text:
Link (YouTube)
There's a jumpscare right around the 14:30 mark here, and it doesn't make any sense. It's a jumpscare for the audience and not the characters, which is a problem I'd just been complaining about a few seconds earlier. Mike is looking through the binoculars and a face appears. For one thing, the face is very close. Since the characters are standing on top of a steep slope / small cliff, I have no idea how anyone could stand that particular distance in front of the binoculars without hovering above the ground. More importantly, Mike gives no reaction whatsoever. Either Mike is in on this murder (in the style of Scream) or the storyteller is engaging in flagrant shenanigans.
Josh suggested that maybe it was Jessica jumping in front of the binoculars for a second, but if you freeze the frame you get:
I don't… I don't think that's a teenage girl.
Mass Effect Retrospective
A novel-sized analysis of the Mass Effect series that explains where it all went wrong. Spoiler: It was long before the ending.
The Biggest Game Ever
How did this niche racing game make a gameworld so massive, and why is that a big deal?
Why Batman Can't Kill
His problem isn't that he's dumb, the problem is that he bends the world he inhabits.
A Star is Born
Remember the superhero MMO from 2009? Neither does anyone else. It was dumb. So dumb I was compelled to write this.
Spec Ops: The Line
A videogame that judges its audience, criticizes its genre, and hates its premise. How did this thing get made?


text:
Abstract: Caringo's boundless object storage paired with rapid enterprise search. Search billions of stored objects and return relevant content in seconds.
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subset: commoncrawl


text:
Key words: Seismic Design, Steel Structures, NEHRP Recommended Seismic Provisions, AISC Seismic Provisions, R
Factor, Ductility, System Overstrength, Capacity Design, 1994 Northridge Earthquake, Moment-Resisting
Frames, Brittle Fracture, Moment Connections, Concentrically Braced Frames, Buckling, Braces,
Eccentrically Braced Frames, Links.
Abstract: Seismic design of steel building structures has undergone significant changes since the Northridge,
California earthquake in 1994. Steel structures, thought to be ductile for earthquake resistance, experienced
brittle fracture in welded moment connections. The latest AISC Seismic Provisions reflect the significant
research findings that resulted from the Northridge earthquake. This chapter first starts with a description of
the seismic design philosophy, the concept of system parameters (R, Cd, and o) and capacity design.
Background information for the seismic requirements in the AISC Seismic Provisions of Moment Frames,
Concentrically Braced Frames, and Eccentrically Braced Frames are then presented. Design examples are
provided for each of the three structural systems.
410 Chapter 9
9. Seismic Design of Steel Structures 411
Cd, to estimate the Design Story Drift, s, in the AISC LRFD Specification (1993), the AISC
Figure 9-1: Seismic Provisions require that the columns be
checked for two additional special load
Cd e combinations using the amplified horizontal
s = (9-3)
I earthquake load effects, oE:
Table 9-1. Steel framing systems and design parameters (NEHRP 1997)
Frame System R o Cd
Bearing Wall Systems
Ordinary Concentrically Braced Frames (OCBFs) 4 2 3
Building Frame Systems
Eccentrically Braced Frames (EBFs)
Moment connections at columns away from links 8 2 4
Non-moment connections at columns away from links 7 2 4
Special Concentrically Braced Frames (SCBFs) 6 2 5
Ordinary Concentrically Braced Frames(OCBFs) 5 2 4
Moment Resisting Frame Systems
Special Moment Frames (SMFs) 8 3 5
Intermediate Moment Frames (IMFs) 6 3 5
Ordinary Moment Frames (OMFs) 4 3 3
Special Truss Moment Frames (STMFs) 7 3 5
Dual Systems with SMFs Capable of Resisting at Least 25% of Prescribed Seismic
Eccentrically Braced Frames (EBFs)
Moment connections at columns away from links 8 2 4
Non-moment connections at columns away from links 7 2 4
Special Concentrically Braced frames (SCBFs) 8 2 6
Ordinary Concentrically Braced Frames (OCBFs) 6 2 5
Table 9-1. Seismic design of three widely used Grade 65 steel for which the only expected
systems (moment-resisting frames, inelastic behavior is yielding at the column
concentrically braced frames, and eccentrically base.
braced frames) that are presented later in this The specified minimum yield strength is
chapter makes use of these parameters. used to design the structural components that
are expected to yield during the design
9.1.3 Structural Steel Materials earthquake. However, to estimate the force
demand these components would impose on
The ductility of steel generally reduces with other structural components (including
an increase of the yield stress. Therefore, the connections) that are expected to remain elastic,
AISC Seismic Provisions permit only the the expected yield strength, Fye, of the energy
following grades of steel for seismic design: dissipating components needs to be used for
ASTM A36, A53, A500 (Grades B and C), capacity design:
A501, A572 (Grades 42 or 50), A588, A913
(Grade 50 or 65), or A992. Further, for those F ye = R y F y (9-6)
structural members that are designed to yield
under load combinations involving o times the For rolled shapes and bars, the AISC Seismic
design seismic forces, the specified minimum Provisions stipulate that Ry shall be taken as 1.5
yield strength, Fy, shall not exceed 50 ksi unless for A36 and 1.3 for A572 Grade 42. For rolled
the suitability of the material is determined by shapes and bars of other grades of steel and for
testing or other rational criteria. This limitation plates, Ry shall be taken as 1.1 (SSPC 1995).
does not apply to columns of A588 or A913
414 Chapter 9
Figure 9-2. (a) Geometry considering finite dimensions of members, (b) Typical moment diagram under lateral loading, and
(c) Corresponding member forces on beams, columns, and panel zones
9. Seismic Design of Steel Structures 415
9.2 Behavior and Design of connections can be used in such frames. Beam-
Moment-Resisting Frames to-column connections in IMFs are required to
have an inelastic rotation capacity of 0.02
radian. Other requirements are listed in the
9.2.1 Introduction AISC Seismic Provisions (1997b).
Ordinary moment frames (OMFs) are less
Steel moment-resisting frames (SMFs) are ductile than IMFs, and are expected to sustain
rectilinear assemblies of columns and beams only limited inelastic deformations in their
that are typically joined by welding or high- components and connections in the design
strength bolting or both. Resistance to lateral earthquake. Beam-to-column connections in
loads is provided by flexural and shearing OMFs are required to have an inelastic rotation
actions in the beams and the columns. Lateral capacity of 0.01 radian. FR and PR connections
stiffness is provided by the flexural stiffness of can be used in OMFs. Because OMFs are less
the beams and columns; the flexibility of the ductile than IMFs, an OMF must be designed
beam-column connections are often ignored for higher seismic forces than an IMF; an OMF
although such flexibility may substantially is designed for earthquake loads calculated
increase deflections in a moment-resisting using a value of R equal to 4.
frame. Components of an SMF together with The remainder of this section addresses
sample internal actions are shown in Figure. 9- issues associated with the design, detailing, and
2. testing of special moment frames and
The AISC Seismic Provisions define three components. The design philosophy for such
types of seismic steel moment-resisting frames: frames is to dissipate earthquake-induced
Ordinary Moment Frames, Intermediate energy in plastic hinging zones that typically
Moment Frames, and Special Moment Frames. form in the beams and panel zones of the frame.
