used in these cases. This part of the
report will focus on these three connections contained in this CISC
Document1
-
Identify undesirable brittle failure modes, and the primary
and other yielding mechanisms.
Determine the probable peak rotational capacity of the
primary yielding mechanism.
Determine the dimensions of the elements so that they have
nominal resistances ( = 1) against all brittle failure modes
at least equal to the probable yield capacity of the primary
yielding mechanism, to assure that this mechanism occurs
before the others.
When the plastic hinges are expected to form in the beams,
the probable plastic moment at the location of the hinge is:
M pr  C pr R y Fy Z e
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ALFREDO BOHL
Where:
C pr 
Fy  Fu
2 Fy
Z e  bt (d  t ) 
w
d  2t 2
4
Where:
-
-
-
Mpr: Probable peak plastic hinge moment.
Cpr: Factor that considers effects of strain hardening,
additional reinforcement, among others.
RyFy: Probable yield stress, where Ry = 1.1. The product
RyFy must be at least 385 MPa, and Fy should not be less
than 350 MPa.
Ze: Effective plastic modulus of the beam. It is equal to the
plastic modulus of the beam, Zb, when the section is not
reduced.
Fu: Specified minimum tensile strength.
b: Flange width of the section.
t: Flange thickness of the section.
d: Depth of the section.
w: Web thickness of the section.
Figure No.22: Shear at plastic hinges
Source: CISC 2004: 25.
The flexural and shear strength demands at different critical
sections can also be determined from equilibrium:
For a wide-flange section, the plastic modulus can be
calculated using the expression shown above (Wong 2003: 2).
The shear at the plastic hinge location can be determined
from static equilibrium of the beam, as it is shown in the following
figure:
Figure No.23: Strength demands at critical sections
Source: CISC 2004: 25.
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We will expose the design philosophy and general
requirements of these three connections.
Bolted unstiffened end plate connection (BUEP)
The BUEP connection consists of the beam being welded
to an end plate, extended above and below the flanges. The beam
flange-to-plate joints have complete-penetration-groove welds, and
the beam web is connected to the plate with fillet or completejoint-penetration-groove welds. Then, the end plate is bolted to the
column using eight bolts. This type of connection can be used for
type D, MD and LD frames. The connection is showed in the
following figure:
ALFREDO BOHL
type LD frames, panel zone yielding may occur alone. There must
not be any significant yielding in the end plate, bolts and welds.
The connection must be proportioned to preclude the following
failure modes:
Mode 1: Bolt tension
This failure mode is avoided by selecting a bolt type that
can resist the moment at the column face. The following equation
must be satisfied:
0.75 Ab Fu 
M cf
2d1  d 2 
Where:
-
Ab: Nominal cross-sectional area of one bolt.
Fu: Minimum tensile strength of the bolt, equal to 825 MPa
for bolts A325M, and 1035 MPa for bolts A490M.
Mcf: Moment at the face of the column.
d1: Defined in figure No.24.
d2: Defined in figure No.24.
Mode 2: Bolt shear
This failure mode is avoided satisfying the following
equation:
Figure No.24: Bolted unstiffened end plate connection
Source: CISC 2004: 26.
The basic idea in the design procedure is that yielding in
the connection can occur as a combination of beam flexure and
panel zone yielding simultaneously, or beam flexure alone. For
Document1
3 Ab 0.5 Fu   Vcf
Where Vcf is the shear at the column face. A comment
regarding this empirical formula is that the factor of three in the
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right hand side is part of the test results that were performed to
derive it. Given that Ab is the area of only one bolt, this formula
seems to be too conservative, considering that this connection has
eight bolts.
Mode 4: End plate shear
This failure mode is avoided if the end plate has this
minimum thickness:
Mode 3: End plate flexure
tp 
This failure mode is avoided if the end plate has this
minimum thickness:
tp 
 1 1
2  bp

   p f  s  
p

g  2
 f s
 d b 1 

 
p

 f 2 
M cf
1.1Fyp b p d p  t b 
Where:
M cf

bp
0.8Fyp d b  pt 
 2

ALFREDO BOHL
-
dp: Depth of the plate.
tb: Beam thickness.
Mode 5 a: Beam flange tension effect on column
flange without continuity plates
Where:
s  bp g
If the column flange thickness satisfies the following
equation, proceed to check mode 6. If not, continuity plates or a
bigger column cross-section should be used:
Where:
-
tp: End plate thickness.
Fyp: End plate yield strength, taken as 250 MPa.
db: Depth of the beam.
pt: Defined in figure No.24.
bp: Defined in figure No.24.
pf: Defined in figure No.24.
s: Defined in equation.
g: Defined in figure No.24.
tc 
 M cf 

