1960's CONCRETE STRUCTURE SEISMIC IMPROVEMENT WITH ISAAC TECHNOLOGY ACCORDING TO NTC … · 8 1960’s CONCRETE STRUCTURE SEISMIC IMPROVEMENT WITH ISAAC TECHNOLOGY ACCORDING TO NTC

1960's CONCRETE STRUCTURE SEISMIC IMPROVEMENT WITH ISAAC TECHNOLOGY ACCORDING TO NTC 2018.

Technical Report by Eng. A. Bussini, Eng. A. Torti, Eng. M. Cortes.

isaacantisismica.com

ISAAC [email protected]

2 1960’s CONCRETE STRUCTURE SEISMIC IMPROVEMENT WITH ISAAC TECHNOLOGY ACCORDING TO NTC 2018. Technical Report by Eng. A. Bussini, Eng. A. Torti, Eng. M. Cortes. v1.0

All contents are the exclusive property of ISAAC srl, and are protected by copyright and other intellectual property laws.

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1960’s CONCRETE STRUCTURE SEISMIC IMPROVEMENT WITH ISAAC TECHNOLOGY ACCORDING TO NTC 2018. Technical Report by Eng. A. Bussini, Eng. A. Torti, Eng. M. Cortes. v1.0

1. Introduction .................................................................................................... 71.1 Scope of this work ......................................................................................................... 8

2. Case study: ELSA building ..................................................................... 92.1 Description ......................................................................................................................... 9

2.2 Numerical model .......................................................................................................... 11

2.2.1 Materials and sections ................................................................................. 12

2.2.2 Vertical loads ...................................................................................................... 13

2.2.3 Non-linear behavior: plastic hinges .................................................. 13

2.2.4 Modal behavior ................................................................................................. 14

2.3 Analysis: non-linear static ................................................................................... 15

2.3.1 Main settings ....................................................................................................... 15

2.3.2 Capacity curves ................................................................................................ 16

3. Seismic risk classification .................................................................... 173.1 Definitions ......................................................................................................................... 17

3.2 Limit states ...................................................................................................................... 17

3.3 Seismic risk ..................................................................................................................... 17

3.4 Security index (indice di sicurezza, IS-V) ................................................ 18

3.5 Expected average annual loss (perdita annuale media attesa,

PAM) ................................................................................................................................... 19

3.6 Seismic risk classification of the case study: Pushover ........... 21

3.6.1 Operational Limit State (SLO) .............................................................. 24

3.6.2 Damage Limit State (SLD) ................................................................... 26

3.6.3 Life Safeguard Limit State (SLV) ...................................................... 27

INDEX


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3.6.4 Collapse Limit State (SLC) ................................................................. 30

3.7 Seismic risk classification: Pushover results ............................... 31

3.7.1 Results: IS-V .................................................................................................... 31

3.7.2 Results: PAM .................................................................................................. 32

3.7.3 Result: Seismic risk class ..................................................................... 32

3.8 Seismic risk classification of the case study: non-linear time

history analysis ....................................................................................................... 33

3.8.1 Operational Limit State (SLO) ........................................................... 36

3.8.2 Damage Limit State (SLD) ................................................................. 37

3.8.3 Life safeguard Limit State (SLV) ................................................... 38

3.8.4 Collapse Limit State (SLC) ................................................................. 40

3.9 Seismic risk classification: non-linear time history results ... 43

3.9.1 Results: IS-V ................................................................................................... 43

3.9.2 Results: PAM ................................................................................................. 43

3.9.3 Result: Seismic risk class .................................................................... 44

4. Seismic performance improvement: ISAAC device ............. 454.1 ISAAC device modelling and simulation .............................................. 45

4.2 Identification and control of the structure ......................................... 46

4.3 Seismic risk class improvement evaluation: non-linear time

history analysis ....................................................................................................... 47

4.3.1 Operational Limit State ........................................................................... 48

4.3.2 Damage Limit State ................................................................................. 49

4.3.3 Life safeguard Limit State .................................................................. 50

4.3.4 Collapse Limit State ................................................................................. 52

4.4 Seismic risk class improvement evaluation: Results ................. 55

4.4.1 Results: IS-V ................................................................................................... 55

4.4.2 Results: PAM ................................................................................................. 55

4.4.3 Result: Seismic risk class .................................................................... 56

5. ISAAC device solution: advantages .............................................. 57


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Earthquakes are among the most dangerous natural risks in Italy for people and infrastructure.

This becomes evident when looking at Table 1. In around 45 years there have been more than 4,650 fatali-

ties and an estimated reconstruction cost of 121 billion Euros.

