This document presents a fiber macro-model for simulating the in-plane and out-of-plane response of infilled frames. The model uses 4 strut elements with distributed plasticity to account for the masonry arching mechanism and two-dimensional effects. It was validated using experimental tests on infilled steel and reinforced concrete frames, showing it can accurately capture the out-of-plane response and the effects of prior in-plane damage. The model provides an effective way to integrate in-plane and out-of-plane behavior in a simplified manner suitable for structural analysis.

1. Fabio Di Trapani Ph.D
Politecnico di Torino
Department of Structural, Building and Geotechnical Enginering (DISEG)
MODELLING IN-PLANE AND OUT-OF-PLANE RESPONSE OF
INFILLED FRAMES THROUGH A FIBER MACRO-MODEL
F. Di Trapani, P.B. Shing, L. Cavaleri
MODELLING IN-PLANE AND OUT-OF-PLANE RESPONSE OF
INFILLED FRAMES THROUGH A FIBER MACRO-MODEL
F. Di Trapani, P.B. Shing, L. Cavaleri

2. Outline
• Background
• Proposed Approach
• Validation Tests
• Conclusions

3. BACKGROUND

4. INFILL-FRAME INTERACTION UNDER SEISMIC LOADS
• In-Plane
• Out-of-plane

5. OUT-OF-PLANE ARCHING MECHAINSM
(MacDowell et al. 1956a and 1956b, Monk 1958, Angel 1994,
Bashandy et al. 1995, Klingner et al. 1996, Abrams et al. 1996)
k
t
h
f
q m
a 2






∝
Compressive Strength of
Masonry
Slenderness ratio of the
wall
ULTIMATE OOP LOAD
Restrain condition

6. IN-PLANE / OUT-OF-PLANE INTERACTION
• Infills are more vulnerable out-of-plane if they suffer of have suffered, simultaneous or
previous in plane damage
• 3D Structural models should account form both the mechanisms and the reciprocal
interaction
Out-of-plane failure of the infills

7. AVAILABLE IP-OOP INTEGRATED MACROMODELS
Hashemi and Mosalam (2007)
FEATURES
• 3D S.A.T. model
• 8 compression only struts
• 1 tension link

8. AVAILABLE IP-OOP INTEGRATED MACROMODELS
Kadysiewski and Mosalam (2009)
FEATURES
• 1 strut with symmetric elastic-perfectly plastic behaviour
• IP/OOP Interaction is introduced by calibrating the fibers composing
the cross-section

9. PROPOSED APPROACH

10. NEEDS FOR AN EFFECTIVE IP-OOP INTEGRATED MACROMODEL
Considering arching mechanism without using fictitious
expedients
Responsive to reciprocal IP/ OOP damage
Simply integrated in a 3D model

11. ARCHING MECHANISM IN FIBER-SECTION ELEMENTS
Fiber-section diagonal in flexure
NO TENSION
Uncracked cross-section
OOP response of the fiber cross-section
Cracked cross-section

12. ARCHING MECHANISM IN FIBER-SECTION ELEMENTS
Axial Force
coupled with
Bending moment
arises
)()()(
)(
)(
)( xxx
xM
xN
x ss
T
0s
T
s
ekks =





=





=
κ
ε
κε
κε
s
22T0
s
21T
s
12T0
s
11T
kkxM
kkxN
,,
,,
)(
)(
+=
+= N and M are
coupled
Formulation of fiber section DB elements
Cross section tangent stiffness matrix Full matrix

13. PROPOSED IP / OOP MACROMODEL
FEATURES
• 2 diagonal struts working in-plane and out-of-plane
• 1 horizontal and 1 vertical struts working out-of-plane
• Each strut is divided in two parts
• Mid-span nodes have independent displacements in x,y plane while are
constrained to move together along z direction

14. PROPOSED IP / OOP MACROMODEL [DIAGONAL STRUTS]
In-Plane Identification
t= actual thickness
w=1/3 d (or other)
Approximate the response in compression using a
concrete-type law in compression
Axial Load
Axial Displ
Force displacement relationship

15. PROPOSED IP / OOP MACROMODEL [DIAGONAL STRUTS]
Masonry
Diagonal struts
00 mmd ff <
The strength of the diagonal is in general lower than the
strength of the masonry
2
0






∝
t
d
wf
q dm
a 2
0






=
t~
d
w~f dmd
dw t dw~ t
~
twtw dd
~~=
Cross section area is
maintained constant
t
tw
wt
f
f
t d
d
0md
0m
~
~;
~
==
Ultimate OOP capacity equivalence
Out-of-Plane Identification
Surrogate dimensions

16. PROPOSED IP / OOP MACROMODEL [HORIZ. AND VERT. STRUTS]
t actual thickness
actual stress-strain law of masonry
widths
θθ sin
;
cos
d
v
d
h
w
w
w
hw −=−= l
Masonry
εεεεm0, fm0
εεεεmu, fmu

17. VALIDATION TESTS

18. VALIDATION TESTS
Experimental tests used for valitaion
• Angel & Abrams (1994, 1996) RC Frames
• Dawe & Seah (1989) Steel Frames
• Flanagan & Bennett (1999) Steel Frames

19. VALIDATION TESTS
Lateral displacement history
Brick Masonry infillsConcrete unit Masonry infills
Specs. by Angel, Abrams (1994, 1996)

20. IP Damage Simulation
(OpenSees)
History of displacements
Specs. by Angel, Abrams (1994, 1996)
IP Response
VALIDATION TESTS

21. OOP Push Simulation (OpenSees)
Experimental
Proposed Model
VALIDATION TESTS

22. OOP Push Simulation (OpenSees)
Response of
the Diagonals
Response of
H + V Struts
VALIDATION TESTS

23. Specs. by Dawe & Seah (1989) and Flanagan & Bennett (1999)
Dawe & Seah Flanagan & Bennett
VALIDATION TESTS

24. Specs. by Dawe & Seah (1989) and Flanagan & Bennett (1999)
Dawe & Seah
Flanagan & Bennett
Experimental
Proposed Model
Experimental
Proposed Model
VALIDATION TESTS

25. TESTING IN-PLANE / OUT OF PLANE INTERACTION
SPEC. 2 by Abrams
SPEC. 4 by Abrams

26. CONCLUSIONS

27. CONCLUSIONS
- A simplified macro-model for the assessment of both in plane – out of plane
behavior of the infilled frame was developed and validated.
- The model provides the use of 4 struts modeled with distributed plasticity fiber
elements in order to account both arching mechanism and 2D effect.
- The reliability of the model has been tested simulating the experimental tests on
real infilled steel and RC frames.
- Validation tests have shown a good accuracy of the model to capture the OOP
response including also the damage induced by a previous IP history of
displacements.

28. THANK YOU
fabio.ditrapani@polito.it