Seismic Performance and Design of Japanese Steel ChevronBraced Moment-Resisting Frames
Ilanildo DIAS
Candidate for the Degree of Doctor of Engineering
Supervisor: Professor Dr. Taichiro Okazaki
Division of Architectural and Structural Design

1. Introduction
Steel braced frames are widely used for buildings in highseismicity regions due to their versatility in meeting stiffness
and strength requirements. Japanese engineers often choose
to place the braces in a “chevron” (or V or inverted-V)
arrangement within a moment-resisting frame (MRF). In such
systems, hereafter referred to as chevron-braced MRFs, thedesign of the beam intersected by braces poses a design
challenge because this beam yields due to forces delivered by
the tension and compression braces in combination withforces produced by moment-frame action. The energy
dissipating mechanism of chevron-braced MRFs is dependent
on the loading history due to the statically indeterminate
nature of the structural system and highly complex cyclicloading response of the steel braces. Despite the very wideuse, limited design guidance is provided by the Japanesedesign codes and standards on how to proportion the beams
and braces and how to detail the bracing connections. The
lack of guidance has allowed engineers to choose a very wide
variety of designs, and this situation is at least partly
responsible for the damage observed in steel chevron-braced
MRFs after even the most recent earthquakes.
In order to address the above-mentioned concerns, acomputational study was conducted with the following
objectives: (1) to further the understanding of the seismic
performance of steel chevron-braced MRFs, and thereby
identify design concerns; (2) to derive proportion rules for thebeams and braces in steel chevron-braced MRFs; (3) to derivebracing requirements to control the beam intersected bybraces against severe transverse forces and torsional moments
delivered by the braces, in addition to bending moments
produced by moment-frame action; and (4) to assess theseismic performance of Japanese steel buildings that employ
steel chevron-braced MRFs.

2. Plastic Mechanism and Plastic Strength
As shown in Fig. 1, chevron-braced MRFs may be
decomposed into a pair of braces, placed in angle α withrespect to beams, and an MRF. The lateral strength of thebraced frame, 𝐻, may be considered the sum of contributionsof the MRF, 𝐻𝑓 , and of the pair of braces, 𝐻𝑏 , such that 𝐻 =𝐻𝑏 + 𝐻𝑓 . The values 𝐻𝑏 and 𝐻𝑓 depend on the energydissipation mechanism developed by the system. Conversely,
the Japanese building code recognizes the proportion oflateral strength carried by the braces, β , as an importantdesign parameter that dictates the ductility category of thestructural system.
Many countries detail braced frames as concentricallybraced frames (CBFs) that are detailed to resist the entire
lateral force by braces. Khatib et al.1) explained that,
depending on the strength of the beam intersected by braces,
chevron CBFs can fail in one of two mechanisms: A “weakbeam” mechanism will form if the beam yields in the middle
due to the force unbalance before the tension brace develops
its yield strength; A “strong-beam” mechanism will form if
the tension brace develops its yield strength while the beamremains elastic. Assuming that yielding of the column andcolumn panels are prevented, the contribution of the pair ofbraces to the lateral strength of the chevron-braced MRFs,
β0 = 𝐻𝑏 ⁄𝐻 , for each mechanism can be expressed as follows:
Strong- beam mechanism:(1 + 𝑥)𝑟0
2 + (1 + 𝑥)𝑟0
𝜅 + 𝑥 ∙ 𝑟0
β0 =2 + 𝑥 ∙ 𝑟0β0 =Weak-beam mechanism:

(1)
(2)

In the above equations, 𝑟0 = (𝑁𝑦 ℎ cos α)⁄(𝑀𝑝 ) is ameasure of the relative horizontal strength of the braces withrespect to the beam, 𝑥 = 𝑁𝑢 ⁄𝑁𝑦 is the compression-totensile strength ratio of the brace, κ, 1 ≤ κ ≤ 2, is the limiting
value for the ratio of the maximum possible force unbalance,
𝑉𝑚𝑎𝑥 = (𝑁𝑡 − 𝑁𝑢 ) sin α , over the plastic resistance of thebeam, 𝑉𝑏0 = 4𝑀𝑝 ⁄𝑙 , when subject to reverse end moments
𝑀𝑝 . The strong-beam mechanism controls when 𝑟0 ≤2κ⁄((1 − 𝑥)) and the weak-beam mechanism controls
otherwise. In reality, when 2⁄(1 − 𝑥) ≤ 𝑟0 ≤ 2κ⁄(1 − 𝑥) ,the braces and the beam may both yield to form a combined
mechanism. Fig. 2 shows the relationship between β0 and
𝑟0 for κ = 1.0 and 1.5, computed for three different valuesof brace slenderness ratio, λ 40, 80, and 120. The figure
shows that, regardless of λ , β0 is a monotonicallyκ = 1.51