C1
d

t
b
b


2 Fyc c
Where:
C1 
g
 k1
2
Where:
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tc: Column flange thickness.
C1: Defined in equation.
Fyc: Column yield strength.
c: Defined in figure No.24.
k1: Distance from centerline of column web to flange toe of
fillet, is a property of the section found in the tables of the
CISC HSC.
ALFREDO BOHL
Where:
-
Yc: Defined in equation.
s: Defined in equation.
C1: Defined in equation.
C2: Defined in equation.
bc: Width of column flange.
Mode 5 b: Beam flange tension effect on column
flange with continuity plates
Mode 6: Beam flange compression effect on column
without continuity plates
If continuity plates are provided and the column flange
thickness satisfies the following equation, proceed to check mode
7. This is the minimum thickness that the column flange can have:
If the column web thickness satisfies the following
equation, continuity plates or a bigger column cross-section should
be used:
M cf
tc 
wc 
2d b  t b 
0.8 Fyc Yc
Document1
d b  t b 6k e  2t p  t b Fyc
Where:
Where:
2 
c
 1
4
Yc    s 
   C 2  C1  
2
 C 2 C1 
c
g
C1   k1
2
b g
C2  c
2
C1C 2
2bc  4k1 
s
C 2  2C1
M cf
-
2

s
wc: Column web thickness.
ke: Is the k-distance of the column section for engineering
design, is a property of the section found in the table No.4.1
of this CISC publication.
If continuity plates are provided, they must satisfy the
following requirements:
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For one-sided connections, their thickness must be at least
half of the thickness of the beam flanges.
For two-sided connections, their thickness must be at least
equal to the thickness of the thicker beam flange.
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Usually, it is less expensive to use a bigger column section
than to use continuity plates. The arrangement of continuity plates
in one-sided connections is shown in the following figure:
ALFREDO BOHL
Where:
-
w’: Panel zone thickness.
Cy: Defined in equation.
Mc: Moment at the centerline of the column.
h: Average storey height.
db: Distance from one edge of the end plate to the centre of
the beam flange at the opposite direction.
RycFyc: Probable yield stress of the column.
dc: Depth of the column.
Se: Effective section modulus of the beam. It is equal to the
section modulus of the beam, Sb, when the section is not
reduced.
The average storey height is calculated using the heights
above and below the connection, except in the following cases:
Figure No.25: Continuity plates for one-sided connection
Source: CISC 2004: 32.
-
Mode 7: Panel zone shear
-
For one-sided connections, this failure mode is avoided if
the panel zone has this minimum thickness:
 h  db 
CyM c 

