![Application example: Case-study RC buildings
The OOP behaviour of the case-study infill panels was modelled by applying the herein proposed semi-
empirical approach. The IP behaviour was modelled by applying Panagiotakos and Fardis model, with
softening stiffness equal to -3.6% of the predicted elastic stiffness of the infill, based on Guidi et al. IP
tests’ results on strong masonry infills.
The infill wall behaviour degradation was modelled through the herein proposed empirical approach.
The IP degradation was modelled with backbones defined at steps of 0.05 times the dOOP,u (16.3 mm)
displacement while the OOP degradation was modelled with backbones defined at steps of 0.05 times
the IDRu (1.80%).
0 5 10 15 20
0
100
200
300
OOP Displacement [mm]
OOPForce[kN]
0 10 20 30 40 50
0
200
400
600
IP Displacement [mm]
IPForce[kN]
MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS](https://image.slidesharecdn.com/presentationriccididomenicoverderame-170704232713/85/Modelling-the-out-of-plane-behaviour-of-URM-infills-and-the-in-plane-out-of-plane-interaction-effects-24-320.jpg)
![Application example: NLTH Analysis procedure
Seven bidirectional ground motions recorded on type A soil were selected
The two components of each ground motions were contemporarily matched to the design 5%-damped
response spectrum at Damage Limitation Limit State (DL) and at Life Safety Limit State (LS) through
the RspMatchBi (Grant, 2010) software.
0 1 2 3 4
0
0.2
0.4
0.6
0.8
1
T [s]
S
a
(T)[g]
mean
EC8 target
Spectral matching period
range: 0.035 s -1.100 s
All components matched to the
0.35 g design spectrum at LS
0 1 2 3 4
0
0.2
0.4
0.6
0.8
1
T [s]
S
a
(T)[g]
mean
0 1 2 3 4
0
0.2
0.4
0.6
0.8
1
T [s]
S
a
(T)[g]
mean
NS component EW component
MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS](https://image.slidesharecdn.com/presentationriccididomenicoverderame-170704232713/85/Modelling-the-out-of-plane-behaviour-of-URM-infills-and-the-in-plane-out-of-plane-interaction-effects-25-320.jpg)
![Application example: NLTH Analysis procedure
Incremental Dynamic Analyses were carried out to obtain for each horizontal direction an incremental
PGA vs maximum IDR curve.
For records scale factor determination, a bisection procedure was implemented in order to define the
PGA associated to the first OOP infill collapse and removal from the structural model with a precision
equal to +/- 0.01 g.
Mass and tangent-stiffness proportional Rayleigh damping rules for two control vibration mode were
applied.
20 40 60 80 100 120 140
0
50
100
150
200
250
300
350
400
Mode
Modes frequencies [rad/s]
OOP infill natural frequency [rad/s]
Control modes (1 and 131)
Rayleigh damping ratios (scaled for 104
)
Three groups of modes were recognizable from modal analysis.
- A first group of global “lower” modes corresponding to lower frequencies/modes involving the whole
structure;
MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS](https://image.slidesharecdn.com/presentationriccididomenicoverderame-170704232713/85/Modelling-the-out-of-plane-behaviour-of-URM-infills-and-the-in-plane-out-of-plane-interaction-effects-27-320.jpg)
![Application example: NLTH Analysis procedure
Incremental Dynamic Analyses were carried out to obtain for each horizontal direction an incremental
PGA vs maximum IDR curve.
For records scale factor determination, a bisection procedure was implemented in order to define the
PGA associated to the first OOP infill collapse and removal from the structural model with a precision
equal to +/- 0.01 g.
Mass and tangent-stiffness proportional Rayleigh damping rules for two control vibration mode were
applied.
20 40 60 80 100 120 140
0
50
100
150
200
250
300
350
400
Mode
Modes frequencies [rad/s]
OOP infill natural frequency [rad/s]
Control modes (1 and 131)
Rayleigh damping ratios (scaled for 104
)
Three groups of modes were recognizable from modal analysis.