λ = 80λ =1200.8

λ = 40λ = 400.6
λ =120λ = 80κ = 1.0

0.4
0.2

h

α

0
0

2

4

6

8

10

l

Fig. 1. Strength decomposition of chevron-braced MRFs.

Fig. 2. Relationship between β0 and 𝑟0 .

12

3. Numerical Model and Validation
The general-purpose finite-element-method (FEM)
analysis software ADINA2) was used to carry out numericalsimulation. Fig. 3 outlines a typical 3D model. The modelcomprised 4-node quadrilateral shell elements with 6 degreesof-freedom per node, 4 integration points in plane and 5
integration points across thickness. Material nonlinearity wasincorporated by the von Mises yield condition and an
associated flow rule. Cyclic hardening was accounted for by
the Armstrong-Frederick combined nonlinear isotropic andkinematic hardening rule calibrated against material tests on
Japanese SN 400 and SM 490 steel by Yamada et al.3).
Loading and boundary conditions were according to tests
by Seki et al. 4). Load was applied at the top end of the North
column in displacement control. Numerical simulation
reproduced the experimental behavior by Seki et al. 4) quite
adequately, from brace buckling, formation of a weak-beammechanism, deformation of the beam intersected by braces,
and local flange deformation of the beam at plastic hinges.

4. Beam Bracing Requirements
The beam intersected by braces is subjected to large
horizontal and vertical forces and torsional moment deliveredby the braces. A parametric study was conducted to examine
the lateral bracing requirements for this beam. Models ofSpecimens 4, 5 and 6 by Seki et al.4) were perturbed withspring stiffnesses 𝐾𝑅 and 𝐾𝐻 at the brace-to-beam joint
equal reference values 𝐾𝑅0 or 𝐾𝐻0 times 0, 1 or ∞, where
𝐾𝑅0 and 𝐾𝐻0 are the theoretical stiffness of the beam. The 3
specimens represented cases with large braces with respect tothe beam with β0 = 0.83 to 0.86 and different bracing
connections: Specimens 4 and 5 supplied large rotational
fixity while Specimen 6 supplied small rotational fixity;
Specimens 4 and 6 oriented the braces to buckle out of plane
while Specimen 5 oriented the braces to buckle in plane.
Fig. 4 plots for Model 4 employing case (e) 𝐾𝑅 = ∞ &𝐾𝐻 = ∞, the torsional moment delivered to the beam by eachbrace over the loading history. The moments were negligible
until the brace buckled, after which the moments grew larger
with increasing loading amplitude. The compression andtension braces delivered moment in opposing direction
because the two braces were forced by the rigid bracing
connections to buckle in the same out-of-plane orientation.
ux uy uz θx θy θz