1. INTRODUCTION.

EVENT YEAR DEATH TOLL INTEVENTIONSACTIVATION PERIOD

UPDATED AMOUNT2014 (MILLIONS €)

Valle del Belice (*)

Friuli Venezia Giulia (*)

Irpinia

Marche / Umbria (*)

Puglia / Molise (*)

Abruzzo (**)

Emilia Romagna (**)

Totale

1968

1976

1980

1997

2002

2009

2012

MAGNITUDE (Mw)

6.1

6.4

6.9

6.0

6.0

6.3

6.0

1968-2028

1976-2006

1980-2023

1997-2024

2002-2023

2009-2029

2012-

9,179

18,540

52,026

13,463

1,400

13,700

13,300

121,608

370

989

2,914

11

30

309

27

(*) final data on the resources allocated by the state

(**) expenditure forecasts of the local authorities responsible for reconstruction

Table 1 - Summary of main earthquakes between 1968-2012, moment magnitude, death toll and updated earthquake costs borne by the state. Source: National Council of Engineers study center (2014).

This is due to the typical seismicity in the territory, but also due to the rather high vulnerability of the Italian

building heritage.

After the decade of 1960’s, the Italian design code of building and infrastructure for seismic actions has

improved significantly the definition of earthquake action on structures, seismic structural detailing of new

buildings for different materials, assessment and retrofitting of existing structures.

Concerning this last one, in 2017 the Italian government launched a strong state incentive through tax de-

traction at national scale for earthquake damage mitigation, encouraging private and productive sectors to

invest in seismic retrofitting of their existing buildings which don’t fulfil the national building code require-

ments (Norme Tecniche per le Costruzioni, NTC).


In order to support qualified professionals for the structural assessment of existing structures and the

later retroffiting, the Superior Council of Public Works (Consiglio Superiore dei Lavori Pubblici) created

the “Guidelines for Seismic Risk Classification of Constructions” (Linee Guida per la Classificazione del

Rischio Sismico delle Costruzioni), providing a risk class scale of 7 grades which can be calculated through

two methods: a simplified method, with limited applications; and conventional approach, applicable for any

structural typology and using the normal analysis method required by the NTC.

The conventional method is addressed by calculation of two parameters defined in the guidelines: the

“Expected Average Annual Loss” (Perdita Annuale Media Attesa, PAM) which is related to the recon-

struction cost and the “Security Index” (Indice di Sicurezza, IS-V), which is related to the ratio of the capacity

PGA (Peak Ground Acceleration) and demand PGA of the structure for the safeguard limit state.

Notice that this scale was created with the purpose of seismic update (adeguamento sismico) and seismic

retrofitting (miglioramento sismico) of existing buildings, therefore, the seismic risk classification should be

done to assess either previous and subsequent state of the building, leading to a risk class jump toward a

better seismic performance.

1.1 SCOPE OF THIS WORK.

Even if previous technical guidelines and the NTC application newsletter are available to help the professio-

nal community with seismic risk classification of buildings, there is a lack of practical and public examples

with explicit procedures of calculation and quantification, and professionals in practice rely most of the

technical responsibility of this crucial steps to available commercial black-box structural analysis software

capable of automatic seismic risk classification through the setting of the structural model.

Considering the above mentioned, the aim of this work is to document and describe the technical steps

of a seismic risk classification for a reinforced concrete building with typical design specification from the

construction code in force in the 1960’s.

Furthermore, this document was deliberately written in English to reach also the international community of

professionals and academics in Civil Engineering either in Italy and abroad, trying to bring them closer an

example and application of the Italian seismic classification approach, construction code interpretation and

professional practices, which are mostly available only in Italian language.

This report has been developed in different sections, which are briefly described in the following: section

2 is a description of the selected case study building and the numerical model parameters, including the

numerical analysis type and results.

Section 3 is devoted to a more detailed explanation of the seismic risk classification procedure and results

presentation for the case study.

Section 4 introduces an innovative alternative for seismic retrofitting through the implementation of an ISAAC device on the building. This is an active control mass damper connected to sensors placed in the structure which feed a computer with acceleration data due to microtremors (on normal operational state) or earthqua-kes (on eventual case) to obtain the dynamic identification of the building and give feedback to

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the mass damper control system in order to reduce building oscillation.A numerical example for the case study building is performed with a non-linear time-history analysis using artificial earthquake time histories prescribed by the code NTC2018.

Results of controlled and non-controlled cases are presented, and the calculation of the seismic risk class jump are discussed.

For a case study it was selected a 1:1 scale building model from the research project “Assessment and Retrofitting of Full-Scale Models of Existing RC frames” of the European Laboratory for Structural Asses-

sment (ELSA) at Ispra-Italy performed in the mid 2000’s.

The experimental model is shown in Figure 1. The main reasons for the selection of this building is because

it represents the typical building design practices of the late 1950’s and 1960’s, such as low seismic coef-

ficient (8%), concrete C16/20, steel S235 for rounded bars, typical lap-splicing, bent stirrups, lack of shear

reinforcement in joints and Strong beam – Weak Column plastic behavior.

This building typology represents a significant part of the existing RC buildings in Italy, one of the target

markets for the ISAAC seismic protection system.

2. CASE STUDY: ELSA BUILDING.2.1 DESCRIPTION.

Figure 1 - ELSA structure chosen as case study.


The building is a 4-story RC frame with masonry infills in the long direction only. The axes and sections

definition are illustrated in Figure 2.