All three framing systems are designed Columns and beam-to-column connections are
assuming ductile behavior of varying degrees, typically designed to remain elastic using
for earthquake forces that are reduced from the capacity design procedures.
elastic forces by a response modification factor,
R (see Table 9-1 for values of R). 9.2.2 Analysis and Detailing of Special
SMFs are considered to be the most ductile Moment Frames
of the three types of moment frames considered
by AISC. For this reason, and due to their Because the SMF is a flexible framing
architectural versatility, SMFs have been the system, beam and column sizes in SMFs are
most popular seismic framing system in high often selected to satisfy story drift
seismic regions in the United States. SMFs are requirements. As such, the nominal structural
designed for earthquake loads calculated using strength of an SMF can substantially exceed the
a value of R equal to 8. Stringent requirements minimum base shear force required by the
are placed on the design of beams, columns, NEHRP Recommended Provisions. When
beam-to-column connections, and panel zones. analyzing SMFs, all sources of deformation
Beam-to-column connections in SMFs are should be considered in the mathematical
required to have a minimum inelastic rotation model. NEHRP stipulates that panel zone
capacity of 0.03 radian. deformations must be included in the
Intermediate Moment Frames (IMFs) are calculation of story drift.
assumed to be less ductile than SMFs but are The AISC Seismic Provisions prescribe
expected to withstand moderate inelastic general requirements for materials and
deformations in the design earthquake. IMFs connections that are particularly relevant to
are designed using a value of R equal to 6; fully SMF construction:
restrained (FR) or partially restrained (PR)
416 Chapter 9
1. Steel in SMF construction must comply gyration about the weak axis for out-of-plane
with the requirements described in buckling.
Section 9.1.3. In addition, a minimum
Charpy V-notch toughness of 20 ft-lbs at 9.2.4 Beam-to-Column Connections
70F is required for thick materials in
SMFs: ASTM A6 Group 3 shapes with Introduction
flanges 1 inches or thicker, ASTM A6
Groups 4 and 5 shapes, and plates that For discussion purposes, a beam-to-column
are 1 inches or greater in thickness in connection includes the beam-column panel
built-up members. zone and the beam-to-column joints.
Connections in an SMF need to satisfy three
2. Calculation of maximum component
criteria: (1) a sufficient strength to develop the
strengths (e.g., for strong column-weak
full plastic moment of the beam, (2) a sufficient
beam calculations) for capacity design
stiffness to satisfy the assumption of a fully
must be based on the expected yield
rigid (FR) connection, and (3) a large post-yield
strength, Fye (see Eq. 9-6).
deformation capacity without significant loss of
3. To prevent brittle fractures at the welds, strength. Prior to the 1994 Northridge,
AISC prescribes that welded joints be California earthquake, the welded flange-bolted
performed in accordance with an web steel moment connections were assumed
approved Welding Procedure by design professionals to easily satisfy all
Specifications and that all welds used in three criteria. Unfortunately, many moment-
primary members and connections in the resisting connections suffered extensive
seismic force resisting system be made damage during this earthquake. In addition to
with a filler metal that has a minimum brittle fracture in the groove welded
Charpy V-notch toughness of 20 ft-lbs at connections (mostly in the beam bottom
minus 20F. flange), other types of fracture that were seldom
observed in laboratory testing prior to the
9.2.3 Beam Design Northridge earthquake were also reported.
Figure 9-3a shows cracks extending into the
A beam in a steel SMF is assumed to be able column panel zone, and Figure 9-3b presents a
to develop its full plastic moment (Mp) divot pullout from the column flange. The
calculated as causes of failure are discussed in Bruneau et al.
M p = Z b Fy (9-7) The poor performance of welded moment-
frame connections in more than 200 multistory
where Z b is the plastic section modulus. In buildings in the Northridge earthquake led to
the development of a national program, funded
order to prevent premature beam flange or web
by the Federal Emergency Management
local buckling, and to maintain this moment for
Agency (FEMA), to investigate the causes of
large plastic deformations, the width-thickness
ratios of the web and flange elements should be failure and to develop alternative connections
for repair, rehabilitation, and new construction.
limited to the values of ps given in Table 9-2.
Part of the FEMA program involved full-scale
(The p values are for non-seismic design.) In testing of large-size steel beam-column
addition, both flanges of the beam must be connections (SAC 1996). The laboratory testing
laterally braced near potential plastic hinges; of the pre-Northridge prequalified welded
the unbraced length of the beam must not flange-bolted web connection replicated many
exceed 2500 ry /Fy, where ry is the radius of of the failure modes observed in the field after
the earthquake. The mean value of beam plastic
9. Seismic Design of Steel Structures 417
rotation capacity from all of the tests of the pre- welded connections are considered in this
Northridge connection detail was 0.004 radian section.
(Whittaker et al. 1998), which was significantly These connection details fall in one of the
less than the target value of 0.03 radian. In two categories: weakening the beam cross-
response to these findings, the 1997 AISC section away from the face of the column, or
Seismic Provisions require that (1) the design of reinforcing the beam cross-section at the
beam-to-column joints and connections in column face. Only non-proprietary moment
SMFs must be based on qualifying tests of at connections are discussed.
least two specimens, and (2) each connection
must develop a plastic rotation of 0.03 radian. Reinforced Connections
hardening in the beam beyond the welded flange-plate connection because the
reinforcement. Although it may be tempting to beam flanges are not welded to the column
assume a linear distribution of bending moment flange. The bottom welded flange plate can be
along the length of the beam to size the shop welded to the column, thereby eliminating
reinforcement, the effects of gravity load on the one field groove weld, and providing an
beam bending moment diagram, if significant, erection seat for the beam.
must be carefully considered. For all of the Welded triangular and straight haunch
connection details described below, notch- reinforced connections (see Figures 9-4c and d)
toughness rated weld filler metal, qualified underwent extensive laboratory testing
welders, and high quality inspection should be following the Northridge earthquake (e.g., SAC
specified. 1996, Gross et al. 1998) because both
Immediately after the Northridge reinforcements could be used for seismic repair
earthquake, cover plates (see Figure 9-4a) have and retrofit. Most of the haunch connection
been one of the more popular strategies for tests conducted to date incorporated a haunch to
reinforcing beam-to-column connections. the bottom flange, although the addition of
Testing has been completed at a number of haunches to both the top and bottom flanges
laboratories and significant data are available was also considered. Of the different types of
(e.g., Engelhardt and Sabol 1996, and SAC haunch details tested to date, the triangular T-
1996). In most cases, the bottom cover plate is shaped haunches appear to be the most effective
rectangular and wider than the beam bottom (Yu et al. 2000). Large plastic rotations were
flange, and the top cover plate is tapered and achieved with this type of connection. Vertical
narrower than the beam top flange. This rib plates (see Figure 9-4e) can also be used to
configuration permits the bottom cover plate to reduce the stress demand in the welded joint
be used as an erection seat, and facilitates (Chi and Uang 2000).
down-hand welding in the field. Welded, not
bolted, web connections are recommended as Reduced Beam Sections
an effective way of reducing the thickness of
the cover plates. Although a significant number An alternative to relocating the plastic hinge
of cover plated connection specimens have away from the face of the column is to reduce
achieved beam plastic rotations exceeding 0.03 the plastic moment of the beam at a short
radian, Hamburger (1996) reported a failure distance from the column face. Beam sections
rate of approximately 20 percent for cover- can be reduced by tapering the flanges, or by
plated connections in laboratory tests. Another radius-cutting the flanges as shown in Figure 9-
concern with the cover-plate connection is that 5. The latter approach appears to be the most
the seam between the flange cover plate and the promising because the re-entrant corners of the
beam flange acts as a notch at the column face tapered flange profile tend to promote pre-
that may lead to cracks propagating into the mature fracture in the beam flanges.
column flange and beyond. Further information Originally proposed and tested by Plumier
is available in SAC (1997). (1990), the use of the reduced beam section
The welded flange-plate connection (see (RBS), also termed the dogbone by many
Figure 9-4b) is closely related to the cover-plate design professionals, has seen broad support
connection, with the major difference being that from engineers, steel producers, and fabricators.
only the flange plates are groove welded to the Both reduced-beam-section profiles have
column (Jokerst and Soyer 1996, Noel and achieved plastic rotations in excess of 0.03
Uang 1996). As such, flange plates of the radian. Additional information is provided in
welded flange-plate connection are thicker than Iwankiw and Carter (1996), Chen et al. (1996),
the comparable cover plates shown in Figure 9- Engelhardt et al. (1996), and Zekioglu et al.
4a. There is no notch effect associated with the (1996).