Fig. 5(a) plots for Model 4 employing cases (a) 𝐾𝑅 = 0& 𝐾𝐻 = 0, (d) 𝐾𝑅 = 𝐾𝑅0 & 𝐾𝐻 = 𝐾𝐻0 , and (e) 𝐾𝑅 = ∞& 𝐾𝐻 = ∞, the torsional moment delivered to the beam by
the braces, T, against the story drift angle. The yielding
torsional moment, 𝑇𝑦 , of the beam is shown for reference.
Model 4a which resisted torsional moment solely by thebeam, drew a large moment of 1.04 𝑇𝑦 . Model 4d drew
substantial moment of 0.61𝑇𝑦 , of which the moment resistedby the rotational spring was 0.37𝑇𝑦 . Model 4e drew 1.24Ty,
but the moment was nearly fully resisted by the springs. Cases(d) and (e) developed the maximum torsional moment when
the second brace buckled. Fig. 5(b) shows the monotonic
loading response of the same Model 4. Model 4e drew
torsional moment much greater than 𝑇𝑦 because the tension
brace remained completely straight and did not cancel the
moment delivered by the compression brace. In comparison,
Models 4a and 4d drew much smaller moment because thebeam twisted and thereby allowed the tension brace toproduce a cancelling moment. Although not included in the
figures, Model 5, which had the braces oriented to buckle inplane, and Model 6, which adopted a flexible bracing
connection, drew small torsional moment from the braces for
all lateral bracing cases.
The results suggest that a lateral bracing system thatprovides 𝐾𝑅 = 𝐾𝑅0 and 𝐾𝐻 = 𝐾𝐻0 at the brace-to-beamnode can effectively restrain twist and out-of-plane deflectionof the beam. Interestingly, although the results showed thatthe lateral bracing cases lead to substantial difference intwisting and out-of-plane deformation of the beam intersectedby braces, the bracing cases had negligible effect on theoverall cyclic performance of the models (Fig. 6).
For chevron-braced MRFs employing rigid bracing
connections and with the braces oriented to buckle out ofplane, as in Model 4, the torsional moment demand on the
beam may be evaluated based on three different conditions:(1) immediately after brace buckling, 𝑇1 ; (2) at large story
drift, say ±0.02 rad which is a typical design limit inengineering practice, 𝑇2 ; and (3) at large story drift but
assuming unidirectional loading stroke such that second bracebuckling does not occur, 𝑇3 . The torsional moment deliveredby the braces maybe decomposed into four components, twoTorsional Moment [kN.m]

increasing function of 𝑟0 . Larger κ leads to larger β0. A key
design issue is that κ varies depending on the loading history
experienced by the system.

South Brace

North Brace±0.002 ±0.00375 ±0.005 ±0.0075 ±0.01 ±0.015±0.02 ±0.03 ±0.04

RR F F RR[rad]Loading Cycle

Fig. 4 Torsional moment delivered by each brace for Model 4e＋ux uy uz θx θy θz
RR F RRRy
Not present inSeki et. al [4]

x

z

South

ux uy uz θx θy θz
F R F RRRux uy uz θx θy θz

North

RF F RRR

F - fixed
R - released

Fig. 3. CBF FE Numerical model

Torsional Moment, T [kN.m]

－

8

(a)

4

8

4a

Ty

0
-4

–Ty

4d

4e

-8
-12
-0.04

–T11
–T

-0.02

(b)

4

0

0.02

0

4a

–T22
–T

4d

-8

4e

-4

-12
0.04
0

0.01

0.02

0.03

–Tyy
–T
–T33
–T

0.04

Story Drift Angle [rad]Fig. 5 Torsional moment delivered by the braces: (a) Model 4; (b)Model 4 under monotonic loading

250
0

4a
4d
4e

-250

(b)

(a)

-500
-0.04 -0.02

0

0.02

0.04 00.02

0.04

Story Drift Angle [rad]Fig. 6. Effect of lateral bracing on the behavior of Model 4: (a)cyclic loading; (b) monotonic loadingfrom each brace: the product of brace axial force andeccentricity between line of action of the deformed brace andbeam centroid; and out-of-plane bending moment in thebrace. The following equations are proposed:
𝑇1 = 𝑁𝑐𝑟 × 𝑒𝐶1 + 𝑀𝐶1(3)

𝑇2 = 0.3𝑁𝑐𝑟 × 𝑒𝐶2 + 𝑀𝐶2 − 𝑁𝑡,max × 𝑒𝑇2 − 𝑀𝑇2(4)

𝑇3 = 0.3𝑁𝑐𝑟 × 𝑒𝐶2 + 𝑀𝐶2(5)𝑁𝑡,max = min. {(κ4𝑀𝑝 1∙+ 0.3𝑁𝑐𝑟 ), 𝑁𝑦 }𝑙 sin α(6)In the above equations, 𝑀𝑇 and 𝑀𝐶 are the out-of-planebending moment at the end of the tension and compression
brace, respectively, computed from the flexure-and-axial
force interaction equation; 𝑁𝑡,max is the maximum tensile
force that the brace can develop4), where, in this study, κ =1.5; and 𝑒𝐶 and 𝑒𝑇 are the eccentricity of the compression
and tension braces, respectively. Further, 𝑇1 assumes thatthe compression brace maintains a relatively large force of
𝑁𝑐𝑟 while the tension brace is straight, and therefore, delivers
zero torsional moment; 𝑇2 assumes that the tension brace isdeformed out of plane, and therefore, delivers cancelling
torsional moment; 𝑇3 assumes that the tension brace has
never buckled, and therefore, delivers zero torsional moment;
𝑇2 and 𝑇3 sample the brace eccentricity at a story drift of±0.02 rad, and assumes that the force in the compressive
races has reduced to 0.3 × 𝑁𝑐𝑟 . The computed torsional
moments are indicated in Fig. 5. For cyclic loading, 𝑇1 wasconservative but 𝑇2 was close to simulation. For monotonic
loading, 𝑇3 was conservative by 15%.

