1. Pushover Analysis
an
Inelastic Static Analysis Methods
courtesy of Barış Binici

2. Target Performance
Dictated by codes (DBYBHY 2007, Section 1.2.1):
“....The objective of seismic resistant design is
to have no structural/nonstructural damage
in low magnitude earthquakes, limited and
repairable damage in moderate earthquakes
and life safety for extreme earthquakes...”

3. Current Status
)(
)(
1
1
TR
TAW
V
a
t 
• Equivalent Lateral Force Procedure
- Assume global ductility (Ra)
- Detail accordingly
• Modal Superposition Procedure
- Include higher mode effects
• Time History Analysis
- Rarely used
- Tedious and requires hysteretic models

4. Critique of Current Practice
Advantages :
- Simple to use
- Have proven to work
- Became a tradition all over the world
- Uncertainty is lumped and easier to deal with
Disadvantages :
- No clear connection between capacity and demand
- No option for interfering with the target performance
- No possibility of having the owner involved in the decision
process
- Not easily applicable to seismic assessment of existing
structures

5. DBYBHY 2007 (Chapter 7)
- Evaluation and Strengthening of Existing Buildings
is based on structural performances.
- 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

6. 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.
Düzce Ground Motion
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0 5 10 15 20 25 30
Sec.
Acceleration(g)

7. 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.

8. 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

9. Section Damage Levels
Damage levels are established based on concrete outermost
compressive fiber strain and steel strain (for nonlinear analysis
procedure).

10. Section Damage Levels
How should these values be decided?
- Construction practice
- Experience of engineers
- Input of academicians

11. Curvature demand at target curvatures
Φp = θp / Lp
Φt = Φy + Φp
0
100
200
300
400
500
600
0.0000 0.0200 0.0400 0.0600 0.0800 0.1000 0.1200
Eğrilik
(rad/m)
Moment
(kN.m)
AK
GV GÇ
(Φt)(Φy)

12. How do we estimate strains from
a structural analysis?
Strain
Moment
Curvature
Moment
My
øy øu
Moment
Plastic
Rotations
My
θpu
θpu =(øu – øy) Lp OR
θp =(ø – øy) Lp
Where Lp = 0.5h
Utilize this idealized
moment-rotation
response in inelastic
structural analysis

13. 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
h
Lp
Elastic
Beam-
Column
Element
Plastic
Hinges
Rigid End
zones

14. Elastic Parts
For regions other than plastic hinging occurs, cracking is expected therefore
use of cracked stiffness is customary (0.4-0.8) EIo
Eğrilik
Moment
EIo
0.4-0.8EIo
Curvature

15. Pushover Analysis

16. Steps of Pushover Analysis:
A Simple Incremental Procedure
1. Build a computational model of the structure

17. Steps of Pushover Analysis
2. Define member behavior
– Beams: Moment-rotation relations
– Columns: Moment-rotation and Interaction Diagrams
– Beam-column joints: Assume rigid (DBYBHY 2007 )
– Walls: Model as beam columns but introduce a shear
spring to model shear deformations
– Use cracked rigidities for elastic portions

18. Steps of Pushover Analysis
3. Apply gravity loads
1.0 G + n Q n=0.3 (live load reduction factor)
(if the interaction diagrams will not be used a good
estimate of the moment capacity of column hinges
needs to be made)
Possibilities:
- Based on initial gravity load analysis
- Based on a beam hinging mechanism
- Based on elastic lateral force analysis with an
assumed reasonable Ra value.

19. Steps of Pushover Analysis
4. Specify a Lateral Load Profile:
(Inverted triangular, constant, first mode shape are some of the
possibilities)
It is a good idea to have a spreadsheet page ready
indicating all members, current load increment
5. Lateral Load Incrementing:
Step 1:
Elastic analysis is valid up to the formation of the first hinge,
i.e. when the first critical location reaches its moment
capacity.
• Find the lateral loads that cause first hinge formation (V1).
• Record all member forces and deformations (F1, d1).

