Dynamic Analysis with Examples – Seismic Analysis

OpenSees Days in Portugal
@FEUP
p. 1
Dynamic Analysis Notes
Dr. André R. Barbosa
July 03, 2014
OpenSees
Days
in
Portugal
@Faculdade
de
Engenharia
at
Univ.
do
Porto
DYNAMIC
ANALYSIS
(Seismic
and
Tsunami
loadings)
André
R.
Barbosa,
Ph.D.,
P.E.
July
03,
2014

@FEUP
p. 2
July 03, 2014
2
Outline
• Moment-‐interac8on
diagrams
as
an
applica8on
of
sec8on
analysis
using
OpenSees.exe
• Modeling
a
1-‐bay,
2-‐story
RC
concrete
frame
– Nonlinear
material
and
nonlinear
geometry
• What
can
else
can
we
do
using
OpenSees?
– Building
example
– Bridge
example
– Soil-‐structure-‐fluid-‐interac8on?

@FEUP
p. 3
July 03, 2014
Moment
interacOon
diagrams
RC
sec8on
behavior
under
Combined
Bending
and
Axial
Load
https://www.dropbox.com/s/evzcz6er3ep0jen/Ex1_MP_Interaction_Diagram.zip

Development
of
M-‐N
interac8on
diagrams
@FEUP
p. 4
Interaction Diagram
(Failure Envelope)
July 03, 2014
Concrete crushes
before steel yields
Steel yields before
concrete crushes
Moment
Axial Load, P
Failure Criterion: ecu = 0.003

@FEUP
p. 5
July 03, 2014
General
Procedure
– For
various
levels
of
axial
load,
increase
curvature
of
the
sec8on
un8l
a
concrete
strain
of
0.003
is
reached.
– Files
used:
• model.tcl
• Mp.tcl
– Output:
• mp.out
Moment = f(c)
Axial Load, P
P
M

@FEUP
p. 6
Zero-Length Section
≡
= Δ = Δ
July 03, 2014
Zero
Length
Sec8on
Element
for
RC
Sec8on
Analysis
y
z
y
x
L 1
u u
L
L
ε
χ = Δ θ = Δ
θ

@FEUP
p. 7
Concrete01
$Fy $b*E0
July 03, 2014
$fpcu
2*$fpc/$epsc0
Concrete01
$fpc
$epsU $eps0
strain
stress
$E0
strain
stress
$Fy
$b*E0
y
As1 =
4 No. 8 bars
As2 =
4 No. 8 bars
z
y1
-y1
z1 -z1
cover
Fiber sec8on
Steel01
Core concrete
Cover concrete

Reinforced
Concrete:
Mechanics
and
Design
(4th
Edi8on)
by
James
G.
MacGregor,
James
K.
Wight
M C y a F y d
= ⎛ − ⎞ + − ⎜⎝ ⎟⎠ Σn
n i
⎛ ⎞
= ⎜ ⎟ ⎝ − ⎠ s y
c d Z
@FEUP
p. 8
P C F
0.003 ; where =
0.003
i
if < i a d
else
July 03, 2014
Interac8on
Diagram
= +Σn
n
c si
=1
i
( ) c si
2 i
=1
1 1
1
ε ε
ε
s
ε = ⎛ − ⎞0.003
⎜⎝ ⎟⎠
si
c d
c
= ε ; ≤ si si s si y f E f f
1 = 1.05 0.05
c f
psi
1000
β
⎛ ′ ⎞
− ⎜ ⎟
⎝ ⎠
( )( ) 1 = 0.85 ′ ; =β c c C f ab a c
= (positive in compression) si si si F f A
= ( −0.85 ′) si si c si F f f A
y = h
for symmetric sections
2

@FEUP
p. 9
July 03, 2014
Interac8on
Diagram

Modeling
a
1-‐bay,
2-‐story
RC
frame
Beam
column
element
with
(elas8c)
RC
@FEUP
p. 10
July 03, 2014
fiber
sec8on
https://www.dropbox.com/s/ove56qgu7dqg54r/Ex2_ElasticFrame.zip