9. Seismic Design of Steel Structures 419
(a) Beam bottom flange weld fracture propagating through column flange and web
(b) Beam bottom flange weld fracture causing a column divot fracture
Figure 9-3. Examples of brittle fracture of steel moment frame connections (courtesy of David P. Osullivan, EQE
International, San Francisco)
420 Chapter 9
Figure 9-4. Reinforced moment connections: (a) cover plates, (b) welded flange plates, (c) triangular haunches,
(d) straight haunch, (e) rib plates
9. Seismic Design of Steel Structures 421
earthquake actions. Assuming that the flanges restrained joints, such as continuity plates,
resist 100 percent of the moment and that the induces residual stress in steel members. In
distance between the centroids of the flanges is addition to the normal variation of material
95 percent of the beam depth, compression and properties in the column, the process of mill
tension flange forces as shown in Figure 9-6b rotary straightening of the W-shaped member
can replace the beam moments. alters the mechanical properties by cold
working in the k area. (The k area is
defined by AISC as the region extending from
about the midpoint of the radius of the fillet into
the web approximately 1 to 1.5 in. beyond the
point of tangency between the fillet and web.)
As a result, a reduction in ductility and
toughness in the k area may occur. In some
cases, values of Charpy V-notch toughness less
than 5 ft-lb at 70 F have been reported. Since
welding in the k area may increase the
likelihood of fracture, a recent AISC Advisory
(1997a) has suggested that welds for the
continuity plates be stopped short of the k
area. Fillet welds and/or partial joint penetration
welds, proportioned to transfer the calculated
forces, are preferred to complete joint
penetration welds.
in the parentheses represents the contribution of calculated using the specified load
column flanges (assumed to be linearly elastic) combinations. In addition, the column axial
to the shear strength of the panel zone. The strength should be sufficient to resist the axial
equation used to calculate Vn assumes a level of forces produced by the special load
shear strain of 4 y in the panel zone, where y combinations of Eqs. 9-4 and 9-5. Additional
is the yield shearing strain. strength is required if either the welds are
A panel zone must also be checked for a partial penetration groove welds or the welds
minimum thickness ( t ) to prevent premature are subjected to net tension forces. Column
local buckling under large inelastic shear splices using fillet welds or partial joint
deformations: penetration groove welds shall not be located
within 4 feet or one-half the column clear
(d z + w z ) height of beam-to-column connections, which
t= (9-13) is less.
Special moment frames are designed using
the strong column-weak beam philosophy
In this empirical equation, d z is the depth of
because such an approach improves the energy
the panel zone between the continuity plates,
dissipation capacity of the frame, promotes
and wz is the width of the panel zone between
plastic hinge formation in the beams, increases
the column flanges. If doubler plates are used to
the seismic resistance of the frame, and
satisfy this equation for t , the plates must be
ostensibly prevents the formation of a soft story
plug welded to the column web such that the
mechanism. Seismic regulations seek to achieve
plates do not buckle independently of the web.
a strong column-weak beam system by ensuring
If used, doubler plates must be welded to the
that, at a beam-to-column connection, the sum
column flanges using either a complete joint
of the column plastic moments exceeds the sum
penetration groove weld or a fillet weld that
of the beam plastic moments. With few
develops the design shear strength of the full
exceptions, AISC (1997) requires that:
doubler plate thickness. When such plates are
welded directly to the column web and extend M *pc
beyond the panel zone, minimum weld size can > 1.0 (9-14)
be used to connect the top and bottom edges to M *pb
the column web. However, because of the cold
working due to the rotary straightening practice
where M *pc is the sum of the moment
and the resulting variations of material capacities in the columns above and below the
properties exhibited in the column k areas, joint at the intersection of the beam and column
the AISC Advisory (1997) suggested that, as an centerlines, and M *pb is the sum of the
interim measure, the design engineer increase moment demands in the beams at the
the column size to avoid the use of doubler intersection of the beam and column
plates. centerlines.
The value of M *pc is determined by
9.2.6 Column Design
summing the projections of the nominal
The column of an SMF must be designed flexural strength of the columns above and
per the LRFD Specifications (1997) as a beam- below the connection to the beam centerline,
column to avoid axial yielding, buckling, and with a reduction for the axial force in the
flexural yielding. Columns are routinely spliced column. M *pc can be conservatively
by groove welding. Such connections are approximated as Z c ( Fyc Puc / Ag ) , where
required to have sufficient strength to resist the
Ag is the gross area of the column, Puc is the
imposed axial, shearing, and flexural forces
required column compressive strength, Zc is the
9. Seismic Design of Steel Structures 425
plastic section modulus of the column, and Fyc elements of the column section shall be limited
is the minimum specified yield strength of to the ps values in Table 9-2 because plastic
column. The value of M *pb is calculated by hinge formation in the column may occur due
to the shift of inflection point during an
summing the projection of the expected beam
earthquake. Otherwise, columns shall comply
flexural strengths at the plastic hinge locations
with the limiting values of p in the same table.
to the column. M *pb can be approximated as
(1.1R y Fy Z + M v ) , where Z is the plastic
9.3 Behavior and Design of
modulus of the beam section at the potential Concentrically Braced
plastic hinge location, and Mv accounts for the
additional moment due to shear amplification
from the location of the plastic hinge to the
column centerline. As illustrated in Figure 9-7,
for reinforced connections using haunches or 9.3.1 Design Philosophy
vertical ribs, SAC (1996) suggests that plastic
hinges be assumed to be located at a distance sh Concentrically braced frames are frequently
= d/3 from the toe of haunch or ribs. For cover used to provide lateral strength and stiffness to
plated connections, SAC recommends that the low- and mid-rise buildings to resist wind and
plastic hinge be located at a distance sh = d/4 earthquake forces. Although some architects
beyond the end of cover plate. When the ratio favor the less intrusive moment frames, others
in Eq. 9-14 is no greater than 1.25, the width- have found architectural expression in exposing
to-thickness ratios of the flange and web braced frames which the public intuitively
Figure 9-7. Assumed beam plastic hinge locations (Adapted from Interim Guidelines Advisory No. 1, SAC 1997)
426 Chapter 9
associates with seismic safety in some connections undamaged, thus allowing the
earthquake-prone regions. However, for those structure to survive strong earthquakes without
frames to provide adequate earthquake losing gravity-load resistance.
resistance, they must be designed for Past earthquakes have demonstrated that this
appropriate strength and ductility. This is idealized behavior may not be realized if the
possible for many of the concentrically braced braced frame and its connections are not
frame (CBF) configurations shown in Figure 9- properly designed. Numerous examples of poor
8, but not all, as described in this section. seismic performance have been reported
In a manner consistent with the earthquake- (Tremblay et al. 1995, 1996; AIJ 1995). As
resistant design philosophy presented elsewhere shown in Figure 9-9, braces with bolted
in this chapter, modern concentrically braced connections have fractured through their net
frames are expected to undergo inelastic section at bolt holes, beams and columns have
response during infrequent, yet large suffered damage, and welded and bolted
earthquakes. Specially designed diagonal braces connections have fractured. Collapses have
in these frames can sustain plastic deformations occurred as a consequence of such uncontrolled
and dissipate hysteretic energy in a stable inelastic behavior.
manner through successive cycles of buckling The design requirements necessary to
in compression and yielding in tension. The achieve adequate strength and ductility in
preferred design strategy is, therefore, to ensure concentrically braced frames are presented in
that plastic deformations only occur in the this section. Two types of systems are permitted
braces, leaving the columns, beams, and by the AISC Seismic Provisions: Special
(b) Severe distortion of beam without lateral support at location of chevron braces
Beyond this difference, the hysteretic curve dissipation. The energy absorption capability of
repeats itself in each subsequent cycle of axial a brace in compression depends on its
loading and inelastic deformations, with a shape slenderness ratio (KL/r) and its resistance to
similar to the OABCDEF of Figure 9-10. local buckling during repeated cycles of
inelastic deformation.