h 

w' 
0.90.6 R y Fyc d c d b  t b 
When the column has a pinned base, it is the sum of the
storey height below and half of the storey height above.
In top level connections, it is the storey height for pinned
base columns, and half of it otherwise.
For two-sided connections, plastic hinges can be formed in
both beams. The same expressions apply for this case. If doubler
plates are used, then w’ can be taken as the sum of the thicknesses
of the column web and the doubler plates. Also, the following
equation must be satisfied:
d 'b'
 90
w'
Where:
Cy 
Document1
Se
C pr Z e
Where:
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d’: Panel zone depth.
b’: Panel zone width.
Usually, it is less expensive to use a bigger column section
than to use doubler plates. The arrangement of continuity and
doubler plates in two-sided connections is shown in the following
figure:
ALFREDO BOHL
The minimum span-to-depth ratio, for type D and MD
frames, is seven; and for type LD frames is five. Also, the
maximum flange thickness of the beam is 19mm, and the
maximum bolt diameter is 1½”.
Bolted stiffened end plate connection (BSEP)
The BSEP connection consists of the beam being welded to
an end plate. The beam flange-to-plate joints have completepenetration-groove welds, and the beam web is connected to the
plate with fillet or complete-joint-penetration-groove welds. The
end plate extensions at the top and bottom of the beam are
stiffened with vertical stiffeners that extend outward from beam
flanges. Then, the end plate is bolted to the column using 16 bolts.
This type of connection can be used for type D, MD and LD
frames. The connection is showed in the following figure:
Figure No.26: Continuity and doubler plates for two-sided connection
Source: CISC 2004: 33.
Other restrictive parameters
The expected location of the plastic hinge measured from
the face of the column, x, is given by:
x  tp 
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db
3
Figure No.27: Bolted stiffened end plate connection
Source: CISC 2004: 27.
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The basic idea in the design procedure is that yielding in
the connection can occur as a combination of beam flexure and
panel zone yielding simultaneously, or beam flexure alone. For
type LD frames, panel zone yielding may occur alone. There must
not be any significant yielding in the end plate, bolts and welds.
The connection must be proportioned to preclude the following
failure modes:
-
ALFREDO BOHL
ts: Defined in figure No.27.
bp: Defined in figure No.27.
Tb: Minimum bolt pretension.
The minimum bolt pretensions are shown in the following
table:
Mode 1: Bolt tension
This failure mode is avoided by selecting a bolt type that
can resist the moment at the column face. The following equations
must be satisfied:
0.75 Ab Fu 
0.75 Ab Fu 
M cf
3.4d 2  d 3 
3.25  10 6 p f
tp
0.895
d bt
1.91
ts
0.591
0.327
Pcf 
0.965
 Tb
Mode 2: Bolt shear
M cf
6 Ab 0.5 Fu   Vcf
d b  tb
Where:
d2: Defined in figure No.27.
d3: Defined in figure No.27.
pf: Defined in figure No.27.
Pcf: Axial force at the column face.
dbt: Diameter of the bolts.
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bp
This failure mode is avoided satisfying the following
equation:
Where:
-
Pcf
Table No.6: Minimum bolt pretensions
Source: AISC-LRFD 1999: 60.
2.58
A comment regarding this empirical formula is that the
factor of six in the right hand side is part of the test results that
were performed to derive it, as in the expression to avoid bolt shear
for BUEP connections. Given that Ab is the area of only one bolt,
this formula seems to be too conservative, considering that this
connection has sixteen bolts.
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Mode 3: End plate flexure
1
 A  3 C3
 m  Ca  f 
1
 Aw  d bt  4
g d
C3   bt  k1
2
4
This failure mode is avoided if the end plate has a
minimum thickness of at least the greater of these two values:
tp 
tp 
154  10 6 p f
0 .9
0 .9
g 0.6 Pcf
0 .1
267  10 6 p f
d bt t s
0.25
0.15
0 .9
Where:
0 .7
d bt t s b p
0 .7
g 0.15 Pcf
bp
-
0 .3
Where g is defined in figure No.27. The column flanges
must be at least as thick as the end plate.
-
Mode 4: End plate shear
This failure mode is avoided by the effect of the stiffeners,
which are proportioned as shown in figure No.27.
Mode 5: Beam flange tension effect on column
flange without continuity plates
If the column flange thickness satisfies the following
equation, proceed to check mode 6. If it is not satisfied and
continuity plates are used, proceed to check mode 7:
tc 
ALFREDO BOHL
 m Pcf C 3
0.9 Fyc 3.5 p b  c 
m: Defined in equation.
C3: Defined in equation.
pb: Defined in figure No.27.
c: Defined in figure No.27.
Ca: Factor equal to 0.128 for bolts A325M and 0.131 for
bolts A490M.
Af: Flange area.
Aw: Web area.
Mode 6: Beam flange compression effect on column
without continuity plates
If the column web thickness satisfies the following
equation, continuity plates or a bigger column cross-section should
be used:
wc 
M cf
d b  t b 6k e  2t p  t b Fyc
The requirements for continuity plates are the same as
those for BUEP connections.
Where:
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ALFREDO BOHL
Mode 7: Panel zone shear
This failure mode is avoided if the same expressions as in
BUEP connections are satisfied. In case of using doubler plates,
