1. CMC/2023
Emerging Structural Technologies 1
Dr Christian Málaga-Chuquitaype (c.malaga@imperial.ac.uk)
Emerging Structural Technologies and Design | Civil and Environmental Engineering
Seismic design of steel structures /
Diseño sísmico de estructuras de acero
Pórticos con arriostres excéntricos
Dr Christian Málaga-Chuquitaype (c.malaga@imperial.ac.uk)
Emerging Structural Technologies and Design | Civil and Environmental Engineering
• Framing system with beam, columns and braces. At least one end
of every brace is connected to isolate a segment of the beam called
a link.
• Resist lateral load through a combination of frame action and truss
action. EBFs can be viewed as a hybrid system between moment
frames and concentrically braced frames.
• Develop ductility through inelastic action in the links.
• EBFs can supply high levels of ductility (similar to MRFs), but can
also provide high levels of elastic stiffness (similar to CBFs)
Eccentrically Braced Frames (EBFs)
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Inelastic Response of EBFs
Energy Dissipation Mechanisms
MRF CBF
EBF
• Design frame so that inelastic behavior is
restricted to links.
§ Links are "fuse" elements of frame.
§ Links are weakest element of frame.
All other frame elements (braces,
columns, beam segments outside of
link, connections) are stronger than
links.
• Detail links to provide high ductility
(stiffeners, lateral bracing).
Design of EBFs - General Approach
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• Link plastic rotation angle
• Forces in links
• Shear vs flexural yielding links
• Link nominal strength
• Post-yield behavior of links
• Examples of experimental
performance of links
EBFs – Link Behavior
Link Behavior: Forces in Links
M
V
P
e e
Will link plastic strength be
controlled by shear or
flexure?
Link length "e" is key parameter
that controls inelastic behavior
Link Behavior: Shear vs Flexural Yielding Links
e
V V
M M
V
M
M
Shear yielding will occur when V
= Vp and M < Mp
or, when:
shear yielding of web along
entire length of link
e ≤
2Mp
Vp
e
Vp Vp
M M
V =Vp
M < Mp
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Flexural yielding will occur when
M = Mp and V < Vp
or, when:
flexural yielding at link ends
e ≥
2Mp
Vp
e
V V
Mp Mp
V <Vp
M = Mp
M = Mp
Simple Plastic Theory (assumes no strain hardening and
no shear - flexure interaction)
SHEAR YIELDING LINK:
FLEXURAL YIELDING LINK:
Shear vs. Flexural Yielding Links
e ≤
2Mp
Vp
e ≥
2Mp
Vp
PREDOMINANTLY SHEAR YIELDING LINK:
PREDOMINANTLY FLEXURAL YIELDING LINK:
COMBINED SHEAR AND FLEXURAL YIELDING:
Post-yield behavior of links
e ≤
1.6Mp
Vp
e ≥
𝟑.𝟎Mp
Vp
1.6Mp
Vp
≤ e ≤
3.𝟎Mp
Vp
Provide best overall structural performance for:
• strength
• stiffness
• ductility
Shear Yielding Links
𝒆 ≤
𝟏. 𝟔𝑴𝒑
𝑽𝒑
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V
e
Link Deformation: (radian)
Δ
γ =
∆
e
Experimental Performance of Shear Links
Engelhardt & Clayton
Experimental Performance of a Shear Link
W10x33 (A992) e = 23" = 1.1 Mp/Vp
Engelhardt & Clayton
Experimental Performance of a Shear Link
W10x33 (A992) e = 23" = 1.1 Mp/Vp
Engelhardt & Clayton
Experimental Performance of a Shear Link
W10x33 (A992) e = 23" = 1.1 Mp/Vp
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Emerging Structural Technologies 8
Experimental Performance of a Shear Link
W10x33 (A992) e = 23" = 1.1 Mp/Vp
gp = ± 0.10 rad
Experimental Performance of a Shear Link
W10x33 (A992) e = 23" = 1.1 Mp/Vp
• Longer links provide less strength, stiffness
and ductility
• Use longer links only when needed for
architectural constraints
e >
1.6Mp
Vp
Longer Links
Experimental Performance of a Flexural Yielding Link
W12x16 (A36) e = 44" = 3.4 Mp/Vp
Engelhardt & Clayton
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Emerging Structural Technologies 9
Experimental Performance of a Flexural Yielding Link
W12x16 (A36) e = 44" = 3.4 Mp/Vp
Experimental Performance of an Intermediate (Shear & Flexural Yielding) Link
W16x36 (A992) e = 48" = 2 Mp/Vp
Experimental Performance of an Intermediate (Shear & Flexural Yielding) Link
W16x36 (A992) e = 48" = 2 Mp/Vp
0
0.04
0.08
0.12
0 1 2 3 4 5
Link Length: e/ (Mp/ Vp)
Link
Plastic