The original experiment was made of two structurally separated specimens (one for each 2D frame in the

long direction), because were made test for both infilled and bare frames, however, for the numerical model

of this work both specimens have been considered as a single structure with infills on every span just in

the long direction.

Figure 2 - study case building details: (a) geometry in elevation; (b) plan geometry (just half of it in long direction); (c) cross sections (cm); (d) infill walls thickness.

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A 3D Finite Element Method model has been done for this structure using SAP2000 V21 software, which

is shown in Figure 3.

Beams and columns have been modelled using frame elements, while the slabs using thin-shell elements.

The masonry infills have been modelled using one frame element on each diagonal with equivalent area

section and material constitutive law according also to other models that have been created of the same

case study and that can be found in the scientific literature.

It is assumed that the overlapping of frames for masonry walls between them and with the RC elements

represents the remaining volume to be filled in every masonry span, so that the total mass of the structure

is well represented.

In the following, the main settings features for the model are presented.

2.2 NUMERICAL MODEL.

Figure 3 - FEM model of the case study building.


For the RC sections, with dimension and rebar detailing as shown previously in Figure 2, a typical UNI EN

206-1:2006 C16/20 concrete and a EN 1993-1-1 per EN 10025-2 S235 rebar steel were selected, as indica-

ted by the documents.

For the masonry infills it was considered the information obtained from previous works that had studied the

same case study, where the infills had been modelled as equivalent compression-only fiber-struts sections

with a volume weight of 6.16 kN/m3, ruled by parabolic stress-strain relations with linear softening, defined

using four main parameters: peak stress fmd0, ultimate stress fmdu, peak strain Ɛmd0, ultimate strain Ɛmdu (Figu-re 4). These parameters were determined individually for each infill span using semi-empirical relationships

which are listed in Table 2.

For the sake of simplicity, the parabolic behavior before the peak value was represented linearly in the FEM

model.

2.2.1 MATERIALS AND SECTIONS.

Figure 4 - Equivalent strut model for infills (from scientific literature).

Table 2 - Geometrical and mechanical parameters of equivalent struts.

INFILL TYPE YEAR w (mm) t (mm) fmd0 (MPa) fmdu (MPa) εmdu (-) εmdu (-)

Between col. A-B

Between col. B-C/C-D

Between col. A-B


Between col. A-B


Between col. A-B


1

1

2

2

3

3

4

4

NAME

tamp_AB1

tamp_BC/CD1

tamp_AB2

tamp_BC/CD2

tamp_AB3

tamp_BC/CD3

tamp_AB4

tamp_BC/CD4

1,11

1,19

1,11

1,22

1,10

1,24

1,10

1,26

0,38

0,33

0,37

0,31

0,36

0,29

0,35

0,26

0,0097

0,010

0,0098

0,010

0,0098

0,0101

0,0098

0,0102

0,0018

0,0016

0,0018

0,0015

0,0018

0,0014

0,0017

0,0013

1146,3

1382,9

1127,9

1269,8

1109,7

1165,2

1091,5

1068,5

120

120

120

120

120

120

120

120

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The loads were considered according to the material and frame/area section definitions from previous

section, besides on what is described in NTC2018 for non-structural elements and live loads.

2.2.2 VERTICAL LOADS.

LOAD NAME DESCRIPTION VALUE

Dead

Dead_G2

Sovraccarico

Dead loads of structural elements

Dead load of non-structural elements

Live load

Depending on section and material

1,2 kN/m2

2,0 kN/m2

Table 3 - Vertical load definition.

In order to improve the modeling of plastic incursion and non-linear behavior of sections during an extreme

event, localized hinge elements on frames were defined as follows:

On columns:

• Axial-flexural interaction fiber hinges (P-M2-M3) which work in both long and short direction.

They are placed in the 10% and 90% of the relative length of each frame member and each hinge

has a length of 10% of the relative total frame length.

For instance, a column of 2.7m length in the ground floor develops two hinges of 27cm length, placed

from bottom to top centered at 0.27m and 2.43m height.

• Force-controlled shear hinge working in long direction only (V2). They are placed in the 50% of the

relative length of each member.

The reason of this position is to not reduce the element length of the axial-flexural fiber hinges.

On beams:

• Axial-flexural interaction fiber hinges (P-M2-M3) which work in both long and short direction.

They are placed in the 10% and 90% of the relative length of each frame member and each hinge

has a length of 10% of the relative beam length.

On infills:

• Axial-only displacement-controlled hinge (P) following the mean of the constitutive laws values re-

ported in Table 2, places in the 50% of the relative length of each infill element.

A general layout of the hinges on the model for one of the longitudinal axes can be observed in Figure 5.

The constitutive laws of Axial-flexural fiber hinges and force-controlled hinges are automatically derived

from the material properties by the software, while for the infills axial hinges, where defined specific plastic

behavior derived from the equivalent strut model from Figure 5.