the same requirements also apply.
Other restrictive parameters
The expected location of the plastic hinge measured from
the face of the column, x, is given by:
x  t p  Ls
Where Ls is the horizontal length of the stiffener. The
minimum span-to-depth ratio, for type D and MD frames, is seven;
and for type LD frames is five. Also, the maximum flange
thickness of the beam is 25mm, and the maximum bolt diameter is
1½”.
Figure No.28: Reduced beam section connection
Source: CISC 2004: 28.
Reduced beam section connection (RBS)
The RBS connection is one in which the acting forces are
kept within its resistance by reducing the flexural resistance of the
beam at a certain distance from the connection, so that yielding and
plastic hinging occurs in the beam. The top and bottom beam
flanges have circular radius cuts for this purpose. The flanges of
the beam are connected to the columns only with complete joint
penetration groove welds. A shear tab, that can be bolted or
welded, is used for the web connection. This type of connection
can be used for type D and MD frames, not type LD frames. The
connection is showed in the following figure:
Document1
Since the beam has been weakened, the frame drifts will be
larger. It has been observed that this increase in the drift varies
between 7 to 9% for flange reductions of 40 to 50%, respectively.
So, if a model with beam elements has been used to analyze the
structure, the drifts obtained must be increased by 7 to 9%.
The basic idea in the design procedure is that yielding in
the connection can occur as a combination of the reduced beam
flexure and panel zone yielding simultaneously, or as reduced
beam flexure alone. There must not be any significant yielding in
the beam-flange-to-column joints and the beam web. The
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connection must be proportioned to preclude the following failure
modes:
We then calculate the moment at the face of the column,
Mcf, using the scheme shown in figure No.23. The flexural failure
is avoided satisfying the following equation:
Mode 1: Connection flexure
M cf  R y Fy Z b
The location, length and depth of the beam flanges
reduction is selected between these limits:
Where:
0.50b  a  0.75b
0.65d  s  0.85d
0.20b  c  0.25b
Where:
-
a: Defined in figure No.28, usually taken as 0.5b.
b: Width of the beam.
s: Defined in figure No.28, usually taken as 0.65d.
d: Depth of the beam.
c: Defined in figure No.28, usually taken as 0.2b.
The width of the reduced beam flange should have a
maximum value of 14.6t, where t is the thickness of the flange.
Then, the effective plastic modulus of the reduced section of the
beam, Ze, must be determined, using:
ALFREDO BOHL
-
RyFy: Probable yield stress, taken as 385 MPa.
Zb: Plastic modulus of the gross beam section.
If this equation is not satisfied, the value of c is increased
and all previous steps are repeated, taking into consideration that it
c must not be greater than 0.25b. Once the final dimensions of the
reduced section are determined, we calculate the moment at the
face of the column and the moment at the column centerline using
these values and the scheme in figure No.23.
Mode 2: Connection shear
The shear at the face of the column is determined by the
following equation:
Vcf 
c  0.2b
be  0.6b
2M cf
L  dc
 Vg
Where:
-
With this, we calculate the probable peak plastic hinge
moment, using Cpr = 1.15:
Vcf: Shear at the face of the column.
Vg: Shear due to gravity loads, as shown in figure No.22.
M pr  C pr R y Fy Z e
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This shear force is used to design the connection of the
beam to the column. If a complete joint penetration groove weld is
used, no further calculations are required. If a bolted shear tab is
used, the tab and the bolts must be designed to resist this shear
force, using a resistance factor of unity ( = 1). The tab must be
connected to the column using complete joint penetration groove
welds or full depth fillets.
ALFREDO BOHL
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:
Mode 3: Panel zone shear
xa
This failure mode is avoided if the same expressions as in
BUEP and BSEP connections are satisfied. In case of using
doubler plates, the same requirements also apply.
s
2
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.
Continuity plates
If the column flange thickness, in milimetres, is less than
the greater of the following two expressions, then continuity plates
must be provided to the connection:
t c  0.4 1.8bb t b
tc 
R yb Fyb
R yc Fyc
bb
6
Where:
-
bb: Unreduced beam flange width.
tb: Beam flange thickness.
RybFyb: Probable yield stress of the beam.
RycFyc: Probable yield stress of the column.
Document1
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,
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ALFREDO BOHL
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 frictiondamped 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.
Figure No.29: Special truss moment frame
Source: USACE: 7-103.
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:
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-todepth 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.
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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.
Vne 
3.4 R y M nc
Ls
ALFREDO BOHL
 L  Ls
 0.07 EI 
3
 Ls

