Authors: Salvatore Sessa, Roberto Serpieri, Luciano Rosati

1. Outline Introduction Confined LSh Examples Conclusions References
Implementation and Finite-Element analysis of shell elements
confined by Through-the-Thickness uniaxial devices
S. Sessa [salvatore.sessa2@unina.it], R. Serpieri, L. Rosati
OpenSees Days Europe – Porto
University of Naples Federico II
June, 20th, 2017
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

2. Outline Introduction Confined LSh Examples Conclusions References
Work Outline
1 Introduction
Motivations and objectives
2 Confined layered shell formulation
Continuum Formulation
3 Examples
4 Conclusions
5 References
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

3. Outline Introduction Confined LSh Examples Conclusions References
Motivations and objectives
Confinement in civil structures
Confinement is an important issue in presence of non–linear
materials and specifically:
Masonry
Reinforced concrete
because of its benefical consequences, confinement techniques are
used in structural retrofit.
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

4. Outline Introduction Confined LSh Examples Conclusions References
Motivations and objectives
Confinement in masonry structures
Figure: Steel net retrofit
Transverse links reduce the
out–of–plane deformation of masonry
walls
The external surfaces of the wall are
constrained together by steel nets,
ribbons or reinforced concrete layers.
See [Pinho et al., 2015],
[Valluzzi et al., 2004] and
[Oliveira et al., 2012]
Source: www.FibreNet.it
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

5. Outline Introduction Confined LSh Examples Conclusions References
Motivations and objectives
Confinement in masonry structures
Figure: Kevlar link Figure: Carbon link
No prescriptions for masonry structures
Source: http://www.olympus-frp.com
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

6. Outline Introduction Confined LSh Examples Conclusions References
Motivations and objectives
Confinement in r.c. shear walls
Figure: Steel stirrups. Source:
www.constructioncost.co
Transverse links bond
together reinforcement
bars of the two shear wall
surfaces.
EC2 Prescriptions:
the code takes into
account the
importance of
transversal
reinforcements
it substantially
extends column
prescriptions to
shear walls.
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

7. Outline Introduction Confined LSh Examples Conclusions References
Motivations and objectives
Confinement – Strength increment approach
Introduced in [Mander et al., 1988] and widely employed.
Confinement devices are not included in the global analysis:
[Berto et al., 2002]
[Corradi et al., 2007]
[Mirmiran et al., 2000]
The approach proved to be accurate enough for common
practice:
[Krevaikas and Triantatillou, 2005]
[Ilyas et al., 2009]
The approach focuses on frame elements.
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

8. Outline Introduction Confined LSh Examples Conclusions References
Motivations and objectives
Confinement effects in reinforced concrete structures
Figure: Mander
constitutive model
In–plane confinement investigated by
[Mostofinejad and Anaei, 1982]
Experimental campaigns carried out in
[Deng et al., 2008],
[Lau and Cruz-Noguez, 2013] and
[Medani et al., 2008]
Confinement plays a major role in shear
wall ductility
[Mostofinejad and Anaei, 2012] with
differences from the column case.
Out–of–plane confinement still under
investigation.
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

9. Outline Introduction Confined LSh Examples Conclusions References
Motivations and objectives
Confined (jacketed) masonry bibliographical survey
Similar experimental results and jacketing retrofit strategies are
shown in:
[Corradi et al., 2007]
[Borri et al., 2011]
[Ilyas et al., 2009]
[Zucchini, 2011]
On the contrary, confined reinforced concrete shells are not really
investigated.
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

10. Outline Introduction Confined LSh Examples Conclusions References
Motivations and objectives
Shell element in OpenSees
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

11. Outline Introduction Confined LSh Examples Conclusions References
Motivations and objectives
Shear wall elements and constitutive models –
bibliographical survey
The finite element currently implemented in OpenSees is the
ShellMITC4:
4 nodes of 6 DOFs
in–plane, flexural and drilling behaviour (Mindlin plate)
its geometry is defined by means of a layered section
(LayeredShell)
it requires a triaxial, plane–stress material
Reference: [Dvorkin and Bathe, 1984]
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

12. Outline Introduction Confined LSh Examples Conclusions References
Continuum Formulation
Mindlin shell–plate element
Figure: Layered confined shell section
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