- A first group of global “lower” modes corresponding to lower frequencies/modes involving the whole
structure;
- A second group of local modes involving infills excited in the OOP direction corresponding to
intermediate frequencies very close the infill natural frequency in the OOP direction;
MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS](https://image.slidesharecdn.com/presentationriccididomenicoverderame-170704232713/85/Modelling-the-out-of-plane-behaviour-of-URM-infills-and-the-in-plane-out-of-plane-interaction-effects-28-320.jpg)
![Incremental Dynamic Analyses were carried out to obtain for each horizontal direction an incremental
PGA vs maximum IDR curve.
For records scale factor determination, a bisection procedure was implemented in order to define the
PGA associated to the first OOP infill collapse and removal from the structural model with a precision
equal to +/- 0.01 g.
Mass and tangent-stiffness proportional Rayleigh damping rules for two control vibration mode were
applied.
20 40 60 80 100 120 140
0
50
100
150
200
250
300
350
400
Mode
Modes frequencies [rad/s]
OOP infill natural frequency [rad/s]
Control modes (1 and 131)
Rayleigh damping ratios (scaled for 104
)
Three groups of modes were recognizable from modal analysis.
- A first group of global “lower” modes corresponding to lower frequencies/modes involving the whole
structure;
- A second group of local modes involving infills excited in the OOP direction corresponding to
intermediate frequencies very close the infill natural frequency in the OOP direction;
- A third group of global “higher” modes corresponding to higher frequencies/modes involving the
whole structure.
MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS
Application example: NLTH Analysis procedure](https://image.slidesharecdn.com/presentationriccididomenicoverderame-170704232713/85/Modelling-the-out-of-plane-behaviour-of-URM-infills-and-the-in-plane-out-of-plane-interaction-effects-29-320.jpg)
![Incremental Dynamic Analyses were carried out to obtain for each horizontal direction an incremental
PGA vs maximum IDR curve.
For records scale factor determination, a bisection procedure was implemented in order to define the
PGA associated to the first OOP infill collapse and removal from the structural model with a precision
equal to +/- 0.01 g.
Mass and tangent-stiffness proportional Rayleigh damping rules for two control vibration mode were
applied.
20 40 60 80 100 120 140
0
50
100
150
200
250
300
350
400
Mode
Modes frequencies [rad/s]
OOP infill natural frequency [rad/s]
Control modes (1 and 131)
Rayleigh damping ratios (scaled for 104
)
Three groups of modes were recognizable from modal analysis.
- A first group of global “lower” modes corresponding to lower frequencies/modes involving the whole
structure;
- A second group of local modes involving infills excited in the OOP direction corresponding to
intermediate frequencies very close the infill natural frequency in the OOP direction;
- A third group of global “higher” modes corresponding to higher frequencies/modes involving the
whole structure.
In this study, the first control mode corresponds the first
natural frequency of the infilled structure, while the
second control mode corresponds to the second group
mode associated to the frequency closer to the infill
natural frequency in the OOP direction.
A damping ratio equal to 2% was assigned to each
control mode.
MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS
Application example: NLTH Analysis procedure](https://image.slidesharecdn.com/presentationriccididomenicoverderame-170704232713/85/Modelling-the-out-of-plane-behaviour-of-URM-infills-and-the-in-plane-out-of-plane-interaction-effects-30-320.jpg)
![Application example: NLTH Analysis results
Median IDA curves in each direction for W/ and W/O models of all case-study buildings are shown in
the following figures
0 1 2 3 4 5
0
0.2
0.4
0.6
0.8
1
8P15-X
maximum IDRX
[%]
PGA
X
[g]
W/O Model
W/ Model
0 1 2 3 4 5
0
0.2
0.4
0.6
0.8
1
8P15-Z
maximum IDRZ
[%]
PGA
Z
[g]
W/O Model
W/ Model
0 1 2 3 4 5
0
0.2
0.4
0.6
0.8
1
8P35-X
maximum IDRX
[%]
PGA
X
[g]
W/O Model
W/ Model
0 1 2 3 4 5
0
0.2
0.4
0.6
0.8
1
8P35-Z
maximum IDRZ
[%]
PGA
Z
[g]
W/O Model
W/ Model
MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS
Mean OOP collapse PGAs are shown in the following table. They are, as expected, lower than the ones
predicted by applying a code-based approach (0.41 g for 8P15 case-study building and 0.38 g for the
8P35 case-study building), especially if IP-OOP interaction is accounted for (W/ model). Moreover, the
first OOP infill collapse does not occur necessary at last storeys but at intermediate storeys due to
IP-OOP interaction effects.