9.3.3 Design Requirements
Limits on Effective Slenderness Ratio
Concentrically braced frames exhibit their
best seismic performance when both yielding in As can be deduced from Figure 9-10,
tension and inelastic buckling in compression slenderness has a major impact on the ability of
of their diagonal members contribute a brace to dissipate hysteretic energy. For a
significantly to the total hysteretic energy very slender brace, segment OA is short while
Figure 9-11. Brace Hysteresis loops by experimentation. (Nakashima and Wakabayashi 1992, referring to a figure by
Shibata et al. 1973, with permission from CRC Press, Boca Raton, Florida)
9. Seismic Design of Steel Structures 431
Figure 9-12. Schematic hysteretic behavior of braces of short, long, and intermediate slenderness (Nakashima and
Wakabayashi 1992, with permission from CRC Press, Boca Raton, Florida).
segment AB is long, resulting in poor energy further and further to be able to dissipate the
dissipation capacity in compression. For stocky same amount of energy at each cycle, perhaps
braces, the reverse is true, and segment AB leading to collapse due to second-order effects.
(i.e., elastic buckling) may not exist. Seismic detailing provisions typically limit
Slenderness has no impact on the energy brace slenderness to prevent the above problem
dissipation capability of braces in tension. and to ensure good energy dissipation capacity.
Typical hysteretic loops obtained Many seismic codes require:
experimentally for axially loaded members of
intermediate and large slenderness ratios are KL 720
shown in Figure 9-11, where the parameter r Fy
(= Kl /( r) Fy / E ) is a non-dimensional
slenderness ratio (Nakashima and Wakabayashi
1992). Schematic illustrations of simplified where Fy is in ksi. For ASTM A992 or A572
hysteresis loops for short, intermediate and long Grade 50 steel, this corresponds to an effective
braces are shown in Figure 9-12. slenderness ratio of 102. Recently, the AISC
Very slender brace members (such as bars Seismic Provisions (1997) have relaxed this
or plates) can result from a practice called limit to:
tension-only design, often used prior to the
promulgation of modern seismic provisions for KL 1000
steel buildings, and still used in non-seismic r Fy
regions. In that design approach, the tension
brace is sized to resist all the lateral loads, and
for bracing members in SCBFs, but kept the
the contribution of the buckled compression
more stringent limit of Eq. 9-15 for OCBFs.
brace is ignored. While tension-only design
Nevertheless, the authors recommend the use of
may be acceptable for wind resistance, it is not
Eq. 9-15 for both SCBFs and OCBFs.
permissible for earthquake resistance. As
shown in Figure 9-13, braced frames with very
Limits on Width-to-Thickness Ratio
slender members must progressively drift
432 Chapter 9
Figure 9-13. Hysteretic Behavior of Single-Story braced frame having very slender braces
The plastic hinge that forms at mid-span of a suffer low-cycle fatigue and fracture after a few
buckled brace may develop large plastic cycles of severe inelastic deformations
rotations that could lead to local buckling and (especially when braces are cold-formed
rapid loss of compressive capacity and energy rectangular hollow sections). For these reasons,
dissipation during repeated cycles of inelastic braces in SCBFs must satisfy the width-to-
deformations. Past earthquakes and tests have thickness ratio limits for compact sections. For
shown that locally buckled braces can also OCBFs, braces can be compact or non-
9. Seismic Design of Steel Structures 433
compact, but not slender, i.e., b / t r per Figure 9-14c, the intent does. Codes generally
LRFD Specification. Based on experimental waive this requirement if nearly elastic
evidence, more stringent limits are specified for response is expected during earthquakes,
some types of structural shapes. In particular, something achieved in the AISC Seismic
the width-to-thickness ratio of angles (b/t), the Provisions by the special load conditions
outside diameter to wall thickness ratio of described in Section 9.1. Note that in
unstiffened circular hollow sections (D/t), and calculating the strength of an OCBF, the AISC
the outside width to wall thickness ratio of Seismic Provisions also require that cPcr (=
unstiffened rectangular sections must not 0.9cPcr) be used instead of cPcr, for the
exceed 52/ F y , 1300/Fy, and 110/ F y , reasons described in the previous section. There
is no such requirement for SCBFs, but the
respectively (see Table 9-2). Note that the
authors prefer to observe this requirement for
AISC Seismic Provisions (1997) define b for
both OCBFs and SCBFs, recognizing, however,
rectangular hollow sections as the out-to-out
that the tension brace may have sufficient
width, not the flat-width (= b3t) as defined in
strength to accommodate the strength
the AISC Specifications (AISC 1994).
degradation of the compression brace upon
repeated cycling, and that such a force
redistribution may be considered when
calculating the strength of the braced panel
Energy dissipation by tension yielding of
using cPcr. This approach is not recommended
braces is more reliable than buckling of braces
for V- and inverted-V-types of OCBF.
in compression. To provide structural
redundancy and a good balance of energy
9.3.4 Bracing Connections Design
dissipation between compression and tension
members, structural configurations that depend
predominantly on the compression resistance of
When a brace is in tension, net section
braces should be avoided. Examples of poor
fracture and block shear rupture at the end of
braced frames layout are shown in Figure 9-14,
the brace must be avoided. Likewise, the brace
together with recommended alternatives. Four
connections to beams and columns must be
braces in compression and only one brace in
stronger than the braces themselves. Using
tension resist the load applied on the 5-bay
capacity design, calculation of brace strength
braced frame shown in Figure 9-14a. All braces
must recognize that the expected yield strength
in the braced-core of Figure 9-14c are in
of the brace, Fye, will typically exceed its
compression to resist the torsional moment
specified minimum yield strength, Fy (see Eq.
resulting from seismically-induced inertial
9-6). Thus, connections must be designed to
force acting at the center of mass. (For
resist an axial force equal to RyFyAg. However,
simplicity, columns resisting only gravity loads
when plastic analysis is used to demonstrate
are not shown in that figure.) Better designs are
that braces are unlikely to yield, connections
shown in Figures 9-14b and 9-14d for each of
may be designed for the maximum force
these cases, respectively.
obtained from such an analysis.
Seismic design codes attempt to prevent the
Connections must also be able to resist the
use of non-redundant structural systems by
forces due to buckling of the brace. If strong
requiring that braces in a given line be deployed
connections permit the development of a plastic
such that at least 30% of the total lateral
hinge at each end of a brace, they should be
horizontal force acting along that line is resisted
designed to resist a moment equal to 1.1RyMp of
by tension braces, and at least 30% by
the brace in the direction of buckling.
compression braces. Although the wording of
Otherwise, the connecting elements will
such clauses does not cover the case shown in
themselves yield in flexure (such as gussets out
434 Chapter 9
Figure 9-14. Brace configurations to ensure structural redundancy and balanced energy dissipation between compression
and tension members: (a and c) poor configurations; (b and d) acceptable configurations
9. Seismic Design of Steel Structures 435
of their plane); these must then be designed to with the further specification that the maximum
resist the maximum brace compression force in axial tension forces in columns need not be
a stable manner while undergoing the large taken larger than the value corresponding to
plastic rotations that result from brace buckling. foundation uplift. For SCBFs, the Provisions
Astaneh-Asl et al. (1986) suggested providing a also require that columns satisfy the same
clear distance of twice the plate thickness width-to-thickness ratio limits as braces (i.e.,
between the end of the brace and the assumed ps in Table 9-2).
line of restraint for the gusset plate to permit Partial penetration groove welds in column
plastic rotations and to preclude plate buckling splices have been observed to fail in a brittle
(see Figure 9-15). manner (Bruneau and Mahin 1990). When a
welded column splice is expected to be in
tension under the loading combination shown in
Eq. 9-5, the AISC Seismic Provisions mandate
that the partial joint penetration groove welded
joints in SCBFs be designed to resist 200% of
the strength required by elastic analysis using
code-specified forces. Column splices also need
to be designed to develop at least the nominal
shear strength of the smaller connected member
and 50% of the nominal flexural strength of the
smaller connected section.