13. Outline Introduction Confined LSh Examples Conclusions References
Continuum Formulation
Mindlin shell–plate element
SH
EV = Em
1 Em
2 γm
12 κb
1 κb
2 2κb
12 γs
13 γs
23
T
SH
σV =
∂Φ
∂
SH
EV
=
∂Φ
∂Em
1
∂Φ
∂Em
2
∂Φ
∂γm
12
∂Φ
∂κb
1
∂Φ
∂κb
2
∂Φ
∂2κb
12
∂Φ
∂γs
13
∂Φ
∂γs
23
T
u = u(m)
+ θ × zˆz + uz (z) ˆz; ε = sym (u ⊗ )
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

14. Outline Introduction Confined LSh Examples Conclusions References
Continuum Formulation
Mindlin shell–plate element
Set trial generalized strain
SH
EV
Compute (5–elements) strain: ε0V (z) =
0
PV (z)
SH
EV
Compute stress
Compute generalized shell forces
SH
σV =
∂Φ
∂
SH
EV
=
h/2
−h/2
∂Φ
∂εV
(z)
∂εV
∂
SH
EV
(z) dz =
h/2
−h/2
0
P
T
V σV dz
Houston! We’ve got a problem...
Strain component ε33 is not defined by the generalized shell strain.
Classical approach assumes planar state for either stress or strain!
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

15. Outline Introduction Confined LSh Examples Conclusions References
Continuum Formulation
Confined shell section formulation
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

16. Outline Introduction Confined LSh Examples Conclusions References
Continuum Formulation
Mindlin shell–plate element
Constitutive tangent operator is partitioned with respect the 3rd
component:
CV =
∂σV
∂εV
=
0 0
CV
0 3
CV
3 0
CV
3 3
CV
˙σ0V (z) =
0 0
CV (z) ·
0
PV (z)
˙SH
EV +
0 3
CV (z) ˙εz (z)
˙σz (z) =
3 0
CV (z) ·
0
PV (z)
˙SH
EV +
3 3
CV (z) ˙εz (z)
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

17. Outline Introduction Confined LSh Examples Conclusions References
Continuum Formulation
Confined shell section formulation
Figure: Layered
confined shell section
Equilibrium and compatibility conditions are
enforced through the section thickness:
σ33 (P, z) + µs
σs
(P) = 0; −h/2 ≤ z ≤ h/2
h/2
−h/2
ε33 (P, z) dz = εs
(P) h
The transverse stress is constant along the
shell section and it is in equilibrium with the
stirrup stress;
The total expansion of the shell section has
to be equal to the stirrups stretching.
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

18. Outline Introduction Confined LSh Examples Conclusions References
Continuum Formulation
Confined shell section formulation - Synoptic table
ε0V (z) =
0
PV (z)
SH
EV
σ33 (P, z) + µs
σs
(P) = 0; −h/2 ≤ z ≤ h/2
h/2
−h/2
ε33 (P, z) dz = εs
(P) h
SH
σV =
∂Φ
∂
SH
EV
=
h/2
−h/2
∂Φ
∂εV
(z)
∂εV
∂
SH
EV
(z) dz =
h/2
−h/2
0
P
T
V σV dz
˙σ0V (z) =
0 0
CV (z) ·
0
PV (z)
˙SH
EV +
0 3
CV (z) ˙εz (z)
˙σz (z) =
3 0
CV (z) ·
0
PV (z)
˙SH
EV +
3 3
CV (z) ˙εz (z)
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

19. Outline Introduction Confined LSh Examples Conclusions References
Continuum Formulation
Confined shell section formulation
Enforcing equilibrium and compatibility between core material
and stirrup, we get an implicit system of equations;
The transversal equilibrium is solved by a Newton–Raphson
algorithm
The tangent operator is provided in closed form.
Reference: [Sessa et al., 2017]
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

20. Outline Introduction Confined LSh Examples Conclusions References
Continuum Formulation
Confined shell section formulation - Tangent operator
3 3
CV (z) ∂ ˙uz
∂z (z) − µs
h
S
C [ ˙uz (h/2) − ˙uz (−h/2)] = −
3 0
CV (z) ·
0
PV (z)
˙SH
EV
∂ ˙uz
∂z (z) − µs
h
S
C [ ˙uz (h/2) − ˙uz (−h/2)] 1
3 3
C V (z)
= − 1
3 3
C V (z)
3 0
CV (z) ·
0
PV (z)
˙SH
EV
h/2
−h/2
∂ ˙uz
∂z (z) dz −
h/2
−h/2
µs
h
S
C [ ˙uz (h/2) − ˙uz (−h/2)] 1
3 3
C V (z)
dz =
−
h/2
−h/2
1
3 3
C V (z)
3 0
CV (z) ·
0
PV (z)
˙SH
EV dz
˙h = ˙uz (h/2) − ˙uz (−h/2) =
−
h/2
−h/2
1
3 3
C V (z)
3 0
CV (z)·
0
PV(z)
˙SH
EV dz
1− µs
h
S
C
h/2
−h/2
1
3 3
C V (z)
dz
˙σ0V (z) =
0 0
CV (z)
0
PV (z) +
0 3
CV (z)
3 3
C V (z)
⊗ −
0
P
T
V
3 0
CV (z) + µs
h
S
C V
˙SH
EV
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