Clearly, if IP-OOP interaction is considered, at equal PGA a greater probability of OOP infill collapse is
expected.](https://image.slidesharecdn.com/presentationriccididomenicoverderame-170704232713/85/Modelling-the-out-of-plane-behaviour-of-URM-infills-and-the-in-plane-out-of-plane-interaction-effects-32-320.jpg)
Modelling the out-of-plane behaviour of URM infills and the in-plane/out-of-plane interaction effects
- 1. Modelling the out-of-plane behaviour of URM infills and the in-plane/out-of-plane interaction effects Paolo Ricci, Mariano Di Domenico, Gerardo M. Verderame University of Naples Federico II Department of Structures for Engineering and Architecture Via Claudio 21 – 80125 – Naples – Italy e-mail: paolo.ricci@unina.it OPENSEES DAYS EUROPE 2017 1st European Conference on OpenSees Porto, Portugal, 19-20 June 2017
- 2. Purposes of the present study 4. Out-of-plane seismic safety check of the infill walls of case-study RC frames 1. Definition of an empirical-based Out-Of-Plane (OOP) infill model 2. Definition of an empirical-based In-Plane (IP) - OOP interaction model - by applying an Eurocode-based approach 5. Safety check results’ comparison - by applying the proposed model in a non-linear dynamic framework MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS 3. Implement the proposed model in OpenSees
- 3. Empirical-based OOP infill model OOPforce OOP displacement Based on pure OOP and combined IP+OOP tests carried out by: - Dawe and Seah (1989) - Angel et al. (1994) - Flanagan and Bennett (1999) - Calvi and Bolognini (2001) - Hak et al. (2014) - Furtado et al. (2015) A trilinear backbone has been assumed for the OOP behaviour of IP-undamaged and IP-damaged URM infills MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS
- 4. Empirical-based OOP infill model OOPforce OOP displacement Based on pure OOP and combined IP+OOP tests carried out by: - Dawe and Seah (1989) - Angel et al. (1994) - Flanagan and Bennett (1999) - Calvi and Bolognini (2001) - Hak et al. (2014) - Furtado et al. (2015) A trilinear backbone has been assumed for the OOP behaviour of IP-undamaged and IP-damaged URM infills Fcrack Kcrack Fcrack = 0.31 fm ′ 0.05 t w h1.66 Kcrack = 1 α Et3 12 (1 − ν2) w h empirical formulation μobs/pred = 1.02 Timoshenko, 1959 μobs/pred = 0.99 MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS
- 5. Empirical-based OOP infill model OOPforce OOP displacement Based on pure OOP and combined IP+OOP tests carried out by: - Dawe and Seah (1989) - Angel et al. (1994) - Flanagan and Bennett (1999) - Calvi and Bolognini (2001) - Hak et al. (2014) - Furtado et al. (2015) A trilinear backbone has been assumed for the OOP behaviour of IP-undamaged and IP-damaged URM infills Fmax = 1.95 fm ′ 0.35 t1.59 w h1.96 Kmax = 6.56 Ew (h/t)3 empirical formulation μobs/pred = 1.01 Kadysiewski and Mosalam, 2008 μobs/pred = 0.82 Fmax Kmax MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS
- 6. Empirical-based OOP infill model OOPforce OOP displacement Based on pure OOP and combined IP+OOP tests carried out by: - Dawe and Seah (1989) - Angel et al. (1994) - Flanagan and Bennett (1999) - Calvi and Bolognini (2001) - Hak et al. (2014) - Furtado et al. (2015) A trilinear backbone has been assumed for the OOP behaviour of IP-undamaged and IP-damaged URM infills dmax du du = 3.7dmax empirical formulation μobs/pred = 1.00 MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS
- 7. Empirical-based IP-OOP interaction model An empirical approach is used to model IP-OOP interaction effects. To model IP action effects on infills OOP behaviour, experimental data are related to the maximum IDR ratio attained during tests normalized with respect to the IDR corresponding to the complete IP resistance loss, IDRu MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS
- 8. Empirical-based IP-OOP interaction model An empirical approach is used to model IP-OOP interaction effects. To model IP action effects on infills OOP behaviour, experimental data are related to the maximum IDR ratio attained during tests normalized with respect to the IDR corresponding to the complete IP resistance loss, IDRu 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 IDR/IDRu F crack,dam /F crack,undam 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 IDR/IDRu K crack,dam /K crack,undam 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 IDR/IDRu K max,dam /K max,undam 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 IDR/IDRu F max,dam /F max,undam 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 IDR/IDRu d u,dam /d u,undam Fcrack,dam Fcrack,undam = 0.11 IDR IDRu −0.89 Kmax,dam Kmax,undam = 0.12 IDR IDRu −0.69 Kcrack,dam Kcrack,undam = 0.07 IDR IDRu −0.76 Fmax,dam Fmax,undam = 0.27 IDR IDRu −0.37 MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS Effects of IP damage on OOP response parameters:
- 9. Empirical-based IP-OOP interaction model An empirical approach is used to model IP-OOP interaction effects. To model OOP action effects on infills IP behaviour, experimental data by Flanagan and Bennett are related to the maximum OOP displacement attained during tests, dOOP, normalized with respect to the OOP collapse displacement of the reference undamaged specimen, dOOP,u MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS Effects of OOP damage on IP response parameters: 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 dOOP /dOOP,u F IP,dam /FIP,undam
- 10. Empirical-based IP-OOP interaction model Based on the proposed degradation relationships, the OOP and IP backbones for the undamaged infill are modified as shown in the following figures. MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS OOPforce OOP displacement IPforce IP displacement IDR IDRu = 0 dOOP dOOP,u = 0
- 11. Empirical-based IP-OOP interaction model Based on the proposed degradation relationships, the OOP and IP backbones for the undamaged infill are modified as shown in the following figures. MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS OOPforce OOP displacement IPforce IP displacement IDR IDRu = 0.2 dOOP dOOP,u = 0.2
- 12. Empirical-based IP-OOP interaction model Based on the proposed degradation relationships, the OOP and IP backbones for the undamaged infill are modified as shown in the following figures. MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS OOPforce OOP displacement IPforce IP displacement IDR IDRu = 0.4 dOOP dOOP,u = 0.4 How can we model the evolution of the OOP response backbone due to the increasing IP damage (and vice-versa) during the NLTH analysis?
- 13. Model implementation in OpenSees OOPforce OOP displacement IDR IDRu = 0 Consider the OOP backbone for the IP-undamaged infill (backbone 1) MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS
- 14. Model implementation in OpenSees OOPforce OOP displacement IDR IDRu = 0 IDR IDRu = 0.2 Consider the OOP backbone for the IP-undamaged infill (backbone 1) Consider an OOP backbone for the IP-damaged infill (backbone 2) MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS
- 15. Model implementation in OpenSees OOPforce OOP displacement IDR IDRu = 0 𝑎𝑎𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 IDR IDRu = 0.2 Consider the OOP backbone for the IP-undamaged infill (backbone 1) Consider an OOP backbone for the IP-damaged infill (backbone 2) Consider backbone 2 mirrored with respect to displacement axis (auxiliary backbone 2) MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS uniaxialMaterial Parallel tagAuxBb#2 tagBb#2 -factors -1
- 16. Model implementation in OpenSees OOPforce OOP displacement IDR IDRu = 0 𝑎𝑎𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 IDR IDRu = 0.2 Consider the OOP backbone for the IP-undamaged infill (backbone 1) Consider an OOP backbone for the IP-damaged infill (backbone 2) Consider backbone 2 mirrored with respect to displacement axis (auxiliary backbone 2) Backbone 2 and Auxiliary backbone 2 are mutually-neutralizing MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS
- 17. Model implementation in OpenSees OOPforce OOP displacement IDR IDRu = 0 𝑎𝑎𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑎𝑎𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 IDR IDRu = 0.2 Consider the OOP backbone for the IP-undamaged infill (backbone 1) Consider an OOP backbone for the IP-damaged infill (backbone 2) Consider backbone 2 mirrored with respect to displacement axis (auxiliary backbone 2) Backbone 2 and Auxiliary backbone 2 are mutually-neutralizing Backbone 1 is the one defining the OOP behaviour of the infill MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS
- 18. Model implementation in OpenSees OOPforce OOP displacement 𝑎𝑎𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 IDR IDRu = 0.2 If IDR/IDRu>0.2 backbone 1 is removed MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS
- 19. Model implementation in OpenSees OOPforce OOP displacement IDR IDRu = 0.2 If IDR/IDRu>0.2 backbone 1 is removed… … as well as auxiliary backbone 2 MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS
- 20. Model implementation in OpenSees OOPforce OOP displacement IDR IDRu = 0.2 𝑎𝑎𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 If IDR/IDRu>0.2 backbone 1 is removed… … as well as auxiliary backbone 2 So, if IDR/IDRu>0.2, backbone 2 starts defining the OOP behaviour of the infill MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS
- 21. The proposed model has been conceived to: 1. Reproduce the OOP behaviour of URM infills; 2. Take into account the OOP strength degradation due to IP damage and vice-versa; 3. Take into account the OOP stiffness degradation due to IP damage and vice-versa; 4. Allow modelling the IP and OOP behaviour of infills – and the corresponding degrading rules – adopting any trilinear material model as well as any hysteretic rule. Model implementation in OpenSees MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS
- 22. OOP behaviour IP behaviour Node OOP mass ‘Real’ ZeroLength Element ‘Auxiliary’ ZeroLength Element Beam/Column Element Hinge Mid-span Node Model implementation in OpenSees MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS
- 23. Application example: Case-study RC buildings Two case eight-storey RC buildings designed addressing EC2 and EC8 provisions are considered. Each building has been designed on A type soil. The two buildings differs for the design PGA at Life Safety Limit State, which is equal to 0.15 g (8P15 case-study building) and 0.35 g (8P35 case-study building) and at Damage Limitation Limit State, which is equal to 0.06 g and 0.14 g (i.e., 0.4 times the PGA at LS), respectively. The inter-storey height, h, is 3 m for all storeys. All bays width, w, is 4.5 m. Eurocode 8 Type I spectrum was adopted. A behaviour factor equal to 4.68 was applied. RC elements non-linearity was modelled by applying a code-based approach, with an elastic-perfectly plastic backbone provided of the cracking point and with chord rotation at yielding determined accordingly to the formulation proposed in EC8, part 3. 22.5 m 13.5m X Z The case-study buildings are infilled by one-leaf 300 mm thick URM walls. Masonry mechanical properties are the ones calculated for masonry wallets tested by Guidi et al. for mechanical characterization of “strong” URM infills. MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS
- 24. Application example: Case-study RC buildings The OOP behaviour of the case-study infill panels was modelled by applying the herein proposed semi- empirical approach. The IP behaviour was modelled by applying Panagiotakos and Fardis model, with softening stiffness equal to -3.6% of the predicted elastic stiffness of the infill, based on Guidi et al. IP tests’ results on strong masonry infills. The infill wall behaviour degradation was modelled through the herein proposed empirical approach. The IP degradation was modelled with backbones defined at steps of 0.05 times the dOOP,u (16.3 mm) displacement while the OOP degradation was modelled with backbones defined at steps of 0.05 times the IDRu (1.80%). 0 5 10 15 20 0 100 200 300 OOP Displacement [mm] OOPForce[kN] 0 10 20 30 40 50 0 200 400 600 IP Displacement [mm] IPForce[kN] MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS
- 25. Application example: NLTH Analysis procedure Seven bidirectional ground motions recorded on type A soil were selected The two components of each ground motions were contemporarily matched to the design 5%-damped response spectrum at Damage Limitation Limit State (DL) and at Life Safety Limit State (LS) through the RspMatchBi (Grant, 2010) software. 0 1 2 3 4 0 0.2 0.4 0.6 0.8 1 T [s] S a (T)[g] mean EC8 target Spectral matching period range: 0.035 s -1.100 s All components matched to the 0.35 g design spectrum at LS 0 1 2 3 4 0 0.2 0.4 0.6 0.8 1 T [s] S a (T)[g] mean 0 1 2 3 4 0 0.2 0.4 0.6 0.8 1 T [s] S a (T)[g] mean NS component EW component MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS
- 26. Application example: NLTH Analysis procedure Incremental Dynamic Analyses were carried out to obtain for each horizontal direction an incremental PGA vs maximum IDR curve. For records scale factor determination, a bisection procedure was implemented in order to define the PGA associated to the first OOP infill collapse and removal from the structural model with a precision equal to +/- 0.01 g. MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS
- 27. Application example: NLTH Analysis procedure Incremental Dynamic Analyses were carried out to obtain for each horizontal direction an incremental PGA vs maximum IDR curve. For records scale factor determination, a bisection procedure was implemented in order to define the PGA associated to the first OOP infill collapse and removal from the structural model with a precision equal to +/- 0.01 g. Mass and tangent-stiffness proportional Rayleigh damping rules for two control vibration mode were applied. 20 40 60 80 100 120 140 0 50 100 150 200 250 300 350 400 Mode Modes frequencies [rad/s] OOP infill natural frequency [rad/s] Control modes (1 and 131) Rayleigh damping ratios (scaled for 104 ) Three groups of modes were recognizable from modal analysis. - A first group of global “lower” modes corresponding to lower frequencies/modes involving the whole structure; MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS
- 28. Application example: NLTH Analysis procedure Incremental Dynamic Analyses were carried out to obtain for each horizontal direction an incremental PGA vs maximum IDR curve. For records scale factor determination, a bisection procedure was implemented in order to define the PGA associated to the first OOP infill collapse and removal from the structural model with a precision equal to +/- 0.01 g. Mass and tangent-stiffness proportional Rayleigh damping rules for two control vibration mode were applied. 20 40 60 80 100 120 140 0 50 100 150 200 250 300 350 400 Mode Modes frequencies [rad/s] OOP infill natural frequency [rad/s] Control modes (1 and 131) Rayleigh damping ratios (scaled for 104 ) Three groups of modes were recognizable from modal analysis. - A first group of global “lower” modes corresponding to lower frequencies/modes involving the whole structure; - A second group of local modes involving infills excited in the OOP direction corresponding to intermediate frequencies very close the infill natural frequency in the OOP direction; MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS
- 29. Incremental Dynamic Analyses were carried out to obtain for each horizontal direction an incremental PGA vs maximum IDR curve. For records scale factor determination, a bisection procedure was implemented in order to define the PGA associated to the first OOP infill collapse and removal from the structural model with a precision equal to +/- 0.01 g. Mass and tangent-stiffness proportional Rayleigh damping rules for two control vibration mode were applied. 20 40 60 80 100 120 140 0 50 100 150 200 250 300 350 400 Mode Modes frequencies [rad/s] OOP infill natural frequency [rad/s] Control modes (1 and 131) Rayleigh damping ratios (scaled for 104 ) Three groups of modes were recognizable from modal analysis. - A first group of global “lower” modes corresponding to lower frequencies/modes involving the whole structure; - A second group of local modes involving infills excited in the OOP direction corresponding to intermediate frequencies very close the infill natural frequency in the OOP direction; - A third group of global “higher” modes corresponding to higher frequencies/modes involving the whole structure. MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS Application example: NLTH Analysis procedure
- 30. Incremental Dynamic Analyses were carried out to obtain for each horizontal direction an incremental PGA vs maximum IDR curve. For records scale factor determination, a bisection procedure was implemented in order to define the PGA associated to the first OOP infill collapse and removal from the structural model with a precision equal to +/- 0.01 g. Mass and tangent-stiffness proportional Rayleigh damping rules for two control vibration mode were applied. 