9.4.1 Introduction
Elastic Stiffness
Figure 9-19. Variations of lateral stiffness with respect to link length (Hjelmstad and Popov 1994)
438 Chapter 9
Figure 9-20. Kinematic mechanism and link plastic angle of a K-type EBF
ensure that the deformation capacity of the link where Vp is the shear strength of the link.
is not exceeded, it is obvious from Eq. 9-17 that Substituting Eq. 9-17 into Eq. 9-19b, the
the link length cannot be too short. Note that resulting ultimate strength of the EBF frame is
the kink that forms between the link and the
beam outside the link also implies damage of Vp L
the concrete slab at the ends of the link. Pu = (9-20)
9. Seismic Design of Steel Structures 439
As long as the link yields in shear, the above moment, Mp. A shear hinge is said to form
equation shows that the ultimate strength is when the shear reaches Vp. The plastic moment
independent of the link length. This simple and shear capacities are respectively computed
plastic theory can also be applied to multistory as follows:
frames (Kasai and Popov 1985).
Once the link length exceeds a threshold Mp = Fy Z (9-21a)
value, flexure and shear dominates the link
strength. The ultimate strength of the frame Vp = 0.6 F y (d 2t f )t w (9-21b)
then decreases with an increase in link length.
Figure 9-21 illustrates the strength variations.
This figure also indicates that the ultimate
strength of an EBF with short links is
significantly larger than that of a moment frame
(i.e., e/L = 1.0).
2M p
e0 = (9-22)
2M p
Figure 9-21. Variations of EBF ultimate strength with e/L V= (9-23)
(Kasai and Popov 1985) e
due to strain hardening and, therefore, flexural Based on experimental results, the link
hinges can develop. To avoid low-cycle fatigue deformation capacity, a, as given by the AISC
failure of the link flanges due to high strains, Seismic Provisions is shown in Figure 9-24.
these end moments are limited to 1.2Mp, and the The calculated rotation angle, p, cannot exceed
maximum length (e0 in Eq. 9-22) for a shear a.
link was modified as follows (Kasai and Popov
2(1.2 M p ) 1.6 M p
e0 = = (9-24)
1.5V p Vp
Longer Links
V pa = V p 1 ( Pu / Py ) 2 (9-26)
to the link web shall have a design strength to At the connection between the diagonal
resist a force of AstFy, where Ast is the stiffener brace and the beam, the intersection of the
area. The design strength of fillet welds brace and beam centerlines shall be at the end
fastening the stiffener to the flanges shall be of the link or within the length of the link (see
adequate to resist a force of AstFy/4. Figure 9-26a). If the intersection point lies
outside the link length, the eccentricity together
Lateral Bracing of Link
with the brace axial force produces additional
To ensure stable hysteresis, a link must be moments in the beam and brace.
laterally braced at each end to avoid out-of- The diagonal brace-to-beam connection at
plane twisting. Lateral bracing also stabilizes the link end of the brace shall also be designed
the eccentric bracing and the beam segment to develop the expected strength of the brace.
outside the link. The concrete slab alone cannot No part of this connection shall extend over the
be relied upon to provide lateral bracing. link length to reduce the link length, e. If the
Therefore, both top and bottom flanges of the connection is designed as a pin (see Figure. 9-
link beam must be braced. The bracing should 26b), the gusset plate needs to be properly
be designed for 6 percent of the expected link stiffened at the free edge to avoid local
flange strength, RyFybf tf. buckling (Roeder et al. 1989).
Diagonal Brace
links in the bottom two stories dissipated most forces need not exceed those computed by the
of the energy (Whittaker et al. 1989). first procedure. Therefore, the first design
Therefore, this design procedure may be procedure will generally produce a more
appropriate for low-rise buildings and the upper conservative design for columns.
stories of medium- and high-rise buildings but
may be too conservative in other instances. 9.5 Design Examples
The alternative design procedure permitted
by the AISC Seismic Provisions is to amplify
9.5.1 General
the design seismic axial forces and moments in
columns by the overstrength factor, o (= 2.0,
A six-story office building having the floor
see Table 9-1). See Eqs. 9-4 and 9-5 for the
plan shown in Figure 9-27 is used to
load combinations. The computed column
demonstrate the seismic design procedures. The where hn (ft) is the building height, and the
design follows the AISC Seismic Provisions coefficient CT is equal to 0.035, 0.030, and 0.02
(1997) and the Load and Resistance Factor for SMFs, EBFs, and SCBFs, respectively.
Design Specification for Structural Steel Alternatively, the value of T obtained from a
Buildings (1993). Special Moment-Resisting dynamic analysis can be used in design, but the
Frames (SMFs) are used in the E-W direction, period thus obtained cannot be taken larger than
and their design is presented in Section 9.5.2. CuTa for the calculation of required structural
Braced frames provide lateral load-resistance in strengths, where Cu = 1.2
the N-S direction; these are designed as Special
Concentrically Braced Frames (SCBFs) in
Section 9.5.3 and Eccentrically Braced Frames
(EBFs) in Section 9.5.4, respectively.
The design gravity loads are listed in Table
9-3. The NEHRP Recommended Provisions
(1997) are the basis for computing the design
seismic forces. It is assumed that the building is
located in a high seismic region with the
following design parameters:
SS = 1.5 g
Figure 9-28. Elastic design response spectrum
S1 = 0.6 g
Site Class = B
I = 1.0 (Seismic User Group I) for this design example. To establish seismic
Seismic Design Category = D forces for story drift computations, however,
this upper limit is waived by the NEHRP
The design response spectrum is shown in Recommended Provisions. Recognizing that the
Figure 9-28. analytically predicted period of a multistory
The design follows the Equivalent Lateral SMF is generally larger than CuTa, this upper
Force Procedure of the NEHRP Recommended bound value is used to compute the design base
Provisions. The design base shear ratio, Cs, is shear ratio for preliminary design. Based on Eq.
computed as follows: 9-1, the design base shear ratios for the three
types of frames are listed in Table 9-4.
S The following two load combinations are to
Cs = DS (9-29) be considered:
where S D1 (= 0.4 g) and S DS (= 1.0 g) are the
design spectral response accelerations at a 0.9D 1.0E (9-32)
period of 1.0 second and in the short period
range, respectively. The values of R for the where E = QE + 0.2 SDSD. The Redundancy
three framing systems considered in this Factor, , is
example are listed in Table 9-4. The NEHRP
empirical period formula is used to compute the 20 20
approximate fundamental period, Ta: = 2 = 2 = 1.13 (9-33)
rmax A 0.25 8549
0.4 0.059
C1 = 1.05(C s ) = 1.05(1.13) = Member Proportions
(where 1.05 accounts for torsion) For brevity in this design example, detailed
calculations are presented only for the beams on
the fourth floor and the columns above and
T = 0.25 = 1.44 T below that floor (see Figure 9-29). The portal
0.059 / T method is used for preliminary design.
Assuming that the point of inflection occurs at
Solving the above equation gives a value of T the mid-length of each member:
equal to 2.0 seconds. For this value, however,
S D1 0.4 2F1 + 3F2 = 0.94(109) = 102.5 kips
Cs = =
= 0.025 < 0.044 S DS F1 = F2/2, F2 = 25.6 kips
and C s = 0.044 controls. That is, the minimum Consider the interior beam-column assembly
seismic base shear for drift computations is shown in Figure 9-29. Summing the moments
at the point of inflection at point P, the beam
V = 1.05 0.044W = 0.052W shear, F3, is calculated to be:
Since the base shear ratios for strength and drift 12F2 = 25F3, F3 = 12.3 kips
designs are 0.047 and 0.044, respectively, a
scaling factor of 0.94 (= 0.044/0.047) can be The story drift due to column and girder
used to reduce the story shears listed in Table 9- deformations is:
5 for drift computations.
Figure 9-30. Reduced beam section and the welded beam-column connection details.
