Non Linear Analysis Pushover
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Transcript of Non Linear Analysis Pushover
Introduction
of
Pushover Analysis
“Everything should be made as simple as possible.
But not simpler.”
-Einstein
Overview
1. What is pushover analysis?
2. Why Pushover Analysis ?
3. Analysis Procedure.
4. Examples.
5. Point to be considered.
Push-over analysis is a technique by which a computer model
The intensity of the lateral load is slowly increased and the sequence
Push-over analysis can provide a significant insight into the weak
What is Push-Over Analysis?
What is Push-Over Analysis?
Static Nonlinear Analysis technique, also known as sequential yield
It is one of the analysis techniques recommended by FEMA 273/274
Proper application can provide valuable insights into the expected
Why Push-Over Analysis?
Why Push-Over Analysis?
To get the performance level of structure in case of seismic load.
Elastic analysis cannot predict failure mechanism and account for
Certain part will yield when subject to earthquake.
The use of inelastic procedure for design and evolution is an attempt
Analysis Procedure
SAP2000 NL
Create 3D Model
Assign end offsets
Design Structure
Assign Hinge properties
Beams – M3, V2
Columns –PMM, V2
Define Static Pushover
Cases
Gravity Pushover
(Force controlled) DL+0.25LL
Lateral Pushover
(Displacement controlled)
Define Load case(Lateral Load at centre of mass)
Analyze
Run analysis, Run Now
Pushover Analysis Procedure
Establish Performance point
Base shear Vs Roof Displacement
Sequential Hinge Formation
Modeling of Structural elements
Beams and columns 3D Frame elements
Slab Diaphragm action
(ignore the out of plane stiffness)
Load Assign load to respective member
Beam column joints End offsets (Rigid zone factor 1)
Inclusion of appendages Include water tanks, cantilever slabs
Stairway slabs Transfer load to respective member
Shear Walls Wide Column Elements
Infill walls Equivalent strut method
Foundation
Isolated footings
Single pile
Multiple piles
Plinth beams
Hinged at the bottom of foundation
Fixed at five times the diameter of pile
Fixity of columns at top of pile cap
Frame elements
Modeling of Structural elements
Concrete Properties
• Cube compressive strength, fck ( f’c= 0.8 fck )
• Modulus of Elasticity of concrete ( )
Reinforcing Steel Properties
• Yield strength of steel
• Modulus of Elasticity of steel Es
5000c ckE f
Material Properties
Material Properties
Define - Material
Modeling of Beams and Columns
3D Frame Elements
Cross Sectional dimensions, reinforcement details, material type
Effective moment of inertia
Beams Rectangular 0.5 Ig
T-Beam 0.7 Ig
L-Beam 0.6 Ig
Columns 0.7 Ig
Modeling of Beams
Define – Frame/Cable Sections
Modeling of Columns
Define – Frame/Cable Sections
Modeling of Beam Column Joints
Select Frame Sections
Modeling of Slab
Select Joints at each floor and assign different diaphragm to each
floor
Modeling of Hinge
A performance level describes a limiting damage condition
which may be considered satisfactory for a given building
and a given ground motion.
The limiting condition is described by the physical damage
within the building, the threat to life safety of the building’s
occupants created by the damage, and the post earthquake
serviceability of the building.
The four building performance levels:
1. Operational
2. Immediate occupancy
3. Life safety
4. Structural Stability
Performance Level
Performance Level
Operational: This is the performance level related to
functionality and any required repairs are minor.
Immediate Occupancy: This corresponds to the most
widely used criteria for essential facilities. The building’s
spaces and systems are expected to be reasonably usable.
Life Safety: This level is intended to achieve a damage state
that presents an extremely low probability of threat to life
safety, either from structural damage or from falling or
tipping of nonstructural building component.
Structural Stability: This damage state addresses only the
main building frame or vertical load carrying system and
requires only stability under vertical loads.