21. Outline Introduction Confined LSh Examples Conclusions References
Continuum Formulation
Confined shell section formulation - Tangent operator
˙σ0V (z) =
0 0
CV (z)
0
PV (z) +
0 3
CV (z)
3 3
C V (z)
⊗ −
0
P
T
V
3 0
CV (z) + µs
h
S
C V
˙SH
EV
˙SH
σV = HV
˙SH
EV
HV =
h/2
−h/2
0
P
T
V
0 0
CV (z)
0
PV (z) +
0
P
T
V
0 3
CV (z)
3 3
CV (z)
⊗ −
0
P
T
V
3 0
CV (z) +
µs
h
S
C V dz
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

22. Outline Introduction Confined LSh Examples Conclusions References
Continuum Formulation
Implementation in OpenSees
The OpenSees object–oriented nature makes it possible to
implement the TTJS formulation in a single object:
LayeredConfinedShell
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

23. Outline Introduction Confined LSh Examples Conclusions References
Continuum Formulation
Implementation in OpenSees
Objects needed by LayeredConfinedShell:
A previously defined uniaxialMaterial object (transverse ties)
A previously defined set of ndMaterial objects (core layers)
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

24. Outline Introduction Confined LSh Examples Conclusions References
Path–following analysis
Qv
Qx
B
H x
y
z
Steeltrusses
Steeltrusses
Monitored
Gauss point
Qv
B
H x
y
z
Steeltrusses
Steeltrusses
Qz
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

25. Outline Introduction Confined LSh Examples Conclusions References
Path–following analysis
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
0
100
200
300
400
500
600
U [m]
R[kN]
Plane stress
µ=0.2 %
µ=2 %
Zero TT stretch
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
0
10
20
30
40
50
60
70
80
U [m]
R[kN]
Plane stress
µ=0.2 %
µ=2 %
Zero TT stretch
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

26. Outline Introduction Confined LSh Examples Conclusions References
Path–following analysis
(e) µ = 2% (f) Zero TT stretch
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

27. Outline Introduction Confined LSh Examples Conclusions References
Yield surface (Von Mises)
Confinement increases the stress spherical part.
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

28. Outline Introduction Confined LSh Examples Conclusions References
Yield surface (Drucker–Prager)
Drucker Prager strength is proportional to the stress spherical part.
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

29. Outline Introduction Confined LSh Examples Conclusions References
Time history analysis
8 × 4 × 0.8 m Masonry wall
Shell core modeled by
Drucker Prager ndMaterial
Elastic transverse ties
(Kevlar FRP)
Floor masses and loads
Transient analysis:
Emilia-Italy 2012
earthquake accelerogram
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

30. Outline Introduction Confined LSh Examples Conclusions References
Time history analysis
8 × 4 × 0.8 m Masonry wall
Shell core modeled by
Drucker Prager ndMaterial
Elastic transverse ties
(Kevlar FRP)
Floor masses and loads
Transient analysis:
Emilia-Italy 2012
earthquake accelerogram
(Mirandola)
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

31. Outline Introduction Confined LSh Examples Conclusions References
Time history analysis: Results
Through-the-Thickness stress: YouTube
Plastic energy: YouTube
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

32. Outline Introduction Confined LSh Examples Conclusions References
Transient analysis: displacements
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

33. Outline Introduction Confined LSh Examples Conclusions References
Transient analysis: plastic energy
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

34. Outline Introduction Confined LSh Examples Conclusions References
Transient analysis: plastic energy
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

35. Outline Introduction Confined LSh Examples Conclusions References
Conclusions
The LayeredConfinedShell object is capable of computing
the triaxial stress state by enforcing equilibrium and
compatibility.
As the transverse stiffness tends to zero [infinite] the object
shows a plane stress [strain] behavior.
The has a greater computational effort with respect to
condensed shells, but...
...it is far more faster than 3D brick + truss models.
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

36. Outline Introduction Confined LSh Examples Conclusions References
Future challenges
Implementation of non–confined and uniaxial layers;
Implementation of a 4 × 9 DOFs Shell element;
Use of alternative ndMaterials;
Definition of pre–tensioned links.
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

37. Outline Introduction Confined LSh Examples Conclusions References
Thank You for your attention
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