2.2.3 NON-LINEAR BEHAVIOR: PLASTIC HINGES.


Figure 5 - Hinges layout in the long direction of the structural model.

The modal information of the structure is reported in Table 4, while the main modal shapes and those of

particular interest are shown in Figure 6. From this information, it is important to notice that the first and se-

cond mode are translational in the short direction and torsional, respectively. The third and the tenth mode

are predominately translational in the long direction (with the infills). This last two modal cases sums around

96% of the dynamic mass in that direction and are important for the purposes of this work, because it re-

present a 1D dynamic case of a reasonably realistic building model with non-linear behavior of two different

materials (concrete and masonry infills), which have been extensively used in existing buildings in southern

Europe. Hence, for the purpose of quantitively assessing the effectiveness of the ISAAC system on the

damage reduction during an earthquake through the inter-story drifts reduction, the transversal direction of

the structure is not considered at this stage in the dynamic analysis.

2.2.4 MODAL BEHAVIOR.

MODE PERIOD (s) MODAL MASS (X) MODAL MASS Y MODAL MASS Z

1

2

3

4

5

6

7

8

9

10

0,694

0,508

0,281

0,230

0,177

0,135

0,112

0,100

0,099

0,098

FREQUENCY (Hz)

1,440

1,967

3,557

4,341

5,649

7,378

8,899

9,927

10,020

10,150

0,80632

0,01559

1,488E-14

0,11278

0,00272

0,03364

0,00064

0,01643

9,011E-14

4,002E-13

5,046E-20

1,662E-16

1,242E-05

2,318E-15

3,094E-16

3,017E-14

1,375E-15

2,1E-13

0,0897

0,00172

2,615E-14

8,779E-15

0,86977

4,501E-13

5,514E-15

2,846E-14

9,66E-15

2,733E-12

0,00724

0,09546

Table 4 - Modal information of the FEM building model.

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Figure 6 - Mode shapes of interest.

For lateral load analysis, a non-linear static case -the so-called Pushover analysis- was performed.

This consists in a lateral load pushing the structure by incremental steps, calculating the equilibrium state in

each of them, as well as the corresponding internal forces and node displacements, describing, accordingly,

the elastic and plastic behavior of each structural element and its non-linear hinges.

2.3 ANALYSIS: NON-LINEAR STATIC.

According to the NTC2018, it can be assigned a lateral load corresponding to an acceleration proportional

to the fundamental mode shape in the vibration direction. In this case is considered the 3rd mode shape,

which has a mass participation of 87% (the minimum required is 75%).

The incremental load application is performed saving at least 40 steps setting a maximum displacement

control of the top floor, because the total lateral resistance is to be determined and it is expected to obtain

the capacity curves with loss of lateral carrying load.

2.3.1 MAIN SETTINGS.


In the following, the capacity curves on the longitudinal direction are shown (Figure 7).

Notice that in both the directions (positive and negative), the overall structure stiffness is rather similar and

linear until a lateral force of 600kN and displacement of 1cm. After this displacement, however, the positive

X direction smoothly decreases its stiffness until reaching a maximum of around 890kN, while the nega-

tive direction keeps most of its stiffness until around 1.9cm and 1000kN, after of which its lateral strength

linearly decays.

These differences are explained by the lateral asymmetry of the structure. For further analysis, just the po-

sitive direction will be considered, due to its lower and more gradual capacity loss that will lead to a better

description of the failure mechanism later.

2.3.2 CAPACITY CURVES.

Figure 7 - Capacity curve with load in positive X direction.

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3. SEISMIC RISK CLASSIFICATION.3.1 DEFINITIONS.

In the following, some key definitions to better understand seismic risk classification are presented.

3.2 LIMIT STATES.

Under seismic actions, the following limit states are defined, based on the construction performance, inclu-

ding structural, non-structural elements and installations, which are introduced in the NTC 2018.

• Operational Limit State (stato limite di operatività, SLO): after the earthquake, the construction as

a whole, should not suffer damages or significant use interruptions.

• Damage Limit State (stato Limite di danno, SLD): after the earthquake, the construction, as a

whole, suffers damages such as not to put on risk the users and not to significantly compromise the

resistance capacity and stiffness against vertical and horizontal actions. The construction has to be

immediately available, despite the interruptions due to installments damages.

• Life Safeguard Limit State (stato limite di salvaguardia della vita, SLV): after the earthquake, the

construction suffers rupture and collapse of non-structural components and installations and signifi-

cant damage on the structural components associated to a significant loss of stiffness against hori-

zontal actions. However, the construction conserves a part of resistance and stiffness against vertical

actions and a safety margin for collapse prevention against horizontal actions.

• Collapse Limit State (stato limite di colasso, SLC): after the earthquake, the construction suffers

severe rupture and collapse of non-structural components and installments and severe damage of

structural components. The construction preserves a safety margin for vertical actions and exiguous

safety margin for collapse prevention against horizontal actions.

Seismic risk is defined as a mathematical/engineering measure to value the expected damage in buildings

and/or infrastructures after a possible seismic event. It relies on the interaction of three factors:

• Hazard: probability of an expected earthquake to occur. This is described by the seismic zone.