Z (L a 0.5b )
Beam-to-Column Connection Design c 1 0.25b f
2t f (d t f ) 1.1L
Reduced beam section details employing where L (= 142.7 in) is the distance from the
radius-cut (Figure 9-30) is the most promising face of the column to the point of inflection in
beam-to-column connection detail. The key the beam, bf, tf and d are flange width, flange
dimensions of the radius cut include the thickness and beam depth, respectively. To
distance from the face of the column determine the maximum cut dimension, c, it is
(dimension a), the length of the cut (dimension assumed that the strain-hardened plastic
b), and the depth of the cut (dimension c). To moment developed at the narrowest beam
minimize the moment gradient between the section is equal to 1.1 times the plastic moment
narrowest section and the face of column, the of the reduced section (ZRBSFye). The factor 1.1
dimensions a and b should be kept small. accounts for strain hardening. The factor
However, making these dimensions too short limits the beam moment ( Mp) developed at
may result in high strains either at the face of the face of column. The maximum value of
column or within the reduced beam sections. It should range between 0.85 and 1.0. Based on an
has been recommended that (Engelhardt et al. equal to 0.90,
a = 4.0 in = 0.57bf
a (0.5 to 0.75)bf b = 16 in = 0.67d
b (0.65 to 0.85)d
c = 1.375 in 0.20bf
450 Chapter 9
M pd = 1.1R y Z RBS F y
= 1.1 1.1115 50 = 6958 kip in
M pc d z + wz
= 1.32 > 1.0 (OK) t(reqd) = = 0.39 in
M pb
Since both the thicknesses of column web and
Therefore, the strong column-weak beam doubler plate are larger than the required
condition is satisfied. thickness, plug welds are not required to
connect the doubler plate to the column web.
Panel Zone Design See Figure 9.30 for the connection details.
The component of story drift produced by
The unbalanced beam moment, M, for the the panel zone deformation is computed as
panel zone design is determined from the follows (Tsai and Popov 1990):
special load combination in Eq. 9-4, where the
beam moment at the column face produced by V
p =
o (Q E ) is dct pG
M1 = M2 = o (F3/0.94)L 419 0.94 / o
14.66(0.645 + 0.50)29000 / 2.6
= 3.0(12.3/0.94)142.7 = 5602 kip-in
= 0.00070 rad
M = M 1 + M 2 = 11204 kip-in
where G is the shear modulus. The story drift
But the above moment need not be greater than due to the panel zone deformation, P , is:
0.8 M pb . Extrapolating the beam moment at
the plastic hinge location to the column face, P = 0.00070 12 12 = 0.10 in
M pb is computed as follows: The total story drift produced by the column,
b beam, and panel zone deformations is:
M *pd = M pd + V pd a +
2 F2 h(h d b )
c + g + P =
= 6958+ 53(4.0 + 8.0) = 7594 kip in 12 EI c
0.8 M *pb = 0.8(2)(7594) = 12150 kip-in F2 h 2 (L d c )
12 EI g
Therefore, the shear in the panel zone is
= 0.10+0.281+0.10 = 0.48 < 0.52 in (OK)
Vu = = 497 78 = 419 kips
0.95d b h Note that the clear lengths are used to compute
the deformations of the beams and column in
The shear capacity of the panel zone is the above equation.
Vn = 0.75(0.6 )(50.0)(14.66)t p
9.5.3 Special Concentrically Braced
3(14.725)(1.03)2 Frames (SCBFs)
1 +
(23.74)(14.66)t p
The six-story inverted-V braced frame
Equating Vu and Vn to solve for the required shown in Figure 9-32 is analyzed for the loads
panel zone thickness gives tp = 1.14 in. Since specified earlier. The service dead load, live
the column web thickness is 0.645 in, use a 1/2 load, and seismic member forces, calculated
in thick doubler plate. (The column size needs taking into account load-paths and live load
to be increased if the designer prefers not to use reduction, and maximum forces resulting from
doubler plates.) Check Eq. 9-13 for local the critical load combination, are presented in
buckling of the doubler plate: Tables 9-6 and 9-7, where the axial forces and
moments are expressed in kips and kip-ft,
452 Chapter 9
respectively. Cladding panels are assumed braces is presented elsewhere (Bruneau et al.
connected at the columns. Note that the load 1997). Note that this frame geometry leads to
combination 1.2D+0.5L+1.0E governs for the substantial foundation uplift forces. Although
design of all members. not done here, increasing the number of braced
In the first phase of design (called strength bays will reduce the uplift forces.
design hereafter), members are sized without In the second phase of design, (hereafter
attention paid to special seismic detailing called ductile design), the seismic
requirements, as normally done in non-seismic requirements are checked, and design is
applications, and results are also presented in modified as necessary. The special ductile
Tables 9-6 and 9-7. Members are selected per a detailing requirements of braces are first
minimum weight criterion, with beams and checked. Here, all braces are found to have a
braces constrained to be wide-flanges sections slenderness ratio in excess of the permissible
of same width, and columns constrained to be limit (Eq. 9-15), and some also violate the
W14 shapes continuous over two stories. specified flange width-to-thickness ratio limit.
ASTM A992 steel is used for all members, and For example, for the fifth story braces
the effective length factors, K, of 1.0 were (W831), the slenderness ratio is:
respectively used in calculating the in-plane and (KL/r)y = (1.0)(19.21)(12)/2.02
out-of-plane buckling strength of braces.
Additional information on the effects of end-
fixity on the inelastic non-linear behavior of
9. Seismic Design of Steel Structures 453
Table 9-6. Strength design results for columns and W-shape braces (axial force in kips)
Story PD PL PLr PQE or TQE Pua Tub Member cPn KL/r bf/2tf h/tw
from load combination 1.2D + 0.5L + 1.0E (see Eq. 9-34), where E = QE.
from load combination 0.9D - 1.0E (see Eq. 9-35).
Table 9-7. Strength design results for beams (axial force in kips, moment in kip-in)
Level PD MD PL ML PLr MLr PQbE Pua M ua Section cPn bMn KL/r bf /2tf h/tw
Roof - 11.1 - - - 2.0 37.2 42 16.5 W821 64.4 76.5 142.9 6.6 27.5
from load combination 1.2D + 0.5L + 1.0E (see Eq. 9-34), where E = QE.
b. M = 0.
Table 9-8. Strength design results for TS-shape braces (axial force in kips)
Table 9-9. Ductility design results for TS-shape braces (axial force in kips)
Design strengths:
Design Forces in Connections
c Pn = 224 kips, t Tn = t Ag Fy = 513 kips
Connections are designed to resist their
Reduced compression design strength: expected brace tension yield force of RyAgFy.
For example, for the braces in the first story,
0.8( c Pn ) = 0.8(224) = 179 kips <Pu=198 kips this would correspond to a force of
Therefore, the redistributed force demand in the (1.1)(14.4)(46) = 729 kips. The brace gusset
tension brace is: used with tubular braces usually permits out-of-
plane buckling and needs to be detailed per
Tu = Tu + ( c Pn 0.8 c Pn ) = 180 + (224 179) Figure 9-15 to resist the applied axial force
= 225 kips < c Tn = 513 kips (OK) while undergoing large plastic rotation.
Finally, the redundancy requirement is Design Forces in Columns
satisfied by checking that members in tension
carry at least 30% but no more than 70% of the When Pu/ c Pn in columns is greater than
story shear. Note that for bays with the same 0.4 (as is the case here), the AISC Seismic
number of compression and tension braces, Provisions require that columns also be
satisfying the above member slenderness limits, designed to resist forces calculated according to
this is usually not a concern. For example, the special load combinations in Eqs. 9-4 and 9-
check the first story brace as follows: 5. However, these forces need not exceed those
Tu / cos 240 / 0.707 calculated considering 1.1Ry Tn and 1.1Ry Pn of
= = 0.56 the braces. Members designed to satisfy this
requirement are presented in Table 9-10.
which is between 0.3 and 0.7.
9. Seismic Design of Steel Structures 455
Table 9-10. Ductility design results for columns (axial force in kips)
Table 9-11. Ductility design results for beamsa (force in kips, moment in kip-in)
Unbalanced Force
Level Tn 0.3cPn Vertical Horizontal Mux Pu Section bMnx cPn Ratio
Ductility design not required at top story of a chevron braced frame per AISC Seismic provisions.