Lcol
=
36
_
@FEUP
p. 11
P
July 03, 2014
P
H/2
1
2
3
4
H
5
6
A
A
P
P
(1)
(2)
(3)
(4)
(5)
(6)
Linear
Elas8c
Steel
Concrete
Lbeam
=
42
_
Lcol
=
36
_
Cross-‐sec8ons

@FEUP
p. 12
Pushover Analysis
July 03, 2014
Linear
geometry
PDelta
Corotational

@FEUP
p. 13
July 03, 2014
13
Time-history Response Analysis
Linear
geometry
PDelta
Corotational

Modeling
a
1-‐bay,
2-‐story
RC
frame
Beam-‐column
element
with
RC
@FEUP
p. 14
July 03, 2014
nonlinear
fiber
sec8on
https://www.dropbox.com/s/geigqdn3dsrvbyb/Ex3_NonlinearFrame.zip

Lcol
=
36
_
@FEUP
p. 15
July 03, 2014
e
P
P
H/2
1
2
3
4
H
5
6
A
A
P
P
(1)
(2)
(3)
(4)
(5)
(6)
Lbeam
=
42
_
Lcol
=
36
_
Cross-‐sec8ons
s
s
e
Steel02
Concrete02
Material
models

Pushover Analysis Time History Analysis
@FEUP
p. 16
July 03, 2014

@FEUP
p. 17
July 03, 2014
Concrete stress-strain response
Steel stress-strain response
Fiber 2 y
z
Fiber 1
Pushover Analysis
Element 1
Section 5

Time History Analysis Concrete stress-strain response
@FEUP
p. 18
Fiber 2 y
July 03, 2014
z
Steel stress-strain response
Element 1
Section 5

@FEUP
p. 19
July 03, 2014
Building
Example
Barbosa, Conte, Restrepo (2011)

q NEHRP
design
example
(FEMA
451)
Ø Demonstrate
the
design
procedures
(ASCE7-‐05,
ACI318-‐08)
Ø Building
was
@FEUP
p. 20
July 03, 2014
re-‐designed
to
account
for
latest
Seismic
Design
Maps
and
common
prac8ces
in
California
Latitude:
37.87N
Longitude:
-122.29W
Plan
View
Eleva,on
Loca,on

q First….
CHECK
AND
VALIDATE
YOUR
MODEL…
q The
model
Ø Walls:
Nonlinear
truss
modeling
approach
Ø Columns
and
beams:
Force-‐based
beam-‐column
elements
Ø Diaphragms:
Flexible
diaphragms
allowing
for
plas8c
hinge
@FEUP
p. 21
July 03, 2014
Elevation Location
elonga8on

@FEUP
p. 22
July 03, 2014

@FEUP
p. 23
July 03, 2014
Bridge
Example
Soil-structure interaction: Barbosa, Mason, Romney (2013)
Tsunami following earthquake: Carey, Mason, Barbosa, Scott (2014)

out-of-plane cross sectional area of the quadrilateral element. The earthquake motion is to the model as an equivalent force-time series, which is coupled with the dashpot. equivalent force-time series, FE, is calculated as FE = 2ȡE Vs uլg A, where uլg is the velocity-series of the input earthquake motion. Applying the force-time series at the soil-bedrock requires the soil column to have unconstrained horizontal degrees of freedom, accomplished by modeling soil column bedrock interface with rollers (i.e. the vertical degree-is constrained).
@FEUP
Barbosa, Mason, Romney (2013)
p. 24
July 03, 2014
Soil-‐Founda8on-‐Bridge
Model
q Type-‐I
sha
q California,
Oregon,
Washington,
USA
(a)
(b)

@FEUP
p. 25
July 03, 2014
Bridge
Deck
&
Abutments
• Linear
elas8c
beam-‐column
• 10.36
m
W
x
1.67
m
T
x
63.4
m
L
• Area
=
4.56
m2
• Ixx
=
5.98x1012
mm4