  R y Pnt  0.3Pnc Sin 


Where:
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
0.45AgFy, taking  = 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.
-
The width-to-thickness ratio of the elements of the special
segment must not exceed the following limits:
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:
Document1
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.
: Angle of the diagonal elements of the special segment,
measured from the horizontal plane.
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-
Diagonal web elements: 2.5.
Angles: 137 / Fy .
-
Flanges and webs of tee sections in chord elements:
137 / Fy .
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The top and bottom chords of the trusses must be laterally
braced at the ends of the special segment. Intermediate braces are
also required.
and the Sumitomo friction device. Friction dampers offer the
following advantages (UPC: 28 – 29):
-
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 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
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):
-
Document1
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:
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.
ALFREDO BOHL
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Maintenance of contact pressure between sliding surfaces.
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Maintenance of an approximately constant coefficient of
friction between sliding surfaces.
Avoiding brittle failure when the joint reaches the limit of
its sliding range.
ALFREDO BOHL
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:
The BSJ is shown in the following figure:
Figure No.31: Applications of the basic sliding joint
Source: Butterworth 1999: 2.
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:
N slip  nN b 
Where:
-
Nslip: Slip force.
n: Number of bolts.
Nb: Tension in one bolt.
: Coefficient of friction.
Document1
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:
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ALFREDO BOHL
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.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:
M slip  nN b D
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
Document1
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
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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):
L  D  d
ALFREDO BOHL
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:
Where:
-
L: Length of the slot.
: 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
Document1
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
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ALFREDO BOHL
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.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.
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:
Document1
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
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ALFREDO BOHL
described previously. We will show how the Rd factor is
determined using this method.
This method was developed by analyzing a single-degreeof-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-offreedom system of a multi-storey building subjected to a ground
motion.
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:
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:
Document1
a 
Ka
Kf
s 
u max
us
y 
u max
uy
Where:
-
3/14/2016
a: Added stiffness ratio.
Ka: Added stiffness provided by the friction damper.
Kf: Stiffness of the primary system.
s: Slip ratio.
umax: Maximum displacement of the system.
us: Displacement at which the friction damper starts to slip.
y: Yield ductility. In building codes, the common
assumption is that it is equal to the Rd factor.
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uy: Yield displacement.
Rsd 
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:
K eo   a
E do   a
e  o 
ALFREDO BOHL
ln  s  1
s

s3

-
y
 y3
E do
K eo
Keo: Equivalent normalized stiffness.
Edo: Equivalent normalized energy dissipated.
e: Equivalent viscous damping ratio.
o: Viscous damping ratio of the primary system, usually
equal to 2% for steel structures.
o
 B o
K eo
3
4
e
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
equivalent linear system and the primary system. It can be obtained
using the following expression:

1 
R f  Rsd  a 


 s y 
Where:
-
 B e
Where:
ln  y  1
 s  12  y  12
1  e 
1  e 
Recalling the definition of the force reduction factor (ratio
between the elastic and design base shear), and using these
expressions, the authors arrived to the following expression to
determine the Rd factor for steel friction-damped multi-degree-offreedom systems:
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:
Rd 
f e R f  a ,  s  1,  y  1