• Vulnerability: physical evaluation of the consequences of an earthquake.

This is described by the building capacity.

• Exposure: social and economic assessment of the after-earthquake consequences.

This is described by the community preparedness.

3.3 SEISMIC RISK.


Figure 8 - Risk components. Source: blogs.worldbank.org.

3.4 SECURITY INDEX (INDICE DI SICUREZZA, IS-V).

The security index of an existing construction is defined as the ratio between the peak ground acceleration

(PGA) which determines the attainment of the safeguard limit state SLV (capacity named hereafter PGAC)

and the PGA prescribed by the code for SLV performance for the correspondent seismic zone and soil

characteristics (demand named hereafter PGAD).

IS - V = PGAC / PGAD

Once calculated, it is possible to obtain the seismic risk classification by terms of IS-V using the following

scale:SECURITYINDEX

IS-V CLASS

100% < IS-V

80% ≤ IS-V < 100%

60% ≤ IS-V < 80%

45% ≤ IS-V < 60%

30% ≤ IS-V < 45%

15% ≤ IS-V < 30%

IS-V ≤ 15%

A+

A

B

C

D

E

F

Table 5 - Seismic risk class according to security index.

In this context, seismic risk classification according to the Italian guidelines uses an approach based on

two concepts:

• Respect the value of human life protection, through the safety levels provided by the current

construction code. This idea leads to the Security Index.

• Consideration of the possibility of economic and social losses, according to a robust conven-

tional estimation based on reconstruction data after the 2009 Mw 6.1 L’Aquila earthquake.

This cidea leads to the Expected Average Annual Loss.

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3.5 EXPECTED AVERAGE ANNUAL LOSS (PERDITA ANNUALE MEDIA ATTESA, PAM).

The expected average annual loss, hereafter PAM from its acronym in Italian, is related to the repairing

costs (costo di riparazione, CR) due to damages after seismic events along the construction life cycle, di-

stributed annually and expressed as a percentage of the reconstruction cost.

This can be estimated as the area under the curve of the direct economic loss as a function of the mean

annual overcoming frequency λ (the reciprocal of the return period λ=1/Tr) of seismic events that produces

the attainment of each limit states for the construction. Similarly to the IS-V index, the PGA that produces

the corresponding limit state should be calculated (capacity PGACi, where “i” is for each limit state), as well

as the demanding PGA of each limit state (demand PGADi) should be known.

To obtain the return period of each limit state, the computation is the following:

TrC = TrD (PGAC/PGAD)η

Where η = 1/0.41.

For the purpose of curve completion, in addition to the limit states defined in 3.2, also other two limit states

are defined:

• Beginning of Damage Limit State (stato limite inizio danno, SLID): where the economic loss is

equal to zero. At this limit state it is assumed a return period TR = 10 years, therefore λ=0.1.

• Reconstruction Limit State (stato limite di ricostruzione, SLR): Where the damage on the structu-

re is such that it is impossible to intervene on the structure other than demolish and reconstruct it.

The economic loss is set as 100% and the return period equals the one obtained with SLC.

The percentage of reconstruction costs (% of CR) associated to each limit state are presented in Table 6.

LIMIT STATE CR (%)

SLR

SLC

SLV

SLD

SLO

SLID

100

80

50

15

7

0

Table 6 - Percentage of reconstruction cost associated to each limit state.


The plotted values obtained should be interpreted as shown in Figure 9. PAM is the area under this curve,

which can be obtained by simple trapezoidal integration.

Figure 9 - Curve of direct economic loss versus exceedance mean annual frequency λ.

Once PAM has been calculated, the associated class is obtained from Table 7.

EXPECTED AVERAGE ANNUAL LOSS (PAM) PAM CLASS

PAM ≤ 0,50%

0,50% < PAM ≤ 1,0%

1,0% < PAM ≤ 1,5%

1,5% < PAM ≤ 2,5%

2,5% < PAM ≤ 3,5%

3,5% < PAM ≤ 4,5%

4,5% < PAM ≤ 7,5%

7,5% ≤ PAM

A+

A

B

C

D

E

F

G

Table 7 - Seismic risk class according to PAM index.

The seismic risk classification is taken as the lower class between the ones obtained with PAM and IS-V.

21



Figure 10 - Seismic risk classification scale.

Using the capacity curve for the positive x direction obtained with the Pushover method introduced in 2.3,

an estimation of the seismic risk classification can be performed with the following procedure.

Relate the MDOF (Multiple Degrees Of Freedom) structure capacity curve with the equivalent SDOF (Sin-

gle Degree Of Freedom) system capacity curve, by obtaining the equivalent SDOF force F* and displace-

ment d*, defined as:

F*=Fb / Γd*=dc / Γ

with

Γ = (φT Mτ)/(φT Mφ)

where Fb and dc are, respectively, the MDOF base shear and top floor displacement; Γ is the modal partici-

pation factor with the modal shapes φ normalized with respect to the maximum top floor displacement, M

is the modal mass matrix and τ is the influence vector in the analysis direction. Considering the positive x

direction of analysis and a natural period of T=0.281[s], a value of Γ=1.28 is obtained.