the round-HSS braces and from 62 to 145 for the I-section
braces. The relative lateral strength of the braces with respect
to the beam, 𝑟0 , ranged from 1.3 to 11.3 to cover a wide
range of possible mechanisms. The plastic mechanism andβ0 values assumed κ 1.5. Except for Models 8, 10 and 11,
the weak-beam mechanism was expected to control. The
adequacy of κ 1.5 is examined later.
Each model was subjected to monotonic or cyclic loading:
Monotonic, Cyclic-1 and Cyclic-2: Cyclic-1 was the loading
sequence specified for prequalification of MRFs5), adopted by
Seki et al.4); Cyclic-2 was based on the near-fault loading
protocol7) but scaled to two third of the original amplitude.
Cyclic-2 contained two occurrences of negative 0.013 rad andpositive 0.04 rad and otherwise smaller cycles skewed topositive drift.
Fig. 7 plots, for all 16 models, the proportion of the lateralstrength carried by the brace, 𝐻𝑏 ⁄𝐻 , against 𝑟0 . The values
𝐻𝑏 ⁄𝐻 were sampled at 0.02 rad for Monotonic, the end of
the first positive excursion at 0.02 rad for Cyclic-1, and at thefirst 0.04 rad for Cyclic-2. The figure indicates the energydissipation mechanism, either strong-beam, weak-beam, or
combined mechanism, identified based on whether the bracetensile force reached 𝑁𝑦 , the force unbalance between thebraces, 𝑉𝑏 , exceeded 𝑉𝑏𝑚 , or both occurred, where 𝑉𝑏𝑚 isthe maximum force unblance that the beam can sustain given
the end moments, without developing 𝑀𝑝 at the brace-tobeam node. The figure also indicates β0 computed for κ
1.0 and 1.5. The sampled 𝐻𝑏 ⁄𝐻 lied between β0 assuming
κ 1.0 and 1.5: close to β0 assuming κ 1.5 for Monotonic,
but somewhat smaller than β0 assuming κ 1.0 for Cyclic1. With no exception, the sampled 𝐻𝑏 ⁄𝐻 was largest for
Monotonic and smallest for Cyclic-1. When the strong-beammechanism controlled, the sampled 𝐻𝑏 ⁄𝐻 was close to β0 ,1
Combined

0.8
0.6

Sampled

Story Shear [kN]500

β0 for = 1.5

2,
1,
3

= 1.0

8 79

11

0.4

Monotonic
Cyclic-1
Cyclic-2

0.2
0
0

2

4

6

8

10

12

5. Beam Proportion Rule
Sixteen models were used to examine chevron-braced
MRFs over various proportions and bracing connections.
Models 1 to 6 were according to Specimens 1 to 6 reported by
Seki et al.4), but with the eccentricity at the column supports
eliminated. The centroidal distance between the beams was
kept constant at h 2,300 mm, but the centroidal distance
between columns was l
3,000, 4,600 or 6,570 mm, toproduce a brace placement angle of α 57°, 45° or 35°. Eitheran H-250×125×6×9 or H-300×150×6.5×9, which differed by
1.4 in plastic strength, was used for the beams. One of six
sections, a round-HSS with D/t of 18.2 or 27.3 or an I-section
with bf/2tf in the range between 4.2 and 7.8, and d/tw in therange between 8.4 and 23.4, was used for the braces. Eitherof the 6 bracing connections examined by Seki et al.4) wereused. The brace slenderness ratioλranged from 70 to 131 forFig. 7 Sampled 𝐻𝑏 ⁄𝐻 versus 𝑟0 .
1

1

Monotonic
Cyclic-1
Cyclic-2

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

(a)

0
0

0.2

0.4

0.6

0.8

0
1 0

(b)
0.2

0.4

0.6

0.8

Fig. 8 Sampled 𝐻𝑏 ⁄𝐻 versus β0 assuming different κ: (a) κ
1.5; and (b) κ 1.25.