38. Outline Introduction Confined LSh Examples Conclusions References
Berto, L., Saetta, A., Scotta, R., and Vitaliani, R. (2002).
An orthotropic damage model for masonry structures.
International Journal for Numerical Methods in Engineering,
55:127–157.
Borri, A., Castori, G., and Corradi, M. (2011).
Masonry columns confined by steel fiber composite wraps.
Materials, 4:311–326.
Corradi, M., Grazini, A., and Borri, A. (2007).
Confinement of brick masonry columns with CFRP materials.
Composites Science and Technology, 57:1772–1783.
Deng, M., Liang, X., and Yang, K. (2008).
Experimental study on seismic behavior of high performance
concrete shear wall with new strategy of transverse confining
stirrups.
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

39. Outline Introduction Confined LSh Examples Conclusions References
In Proc. 14th World Conference on Earthquake Engineering
(WCEE), Beijing, China, pages 1–8.
Dvorkin, E. N. and Bathe, K.-J. (1984).
A continuum mechanics based fournode shell element for
general nonlinear analysis.
Engineering Computations, 1(1):77–88.
Ilyas, M., Farooq, S. H., Qazi, A. U., and Umair, R. (2009).
Masonry Confinement Using Steel Strips.
Pakistan Journal of Engineering & Applied Sciences, 5:1–9.
Krevaikas, T. D. and Triantatillou, T. C. (2005).
Masonry Confinement with Fiber–Reinforced Polymers.
Journal of Composite for Construction ASCE, 9(2):128–135.
Lau, D. T. and Cruz-Noguez, C. A. (2013).
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

40. Outline Introduction Confined LSh Examples Conclusions References
Developments on Seismic Retrofit of RC Shear Walls with
FRP.
In Proc. 5th International Conference on Advances in
Experimental Structural Engineering, Taipei, Taiwan, pages
1–20.
Mander, J. B., Priestley, M. J. N., and Park, R. (1988).
Theoretical stress–strain model for confined concrete.
Journal of Structural Engineering, 114(8):1804–1826.
Medani, T., Liu, X., Huurman, M., Scarpas, A., and Molenaar,
A. (2008).
Experimental and numerical characterization of a membrane
material for orthotropic steel deck bridges: Part 1:
Experimental work and data interpretation.
Finite Elements in Analysis and Design, 44(9-10):552 – 563.
Mirmiran, A., Zagers, K., and Yuan, W. (2000).
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

41. Outline Introduction Confined LSh Examples Conclusions References
Nonlinear finite element modeling of concrete confined by fiber
composites.
Finite Elements in Analysis and Design, 35(1):79 – 96.
Mostofinejad, D. and Anaei, M. M. (1982).
Ductility of confined concrete masonry shear walls.
Bulletin of the New Zealand National Society for Earthquake
Engineering, 15(1):22 – 26.
Mostofinejad, D. and Anaei, M. M. (2012).
Effect of confining of boundary elements of slender {RC} shear
wall by {FRP} composites and stirrups.
Engineering Structures, 41:1 – 13.
Oliveira, D. V., Silva, R. A., Garbin, E., and Louren¸co, P. B.
(2012).
Strengthening of three-leaf stone masonry walls: an
experimental research.
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

42. Outline Introduction Confined LSh Examples Conclusions References
Materials and structures, 45(8):1259–1276.
Pinho, F. F., L´ucio, V. J., and Bai˜ao, M. F. (2015).
Rubble stone masonry walls strengthened by three-dimensional
steel ties and textile-reinforced mortar render, under
compression and shear loads.
International Journal of Architectural Heritage, 9(7):844–858.
Sessa, S., Serpieri, R., and Rosati, L. (2017).
A continuum theory of throughthethickness jacketed shells for
the elasto-plastic analysis of confined composite structures:
Theory and numerical assessment.
Composites Part B: Engineering, 113:225 – 242.
Valluzzi, M., Da Porto, F., and Modena, C. (2004).
Behavior and modeling of strengthened three-leaf stone
masonry walls.
Materials and Structures, 37(3):184–192.
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017

43. Outline Introduction Confined LSh Examples Conclusions References
Zucchini, L. (2011).
Experimental analysis of fiber reinforced cementitious matrix
(frcm) confined masonry columns.
Technical report, Alma Mater Studiorum Universit´a di
Bologna.
Sessa et al. – Implementation and FE analysis of shell elements confined by TT uniaxial devices Univ. of Naples Federico II
OpenSees Days Europe – 1st European Conference on OpenSees, Porto, 19-20 June 2017