Additionally, in order to get specific values of maximum capacity in terms of yielding force Fy* and ultimate

displacement du*, a bi-linear elastic-perfectly plastic capacity curve is calculated using the concept of equal

energy by imposing the same value for the integral of both functions.

The elastic part is defined imposing the line to intersect the equivalent SDOF capacity curve where it rea-

ches a 60% of the maximum capacity force Fbu*, while the ultimate displacement is imposed as the displa-

cement where the equivalent SDOF capacity curve is equal or larger than the 85% of the maximum capaci-

ty force. By means of minimizing the area between the equivalent SDOF capacity curve and the equivalent

bi-linear capacity curve, is possible to obtain the equivalent yielding force Fy* and displacement dy*.

3.6 SEISMIC RISK CLASSIFICATION OF CASE STUDY: PUSHOVER ANALYSIS.


Figure 12 - Equivalent SDOF capacity curve and bi-linear capacity curve for the case study.

From the equivalent bi-linear capacity curve and the modal mass expression, is possible to deduce the

natural period of the equivalent SDOF structure T*=0.375s.

For determination of the seismic demand, the case study is assumed to be a construction with ordinary

performance level (construction type 2 with nominal project life VN of 50 years) and use class type II (with

class use coefficient CU of 1.0). It is considered to be located in the Italian municipality of Reggio Emilia, sei-

smic zone 3, with global coordinates 44°41’34.1’’N, 10°37’,38.6’’E, on a soil class C and topographic category

T1. The energy dissipation of the structure is an object of study in the further steps; hence, the structure

factor “q” is assumed to be 1.0.

The main parameters of the elastic response spectra according to the NTC 2018 for each of the four limit

states described in 3.2 are reported in Table 8 and plotted in Figure 13.

Figure 11 - Equivalent SDOF system and capacity curves.

This procedure is better illustrated in Figure 11, while the corresponding results for the case study are re-

ported in Figure 12.

23



Table 8 - parameters of elastic design response spectra according to NTC 2018.

LIMIT STATE PGAd (g) Tc* ag (m/s2)

Operativity (SLO)

Damage (SLD)

Life Safeguard (SLV)

Collapse (SLC)

0.0789

0.0919

0.2359

0.2879

F0

2.478

2.496

2.372

2.382

0.516

0.601

1.572

2.006

0.253

0.26

0.29

0.306

Figure 13 - Elastic design response spectra according to NTC 2018.

For determination of the structure seismic capacity, the NTC 2018 recommends verifying the primary

structural elements (ST), non-structural elements (NS) and installations (IM) according to different criteria

depending on the limit state and depending on the use class CU.

The criteria are Stiffness (RIG), Resistance (RES) and Ductility (DUT). This study will cover verification of

primary structural elements only, therefore, just the cases in the red column highlighted in Table 9.

Table 9 - Seismic verifications prescribed by the code depending on the limit state and on the building utilization class.

For each limit state a different structural verification is necessary. In each of these the respective maximum

capacity is estimated in terms of the corresponding design spectrum PGA.

Because it is expected that the capacity could be lower than the demand, on each case the capacity PGA

is estimated by scaling the corresponding design spectrum.

Each limit state verification is be briefly explained and analyzed in the following.


3.6.1 OPERATIONAL LIMIT STATE (SLO).

Regarding this limit state, as can be seen from Table 9, this limit state is not mandatory to assess for this

class use; however, it is needed for PAM index estimation. It is assumed the damage limit state (SLD) veri-

fication, which is in terms of structure stiffness (RIG). This verification is considered satisfied when the de-

formations of the structural elements does not create damages on the non-structural elements that could

potentially make the building temporarily condemned. The verifications can be performed for different type

of connections of the non-structural elements, such as:

A) For masonry infills which are rigidly connected to the structure and interfere with its deformation:

qdr ≤ 0,0050 h for brittle masonry infill

qdr ≤ 0,0075 h for ductile masonry infill

B) For masonry infills which have been designed in order not to have damages as a consequence of

a seismic event due to the inter-story drift drp:

qdr ≤ drp ≤ 0,0100 h

C) For structures with structural ordinary masonry infill: qdr ≤ 0,0020 h

D) For structures with reinforced structural masonry infills: qdr ≤ 0,0030 h

E) For structures with structural confined masonry infills: qdr ≤ 0,0025 h

Where:

• dr is the inter-story drift, this is the difference between the lateral displacement of the upper slab

with respect to the lower slab, computed either in case of linear analysis, or non-linear analysis, on

the model not comprehensive of the masonry infill;

• h is the story height.

Instead, for what concern the constructions that are in utilization class III or IV (CU III or IV), the verification

has to be done also with respect to the operativity limit state (SLO), thus the inter-story drifts have to be

lower than 2/3 of the previously mentioned limits.