20. Steps of Pushover Analysis
Step 2:
Beyond Step 1, yielded element’s critical location cannot
take any further moment. Therefore place an actual
hinge at that location. Conduct an analysis increment for
this modified structure. This load increment should be
selected such that upon summing the force resultant
from this incremental step and previous step, second
hinge formation is reached.
V2 = V1 + ΔV
F2 = F1 + ΔF
d2 = d1 + Δd
Results from Step 1 + Results from an
incremental analysis with a hinge placed at
first yield location = Second Hinge formation

21. Steps of Pushover Analysis
.
.
Step i:
Similar to step 2 but additional hinges form and
incremental analysis steps are conducted for systems
with more hinges. Results are added to those from the
previous step
Vi = Vi-1 + ΔV
Fi = Fi-1 + ΔF
di = di-1 + Δd
Results from Step i-1 + Results from an
incremental analysis with a hinge placed at i-1th
yield location = ith hinge formation

22. 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

23. Example Application: 3 Story- 2 Bay
RC Frame (Courtesy of Ahmet Yakut)
M O D E L
3m
3m
3m
1
2
3
10
11
12
13
14
15
4
5
6
7
8
9
6m 6m
J1
J2
J3
J4
J8
J7
J6
J5 J9
J10
J11
J12

24. 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=10kN/m
DL=15kN/m
DL=15kN/m
LL=2kN/m
LL=2kN/m
LL=2kN/m
EQ=60kN
EQ=40kN
EQ=20kN
SABİT YÜK HAREKETLİ YÜK YATAY YÜK

25. DATA
10-f10
60cm
60cm
Columns
3-f10
3-f10
25cm
50cm
Beams
Steel (fyd=495 Mpa)
Concrete (fcd=25 Mpa)
Clear cover=5 cm
E=2.779E+4 MPa
M+ is the same as M-
Note that if this is a seismic evaluation problem strength values obtained
at site should be used!

26. Section Capacities
Eğrilik
Moment
fy
My
fult
Eleman N My Φy
Φ u l t
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
4 -253,392 166 0,0059 0,085
5 -158,905 143 0,0060 0,099
6 -64,797 119 0,0060 0,113
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
13 5,606 49 0,0073 0,103
14 1,421 50 0,0069 0,102
15 -17,233 53 0,0069 0,099
Elemnaların Moment-eğrilik ilişkileri
elasto-plastik, pekleşmesiz
To be conservative smaller axial load from two load
combinations can be selected (as long as N<Nb)
Idealized member moment curvature
relations for estimated axial load level
Member

27. Effect of Axial Force
• Compute the moment
capacity by accounting for
axial force variation
• Always remain on the yield
surface

28. Step 1
DL=10kN/m
DL=15kN/m
DL=15kN/m
LL=2kN/m
LL=2kN/m
LL=2kN/m
EQ=3kN
EQ=2kN
EQ=1kN
COMBO2: 1.0 DL + 0.3 LL + 1.0 EQ
Detection of first yield (moment
reaches My±5%My )
6
Frame Joint Myield M
Element Label kNm kNm
J1 124.0 -4.33
J2 124.0 20.60
J2 115.5 -22.14
J3 115.5 21.00
J3 107.5 -22.23
J4 107.5 27.35
J5 166.0 6.23
J6 166.0 -0.60
J6 143.0 3.50
J7 143.0 -2.94
J7 119.0 1.52
J8 119.0 -3.29
J9 133.5 16.03
J10 133.5 -20.07
J10 122.0 26.88
J11 122.0 -24.83
J11 110.0 22.95
J12 110.0 -30.82
J2 49.0 -42.74
J6 49.0 -49.58 YIELDED
J3 50.0 -43.24
J7 50.0 -49.28
J4 53.0 -27.35
J8 53.0 -34.34
J6 49.0 -45.48
J10 49.0 -46.95
J7 50.0 -44.83
J11 50.0 -47.79
J8 53.0 -31.05
J12 53.0 -30.82
0.2947
11
12
6
7
4
14
15
Condition
13
5
8
9
3
10
1
2
First yielding stage
Total Base Shear (kN)=
Lateral Disp. at J4 (mm)=
J4 (monitored node )

