3.4 Pushover Analysis
3.4 Pushover Analysis
3.4 Pushover Analysis
an
Inelastic Static Analysis Methods
- Steps:
• Collect information from an existing structure
• Assess whether info is dependable and penalize accordingly
• Conduct structural analysis
- Linear static analysis
- Nonlinear static analysis (Pushover analysis)
- Incremental pushover analysis
- Time history analysis
• Identify for each member the damage level
• Decision based on number of elements at certain damage levels
Time History?
- Actual earthquake response is hard to predict anyways.
- Closest estimate can be found using inelastic time-history analysis.
- Difficulties with inelastic time history analysis:
- Suitable set of ground motion (Description of demand)
- hysteretic behavior models (Description of capacity)
- Computation time (Time)
- Post processing (Time and understanding)
Alternative approach is pushover analysis.
0.6
0.4
Acceleration (g)
0.2
0 Sec.
0 5 10 15 20 25 30
-0.2
-0.4
-0.6
Pushover Analysis
• Definition: Inelastic static analysis of a
structure using a specified (constant or
variable) force pattern from zero load to a
prescribed ultimate displacement.
• Use of it dates back to 1960s to1970s to
investigate stability of steel frames.
• Many computer programs were developed
since then with many features and limitations.
Available Computer Programs
• Design Oriented:
SAP 2000, GTSTRUDL, RAM etc.
• Research Oriented:
Opensees, IDARC, SeismoStrut etc.
What is different?
• User interface capabilities
• Analysis options
• Member behavior options
Section Damage Levels
500
AK
400
GV GÇ
Moment
(kN.m)
Φp = θp / Lp 300
Φt = Φy + Φp 200
100
0
(Φy) (Φt)
0.0000 0.0200 0.0400 0.0600 0.0800 0.1000 0.1200
Eğrilik
(rad/m)
How do we estimate strains from
a structural analysis?
Moment Moment
My
Curvature Strain
øy øu
Moment
θpu =(øu – øy) Lp OR
My Utilize this idealized
θp =(ø – øy) Lp moment-rotation
Where Lp = 0.5h response in inelastic
structural analysis
Plastic
θpu Rotations
Definition of Potential Plastic Hinges
• End regions of columns and beams (center for gravity loads)
are the potential plastic hinges
• Plastic hinges are hinges capable of resisting My (not
significantly more, hardening allowed) undergoing plastic
rotations
Rigid End
zones
Elastic
h Beam- Plastic
Column Hinges
Element
Lp
Elastic Parts
For regions other than plastic hinging occurs, cracking is expected therefore
use of cracked stiffness is customary (0.4-0.8) EIo
0.4-0.8EIo
Moment
EIo
Eğrilik
Curvature
Pushover Analysis
Steps of Pushover Analysis:
A Simple Incremental Procedure
1. Build a computational model of the structure
Steps of Pushover Analysis
Vi = Vi-1 + ΔV
Results from Step i-1 + Results from an
Fi = Fi-1 + ΔF incremental analysis with a hinge placed at i-1th
yield location = ith hinge formation
di = di-1 + Δd
Steps of Pushover Analysis
Step n:
Sufficient number of plastic hinges have formed and
system has reached a plastic mechanism. Note that this
could be a partial collapse mechanism as well. Beyond
this point system rotates as a rigid body.
ANALYSIS DONE
- Plot Base Shear- Roof Displacement
- Check member rotations and identify performance levels
Example Application: 3 Story- 2 Bay
RC Frame (Courtesy of Ahmet Yakut)
MODEL
12 J8 15
J4 J12
3 6 9
3m
11 J7 14
J3 J11
2 5 8 3m
10 J6 13
J2 J10
4 3m
1 7
J1 J5 J9
6m 6m
Assumptions
Assume
• Constant Axial Load on Columns for Analysis Steps
• Rigid-plastic with no hardening or softening moment-rotation behavior for
columns and beams
• plastic hinging occurs when moment capacity is within 5% tolerance
• Load combinations 1.0 DL + 0.3 LL and 1.0 DL + 0.3 LL+1.0EQ to compute
axial load levels
DL=15kN/m LL=2kN/m
EQ=40kN
DL=15kN/m LL=2kN/m
EQ=20kN
DATA
Columns Beams
10-f10
3-f10
60cm 50cm
3-f10
60cm 25cm
Φy
u l t
Eleman
Member N My
kN kNm rad/m rad/m
1 -83,786 124 0,0055 0,111
2 -51,347 115,5 0,0056 0,115
3 -19,872 107,5 0,0056 0,119 My
4 -253,392 166 0,0059 0,085
5 -158,905 143 0,0060 0,099
6 -64,797 119 0,0060 0,113
Moment
7 -124,104 133,5 0,0056 0,105
8 -77,747 122 0,0057 0,112
9 -31,201 110 0,0054 0,118
10 5,606 49 0,0073 0,103
11 1,421 50 0,0069 0,102
12 -17,233 53 0,0069 0,099 fy Eğrilik f ult
13 5,606 49 0,0073 0,103
14 1,421 50 0,0069 0,102
15 -17,233 53 0,0069 0,099
160
SYSTEM IS UNSTABLE
140
120
80
60
40
20
0
0 5 10 15 20 25 30
Roof Displacement (mm)
140
100
SAP2000
80 • hardening/loss of strength
• P-M interaction
60
40
20
• Systematic stiffness approach
0
0 5 10 15 20 25 30