1

6. Seismic Design
A series of 4-, 8-, and 12-story office buildings were
designed. Fig. 9 shows the layout of the 4-story building. The
members were proportioned for Level-2 design requirementsof the Building Standard Law of Japan. Uniformly distributed
dead load of 8 kN/m2, live load of 2.4 kN/m2, and tributary
floor width of 7.5 m were assumed to compute the gravity
loads and masses. All stories were designed for the same 𝐷𝑠 ,although some of the upper stories qualified for smaller 𝐷𝑠 .
Different types of steel braced frames were designed: (A)a chevron-braced CBF following earlier Japanese regulations,assuming the brace develop the same strength 𝑁𝑐𝑟 in tension
or compression, and therefore neglects the interaction
between the braces and the beam; (B) a chevron-braced CBF
assuming the brace develops 𝑁𝑡 in tension and 𝑁𝑢 = 0.3𝑁𝑐𝑟
in compression; and (C) a CBFs where the entire lateral load
is resisted by chevron braces, brace develops 𝑁𝑦 in tension
and 𝑁𝑢 in compression, and the beam is proportioned toremain elastic. Types (A) and (B) employ rigid beam-tocolumn connections and column base connections. Type (C)employ simple beam-to-column connections and column baseconnections. All designs were repeated for 2 different bracing
connections: a flexible or rigid connection, representing the
US and Japan, respectively. Types (A) and (B) were designed
for 𝑟0 = 1.0, 2.0, 4.0 and 8.0. The resulting target β 0 were0.37, 0.50, 0.73 and 0.85 for Type (A), and 0.37, 0.50, 0.83
and 0.87 for Type (B), respectively. Type (C) was, by nature,β β0 = 1.0. For 𝑟0 = 4.0 and 8.0, a weak-beam mechanism
was expected.
For the 4-story systems, Type (A) and (B) with r0 2.0
resulted in very similar designs.
All braces employed a circular tube section. The brace
slenderness ratio ranged from 36 to 104 for the 4-story
systems, 24 to 88 for the 8-story systems, and 24 to 128, forthe 12-story systems.
For all the cases, Type (C) required larger steel tonnage
than both A or B. Type C was designed such that the entire

Round-HSS

Tubular-HSS

4@4m

but when the weak-beam mechanism controlled, the sampled
𝐻𝑏 ⁄𝐻 was between 0.89 and 1.06β0 , 0.74 and 0.92β0 , and0.85 and 1.02β0 , assuming κ 1.5, for Monotonic, Cyclic-1
and Cyclic-2, respectively. Monotonic and Cyclic-2 tended tostretch the tension braces more than Cyclic-1, and thereby
develop larger unbalance force to promote a weak-beammechanism. Cyclic-1 tended to produce smaller unbalance
force than predicted, and thereby, allow the MRF to develop
larger lateral strength than predicted. Models 1 to 3 and 7 to
9, with 2.8 ≤ 𝑟0 ≤ 4.1 , did not necessarily develop thepredicted mechanism. Except for Model 8, Cyclic-1 produced
the same mechanism as predicted, but Monotonic and Cyclic2 caused disagreement in more models: Models 1, 2, 3, 7 and
9, which were predicted to develop a weak-beam mechanism
instead developed a combined mechanism.
Fig. 8 explores the appropriate design value for κ byplotting the predicted β0 against the sampled 𝐻𝑏 ⁄𝐻 fromthe 3 loading protocols, assuming κ 1.5, and 1.25. Larger κ
gives larger β0 . The prediction with κ 1.5 matched thesimulation for Monotonic but substantially overpredicted for
Cyclic-1. In comparison, the prediction with κ 1.25 matched
Monotonic and Cyclic-2 but overpredicted Cyclic-1 for mostmodels. A better match over the 16 models and 3 loading
protocols was obtained with κ 1.25: the simulated 𝐻𝑏 ⁄𝐻
was between 0.84 and 1.01β0 for Monotonic, 1.01 and 1.2β0
for Cyclic-1, and 0.88 and 1.05β0 for Cyclic-2.