29. Step 2 (Incremental)
ΔEQ=3kN
ΔEQ=2kN
ΔEQ=1kN
Actual hinge at previously yielded
location for the incremental analysis
New
locations at
which yield
moments
within
tolerance are
reached
6
12
0.2865
Total Lateral Disp. at J4 (mm)= 0.5812
Frame M ΔM M + ∆M
Element kNm kNm (kNm)
-4.33 6.39 2.06
20.60 0.76 21.36
-22.14 2.05 -20.10
21.00 -2.18 18.82
-22.23 0.24 -21.99
27.35 -1.82 25.53
6.23 6.47 12.71
-0.60 0.39 -0.21
3.50 2.79 6.29
-2.94 -3.15 -6.09
1.52 1.56 3.08
-3.29 -3.43 -6.72
16.03 6.48 22.51
-20.07 0.20 -19.87
26.88 2.57 29.45
-24.83 -2.26 -27.09
22.95 0.15 23.10
-30.82 -1.80 -32.62
-42.74 1.29 -41.46
-49.58 0.00 -49.58 YIELDED
-43.24 2.42 -40.82
-49.28 -2.36 -51.64 YIELDED
-27.35 1.82 -25.53
-34.34 -1.73 -36.07
-45.48 2.40 -43.08
-46.95 -2.38 -49.33 YIELDED
-44.83 2.35 -42.48
-47.79 -2.41 -50.19 YIELDED
-31.05 1.71 -29.34
-30.82 -1.80 -32.62
13
14
15
9
10
11
12
5
6
7
8
1
2
3
4
Inc. Lateral Disp. at J4 (mm)=
Total Base Shear (kN) =
Total Incremental Load (kN)=
Condition

30. Step 3 (Incremental)
Actual hinges at previously yielded
location for the incremental analysis
New location
at which yield
moment within
tolerance are
reached
ΔEQ=21kN
ΔEQ=14kN
ΔEQ=7kN
42
54
2.94
Total Lateral Disp. at J4 (mm)= 3.5212
Frame M ΔM M + ∆M
Element kNm kNm (kNm)
2.06 57.79 59.85
21.36 12.12 33.48
-20.10 24.68 4.58
18.82 -16.19 2.64
-21.99 -2.12 -24.11
25.53 -18.94 6.58
12.71 56.85 69.56
-0.21 12.18 11.97
6.29 24.58 30.87
-6.09 -13.41 -19.49
3.08 0.99 4.07
-6.72 -34.94 -41.67
22.51 53.65 76.16
-19.87 18.00 -1.88
29.45 18.00 47.45
-27.09 -8.15 -35.24
23.10 -8.15 14.95
-32.62 -18.38 -51.00
-41.46 12.56 -28.90
-49.58 0.00 -49.58 YIELDED
-40.82 14.07 -26.75
-51.64 0.00 -51.64 YIELDED
-25.53 18.94 -6.58
-36.07 -17.61 -53.68 YIELDED
-43.08 12.40 -30.68
-49.33 0.00 -49.33 YIELDED
-42.48 14.40 -28.08
-50.19 0.00 -50.19 YIELDED
-29.34 17.33 -12.01
-32.62 -18.38 -51.00
12
13
14
15
8
9
10
11
1
2
3
4
5
6
7
Inc. Lateral Disp. at J4 (mm)=
Total Base Shear (kN) =
Condition
Total Incremental Load (kN)=

