2. Hossein Agha Beigi & Constantin Christopoulos, Civil
Engineering, University of Toronto, Toronto, Canada.
Timothy Sullivan, Department of Civil Engineering and Architecture,
University of Pavia, Pavia, Italy.
Michele Calvi, UME School, IUSS Pavia, Pavia, Italy.
Authors: 2
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3. GIB system consists pinned brace + gap element
Added to the first story columns of the frame
• Reduces axial load at predetermined rate.
• Increases the post-yield stiffness ratio of the system.
• Reduces/Counteracts the P-delta effects on the
columns, while not increasing the first story lateral
resistance or stiffness
• Increases the lateral deformation capacity of
columns at the first story.
• Protect the upper floors of the structure from damage
by avoiding excessive deformations and reducing the
propensity for collapse.
3
Mechanism used is props and lifts
*Resisting the axial unloading of the existing
columns as the structure sways laterally
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4. 4
Properties of GIB
depends on:
The initial angle of the GIB.
The gap distance.
Mechanical properties of the inclined brace
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5. 5
Beam : 30cm x 50cm. Column
dimensions reduce upto frame height.
Smooth round bars with hooked ends
for anchorage for reinforcement.
Design load on beam 60 KN/m at floor
level and 50KN/m at roof level.
Characteristic yield strength=380MPa.
Compressive Strength=20MPa (conc).
Compressive strength of masonry
Horizontal direction=2.7 MPa
vertical direction=3.84 MPa.
Fundamental period : SS variant and
the GIB variant = 0.78 s, FI variant =
0.32 s.
• SS variant =existing soft story frame, in which masonry infills are
omitted at the ground story but present on all other floors.
• FI variant =considers masonry infills are presented at all levels
(including the ground level.
• GIB variant =SS variant is retrofitted using the GIB system at the
ground level.
• ρs =longitudinal reinforcement ratio.
• CF=confinement factor.
(ratio of the compressive
strength of confined concrete
to that of the unconfined one)
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7. 7
GIB-1L, GIB-1R, GIB-4L, GIB-4R are
exterior columns, share a similar
design and referred to as type GIB-Ex.
GIB-2L, GIB-2R, GIB-3L, GIB-3R are
interior columns, share a similar
design and referred to type GIB-In.
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8. 8
A degraded capacity curve of the desired RC column
is determined.
Degraded capacity curve= envelope of [potential
axial loads (force)–displacement] capacity curves.
It determines, yield resistance, Fy,col,
ultimate resistance, Fu,col,
ultimate drift capacity, θu
critical drift capacity, θcr
(at θcr the lateral resistance starts to degrade)
an ‘effective’ axial force (Peff ) of each column is
determined.
(it will minimize P-delta effects and maximize the lateral
drift capacity of the columns)
• To determine Peff , the maximum lateral drift capacity
v/s range of axial load resulting from analyses in
which P-delta effects were considered.
• Then, the axial load that corresponds to the ultimate
drift capacity of each column Pu is determined
The design procedure of the GIB system for each
column consists of five main steps:
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9. 9
The initial angle of the GIB θGIB, that controls the
lateral resistance, and lateral forces to the upper
floors is determined.
• This selected angle decreases from the yield
resistance (Fy,col) to the ultimate resistance (Fu,col).
The gap distance (Δgap) controls the point at which
the lateral resistance of the existing column starts to
decrease is determined.
The stiffness of the inclined brace defined based on
geometric compatibility between the GIB element
and existing column is determined
• The inclined brace should also be checked for the
buckling resistance.
• Pb = The axial load of the inclined brace
• Pu = The axial load corresponds to ultimate drift
capacity of each column
• P0 = The initial axial force of the column.
From equilibrium condition in vertical direction,
Steel square hollow structural section (HSS) CSA
grade H was used as the inclined brace of GIB.
The specified yield stress was takes as Fy = 350MPa.
Pb = Pu - P0
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10. 10
• The system has a cantilever height of H, and is
subjected to an initial vertical load P0.
• Bernal (1987) showed that as the lateral
displacement Δ increases, the lateral resistance at
the base of this cantilever is reduced according to
the following relationship
Where, Fp and F = lateral resistance of the cantilever
with and without the P-Delta effect,
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11. 11
• Peff to counteracts P-Delta effect for displacements
greater than Δcr. This requires that the reduction of
the lateral resistance (PeffΔ/H) is maintained at a
value as close as possible to P0Δcr/H.
• P-Delta effects are not significant for displacements
smaller than Δcr, Peff is given by
Assume ,
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12. 12
• Moment-rotation relationships for the rotational
spring have been calibrated to experimental results
by Pampanin et al.
Principal tensile stress at first cracking was defined
• Interior
• Exterior
Hardening behavior for the post-cracked area was
assumed
• Interior
• Exterior = zero
The inclined braces were modeled in
SeismoStruct using fiber elements positioned
in series with the nonlinear gap elements.
The contact stiffness of the gap element
100000 kN/mm and provided that the contact
element is modeled as being very stiff.
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13. 13
the comparison of the push over curve of
the six-story frame obtained from the
nonlinear fiber element analysis for the
three different variants: soft story (SS)
variant, full infill (FI) variant and GIB
variant.
o The pushover analysis was run until
either concrete at the core of each
beam column was crushed or the
steel was ruptured
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PUSH OVER CURVE= lateral resistance versus
lateral roof drift ratio)
15. 15
Damage to infill masonry occurs at much lower
levels of drift than traditional RC frame
structures, the lateral roof drift.
Capacity ratio of GIB variant is more than two
times that of the FI variant.
The lateral resistance of the GIB variant is
similar to that of the SS variant, which confirms
that adding the GIB at the first floor of the SS
variant does not increase its lateral resistance.
In second curve , the lateral stiffness of the GIB
variant starts to increase, which indicates that
GIB activates (gap closes) before columns at
the first floor reach their ultimate limit state.
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16. Results from the nonlinear fiber element analysis indicated that the lateral drift capacity of the
GIB variant is significantly increased compared with the other variants, while its lateral stiffness
and resistance are not increased significantly.
Results from the nonlinear dynamic analyses indicated that the lateral drift demand at the first
floor of the GIB variant is significantly greater (almost seven times at the design level) than that
of the full infill variant, but the advantage is that the drift ratio at stories above the first floor are
significantly reduced
16
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