@FEUP
p. 26
July 03, 2014
Bridge
Deck
&
Abutments
• Abutment
(Shamsabadi
et
al.,
2007,
Caltrans
SDC)
• Silty
sand
• S8ffness,
K
=
307
kN/cm/m
• Yield
Force,
Fy
=
1397
kN
• Ini8al
Gap
Opening
=
2.54
cm

@FEUP
p. 27
July 03, 2014
27
Pile
and
Column
• Moment-‐Curvature
Analysis
• f’ c
=
28
MPa
• Fy
=
475
MPa
• E
=
200
GPa
• Long.
steel
ra8o
=
1.0%
• Fiber-‐sec8on:
• Varied
number
of
theta
wedges
and
radial
rings

the Open System for Earthquake Engineering Simulations (OpenSees) finite [10]. The seismic response of the soil-bridge system was analyzed by subjecting seven shallow crustal earthquake motions and seven subduction zone earthquake 1 shows a schematic of the overall soil-bridge system and a cross-section of the bridge column. Barbosa et al. [2] contains more details about the soil-bridge model, of the modeling details have changed, which are documented herein.
@FEUP
p. 28
July 03, 2014
Analysis
Methodology
• Development
of
SFB
Model
• Step
1:
Define
soil
• Step
2:
Define
structural
nodes
and
elements

@FEUP
p. 29
July 03, 2014
Analysis
Methodology
• Step
3:
Gravity
(self-‐weight)
loads
• Soil
self-‐weight
loading
• Connect
pile
to
soil
column
• Structural
self-‐weight
loading

@FEUP
p. 30
July 03, 2014
Analysis
Methodology
• Step
4:
Nonlinear
dynamic
analysis
using
earthquake
mo8ons

response will be dominated by tsunami impact on the much larger deck width. The length tsunami bore is set as twice the open length (defined in Figure 3). The accuracy and PFEM solution depends on the mesh density of the fluid and structure under consideration
3. Schematic of the tsunami bore simulation (Note: pile and soil column are not Tsunami
ensure accuracy and stability, the mesh size for the tsunami bore simulation was mm x 175 mm.
@FEUP
p. 31
July 03, 2014
following
Earthquake
Modeling
q Type-‐I
sha
q California,
Oregon,
Washington,
USA
q In
OpenSees,
use
PFEM:
v Zhu and Scott (2014)
Carey, Mason, Barbosa, Scott (2014)

PFEM procedure. At the conclusion of each time step, the fluid, wall, flume and bridge
column were re-meshed for the subsequent time steps. Figure 5 shows a schematic of the
tsunami simulation.
Tsunami-‐Bridge
Interac8on
Model
@FEUP
p. 32
July 03, 2014
Figure 4. Flow Chart of the three stages comprising the analysis framework.

Tsunami-‐Bridge
Interac8on
Model
q Type-‐I
sha
q California,
Oregon,
Washington,
USA
30
30
25
25
20
20
15
15
10
10
5
5
0
0
−5
−5
30
25
20
15
10
5
0
−20 −15 −10 −5 0 5 10
@FEUP
p. 33
Analysis at 0.575 Sec
Analysis at 0.575 Sec
30
25
20
15
10
5
0
−5
July 03, 2014
Carey, Mason, Barbosa, Scott (2014)
(b)
3.1, and (b) tsunami bore during Step 3.2.
Initial Bore Time 0
−20 5 10
−20 −15 −10 −5 0 5 10
(a)
(b)
Figure 5. (a) Tsunami bore at the end of Step 3.1, and (b) tsunami bore during Step 3.2.
−5
Initial Bore Time 0
−20 −15 −10 −5 0 5 10
Units in meters

@FEUP
p. 34
July 03, 2014
Andre.Barbosa@oregonstate.edu

Dynamic Analysis with Examples – Seismic Analysis

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