Note that columns splices would have to be adequacy of these beams is checked using the
designed to resist the significant uplift forces AISC (1993) beam-column interaction
shown in this table, although the AISC Seismic equations.
Provisions indicate that the tension forces For example, for the W30191 beam on the
calculated in Table 9-10 need not exceed the second floor:
value corresponding the uplift resistance of the
Pu M ux 189 2265
foundation. + =
2 c Pn b M nx 2 (1956) 2398
Design Forces in Beams = 0.05 + 0.94 = 0.99 < 1.0 (OK)
Incidentally, note that this section is a compact
Finally, beams are checked for compliance section.
with the special requirements presented in
Section 9.3. Here, all beams are continuous 9.5.4 Eccentrically Braced Frames
between columns, and are braced laterally at the (EBFs)
ends and mid-span. W30 shapes were chosen to
limit beam depth. The configuration of the split-V-braced EBF
Beams are, therefore, redesigned to resist is shown in Figure. 9-33, and the design seismic
the unbalanced vertical force induced when the forces are listed in Table 9-5. The geometry is
compression braces are buckled and the tension chosen such that the link length is about 10% of
braces are yielded. In this example, this the bay width, and the inclined angle of the
substantial force governs the design. The braces is between 35 to 60 degrees:
corresponding moments and axial forces acting
e = 0.1L = 3 ft = 36 in
on the beams are shown in Table 9-11, along
with the resulting new beam sizes. Note that the
456 Chapter 9
= tan 1 (15 / 13.5) = 48 (first story) Assuming that the braces are rigidly connected
to the link, that the beam can resist 95% of the
link end moment, and that the beam flexural
= tan 1 (12 / 13.5) = 42 (other stories) capacity is reduced by 30% due to the presence
of an axial force:
In this example, detailed design calculations are
only presented for members at the first story to (0.7) R y ( b M p ) 0.85(1.1) R yVn (e / 2)
illustrate the procedure. Unless indicated
otherwise, ASTM A992 steel is used.
1.35Mp/Vn e
For shear links, the above requirement for the
maximum link length is more stringent than
1.6Mp/Vp. The required strengths for the link on
the second floor are
Vu = 1.4 D + 0.5 L + E
= 1.4(1.1) + 0.5(0.4) + 98.0 = 100 kips
M u = 1.4 D + 0.5L + E
= 1.4(8.0) + 0.5(3.0) + 98(3.0 / 2) = 160
Figure 9-33. Eccentrically braced frame elevation Z x = 64.7 in 3 > 40.0 in 3 (OK)
Vn = min {V p , 2 M p e}
2 EI x
Pe1 = = 3817 kips
(OK) ( KL x ) 2
= min {116, 180} = 116 kips
Cm = 0.85
Beam Outside of Link Cm 0.85
Pu 126
The moment at both ends of the link is: 1 1
Pe1 3817
M u = 1.1( R yVn e / 2)
Use B1 = 1.0
= 1.1(1.1 116 3.0/2) = 211 kip-in
( KL) y = 13.5 ft, c Pn = 337 kips
This moment is resisted by both the rigidly
connected brace and the beam outside the link. Pu 8 B1 M u
Assuming that the beam resists 85% of the link + = 0.34 + 0.63
moment, the beam end moment including the R y ( c Pn ) 9 R y ( b M n )
gravity load effect (MD = 8 kip-ft, ML = 3 kip-ft)
is = 0.97 < 1.0 (OK)
Mu = 0.85(211) + 1.2(8.0)
Diagonal Brace
+ 0.5(3.0) = 190 kip-ft
The axial force ratio in the beam is To compute the beam shear, Vb, assume the
beam moment at the column end is zero.
Pu 126
= = 0.212 > 0.125 1.25 R yVn = 160 kips
b Py 0.9 Ag F y
1.25R y Vn (e 2)
Table 9-2):
Vb = = 18 kips
ps = 2.33 u
F y b Py
Fy Therefore, the brace force including the gravity
= 57.2 load effect (VD = 5.7 kips, VL = 2.2 kips) is
Pu = (1.25R yV n + Vb + 1.2V D + 0.5V L ) / sin()
= = 16.7 < ps (OK) = 250 kips
The brace length is 20.2 ft. Selecting a square
Checking the strength of the beam segment as a tubular section TS8 8 1/2 (A500 Grade B
beam-column: steel):
[L p ]
= 6.9 ft < [Lb = 13.5 ft ]< [Lr = 20.3 ft ] c Pn = 366 kips > 250 kips (OK)
458 Chapter 9
b/t = 6.5/0.5 = 13 < p = 190 / F y = 28 (OK) The link rotation capacity is 0.08 rad
because the link length (= 36 in) is smaller than
Once the brace size is determined, it is 1.6 Mp/Vp (= 44.6 in). Thus, the link
possible to determine the link end moment deformation capacity is sufficient.
based on the relative stiffness (I/L) of the brace
and the beam segment outside the link. The Lateral Bracing
moment distribution factor is
Full-depth stiffeners of A36 steel are to be
I br /Lbr
(DF )br = = 0.20 used in pairs at each end of the links. The
I br /Lbr + I b /Lb required thickness of these stiffeners is
Therefore, the moment at the end of brace is t = max {0.75tw, 3/8} = 3/8 in
Lateral bracing similar to that shown in Figure
Mu = 240 (DF)br = 48 kip-ft 9-31 is needed for the links, except that the
bracing needs to be designed for 6% of the
The brace capacity is checked as a beam- expected link flange force, RyFybftf.
b M n = b ( Z x F y ) = 137 kip-ft Link Stiffeners
and the design story drift is The required total design force between the
stiffener and the flanges is
s = C d e I = 4.0( 0.115 ) / 1.0 = 0.46 in
F = Ast Fy/4 = 12.8 kips
Therefore, the link rotation is A minimum fillet weld size of in. satisfies the
L 30.0 0.46 above force requirement.
p = s = = 0.026 rad
e h 3.0 15 12
9. Seismic Design of Steel Structures 459
9-31 Libby, J. R., "Eccentrically Braced Frame Loading, Proc., 5th World Conf. Earthquake Engrg.,
ConstructionA Case Study," Engrg. J., Vol. 18, No. Vol. 1, pp. 845-848, IAEE, Rome, Italy, 1973.
4, pp. 149-153, AISC, 1981. 9-47 SSPC, Statistical Analysis of Tensile Data for Wide-
9-32 Malley, J. O. and Popov, E. P., "Shear Links in Flange Structural Shapes, Chaparral Steel Co.,
Eccentrically Braced Frames," J. Struct. Engrg., Vol. Midlothian, TX, 1994.
110, No. 9, pp. 2275-2295, ASCE, 1984. 9-48 Tanabashi, R., Naneta, K., and Ishida, T., "On the
9-33 Manheim, D. N. and Popov, E. P., "Plastic Shear Rigidity and Ductility of Steel Bracing Assemblage,"
Hinges in Steel Frames," J. Struct. Engrg., Vol. 109, Proc., 5th World Conf. Earthquake Engrg., Vol. 1,
No. 10, pp. 2404-2419, ASCE, 1983. pp. 834-840, IAEE, Rome, Italy, 1974.
9-34 Merovich, A., Nicoletti, J. P., and Hartle, E., 9-49 Teal, E. J., "Seismic Drift Control Criteria," Engrg.
"Eccentric Bracing in Tall Buildings," J. Struct. Div., J., Vol. 12, No. 2, pp. 56-67, AISC, 1975.
Vol. 108, No. ST9, pp. 2066-2080, ASCE, 1982. 9-50 Teal, E., Practical Design of Eccentric Braced
9-35 Nakashima, M. And Wakabayashi, M., Analysis and Frames to Resist Seismic Forces, Struct. Steel Res.
