Design projects and research activities

DESIGN PROJECTS AND RESEARCH ACTIVITIES

Dr. Isabella Vassilopoulou
STRUCTURAL ENGINEER, Ph.D. NTUA, GREECE
ASSOCIATE AT ODOTECHNIKI Ltd

Athens, Greece, 2013

CONTENTS
PROJECT NAME: Pages
A. Entrance Canopies of the Athens Olympic Sports Complex 3-11
B. Railway bridge (integral system) 12-15
C. Viaduct of 14 spans 16-21
D. Doctoral Thesis: Nonlinear Dynamic Response and Design of Cable 22-32
Nets

A B

C D

Dr. ISABELLA VASSILOPOULOU 2
STRUCTURAL ENGINEER, Ph.D. N.T.U.A. and ASSOCIATE AT ODOTECHNIKI Ltd

ENTRANCE CANOPIES
Entrance Canopies of the Athens Olympic Sports Complex
Location: Athens, Greece
Architectural and structural report : CALATRAVA S.A.
Design verification: Associate Professor C. J. Gantes, I. Vassilopoulou
Construction: Joint Venture TERNA S.A. – PANTECHNIKI S.A.
Client: Hellenic Ministry of Culture – General Secretariat of Sport
Dates: design and construction - 2004

Areas of responsibility
Structural design of superstructure
and foundation

•Modeling
•Permanent, variable and seismic
loads
•Loading combinations
•Static and dynamic analysis


ENTRANCE CANOPIES

Plan view (dimensions in m)

ENTRANCE CANOPIES

Section A-A (dimensions in m)

ENTRANCE CANOPIES

Finite Element Software: SOFiSTiK

Model for analysis


ENTRANCE CANOPIES


1 st 2 nd 3 rd

4 th 5 th 6 th

Vibration modes


ENTRANCE CANOPIES

The canopies under construction

Installation of the two arches


ENTRANCE CANOPIES


Installation of the beams


ENTRANCE CANOPIES


Installation of the outer ring


ENTRANCE CANOPIES

General view


RAILWAY BRIDGE
Railway bridge over the river “Dervenios”
Location: Derveni (Railway line Corinth – Patras), Greece
Geotechnical and Structural Design: ODOTECHNIKI Ltd
Construction: MICHANIKI S.A.
Client: ERGOSE S.A.
Dates: design - 2006, construction - 2008
Type: Prestressed frame (integral system) – Total length ~49m

Final design of superstructure and
foundation

•Modeling
•Pretension
•Permanent, variable and seismic
loads
•Foundation bearing capacity
•Preparation of construction drawings

RAILWAY BRIDGE
4.00 48.70 4.00

Elevation view
2.00 8.70 2.00
2.80

7.80

Cross section (dimensions in m)

RAILWAY BRIDGE


Model for analysis and design

RAILWAY BRIDGE

Bridge under construction


VIADUCT
Viaduct from Km 13+774.54 to Km 14+270.40
Location: Tsakona (Tripoli – Kalamata Highway), Greece
Geotechnical and Structural Design: ODOTECHNIKI Ltd
Construction: ALPINE BAU Gmbh – GEK TERNA GROUP
Client: Hellenic Ministry of Infrastructure, Transport and Networks
Dates: design - 2008, construction - 2010
Type: 14 spans with post-tensioned/precast beams – Total length 492m

Final design of superstructure and
foundation

•Modeling
•Pretension
•Permanent, variable and seismic loads
•Foundation bearing capacity
•Supervision of construction drawings


VIADUCT


Model for deck design
Prestressed/precast beams of a typical span

Model for seismic design

VIADUCT
0.16 10 / 10

61
0.
330 10 / 10 L=

1 5
0.

0.14
0.66

0.10
0.10
4
0.4

10 / 10

0.26
10 / 10

540 10 / 10
12 / 10 L= 0.80
2.19
2.18

0.13 404 10 / 10

2.03
0.20
1.97
[(34+19)x2+96]x2
10 12 / 20 10 12 / 20 L= 1.00
0.12
168 10 / 10

0.29
(84x2)
L= 0.45
10 / 10 10 / 10
1O12

0.
58
0.25

0.25

14 / 100

0.12
0.12

0.13
0.15
140 14 / 100 0.16 0.66
L= 0.65 8O18 320 10 / 10 L= 0.90
110 12 / 10 10 / 10
L= 5.00
0.25 0.25 0.25

0.75

Detail of beam reinforcements from the construction drawings
(dimensions in m)

VIADUCT


Construction of foundation Pretension of beams
and pilecaps


VIADUCT


Construction of piers Placement of beams


VIADUCT


Construction of concrete slab Finished bridge


DOCTORAL THESIS
Nonlinear Dynamic Response and Design of Cable Nets
Supervisor: Associate Professor C. J. Gantes
Date: November 2011
http://odotechniki.gr/siteen/pages/publications/associates-research.php

From … … to …

… the Raleigh Arena …the Velodrome
North Carolina, U.S.A. (1953) London, UK (2011)

Vassilopoulou, I., “Nonlinear dynamic response and design of cable nets”, Structural Engineering
International (SEI) – Recent PhD Abstracts, Vol. 22, No. 3, pp. 422-423.