Even if this last consideration is referring to class III and IV structures, the same values are considered for

this case study.

The verifications have to be done by considering the model without the presence of the masonry infills as

illustrated in Figure 14.

25



Figure 14 - FEM of the structure without the masonry infill used for the analysis of the operational and damage limit states.

The verification is conservatively performed using the worst case, which is case c), giving a maximum in-

ter-story drift of 3.6 mm (2/3*0.002*2.7m). Observing the pushover results, the equivalent lateral force at

which this value is surpassed is 199.3kN for the 3rd inter-story drift, as shown in Figure 15. After, the equivalent capacity pseudo-acceleration Sac is computed dividing the base shear by the structu-

re weight, giving:

Sac,SLO = F/W = (199.3kN) / (2842kN)=0.07g

Entering with the equivalent natural period T* on the SLO response spectrum, the ordinate of the spectrum

is scaled varying just the parameter ag until reaching the value of Sac,SLO, then the corresponding value of

the PGAc,SLO is noted, and for this case it is 0.0345g.

Figure 15 - SLO story drift verification.


3.6.2 DAMAGE LIMIT STATE (SLD).

For what concern the damage limit state (SLD), this has to be verified using the same argument as the ope-

rational limit state (SLO) for constructions of utilization class II (CU II), while for what concerns the structures

with utilization class III or IV (CU III or IV), the verification has to be performed in terms of resistance (RES).

This will be briefly described in the verification of the life safeguard limit state (SLV) in the next paragraph.

The analysis of this limit state has to be performed on the model without the presence of the masonry infill,

exactly as it is performed for the operational limit state.

Similarly to the previous limit state, the verification is conservatively performed using the worst case, case

c), giving a maximum inter-story drift of 5.4mm (0.002*2.7m). Observing the pushover results, the equivalent

lateral force at which this value is surpassed is 238.29kN for the 2nd and 3rd inter-story drift, as shown in

Figure 16. After, the equivalent capacity pseudo-acceleration Sac is computed dividing the base shear by

the structure weight, giving:

Sac,SLD = F/W = (238.29kN) / (2842kN) = 0.083g

Entering with the equivalent natural period T* on the SLD response spectrum, the ordinate of the spectrum

is scaled varying just the parameter a_g until reaching the value of Sac,SLD, then the corresponding value of

the PGAc,SLD is noted, and for this case it is 0.036g.

Figure 16 - SLD story drift verification.

27



3.6.3 LIFE SAFEGUARD LIMIT STATE (SLV).

According to the NTC 2018, this state limit has to be verified with respect to:

• the resisting bending moment with and without the presence of the axial load;

• the resisting shear load;

• the resisting torsion;

• the resistance of thick body elements;

• the resistance to cyclic loads;

• the buckling-instability of slender elements.

Moreover, some hypotheses have to be taken into account such as the complete absence of resistance to

tensile loads of the concrete, the perfect adhesion of reinforcement bars with the surrounding concrete and

the conservation of plane sections.

Figure 17 - Extract from the section structural verification in the code NTC2018.

With reference to the NTC2018 and the section subjected to bending moment and axial load shown in Fi-gure 17, the capacity of the element has to be verified in terms of resistance and ductility.

Indeed, the structural check has to be executed by comparing the element capacity and the relative de-

mand due to the load combination applied to the structure following the relation:

MRd=MRd (NEd) ≥ MEd

μΦ= μΦ (NEd) ≥ μƐd

Where:

MRd is the value of the resisting bending moment corresponding to the axial load N_Ed;

NEd is the value of the applied axial load;

MEd is the applied bending moment;

μΦ is the curvature ductility value corresponding to the axial load N_Ed;

μƐd is the demand in terms of the ductility curvature.

Moreover, in case of columns subjected to axial load, a bending moment MEd= e NEΦ due to possible ec-

centricity e that has to be at least equal to 1/200 of the height of the column has to be taken into account

and should not be less than 20mm.


Given this hypothesis, the section verification to be performed is:

(MEyd / MRyd)α+ (MEzd / MRzd )

α ≤ 1

Where:

• MEyd, MEzd are the applied bending moments to the section w.r.t. the axes y and z;

• MRyd, MRzd are the resisting bending moment that correspond to the applied axial load separately

computed respectively for the y and z axes.

The value of the α exponent for a rectangular section can be computed by interpolation using the coeffi-

cient and the following table:

NEd / NRcd

α

0.1

1.0

0.7

1.0

1.0

2.0

0.7

1.5

While for circular and elliptic sections it is assumed that α = 2. The same applies for the shear loads that

have to be verified as:

VRd ≥ VEd

Where VEd is the shear load applied to the element.

Moreover, with reference to the element that is considered cracked by bending moment and without shear

reinforcement, the resisting shear load is evaluated as:

VRd = max{[0,18k (100 ρ1fck )1/3 /γc + 0,15σcp] bwd ; (vmin + 0,15σcp) bwd}

With:

fck in MPa.

k = 1 + (200/d)1/2 ≤ 2.

vmin=0,035 k3/2 fck1/2.

d is the height of the section in mm.