Design of Steel Braces and Braced Frames, in Council, CA, 1979.
Stability and Ductility of Steel Structures under 9-51 Tremblay, R., Bruneau, M., Nakashima, M., Prion,
Cyclic Loading, pp. 309-322, CRC Press, 1992. H.G.L., Filiatrault, M., DeVall, R., Seismic Design
9-36 Noel, S. and Uang, C.-M., Cyclic Testing of Steel of Steel Buildings: Lessons from the 1995 Hyogo-
Moment Connections for the San Francisco Civic ken Nanbu Earthquake, Canadian J. Civil Engrg.,
Center Complex, Report No. TR-96/07, Univ. of Vol. 23, No. 3, pp. 757-770, 1996.
California, San Diego, La Jolla, CA, 1996. 9-52 Tremblay, R., Timler, P., Bruneau, M., Filiatrault, A.,
9-37 Plumier, A., New Idea for Safe Structures in Performance of Steel Structures during the January
Seismic Zones, Proc., Symposium of Mixed 17, 1994, Northridge Earthquake, Canadian J. Civil
Structures Including New Materials, pp. 431-436, Engrg., Vol. 22, No. 2, pp. 338-360, 1995.
IABSE, Brussels, Belgium, 1990. 9-53 Tsai, K.-C., and Popov, E.P., Seismic Panel Zone
9-38 Redwood, R.G., and Channagiri, V.S., Earthquake- Design Effects on Elastic Story Drift of Steel
Resistant Design of Concentrically Braced Steel Frames, J. Struct. Engrg., Vol. 116, No. 12, pp.
Frames, Canadian J. Civil Engrg., Vol. 18, No. 5, 3285-3301, ASCE, 1990.
pp. 839-850, 1991. 9-54 Tsai, K.-C., and Popov, E.P., Steel Beam-Column
9-39 Ricles, J. M. and Popov, E. P., "Composite Action in Joints in Seismic Moment-Resisting Frames, Report
Eccentrically Braced Frames," J. Struct. Engrg., Vol. No. UCB/EERC-88/19, Univ. of Calif., Berkeley,
115, No. 8, pp. 2046-2065, ASCE, 1989. 1988.
9-40 Roeder, C. W. and Popov, E. P., "Eccentrically 9-55 Yu, Q.S., Uang, C.M., and Gross, J., Seismic
Braced Steel Frames For Earthquakes," J. Struct. Rehabilitation Design of Steel Moment Connection
Div., Vol. 104, No. ST3, pp. 391-411, ASCE, 1978. with Welded Haunch, Journal of Structural
9-41 Roeder, C. W., Foutch, D. A., and Goel, S. C., Engineering, Vol. 126, No. 1, pp. 69-78, ASCE,
"Seismic Testing of Full-Scale Steel BuildingPart 2000.
II," J. Struct. Engrg., Vol. 113, No. 11, pp. 2130- 9-56 Uang, C.-M. "Establishing R (or Rw) and Cd Factors
2145, ASCE, 1987. for Building Seismic Provisions," J. Struct. Engrg.,
9-42 SAC, Interim Guidelines: Evaluation, Repair, Vol. 117, No. 1, pp. 19-28, ASCE, 1991.
Modification, and Design of Welded Steel Moment 9-57 Uang, C.-M. and Noel, S., Cyclic Testing of Strong-
Frame Structures, Report FEMA No. 267/SAC-95- and Weak-Axis Steel Moment Connection with
02, SAC Joint Venture, Sacramento, CA, 1995. Reduced Beam Flanges, Report No. TR-96/01, Univ.
9-43 SAC, Interim Guidelines Advisory No. 1, of Calif., San Diego, CA, 1996.
Supplement to FEMA 267, Report No. FEMA 9-58 Uang, C.-M and Fan, C.C, Cyclic Stability of
267A/SAC-96-03, SAC Joint Venture, Sacramento, Moment Connections with Reduced Beam Section,
CA, 1997. Report No. SSRP-99/21, Department of Structural
9-44 SAC, Technical Report: Experimental Investigations Engineering, University of California, San Diego, La
of Beam-Column Subassemblages, Parts 1 and 2, Jolla, CA, 1999.
Report No. SAC-96-01, SAC Joint Venture, 9-59 Whittaker, A. S., Uang, C.-M., and Bertero, V. V.,
Sacramento, CA, 1996. "Seismic Testing of Eccentrically Braced Dual Steel
9-45 SAC, Recommended Seismic Design Criteria for Frames," Earthquake Spectra, Vol. 5, No. 2, pp. 429-
New Moment-Resisting Steel Frame Structures, 449, EERI, 1989.
Report No. FEMA 350, SAC Joint Venture, 9-60 Whittaker, A.S. and Gilani, A., Cyclic Testing of
Sacramento, CA, 2000. Steel Beam-Column Connections, Report No.
9-46 Shibata, M., Nakamura T., Yoshida, N., Morino, S., EERC-STI/96-04, Univ. of Calif., Berkeley, 1996.
Nonaka, T., and Wakabayashi, M., Elastic-Plastic 9-61 Whittaker, A.S., Bertero V.V., and Gilani, A.S.
Behavior of Steel Braces under Repeated Axial Evaluation of Pre-Northridge Steel Moment-
462 Chapter 9


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Patients with a large inter-arm SBP difference need a vascular assessment, because they may develop more complex vascular disease. Those with inter-arm SBP differences of ≥10 mmHg are at greater[s2If !is_user_logged_in()]…
[/s2If][s2If is_user_logged_in()] vascular disease risk and those with differences of ≥15 mmHg are at a greater risk of dying.
"Initial assessment of people with a higher risk of PVD such as smokers and diabetics should include blood pressure measurements of both arms."
-Safraj Shahul Hameed, BDS, MSc, DPH, senior research fellow, Centre for Chronic Disease Control (CCDC), New Delhi, India
Safraj Shahul Hameed, BDS, MSc, DPH, senior research fellow, Centre for Chronic Disease Control (CCDC), New Delhi, India, said that the study has particular relevance for your patients since the latest estimates show that 26% of Indians suffer from uncontrolled hypertension. "This meta-analysis of 28 studies indicates that blood pressure measurements should be done in both arms and that differences could indicate increased risk of PVD," Hameed told mdCurrent-India. "Initial assessment of people with a higher risk of PVD such as smokers and diabetics should include blood pressure measurements of both arms."
Early detection essential
Many patients do not know that they have peripheral vascular disease (PVD), and PVD is a major risk factor for cardiovascular disease and death. When detected early, patients can make lifestyle changes to improve their health. You and your patients can work together to improve their vascular health through steps such as stopping smoking, improving diet, controlling diabetes, controlling high cholesterol, controlling blood pressure, decreasing obesity, exercising, and decreasing stress.
Task Force for the Management of Arterial Hypertension of the European Society of Hypertension (HTN) and of the European Society of Cardiology advised in 2007 that arm SBP differences are due to PVD. Other studies have suggested that differences of more than 10 mmHg lead to poor patient results.
The authors of this study assessed the connection between inter-arm SBP differences and death, and central or peripheral vascular disease. In an invasive assessment using angiography for patients with more than 50% occlusion of the subclavian artery, there was a mean SBP difference of 37 mmHg. A difference of ≥10 mmHg was strongly linked to subclavian stenosis. This was both clinically and statistically significant (P<0.0001). In patients who were evaluated by non-invasive methods, a difference of ≥15 mmHg was associated with PVD, pre-existing cerebrovascular disease, increased cardiovascular mortality, and all-cause mortality. Differences of ≥10 mmHg were also linked to PVD.
Source: Clark CE, Taylor RS, Shore AC, Ukoumunne OC, Campbell JL. Association of a difference in systolic blood pressure between arms with vascular disease and mortality: a systematic review and meta-analysis. Lancet Online January 30, 2012 DOI:10.1016/S0140-6736(11)61710-8.
Access the original journal information here:
Journal publishers are independent from mdCurrent-India and may require a subscription or charge a fee to download the full article.


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