DOCTORAL THESIS
Geometry of a cable net


DOCTORAL THESIS
SDOF Cable net

L/ 2
L: cable span, f/L: sag-to-span ratio

4 (L/ 2,0,-f) 2 (-L/ 2,0,-f)

L/ 2 L/ 2
L/ 2

Plan view Perspective view

I. Vassilopoulou and C.J.Gantes
“Nonlinear dynamic phenomena in a SDOF model of cable net”
Archive of Applied Mechanics, Vol. 82, No. 10, pp. 1689-1703.


DOCTORAL THESIS
SDOF Cable net: Simplified equation of motion
C  K 16(EA) m 3 (P )
wm +
 wm + m wm + w m = 0 m cos( Ωt )
Mm Mm Mm L3
m
Mm

Linear term Nonlinear term

Duffing equation
2 3
w m + 2εμw m + ω m w m + εαw m = p m cos( Ωt )
 

16(EA) m (P0 ) m
where 2εμ=2ζωm εα = pm =
Mm L3
m
Mm

 fm2 2 
4(EA) m (N0 ) m (N0 ) m f m
ωm = ⋅ 8 2 + 2 −4 
Mm L m  L (EA) m (EA) m L2 
 m m 


DOCTORAL THESIS
MDOF cable net: natural frequencies

(1S) (2A)

2
f Eg T0  L  7 gT0
ω1S = 7⋅ ⋅ 3   ω2A = ⋅
L ρL2 EA  f  L ρA

(1A) (1A)

2
f Eg T L
2.5 0  
ω1A = 7⋅ ⋅
L ρL2 EA  f 
I. Vassilopoulou and C. J. Gantes, “Vibration modes and natural frequencies of saddle form cable
nets”, Computer and Structures, Vol. 88, pp.105-119, 2010.

DOCTORAL THESIS
MDOF cable net: natural frequencies

2
Ε: Elastic modulus EA  f  T0: initial pretension
λ2 =  
Α: Cross-sectional area T0  L  f/L: Sag-to-span ratio

λ2≤0.8 ω1S ≤ ω1A < ω2A

0.8 < λ2 ≤ 1.0 ω1A < ω1S ≤ ω2A

1.0 < λ2 ≤ 1.17 ω1A ≤ ω2A < ω1S

1.17 < λ2 ω2A < ω1A < ω1S


DOCTORAL THESIS
MDOF cable net: Dynamic response to harmonic loads

2 node 15
Uniform loading

deflection (m)
1

0
0.30 0.40 0.50 0.60
Ω/ ω1S

Steady-state response (superharmonic
resonance Ω<ω 1S )
3 node 15

deflection (m)
2

P(t)=P 0 cosΩt 1

0
I. Vassilopoulou and C. J. Gantes, “Nonlinear 0.90 1.00 1.10 1.20 1.30 1.40
dynamic behavior of saddle form cable nets Ω/ ω1S
under uniform harmonic load”, Engineering Steady-state response
Structures, Vol. 33, pp. 2762-2771, 2011 (fundamental resonance Ω≈ω 1S )

DOCTORAL THESIS
Approximate method

MODEL (m) PROTOTYPE (p)

Similarity
relations

2
 Np + 1 
(P0 ) m = (P0 ) p  
N + 1
 m 
m model p prototype N number of cables per direction

I. Vassilopoulou and C. J. Gantes,
“Cable nets with elastically deformable edge ring”,
International Journal of Space Structures, Vol. 20, No.1, pp. 15-34, 2005.


DOCTORAL THESIS
Estimation of MDOF cable net response with an equivalent SDOF model

MODEL (m) PROTOTYPE (p)

Similarity
relations

Analytical solution Numerical analysis

I. Vassilopoulou and C.J.Gantes,
“Nonlinear dynamic response of MDOF cable nets estimated by equivalent SDOF models”,
Computational Methods in Earthquake Engineering, Vol. 2, M. Papadrakakis, M. Fragiadakis, V.
Plevris (Eds.), Springer Verlag, 2012 (in press).


DOCTORAL THESIS
Estimation of MDOF cable net response with an equivalent SDOF model
Fundamental Resonance
SDOF response
MDOF response with initial conditions
4 4.0 Ω/ ωp = 1.08
MDOF response with zero initial conditions

deflection (m)
2.0
Steady state amplitude (m)

0.0
3
-2.0

-4.0
2 0 5 10 15 20 25
time (sec)

4.0 Ω/ ωp = 1.08
1

deflection (m)
2.0

0.0
0
-2.0
0.9 1 1.1 1.2 1.3
-4.0
Ω/ωp 0 5 10 15 20 25
time (sec)


DOCTORAL THESIS
MDOF cable net: Dynamic response to wind action

f/L N0/(Aσy) [%] λ2 ω1S[sec-1] f1S[Hz]

2 EA  f 
2 1/20 10 2.59 7.696 1.225
λ =  
T0  L  1/20 19 1.35 6.654 1.059
1/20 30 0.86 6.085 0.968
f/L: sag/span ratio, Ν0: initial cable pretension
A: cross-sectional area σy: yield stress

λ2 2.59 1.35 0.86

Dr. Isabella Vassilopoulou
STRUCTURAL ENGINEER, Ph.D. NTUA, GREECE
ASSOCIATE AT ODOTECHNIKI Ltd

isabella.vassilopoulou@gmail.com
i_vasilopoulou@odotechniki.gr

Athens, Greece, 2013

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