31. ΔEQ=3kN
ΔEQ=2kN
ΔEQ=1kN
Step 4 (Incremental)
Actual hinges at previously yielded
location for the incremental analysis
New location
at which yield
moment within
tolerance are
reached
6
60
0.4692
Total Lateral Disp. at J4 (mm)= 3.9904
Frame M ΔM M + ∆M
Element kNm kNm (kNm)
59.85 8.59 68.44
33.48 2.00 35.48
4.58 3.91 8.49
2.64 -1.96 0.67
-24.11 0.29 -23.82
6.58 -1.96 4.63
69.56 8.43 77.99
11.97 2.07 14.04
30.87 3.95 34.82
-19.49 -1.77 -21.26
4.07 0.50 4.57
-41.67 -3.40 -45.07
76.16 7.95 84.12
-1.88 2.90 1.02
47.45 2.90 50.35
-35.24 -0.50 -35.74
14.95 -0.50 14.45
-51.00 -3.35 -54.36
-28.90 1.91 -26.99
-49.58 0.00 -49.58 YIELDED
-26.75 2.26 -24.49
-51.64 0.00 -51.64 YIELDED
-6.58 1.96 -4.63
-53.68 0.00 -53.68 YIELDED
-30.68 1.88 -28.79
-49.33 0.00 -49.33 YIELDED
-28.08 2.27 -25.81
-50.19 0.00 -50.19 YIELDED
-12.01 3.40 -8.61
-51.00 -3.35 -54.36 YIELDED
13
14
15
9
10
11
12
5
6
7
8
1
2
3
4
Condition
Inc. Lateral Disp. at J4 (mm)=
Total Base Shear (kN) =
Total Incremental Load (kN)=

32. ΔEQ=18kN
ΔEQ=12kN
ΔEQ=6kN
Step 5 (Incremental)
36
96
3.41
Total Lateral Disp. at J4 (mm)= 7.4004
Frame M ΔM M + ∆M
Element kNm kNm (kNm)
68.44 55.34 123.78
35.48 15.86 51.34
8.49 28.66 37.15
0.67 -6.38 -5.71
-23.82 10.42 -13.40
4.63 -15.82 -11.19
77.99 54.50 132.49
14.04 16.03 30.06
34.82 28.70 63.52
-21.26 -6.00 -27.26
4.57 10.75 15.33
-45.07 -15.83 -60.90
84.12 51.48 135.60 YIELDED
1.02 21.43 22.45
50.35 21.43 71.78
-35.74 1.18 -34.57
14.45 1.18 15.62
-54.36 0.00 -54.36
-26.99 12.80 -14.19
-49.58 0.00 -49.58 YIELDED
-24.49 16.80 -7.69
-51.64 0.00 -51.64 YIELDED
-4.63 15.82 11.19
-53.68 0.00 -53.68 YIELDED
-28.79 12.68 -16.12
-49.33 0.00 -49.33 YIELDED
-25.81 16.75 -9.05
-50.19 0.00 -50.19 YIELDED
-8.61 15.83 7.22
-54.36 0.00 -54.36 YIELDED
12
13
14
15
8
9
10
11
1
2
3
4
5
6
7
Condition
Inc. Lateral Disp. at J4 (mm)=
Total Base Shear (kN) =
Total Incremental Load (kN)=

33. Step 6 (Incremental)
ΔEQ=0.06kN
ΔEQ=0.04kN
ΔEQ=0.02kN
0.12
96.12
0.01277
Total Lateral Disp. at J4 (mm)= 7.41317
Frame M ΔM M + ∆M
Element kNm kNm (kNm)
123.78 0.25 124.03 YIELDED
51.34 0.03 51.38
37.15 0.08 37.23
-5.71 -0.03 -5.74
-13.40 0.03 -13.37
-11.19 -0.06 -11.25
132.49 0.26 132.75
30.06 0.02 30.09
63.52 0.07 63.60
-27.26 -0.02 -27.29
15.33 0.04 15.36
-60.90 -0.06 -60.96
135.60 0.00 135.60 YIELDED
22.45 0.09 22.54
71.78 0.09 71.87
-34.57 0.00 -34.57
15.62 0.00 15.63
-54.36 0.00 -54.36
-14.19 0.05 -14.14
-49.58 0.00 -49.58 YIELDED
-7.69 0.06 -7.63
-51.64 0.00 -51.64 YIELDED
11.19 0.06 11.25
-53.68 0.00 -53.68 YIELDED
-16.12 0.05 -16.07
-49.33 0.00 -49.33 YIELDED
-9.05 0.06 -8.99
-50.19 0.00 -50.19 YIELDED
7.22 0.06 7.28
-54.36 0.00 -54.36 YIELDED
13
14
15
9
10
11
12
5
6
7
8
1
2
3
4
Condition
Inc. Lateral Disp. at J4 (mm)=
Total Base Shear (kN) =
Total Incremental Load (kN)=

