Pushover Analysis Final
Pushover Analysis Final
Pushover Analysis Final
Meher Prasad
Department of Civil Engineering Indian Institute of Technology Madras email: prasadam@iitm.ac.in
Dynamic - Loads change with time Nonlinear - Loaded beyond Elastic Limit
Linear Dynamic Response Spectrum Nonlinear Static Nonlinear Dynamic Pushover Analysis Time History
Overview
What is pushover analysis? What are its fundamental techniques? What tools can be used? Common pitfalls in pushover analysis Example of pushover analysis application
Push-over analysis is a technique by which a computer model of the building is subjected to a lateral load of a certain shape (i.e., parabolic, inverted triangular or uniform). The intensity of the lateral load is slowly increased and the sequence of cracks, yielding, plastic hinge formations, and failure of various structural components is recorded. Push-over analysis can provide a significant insight into the weak links in seismic performance of a structure.
A series of iterations are usually required during which, the structural deficiencies observed in one iteration, are rectified and followed by another. This iterative analysis and design process continues until the design satisfies a pre-established performance criteria. The performance criteria for push-over analysis is generally established as the desired state of the building given a roof-top or spectral displacement amplitude.
To obtain the maximum shear strength of the structure, Vb, and the mechanism of collapse. To evaluate if the structure can achieve the collapse mechanism without exhausting the plastic rotation capacity of the members. To obtain the monotonic displacement and global ductility capacity of the structure. To estimate the concentration of damage and IDI (Interstorey Drift Index) that can be expected during the nonlinear seismic response.
V/W (Acceleration)
Using simple modal analysis equations spectral displacement and roof-top displacement may be converted to each other. High-Strength; High-Stiffness; Brittle
Roof-top Displacement
Ordinary Design
V/W (Acceleration)
er io d
Li ne s
Period
DESIGN SPECTRUM
Sequential application of linear analysis software Sequential application of linear analysis software
Plastic Hinge
Curvature diagram along the length of the member
No building can be pushed to infinity without failure. Performance point is where the Seismic Capacity and the
Seismic Demand curves meet.
ATC-40 Method
This is an iterative procedure involving several analyses. For each analysis an effective period for an equivalent elastic system and a corresponding elastic displacement are calculated. This displacement is then divided by a damping factor to obtain an estimate of real displacement at that step of analysis.
V/W (Acceleration)
T0
eff = 0 + 0.05
T e ff
e/B
SRA =
5% damped elastic spectrum
SRV =
Roof-top Displacement
1.
2.
3.
2.
3.
4. 5. 6. 7.
8.
9.
10.
/H(%)
So called higher mode effects as the load distribution changes Limit base moment increases adapts for maximum shear force Limit base shear increases adapts for maximum bending moment Not apparent from linear analysis
N-A Operational
1- A Operational
2- A
NR
NR
NR
NR
1- B Immediate Occupancy
2- B
3- B
NR
NR
NR
1- C
2- C
3- C Life Safety
4- C
5- C
6- C
NR
2- D
3- D
4- D
5- D
6- D
NR
NR
3-E
4-E
No rehabilitation
Extremely rare
50% in 50 years
20% in 50 years
10% in 50 years
Ba s
2% in 50 years
ick Sa fe ty
o
Ob jep c ti v
5. Do not push beyond failure unless otherwise you can model failure
Ultimate Capacity
Lateral Force
Actual
Force or Moment
Displacement
Displacement or Curvature
Joint Detailing
Shear Failure
This failure can be avoided by providing special confining reinforcement over entire column length
0.15
0.1
0.05
IDARC SAP 0.16g 0 0.002 0.004 0.006 0.008 0.25g 0.3g 0.35g
Vb/W
-0.1
-0.15
-0.2
/H
Material Properties
Concrete Properties
Modification Factors
Factors to estimate the expected strength 1.5 times the Concrete compressive strength (fck) Steel yield stress (fy) (Factor of 1.25 used for capacity estimation considering strain hardening of steel)
Knowledge Factors, mk
No 1 2 3 4 5 6 Description of available information Original construction documents, including material testing report Documentation as in (1) but no material testing undertaken Documentation as in (2) and minor deteriorations of original condition Incomplete but usable original construction documents Documentation as in (4) and limited inspection and material test results with large variation. Little knowledge about the details of components mk 1.0 0.9 0.8 0.7 0.6 0.5
Material Properties
Frame Elements
Infill (struts)
Inclusion of appendages
Modeling of Beams
Modeling of Columns
Modeling of Slab
BEAM
y x
MASTER NODE
t L
Beam elements with rigid ends
SLAVE NODE
For axial and torsional rigidity, the full cross-sectional area should be used
BEAM
y x
FOR A, J
SLAVE NODE
For shear along y axis and bending about x-axis (ground motion along y-axis), the walls in the direction of ground motion should be considered as two parallel elements
BEAM
y x
SLAVE NODE
For shear along x axis and bending about y-axis (ground motion along x-axis), the walls in the direction of ground motion should be considered as three parallel elements
BEAM
y x
SLAVE NODE
b a
Lateral Load
1.0
D c A y
Lateral Deformation
V sy = f y A sv
d 0 .6 s v
Vy
Vu = 1.05Vy
=0
0.2 Vy
y
Shear deformation ()
b a
Lateral Load
1.0
D c A y
Lateral Deformation
* ATC 40 Volume 1
3Pu = 1+ 1.5 Ag f ck
Vc = c bd
V sy = f y A sv
d 0 .6 s v
3 Pu 0 .5 A g f ck
Rl = G 0.75 Ag
Where G = Shear modulus of the reinforced concrete section Ag = Gross area of the section l = Length of member
0.2 Vy
y
y Shear
deformation ()
Similarly maximum shear deformation is taken as 15 times the yield deformation. The values were taken as per SAP 2000 manual recommendations.