I-section

12 m

6m

12 m

Fig. 9 Layout of the 4- story building.
“forceBeamColumn”“RigidLink”“Displ. BeamColumn”

Imperfection 0.1%
Gusset Plate“Zero Length Element”

Fig. 10 OpenSees modeling Scheme.

lateral load is carried by the braced frames with the beams andcolumns designed to remain elastic. Compared to Type B with
𝑟0 = 8.0, Type C led to an increase in the steel weight by
148%, 98%, and 99%, for the 4-, 8-, and 12-story systems,
respectively. Between Type A and B, except for 𝑟0 1.0 and
2.0, Type A in general required smaller amount of steel thanType B.
For both Type A and B, designing the braced frame withlarge 𝑟0 value, so that most of the lateral strength is resistedby the braced, leads to lighter braced frame systems.

7. Seismic Performance
The analysis platform OpenSees6) was used to conduct
nonlinear time-history analysis. As shown in Fig. 10, allbraces, and beams were modeled with force-based beamcolumn elements with five integration points according to theGauss-Lobatto quadrature rule. The braces were provided
with an initial imperfection of 0.1% of the brace length.
Between joints, beams were modeled with a single element;
braces were evenly split into two elements. Columns weremodeled with displacement-based beam column element,
evenly split into four elements; Beam and column sections
had each flange and web divided into eight fibers, four inwidth and two in thickness. Brace sections were discretized
into 48 fibers, 12 along circumference and 4 across thickness.
Each fiber was assigned a uniaxial stress-strain relationshipaccording to the Menegotto-Pinto rule with parameters
calibrated based on cyclic-loading material tests by Yamada
et al.3).

600
400

200

200

100

0

0

-200

-100
-200

L/r = 19
D/t=38.8-400-600
Simulated
Experimental
-800
-20
20

(a)

-300
-80

-30

(b)
-10

0

10

20

Axial Displacement [mm]Fig. 11. Simulated versus experimental response for isolated braces.

Story Shear [kN]

400

800

(a)

(b)

200

400

0

0

-200

-400
Simulated
Experimental

-400
-0.04

-0.02

0

0.02

0.04

-800
-0.02

0.00

0.02

Story Drift Angle [rad]Fig. 12
Simulation versus experimental response of the
OpenSees Model: (a) Specimen 2 (Seki et. al [4]), (b) E-Defense
shake table test (Okazaki et al. [8]).