34. Step 7 (Incremental)
ΔEQ=4.8kN
ΔEQ=3.2kN
ΔEQ=1.6kN
9.6
105.72
1.3
Total Lateral Disp. at J4 (mm)= 8.71317
Frame M ΔM M + ∆M
Element kNm kNm (kNm)
124.03 0.00 124.03 YIELDED
51.38 4.04 55.42
37.23 8.81 46.05
-5.74 -3.63 -9.37
-13.37 2.07 -11.30
-11.25 -5.15 -16.40
132.75 35.16 167.90 YIELDED
30.09 -3.63 26.45
63.60 2.03 65.63
-27.29 -2.56 -29.84
15.36 3.01 18.38
-60.96 -5.18 -66.14
135.60 0.00 135.60 YIELDED
22.54 5.95 28.49
71.87 5.95 77.82
-34.57 -1.02 -35.58
15.63 -1.02 14.61
-54.36 0.00 -54.36
-14.14 4.77 -9.37
-49.58 0.00 -49.58 YIELDED
-7.63 5.70 -1.93
-51.64 0.00 -51.64 YIELDED
11.25 5.15 16.40
-53.68 0.00 -53.68 YIELDED
-16.07 5.67 -10.40
-49.33 0.00 -49.33 YIELDED
-8.99 5.57 -3.42
-50.19 0.00 -50.19 YIELDED
7.28 5.18 12.46
-54.36 0.00 -54.36 YIELDED
12
13
14
15
8
9
10
11
1
2
3
4
5
6
7
Total Base Shear (kN) =
Total Incremental Load (kN)=
Condition
Inc. Lateral Disp. at J4 (mm)=

35. Step 9 (Incremental)
39
144.72
12.69
Total Lateral Disp. at J4 (mm)= 21.40317
M ΔM M + ∆M
kNm kNm (kNm)
124.03 0.00 124.03 YIELDED
55.42 -46.64 8.78
46.05 5.74 51.79
-9.37 -44.15 -53.51
-11.30 1.29 -10.01
-16.40 -38.69 -55.09
167.90 0.00 167.90 YIELDED
26.45 -46.22 -19.76
65.63 6.05 71.68
-29.84 -43.74 -73.58
18.38 1.72 20.10
-66.14 -38.78 -104.91
135.60 0.00 135.60 YIELDED
28.49 -24.15 4.35
77.82 -24.15 53.68
-35.58 -21.98 -57.57
14.61 -21.98 -7.37
-54.36 0.00 -54.36
-9.37 52.37 43.00
-49.58 0.00 -49.58 YIELDED
-1.93 45.43 43.51
-51.64 0.00 -51.64 YIELDED
16.40 38.69 55.09 YIELDED
-53.68 0.00 -53.68 YIELDED
-10.40 52.27 41.87
-49.33 0.00 -49.33 YIELDED
-3.42 45.46 42.03
-50.19 0.00 -50.19 YIELDED
12.46 38.78 51.24
-54.36 0.00 -54.36 YIELDED
Condition
Total Incremental Load (kN)=
Total Base Shear (kN) =
Inc. Lateral Disp. at J4 (mm)=
ΔEQ=19.5kN
ΔEQ=13kN
ΔEQ=6.5kN