Ta =
Q3
VB = Ah W
Wi hi Qi = VB 2 W j hj
2
Q2
Q1
Building Data
Building frame system Usage Built in Zone Number of stories Footing Symmetry Material used Plan dimensions Building height Soil Type (assumed) RC OMRF Residential 1999 V G+4 Multiple Piles About Y-axis M15 & Fe 415 25.2m X 13.95m 15.7m Type-II (Medium)
Comments
Visual inspection did not reveal concrete deterioration. Knowledge factor was not applied. Architectural drawings were not available. Location of infill walls was postulated. Geotechnical data was not available. Rebar detailing was not complete in the available structural drawings. Building considered to be noncompliant with IS 13920: 1993 (R = 3). Fixity considered at pile cap. Soil-structure interaction neglected. Elevator walls not considered as lateral load resisting elements.
Structural Parameters
Center of Mass (m)
Xdirection Ydirection
Floor
5 4 3 2 1
ZI Sa Ah = 2R g
Ah = 0.15 VB = 0.15 20270 kN = 3039 kN
Without infill stiffness Analysis methods Vx (kN) Equivalent Static Method EQX EQY 2796 2796 Vy (kN)
3039 -
3039
Without infill Mode T (s) 0.83 0.78 0.42 0.25 0.24 Mass Participation (%) UX 1 2 3 4 5 88.34 2.22 1.23 6.05 0.14 Uy 1.95 86.71 0.47 0.16 8.02 0.73 0.69 0.38 0.22 0.21 T (s)
With infill Mass Participation (%) UX 92.29 1.26 0.72 4.44 0.11 Uy 1.10 90.23 0.59 0.13 6.33
Mode Shapes
Mode Shapes
Mode Shapes
Section
Absolute Capacities
y Pu x
ey
ex Pu
Puz
Y
PuR
MuR,y
P (kN)
M2 (kNm)
M3 (kNm)
P (kN)
M2 (kNm)
M3 (kNm)
P (kN)
M2 (kNm)
M3 (kNm)
Muy1
0 Muy = Pu ey
2 2 M uR = M ux + M uy
Mux = Pu ex
Vu (kN) 1C1 1C2 1C3 1C4 1C5 2C5 250 259 275 282 285 282
Vu is higher of the shear from analysis and the shear corresponding to the flexural capacity Mu (Vu = Mu / Ls)
With Infill
Without Infill
With infill
Without infill
Performance Objective
1.
Design Basis Earthquake + Life Safety (2% total drift) Maximum Considered Earthquake + Collapse Prevention (4% total drift)
2.
Hinge Property
1.2
B IO LS
CP
B IO
0.8
Moment/SF
0.6
LS Life Safety
D A
0 0.005 0.01 0.015 0.02 Rotation/SF 0.025 0.03 0.035 0.04
0.4
CP Collapse Prevention
E
0.2
Ultimate state
Demand Spectrum
Seismic Coefficient, CA Soil Type I Type II Type III Zone II (0.10) 0.10 0.10 0.10 Zone III (0.16) 0.16 0.16 0.16 Seismic Coefficient, CV Type I Type II Type III 0.10 0.14 0.17 0.16 0.22 0.27 0.24 0.33 0.40 0.36 0.49 0.60 Zone IV (0.24) 0.24 0.24 0.24 Zone V (0.36) 0.36 0.36 0.36
1.5VB
3500 3000
2500
2000
1500
1000
Without infill stiffness With infill stiffness
500
0 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
1.5VB
3000
2500
2000
1500
1000
Without infill stiffness With infill stiffness
500
0 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
0.10
0.20
0.30
Retrofitting Scheme
1. 2.
Continuing infill walls only at a few locations. Strengthening of the ground floor columns.
9000
8000
C B A
/h=0.28% /h=0.48% /h=0.75%
7000
6000
5000
VB
4000
3000
2000
/h = 1 %
1000
0 0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
A, /h=0.28%
B, /h=0.48%
C, /h=0.75%
D, /h=1%
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0
5%
0.1
0.2
0.3
0.4
Storey Displacements
18
15
12
H(m)
0
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20
Displacement (m)
IDI
5
B A D C
3 H(m) 2 1 0 0.000
0.005
0.010 IDI
0.015
0.020
FE
V/W (Acceleration)
FI
Roof-top Displacement
FE
V/W (Acceleration)
FI
Roof-top Displacement
FE
V/W (Acceleration) REDUCE SEISMIC DEMAND BY: ADDING DAMPING OR ISOLATION
FI
Roof-top Displacement