f y R f  a ,  s  1,  y  1
Where:
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fe: Elastic base shear.
fy: Design base shear.
ALFREDO BOHL
Conclusions
their flexibility and have high energy dissipation capacity, but their
large inter-storey drifts may cause severe P-delta effects and nonstructural damage. On the other hand, ductile plate walls have very
large stiffness, but may be more expensive. Also, calculating the
tension fields in the plate web and determining the yielding
sequence of the plate and the framing system is still a problem, due
to the limitations of the strip model. The eccentrically braced
frames have a good performance because they combine the ductile
behavior of the moment-resisting frames and the stiffness of the
concentrically braced frames. However, since all the energy
dissipation is restricted to the link, the collapse mechanism forms
once this element has yielded; while other SFRS are more
redundant. The concentrically braced frames have high stiffness,
but cannot be used in tall buildings, since they tend to have a softstorey response due to concentration of inelastic demands in the
lower and upper levels. There may be cases in which the optimum
solution will be a combination of different SFRS.
An overall overview of the seismic design of steel
structures in Canada has been carried out. The design procedures
for SFRS, moment-resisting connections, and some special
framing systems, which are spread in various documents and
publications, have all been organized in this report, to provide a
practical tool for structural engineers. Although this is a very
extensive topic which is constantly in change, the most important
issues about steel seismic design have been presented and
discussed.
Physical testing of connections is important to evaluate
their performance during earthquakes. Alternatively, prequalified
connections may be used for design. However, there may be cases
in which it might not be possible to use the prequalified
connections, and physical tests are usually very expensive and
cannot be afforded by small engineering companies. More research
is needed to develop design procedures for various types of
connections with different element sections, rather than only wideflange sections.
Each of the SFRS presented have their own advantages and
disadvantages, as we have seen, and these must be taken into
consideration to decide which of them is more convenient to
design a particular building. Here we present a summary of them.
Ductile moment-resisting frames absorb less shear forces due to
Finally, it is important to mention that, although the codes
give provisions and recommendations for various kinds of systems,
they do not contain the answers to all of the structural problems
that engineers may encounter. It is necessary to go beyond of what
the code says to find more safe and economic solutions. Systems
So, when designing this type of structures, the structural
designer has to specify the added stiffness ratio, the slip ratio and
the yield ductility, depending on the desired performance of the
structure. Then, the Rd factor can be determined, and the quasistatic analysis may be used to determine the internal forces and
displacements.
This method was developed while the 1995 NBCC was the
current code. Therefore, to be able to adapt this method to the 2005
NBCC, an Ro factor must be assigned to this type of structures.
Overstrength in friction-damped structures arises due to the fact
that energy is first dissipated by friction, and then by yielding.
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CIVL 510
CANADIAN SEISMIC DESIGN OF STEEL STRUCTURES
ALFREDO BOHL
like the special truss moment frame and the friction-damped steel
frame are examples of these, and may be implemented in future
codes.
Sheng-Jin Chen, C. H. Yeh and J. M. Chu (1996) “Ductile Steel
Beam-to-Column Connections for Seismic Resistance”, Journal of
Structural Engineering, Vol. 122, No.11: 1292 – 1299.
References
Joe Wong (2003) “Plastic Analysis of Standard Shapes Loaded by
Impact”, University of British Columbia.
Canadian Institute of Steel Construction (2004) “Handbook of
Steel Construction” (8th. Edition), Quadratone Graphics Ltd,
Toronto, Ontario.
Denis Mitchell, Robert Tremblay, Erol Karacabeyli, Patrick
Paultre, Murat Saatcioglu and Donald L. Anderson (2003)
“Seismic Force Modification Factors for the Proposed 2005
Edition of the National Building Code of Canada”, Canadian
Journal of Civil Engineering, 30: 308 – 327.
Dennis Chu (2003) “Comparative Case Studies of Beam and
Column Design: A Comparison of the Canadian and US
Standards”, University of British Columbia.
Robert Schubak (2005) “CIVL 505: Seismic Response of
Structures” (Lecture Notes, Chapter 6), University of British
Columbia.
Canadian Commission on Building and Fire Codes (2005)
“National Building Code of Canada” (Part 4: Structural Design).
Canadian Institute of Steel Construction (2004) “Moment
Connections for Seismic Applications” (1st. Edition).
American Institute of Steel Construction (1999) “Load and
Resistance Factor Design Specification for Structural Steel
Buildings”.
Web page: www.hnd.usace.army.mil/techinfo/ti/809-04/ch7c.pdf
Web page: www.new-technologies.org/ECT/Civil/truframe.htm
Web page: www.tdx.cesca.es/TESIS_UPC/ AVAILABLE/TDX1217103-104653/03Chapt02.pdf
John W. Butterworth (1999) “Seismic Response of MomentResisting Steel Frames Containing Dual-Level Friction Dissipating
Joints”, NZSEE Conference, Rotorua.
Ian D. Aiken, Douglas K. Nims, Andrew S. Whittaker and James
M. Kelly (1993) “Testing of Passive Energy Dissipation Systems”,
Earthquake Spectra, Vol. 9, No.3.
Yaomin Fu and Sheldon Cherry (1998) “Simplified Seismic Code
Design Procedure for Friction-Damped Steel Frames”, Canadian
Journal of Civil Engineering, 26: 55 – 71.
Federal Emergency Management Agency (2000) “Recommended
Seismic Design Criteria for New Steel Moment-Frame Buildings”
(FEMA 350).
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