Fig. 11 shows the simulated versus experimental
response4,7,8). For an HSS 76.3×4.2 brace with slenderness
ratio, λ 107, the model accurately captured buckling incompression, yielding in tension, and degradation of thecompressive strength. However, for an HSS 139.8×3.6 bracewith λ 19 the model did not reproduce the substantial
reduction in compressive strength observed in the test
because the fiber elements adopted in this model assumes thatplane section remain plane and hence the effects of local
buckling cannot be simulated. The numerical model was
validated against data from cyclic-loading tests conducted by
Seki et al. [4], and dynamic test conducted by Okazaki et al.
[8]. As shown in Fig. 12(a) and 12(b) , the OpenSees model
reproduced the braced frame behavior as accurately as the
FEM model described earlier.
Therefore, the modeling scheme is highly reliable forbraces where the inelastic response was controlled by global
buckling, but it is not suitable for braces with small λ, inwhich the inelastic response is controlled by local buckling.
As observed by Uriz et al.8), force-based beam-column
elements cannot accurately simulate the degradation of thebrace compressive strength for braces with slenderness ratio
smaller than 40. This suggests that the OpenSees model may
not be suitable to model the response of the mid-rise
structures.
Flexible bracing connections were modelled with a zerolength spring. Rigid bracing connection had the braces rigidly
connected at the ends. At the beam-brace-column joints, thecolumn panel zone and segments stiffened by gusset plates,
shown by thick black lines in Fig. 10, were modeled withelastic elements ten times the area and moment of inertia of
the connecting member.
Fig. 13 plots the base shear coefficient versus roof drift
angle obtained from nonlinear pushover analysis of the 4 story models employing flexible bracing connections. Thebase shear exceeded the design base shear, 𝑄𝑢𝑛 , by a factorof 1.17 to 1.62 for the 4-story systems, 1.06 to 1.74 for the 8story systems, and 1.12 to 1.62 for the 12-story systems. Story
drift ratio (not shown here) was distributed uniformly for the
4-story systems but concentrated in the bottom stories for the
8- and 12-story systems. The pushover analysis produced
similar results between Type (A) and (B) with 𝑟0 = 2.0, but
Type (B) with 𝑟0 = 8.0 developed up to 38%, 65%, and 28%
greater strength than Type (A) for the 4-, 8-, and 12-story
systems, respectively.
The models were subjected to a suite of 28 pairs of nearfield ground motions using the procedure described in FEMA
P6959). The ground motions were scaled to match theJapanese Level-2 and Level-3 design spectrum over a periodof 0.2𝑇1 to 2𝑇1 , as shown in Fig. 14. The constant average
acceleration scheme with time increment 0.001s was used for
integration over time. Rayleigh damping with a critical
damping ratio 0.02 was assigned to the first two modes.
Seismic mass was computed as 100% of dead load and 25%of live load. The computed periods of the 4-story systems
ranged from 0.41s in Model C to 0.67s in Model B with 𝑟0 =2.0. For the 8- and 12-story systems the period ranged from
0.86s and 1.17s in Model C to 0.90s and 1.29s in Model A
with 𝑟0 = 2.0, for the 8-, and 12- story systems, respectively.
All models developed large normalized median peak story
shear. For the 4-story systems employing flexible connections,the normalized median peak story shear ranged from 1.39 in
A with 𝑟0 = 8.0 to 1.72 in B with 𝑟0 = 8.0. The braced frame
models designed with Type (A) did not develop theirpredicted plastic strength, H, for all the cases considered using
either the flexible or the rigid bracing connections. For Type(B), the median base shear equaled the predicted plastic
strength for 𝑟0 = 2.0, but for 𝑟0 = 4.0 and 8.0 and Type (C),0.75
Base Shear Coefficient

L/r = 107.5
D/t=18.2

300

Axial Force [kN]

800

Type CType B,
Type B,

0.5

Type A,

0.25

Type A,

0
0

0.01
0.02
0.03
Roof
Drift
[rad]
Roof
drift
Angle
[rad]

0.04

Fig. 13 Pushover response of the 4-story systems.
4

Spectral Acceleration (g)400

Indiv. record
Target Spectra
Mean3

Period range forground motion
scaling;

2

1

0
0

1

2
Period [sec]3

4

Fig. 14 Acceleration response spectra for the 4-story systems.

the median base shear was close to 0.96H, 1.09H, and 1.52H,
respectively, for the 4-story systems, 1.16H, 1.39H and 1.57H,
respectively, for the 8-story systems and 1.02H, 1.10H and1.51H, respectively, for the 12-story systems. The larger
lateral resistance is justified due to the response of the braces
in compression, the post-buckling strength of the braces was
significantly larger than the 0.3× 𝑁𝑐𝑟 assumed in design.
Fig. 15 plots the median and the 84th percentile drift
demands of all the braced frame models under level-2 groundmotions. For all the braced frame systems, the median story
drift demand was smaller than 0.02 rad for all cases. The story
drift demands were similar between Type (A) and (B) for 𝑟0 =2.0, but the demand for Type (A) was notably greater for 𝑟0 =4.0 and 8.0. Type (C) developed smaller drift demands thanany of subcases of (A) or (B). For the 4-story systems, except
for Type (C), the 84th percentile of the maximum drift
exceeded 0.02 rad for all the cases, but Type (B) with 𝑟0 =4.0 and 8.0 had lower 84th percentile drift demands and show
more uniform distribution of the drift. Although designed forthe same base shear coefficient, the median and 84th
percentile demand was significantly smaller for the 8- and 12story systems. This can be attributed to two factors: (i) as
discussed previously, some braced frame cases developed
larger lateral resistance than the predicted plastic strength;and (ii) the suite of ground motions was less severe for the 8and 12-story systems because, as seen in Fig. 14, the groundmotions were scaled over periods beyond the constantacceleration domain of the design spectra.
The rigid bracing connection, which lead to stronger brace
frame systems, reduced the story drift demands in up to 14%
in Type (A) and (B) with 𝑟0 = 8.0 and 9% in Type (C).
For the 4-story systems, the strong-beam mechanism(SB) controlled the energy dissipation mechanism for 82 %of the ground motions for Type (A) and for nearly all theground motions for Type (B) with 𝑟0 = 2.0 and Type (C).
The combined mechanism controlled the inelastic response of
the frames under most of the ground motions for Type (A)with 𝑟0 = 4.0 and 8.0, and Type (B) with 𝑟0 = 4.0, but in only
61% of the ground motions for Type (B) with 𝑟0 = 8.0, withthe weak-beam mechanism controlling for the remaining
ground motions.
Regardless of the design approach and 𝑟0 , the rigid
bracing connection forced yielding of the braces for morecases than the flexible bracing connection.