Moment Rotation Curve for a Typical
Element
Hinge Property
0
0.2
0.4
0.6
0.8
1
1.2
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
Rotation/SF
Mo
men
t/S
FA
BC
DE
IO LSCP
C
1. Point „B‟ corresponds to nominal yield strength and yield rotation y.
2. Point „C‟ corresponds to ultimate strength and ultimate rotation u, following which failure takes place.
3. Point „D‟ corresponds to the residual strength, if any, in the member. It
is usually limited to 20% of the yield strength, and can be taken into
account provided the calculated ultimate rotation is less than 15 y.
4. Point „E‟ defines the maximum deformation capacity and is taken as
15y or u, whichever is greater.
B Yield state
IO Immediate Occupancy
LS Life Safety
CP Collapse Prevention
C Ultimate state
Three way to model the hinge property for member,
Default Hinge Property
ATC 40
User Defined Hinge Property
Hinge Property
Default Hinge Property
Default hinge properties can not be modified.
They also can not be viewed because the default
properties are section dependent.
The default properties can not be fully defined by the
program until the section to which they are apply has
been identified. Thus, to see the effect of the default
properties, the default property should be assigned to a
frame element, and then the resulting generated hinge
property should be viewed.
The built-in default hinge properties for concrete
members are generally based on Tables 9.6, 9.7 and 9.12
in ATC-40.
You should review any generated properties for their
applicability to your specific project.
Default Hinge Properties
• Select the member.
• Assign – Hinge property
Default Hinge Properties
Hinge Properties – ATC 40 (BEAM)
ab
c
Hinge Properties – ATC 40 (BEAM)
• Moment Rotation curve for beam: Following values are required
to define Moment Rotation curve for a element.
• Ast
• Asc
• fc’
• V
• bw
• d
Hinge Properties – ATC 40 (BEAM)
Units:
• V (pound), 1 lb = 4.45 N
• fc’ (lb/in2), 1 lb / in2 = 0.006895 MPa
• bw , d (in), 1 in = 25.4 mm
• ρ = Ratio of nonprestressed tension reinforcement
• ρ’ = Ratio of nonprestressed compression reinforcement
• ρbal = Reinforcement ratio producing balanced strain condition
Hinge Properties – ATC 40 (BEAM)
• Performance level for element
Hinge Properties – ATC 40 (BEAM)
• Procedure: For defining Flexure Hinge
Define- Hinge Property
Define New Hinge Property
Hinge Properties – ATC 40 (BEAM)
Hinge Properties – ATC 40 (Column)
• Moment rotation curve for column: Following values are required
to define the hinge property.
• P
• Ag
• fc’
• V
• bw
• d
Hinge Properties – ATC 40 (Column)
Hinge Properties – ATC 40 (Column)
• Performance level for element
Hinge Properties – ATC 40 (Column)
• Procedure: Defining flexure
hinge
Define - Hinge Property
Define New Hinge Property
Hinge Properties – ATC 40 (Column)
User Defined Hinge Property (Beam)
• Develop the Moment rotation relationship based upon given
cross section, R/F, Spacing of stirrup.
User Defined Hinge Property (Beam)
User Defined Hinge Property (Column)
User Defined Hinge Property (Column)
Pushover Cases
Three Different Pushover Cases are defined as listed below:
1. Gravity push, which is used to apply gravity load
2. Push X, is the lateral push in x – direction (Eqx) , after gravity push
3. Push Y, is the lateral push in y – direction (Eqy) , after gravity push
Pushover - Gravity
Joint – roof centre of mass
Force Controlled –
Refers to systems which are not permitted to exceed their elastic limits
Pushover - Gravity
1. Design Basis Earthquake + Life Safety (2% total drift)
2. Maximum Considered Earthquake + Collapse Prevention (4% total drift)
Determination of the Load pattern: (IS 1893 (part 1) : 2002 )
Q3
Q2
Q1
Lateral Load Pattern
Fundamental
natural period
Design Base
Shear
Design Lateral
Force
d
h.Ta
090
WAV hB
2
2
jj
iiBi
hW
hWVQ
Assign the lateral load at centre of mass at each floor.