36. Step 9 (Incremental)
Frame M ΔM M + ∆M
Element kNm kNm (kNm)
124.03 0.00 124.03 YIELDED
8.78 -1.83 6.95
51.79 0.44 52.22
-53.51 -1.74 -55.25
-10.01 0.30 -9.71
-55.09 0.00 -55.09
167.90 0.00 167.90 YIELDED
-19.76 -1.82 -21.59
71.68 0.44 72.12
-73.58 -1.44 -75.02
20.10 0.64 20.74
-104.91 -1.86 -106.77
135.60 0.00 135.60 YIELDED
4.35 -0.84 3.50
53.68 -0.84 52.83
-57.57 -0.54 -58.11
-7.37 -0.54 -7.91
-54.36 0.00 -54.36
43.00 2.27 45.27
-49.58 0.00 -49.58 YIELDED
43.51 2.03 45.54
-51.64 0.00 -51.64 YIELDED
55.09 0.00 55.09 YIELDED
-53.68 0.00 -53.68 YIELDED
41.87 2.26 44.13
-49.33 0.00 -49.33 YIELDED
42.03 2.08 44.11
-50.19 0.00 -50.19 YIELDED
51.24 1.86 53.10 YIELDED
-54.36 0.00 -54.36 YIELDED
12
13
14
15
8
9
10
11
1
2
3
4
5
6
7
Condition
ΔEQ=0.75kN
ΔEQ=0.50kN
ΔEQ=0.25kN

37. Step 10 (Incremental)
4.2
150.42
1.94
Total Lateral Disp. at J4 (mm)= 23.90917
Frame M ΔM M + ∆M
Element kNm kNm (kNm)
124.03 0.00 124.03 YIELDED
6.95 -5.34 1.61
52.22 2.18 54.40
-55.25 -4.04 -59.29
-9.71 3.14 -6.57
-55.09 0.00 -55.09
167.90 0.00 167.90 YIELDED
-21.59 -5.17 -26.76
72.12 2.35 74.47
-75.02 -4.19 -79.21
20.74 3.00 23.73
-106.77 0.00 -106.77
135.60 0.00 135.60 YIELDED
3.50 -2.09 1.41
52.83 -2.09 50.74
-58.11 0.16 -57.95
-7.91 0.16 -7.75
-54.36 0.00 -54.36
45.27 7.52 52.79 YIELDED
-49.58 0.00 -49.58 YIELDED
45.54 7.18 52.72 YIELDED
-51.64 0.00 -51.64 YIELDED
55.09 0.00 55.09 YIELDED
-53.68 0.00 -53.68 YIELDED
44.13 7.52 51.65 YIELDED
-49.33 0.00 -49.33 YIELDED
44.11 7.18 51.30 YIELDED
-50.19 0.00 -50.19 YIELDED
53.10 0.00 53.10 YIELDED
-54.36 0.00 -54.36 YIELDED
13
14
15
9
10
11
12
5
6
7
8
1
2
3
4
Total Incremental Load (kN)=
Total Base Shear (kN) =
Inc. Lateral Disp. at J4 (mm)=
Condition
ΔEQ=2.1kN
ΔEQ=1.4kN
ΔEQ=0.7kN

38. Collapse Mechanism
S Y S T E M I S U N S T A B L E
Beam sway mechanism is observed
No further lateral load incrementing
possible (only rigid body motion)
0
20
40
60
80
100
120
140
160
0 5 10 15 20 25 30
Roof Displacement (mm)
BaseShear(kN)

39. What did we obtain?
• A simple representation of the capacity curve
• Plastic mechanism and sequence of hinge formation
• Lateral load and displacement capacity
• Ductility and plastic rotation demand
0
20
40
60
80
100
120
140
160
0 5 10 15 20 25 30
Top Displacement (mm)
TotalBaseShear(kN)
Incremental
SAP2000
SAP 2000 built in pushover
analysis options include:
• hardening/loss of strength
• P-M interaction
• Systematic stiffness approach

40. Concluding Remarks
• Nonlinear analysis is becoming a part of
the profession
• It gives us information on displacements
which are indicators of damage
• Never forget that estimating deformations
is harder compared to estimating strength
• Never replace engineering judgment with
any analysis procedure