monotonic pulses and develops a smaller value close tounity under gradually increasing cyclic loading. Rather
than the value κ 1.5 previously used by Seki et al.4), κ
1.25 was more representative over the examined
proportions and loading sequences and better matched thetest results by Seki et al.4).
4. Nonlinear time history analysis suggest that all the brace
frame systems meet the design requirements stipulated by
the Japanese code. For the 4-story systems, the fictitious
mechanism assumed in Type (A) caused no adverse
design result for 𝑟0 smaller than 2.0. For 𝑟0 larger than
2.0, Type (B) showed better seismic performance.
5. The braced frame models with 8- and 12-story systems,
cannot be appropriately modelled using the modelling
scheme discussed here. Japanese mid-rise braced frames
require braces with small slenderness ratio, where theinelastic response is controlled by local buckling. If used,
the lateral strength of the braced frames may besignificantly larger than expected from design.

References[1] I. F. Khatib et al., Seismic behavior of concentrically braced
steel frames, PEER Report 1988/01, Berkeley, CA, USA,(1988).
[2] ADINA R&D, Inc. Theory and Modeling Guide. ADINA 9.3,
(2017).
[3] S. Yamada, et al., Simple hysteresis model of structural steel
considering the Bauschinger effect, J. of Struct. and Const.
Eng., AIJ, 559 225-232, (2002). (In Japanese)[4] A. Seki, et al., Seismic performance of steel chevron braced
frames designed according to Japanese practice, J. Const.
Steel Res., 189, 107066, (2022).
[5] AISC 2016, Seismic provisions for structural steel buildings,
in: ANSI/AISC 341-16, (2016).
[6] F. McKenna, Object oriented finite element programing
frameworks for analysis, algorithms and parallel computing.
Ph.D. thesis, UC Berkeley, California, (1997).
[7] I. Raheem et al., Cyclic loading performance of squat braces-Part 1 Test program and results-, Summaries of TechnicalPapers of Annual Meeting, Structural III, 981-982, (2022).
[8] T. Okazaki, et. al., Dynamic Response of a Chevron
Concentrically Braced Frame, J. of Struct. Eng., vol. 139, no.
4, pp. 515–525, 2013.
[9] P. Uriz et. al., Model for cyclic inelastic buckling of steel
braces, J. Struct. Eng. ASCE, (2008).
[10] FEMA P-695, Quantification of Building Seismic
Performance Factors, FEMA ATC, Washington, US, (2009).

8. Conclusions
3.0

4-Story

8-Story

12-Story

2.0
1.0

Story drift (rad)A numerical study was conducted to examine the seismic
performance of steel chevron-braced MRFs. The torsional
moment delivered by the braces, and the lateral force
resisting system of the system were analyzed. In addition,
the performance of Japanese steel buildings designed using
three different design assumptions, different 𝑟0 values andtwo different bracing connections was investigated. The
main findings are summarized as follows:
1. Lack of lateral bracing of the beam intersected bybraces can lead to severe twist and out-of-plane
deflection of the beam but may not affect the lateralload resistance of the chevron-braced MRF system.
2. A minimum bracing requirement for the beamintersecting the braces at midspan that provides aminimum stiffness equal to the theoretical translation
and rotational stiffness of the beam was recommended.
3. The factor κ changes over the loading sequence, but
generally reaches 1.5 under monotonic loading or large

Median84th Percentile

0.0
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

3.0

4-Story

8-Story

12-Story

2.0

1.0
0.0
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

β0 = Hb/H

Fig. 15 Median peak SDR demands: a) flexible connection; b) rigid
connection.