Do the dynamic analysis to get the mass participation in first mode
and time period of structure.
Pushover - Lateral
Define -
Analysis Case
Pushover - Lateral
Deformation Control –
Refers to systems
which can, and are
permitted to, exceed
their elastic limit in a
ductile manner. Force
or stress levels for
these components are
of lesser important than
the amount or extent of
deformation beyond the
yield point
Analyze
Run Analysis
Run Now
Result
The sequence of Hinge Formation
The Capacity Spectrum
Base shear Vs Roof Displacement
EXAMPLE 1
Building Type RC frame with un-reinforced
brick infill
Year of construction --------------------
Number of stories Ground + 3 Storey
Plan dimensions 30 m 8.8 m
Building height 12.8 m above plinth level
Type of footing Isolated footing
General
Time Period (Dynamic analysis) – 0.95 s
Mass participation(Mode I) – Y = 95 %
Mass participation(Mode II) – X = 95 %
3D Model
Assigned Hinge
User Defined Hinge Property
State of the Hinge at every Increase in Lateral load
Step 2
Step 8
Display -
Deformed Shape
Case
Push X
State of the Hinge
Performance Point ( Capacity spectrum- Z )
Teff = 1.338s
βeff = 10.3%
V = 1761 kN
D = 0.073 m
= 0.57% of H
Sa = 0.137 m/s2
Sd = 0.061 m/s
Performance Point
Demand Spectrum
Capacity Spectrum
Effective Period
Display –
Pushover Curve
Period (s)
Sp
ectr
al A
cce
lera
tio
n C
oe
ffic
ien
t (S
a/g
)
EPA = CACV / T
2.5 CA
Demand Spectrum
EPA: Effective Peak Acceleration
2.5CA = Average value of peak
response
2.5CA = Cv / T
Zone II
(0.10)
Zone III
(0.16)
Zone IV
(0.24)
Zone V
(0.36)
At T = 0.40 for Type I
At T = 0.55 for Type II
At T = 0.67 for Type III
Fig.:Construction of a 5 percent –damped elastic response spectrum
Seismic Coefficient, CA
SoilZone II
(0.10)
Zone III
(0.16)
Zone IV
(0.24)
Zone V
(0.36)
Type I 0.10 0.16 0.24 0.36
Type II 0.10 0.16 0.24 0.36
Type III 0.10 0.16 0.24 0.36
Seismic Coefficient, CV
Type I 0.10 0.16 0.24 0.36
Type II 0.14 0.22 0.33 0.49
Type III 0.17 0.27 0.40 0.60
Demand Spectrum
Capacity Curve – Push X
EXAMPLE 2
Building Type RC frame with un-reinforced
brick infill
Year of construction --------------------
Number of stories Ground + 7 Storey
Plan dimensions 27.3 m 12.6m
Building height 24 m above plinth level
Type of footing Isolated footing
General
Time Period (Dynamic analysis) – 2.19 s
Mass participation(Mode I) – Y = 94 %
Mass participation(Mode II) – X = 5 %
3D Model
State of the Hinge
Capacity spectrum-X
Performance point does not exist.
Capacity spectrum-Y
Performance point does not exist.
Capacity Curve – Push X
Points to be taken care..
1. Do not underestimate the importance of the loading or displacement shape
2. Know your performance objectives before you push the building.
3. If it is not designed, it cannot be pushed.
4. Do not ignore gravity loads.
5. Do not push beyond failure unless otherwise you can model failure.
6. Pay attention to rebar development and lap lengths.
7. Do not ignore shear failure mechanisms.
8. P-Delta effects may be more important than you think.
9. Do not confuse the Push-over with the real earthquake loading.
10. First mode, in which mass participation should be maximum.
11. This is generally valid for building with fundamental periods of vibration
12. Misuse can lead to an erroneous understanding of the performance characteristics
Points to be taken care..