20 40 60 80 100 120 140 0 50 100 150 200 250 300 350 400 Mode Modes frequencies [rad/s] OOP infill natural frequency [rad/s] Control modes (1 and 131) Rayleigh damping ratios (scaled for 104 ) Three groups of modes were recognizable from modal analysis. - A first group of global “lower” modes corresponding to lower frequencies/modes involving the whole structure; - A second group of local modes involving infills excited in the OOP direction corresponding to intermediate frequencies very close the infill natural frequency in the OOP direction; - A third group of global “higher” modes corresponding to higher frequencies/modes involving the whole structure. In this study, the first control mode corresponds the first natural frequency of the infilled structure, while the second control mode corresponds to the second group mode associated to the frequency closer to the infill natural frequency in the OOP direction. A damping ratio equal to 2% was assigned to each control mode. MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS Application example: NLTH Analysis procedure
- 31. Application example: NLTH Analysis procedure Incremental Dynamic Analyses were carried out on two models for each case-study building. - W/ model accounting for: 1. backbone removal during analysis for IP and OOP stiffness, strength and displacement capacity reduction; 2. infill removal at IP collapse displacement attainment; 3. infill removal at OOP collapse displacement attainment (OOP collapse). - W/O model accounting for: 1. backbone removal during analysis for IP and OOP stiffness, strength and displacement capacity reduction; 2. infill removal at IP collapse displacement attainment; 3. infill removal at OOP collapse displacement attainment (OOP collapse). MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS
- 32. Application example: NLTH Analysis results Median IDA curves in each direction for W/ and W/O models of all case-study buildings are shown in the following figures 0 1 2 3 4 5 0 0.2 0.4 0.6 0.8 1 8P15-X maximum IDRX [%] PGA X [g] W/O Model W/ Model 0 1 2 3 4 5 0 0.2 0.4 0.6 0.8 1 8P15-Z maximum IDRZ [%] PGA Z [g] W/O Model W/ Model 0 1 2 3 4 5 0 0.2 0.4 0.6 0.8 1 8P35-X maximum IDRX [%] PGA X [g] W/O Model W/ Model 0 1 2 3 4 5 0 0.2 0.4 0.6 0.8 1 8P35-Z maximum IDRZ [%] PGA Z [g] W/O Model W/ Model MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS Mean OOP collapse PGAs are shown in the following table. They are, as expected, lower than the ones predicted by applying a code-based approach (0.41 g for 8P15 case-study building and 0.38 g for the 8P35 case-study building), especially if IP-OOP interaction is accounted for (W/ model). Moreover, the first OOP infill collapse does not occur necessary at last storeys but at intermediate storeys due to IP-OOP interaction effects. Clearly, if IP-OOP interaction is considered, at equal PGA a greater probability of OOP infill collapse is expected.
- 33. Conclusions 1. An empirical based OOP infill wall model has been defined. 2. An empirical based IP-OOP interaction model has been defined. 3. The proposed model has been implemented in OpenSees. 4. IDA on 8-storey case-study buildings designed addressing EC2 and EC8 provisions were performed 5. The PGA associated to the first OOP collapse is underestimated of about 44% if IP-OOP interaction is neglected. 6. The PGA associated to the first OOP collapse is underestimated of up to 132% if an Eurocode- based approach, which neglects IP-OOP interaction, the primary structure non-linearity and the contribution to the OOP acceleration acting on infills of the primary structure’s higher modes, is applied. Ongoing research is focused on the application of the proposed approach for modelling the infills of a wide range of case-study RC buildings different for number of storeys (2, 4, 6 and 8), designed for different PGA at LS (0.05, 0.15, 0.25 and 0.35 g) and provided of different infills’ layout (‘weak’ thin infills and ‘strong’ thick infills). Numerical analyses are being performed to assess infills acceleration and displacement demand, effective stiffness and behaviour factor accounting for IP- OOP interaction in a non-linear dynamic framework. MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS
- 34. Paolo Ricci, Mariano Di Domenico, Gerardo M. Verderame University of Naples Federico II Department of Structures for Engineering and Architecture Via Claudio 21 – 80125 – Naples – Italy e-mail: paolo.ricci@unina.it Modelling the out-of-plane behaviour of URM infills and the in-plane/out-of-plane interaction effects Thank you for your attention