Pushover Analysis
Pushover Analysis
Pushover Analysis
• Types
– Truss - yielding and buckling
– 3D Beam - major direction flexural and shear
hinging
– 3D Column - P-M-M interaction and shear hinging
– Panel zone - Shear yielding
– In-fill panel - Shear failure
– Shear wall - P-M-Shear interaction!
– Spring - for foundation modeling
Pushover Modeling (Properties)
Force-Deformation Relationship
C
B
Force
D E
A
Deformation
Pushover Modeling (Properties)
Force
Deformation
Pushover Modeling (Beam Element)
Three dimensional Beam Element
Shear Hinge
M
Pushover Modeling (Column Element)
Axial Load - Moment Interaction (Steel)
• Limit of analysis
– Instability - loss of gravity load carrying capacity
– Excessive distortions
Pushover Analysis
The magnitude of lateral loads is incrementally increased, until
the displacement at the same point on the structure reaches a
specified target displacement.
Pushover Analysis
Develop pushover (capacity) curve: Plot of base shear vs roof
displacement
Pushover Analysis
With the increase in magnitude of the loads, weak links and
failure modes are found
Pushover Analysis ( Results)
Pushover Analysis
Modal analysis will allow the base shear and displacement of the
structure to be converted to a spectral acceleration and spectral
displacement of the equivalent SDOF structure.
Pushover Analysis
W g
N
W g
2 N
i i ,1 i i ,1
1 i 1
PF1 i 1
N
N
Wi g (Wii ,1 / g )
N
i i ,1
2
(W 2
/ g )
i i 1 i 1
Pushover Analysis
Curve is plotted between spectral acceleration and spectral
displacement .
This slide shows the state of the structure just after gravity loads
are applied but before any lateral load has been applied.
Now the lateral load is applied. The idealized moments in two
potential hinging regions are shown for the lateral load only.
Insufficient lateral load has been applied to cause yielding.
If the member forces from gravity load are added to the member
forces from the lateral loads it is seen that the moment computed
at the right span, right hinge is well in excess of the capacity.
The program performing the analysis will then compute the
fraction of the lateral load, that when added to the gravity load,
causes first yielding in the structure.
Here the total load V is applied to
the structure which has not yet
yielded.
We have applied too much lateral load. Hence, we want to
compute the portion of load, ψV, that just causes the first
yielding.
The pushover curve is not at the state shown, with
only one hinge present.
We now apply the remainder of the load VR = V(1-ψ). We will
want to determine how much of the remaining load causes the
next hinge to form.
The next hinge will occur at the right of the second story
girder of the right bay.
The second hinge is formed and the stiffness is changed.
The remaining load is applied, and the next hinge location is
found.
It appears that the next hinge will form at the right hand side of
the first story girder in the left bay.
The procedure is continued until adequate displacement has been
obtained. A maximum expected displacement would be 3% of the
height of the structure (as this is in excess of the seismic drift limit
in most codes).
In the capacity-spectrum approach it is
necessary to transform the pushover curve
(in Force-Displacement space) into a
Capacity Curve (in Modal Acceleration-
Modal Displacement Space).
Use of Pushover Curve
Spectral Acceleration
Base Shear
Equivalent SDOF
PF is the participation factor and
MDOF
relates the roof displacement to
the SDOF displacement
Use of Pushover Curve (ATC-40)
Constructing Capacity Spectrum
S a V / W / 1
Acceleration
Spectral Displacement
Use of Pushover Curve (ATC-40)
Estimation of Equivalent Viscous Damping
eq 0 0.05
0 (1 / 4 ) * ( ED / Eso )
Acceleration
Spectral
factor
Spectral Displacement
Use of Pushover Curve (ATC-40)
Estimation of Equivalent Damping
Acceleration
Spectral
Eso
Ed Spectral Displacement
Use of Pushover Curve (ATC-40)
Response Spectrum (5% damping)
2.5CA
CV/T
Acceleration
Spectral
Time Period
Use of Pushover Curve (ATC-40)
Response Spectrum (5% damping)
2.5CA/Bs
Acceleration
Spectral
CV/(T BL)
Time Period
Use of Pushover Curve (ATC-40)
Acceleration-Displacement Response Spectrum
T0
Sd = S a T2/42
Acceleration
Spectral
T0
Performance Point
Demand Spectrum for effective
damping at performance point
Acceleration
Spectral
Capacity Spectrum
Spectral Displacement
Use of Pushover Curve (ATC-40)
Spectral Acceleration
Performance Point
Spectral Displacement
Use of Pushover Curve (ATC-40)
Verification of Acceptance
Expected Performance Point
for given Earthquake
Force Measure
Deformation Measure
Use of Pushover Curve (FEMA-273)
C0 C1 C2 C3 S a T /( 4 )
e
2 2
Use of Pushover Curve (FEMA-273)
Estimate Te using Ke
.6Vy
Estimate Elastic Spectral Displacement
Base Shear
Ke
S a T /(4 ) e
2 2
Roof Displacement
Use of Pushover Curve (FEMA-273)
Calculation of C0
Relates spectral to roof displacement
- use modal participation factor for control
node from first mode
- or use modal participation factor for control
node from deflected shape at the target
displacement
- or use tables based on number of stories and
varies from 1 to 1.5
Use of Pushover Curve (FEMA-273)
Calculation of C3
Modifier for dynamic second order effects
Verification of Acceptance
Target Displacement (or
corresponding deformation) for
given Earthquake
Force Measure
Performance Limits
(IO, LS, CP)
Deformation Measure