Rotation
Capacity:
g
p
(rad)
Shear Yielding Flexural Yielding
Shear +
Flexure
Experimentally Determined Link Plastic Rotation Capacities
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Relación entre la longitud del link y la rigidez lateral del EBF
General Approach
1. Size links for code level forces
2. Size all other members and
connections for maximum forces
that can be generated by links
3. Estimate ductility demand on links;
check that links can supply the
required ductility
4. Detail links to supply high ductility
(stiffeners and lateral bracing)
Design of EBFs
Mult
Mult
Vult Vult
Vult
Mult
Vult
Mult
Espectro de respuesta (acc.) horizontal
0.085 for moment resistant space steel frames,
0.075 for moment resistant space concrete frames and
for eccentric braced steel frames
0.050 for all other structures
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Clasificación Clasificación
where α is the ratio of the absolute value of the smaller-
to-larger bending moments at the two ends of the link.
In designs in which only one plastic hinge forms at one
end in I-sections:
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Demanda de ductilidad
EC8 also provides limits on the rotation θp in accordance with the
expected rotation capacity.
This is given as 0.08 radians for short links and 0.02 radians for
long links, whilst the limit for intermediate links can be
determined by linear interpolation. The code also gives a number
of rules for the provision of stiffeners in short, long and
intermediate link zones.
Diseño por capacidad
However, in this case, Ω is the minimum of the following:
(i) min of Ωi = 1.5 Vp,link,i/VEd,i among all short links, and
(i) min of Ωi = 1.5 Mp,link,i/MEd,i among all intermediate and long links, where VEd,i and MEd,i are the design
values of the shear force and bending moment in link ‘i’ in the seismic design situation, whilst
Vp,link,i and Mp,link,i are the shear and bending plastic design capacities of link ‘i’.
It should also be checked that the individual values of Ωi do not differ from the minimum value by more
than 25% in order to ensure reasonable distribution of ductility.
Connections as well.
Rigidizadores
Specific guidance is given for link stiffeners
in EN1998-1.
Full-depth stiffeners are required on both
sides of the link web at the diagonal brace
ends of the link as indicated in the Figure.
These stiffeners should have a combined
width not less than bf − 2tw and a thickness
not less than 0.75tw or 10 mm whichever is
larger, where bf and tware the link flange
width and link web thickness, respectively.
Rigidizadores
Intermediate web stiffeners in shear links
should be provided at intervals not
exceeding (30tw– d/5) for a link rotation
angle of 0.08 radians, or (52tw– d/5) for
link rotation angles of 0.02 radians or
less, with linear interpolation used in-
between, where d is the section depth.
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Rigidizadores
Flexural links of length greater than 2.6
Mp,link/Vp,linkand less than 5Mp,link/Vp,linkshould be
provided with intermediate web stiffeners
placed at a distance of 1.5 times bf for each
end of the link.
Both requirements apply for links of length
between 1.6 and 2.6Mp,link/Vp,link, and no
intermediate web stiffeners are required in
links of lengths greater than 5 Mp,link/Vp,link.
Rigidizadores
Intermediate link web stiffeners are required to
be full depth.
For links that are less than 600 mm in depth,
stiffeners are required on only one side of the
link web.
.
Estabilidad y deriva de entrepiso
• Inter-storey drift sensitivity coefficient:
• Serviceability
M
V
P
M
V
P
Analysis - Diagonal Brace and Beam Outside of Link
Design of link-to-column
connections should be based
upon cyclic test results that
demonstrate inelastic rotation
capability 20% greater than
that calculated at the design
storey drift. On the other
hand, beam-to-column
connections away from links
are permitted to be designed
as pinned in the plane of the
web.
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Bracing of Link
Bracing shall be provided at both the top and
bottom link flanges at the ends of the link for I-
shaped sections.