ρ1= Asl / (bwd).

σcp= NEd/Ac is the average compression stress of the section.

bw is the minimum width of the section.

Instead when the element is equipped with reinforcement for shear loads the resisting shear load is com-

puted as:

VRd = min(VRsd, VRcd)

29



Where the resisting shear load for the combination of tensile stress and shear is computed as:

VRsd = 0,9 dAsw / sfyd (ctgα + ctgα) sinα

And for the combination of compression stress and shear is computed as:

VRcd = 0,9dbw αc v (fcd (ctgα+ctgθ) / (1+ctg2θ))

For a deeper analysis of verification procedures, the interested reader should check chapter 4.1.2 of the

NTC 2018.

The procedure in this case was carried out verifying the solicitation of every single element separated by

types, for every pushover step on the structure with infills following the above-mentioned resistance criteria.

This has given as result the step, and, therefore, the lateral force where every element failed. The lateral

force corresponding to the step where the first primary element fails is considered for the computation of

the capacity pseudo-acceleration after obtaining the ratio of this value with respect to the structure weight.

The first element to fail is one of the longitudinal beams T50x25 in the 1st floor, as shown in Figure 18, not

satisfying the bending moment verification under an equivalent lateral force of 322.36kN, giving:

Sac,SLV = F / W = (322.36kN / 2842kN )= 0.113g

Figure 18 - Not verified element for SLV limit state.

Entering with the natural period T on the SLV response spectrum, the ordinate of the spectrum is scaled

varying just the parameter ag until reaching the value of Sac,SLV, then the corresponding value of the PGAc,SLV

is noted, and for this case it is 0.048g.


3.6.4 COLLAPSE LIMIT STATE (SLC).

For what concerns the collapse limit state (SLC), this must be analyzed in terms of ductility by verifying the

total ductile capacity of the structure.

The capacity in terms of ductility factor based on the curvature μΦ can be computed separately for the two

principal directions of analysis as the ratio between the curvature corresponding to a reduction of the 15%

of the maximum resistance of the structure in tensile load – or the achievement of the ultimate limit stren-

gth for concrete or steel – and the conventional curvature of first plasticization Φyd expressed as

Φyd = (MRd / M’yd ) Φ’yd

where

• Φ’yd is the minimum between the curvature computed in correspondence of the yielding of the rein-

forcement bars and the curvature computed in correspondence of the maximum peak deformation

(Ɛc2 if the parabole-rectangle model is used or Ɛc3 if the triangle model is used) of the compressed

concrete;

• MRd is the resistant moment of the section to the ultimate limit state (SLU);

• M’yd is the bending moment corresponding to the value Φ’yd and it can be considered as the maxi-

mum resisting bending moment in the substantially elastic field.

The ductility is quantified through the ductility factor that, for each of the parameters usually considered

(curvature, displacement), is the ratio between the maximum value reached by the parameter examined and

the value of the same parameter at the instant of first yielding.

If it is necessary to verify that the ductile capacity of the structure, globally or locally, is bigger than the

corresponding demand, it is necessary to adopt the following procedure with reference to the ductility in

curvature (locally) and the ductility in displacement (globally).

In the following it is reported how the collapse limit state (SLC) has been computed in the case of non-li-

near static analysis with the Pushover method.

Because of the regularity of the structure and relatively low structural redundancy, it is assumed that what

controls this limit state is the global ductility.

The global ductility was obtained from the equivalent SDOF capacity curve, from which the maximum di-

splacement du is noted; this displacement corresponds to the point where lateral force is reduced in 15%

with respect to the maximum capacity. The force in this point is equal to 589.9kN, as shown in Figure 19. Similarly to the previous procedure, the corresponding pseudo-acceleration is computed:

Sac,SLC = F* / W* = (589.9kN / 2220kN) = 0.2657g

31



Figure 19 - Equivalent SDOF capacity curve for SLC limit state verification.

Entering with the equivalent natural period T* on the SLC response spectrum, the ordinate of the spectrum

is scaled varying just the parameter αg until reaching the value of Sac,SLC, then the corresponding value of

the PGAc,SLC is noted, and for this case it is 0.11g.

3.7 SEISMIC RISK CLASSIFICATION: PUSHOVER RESULTS.3.7.1 RESULTS: IS-V.

For the computation of the IS-V coefficient it is only needed the result obtained from the analysis of the

life safeguard limit state, where it has been possible to obtain a capacity PGA, PGAC, of 0.048g while the

demand PGA, PGAD, is of 0.2359g.

Thus, by using the relation:

IS-V = PGAC,SLV / PGAD,SLV = 0.048 / 0.2359 = 20.3%

IS-V coefficient of 20.3% is obtained, corresponding to seismic risk class E, according to Table 5.


3.7.2 RESULTS: PAM.

As it has been done for the non-linear static analysis, the PAM coefficient has been computed and in Table 11 are reported the capacity PGA, PGAC, the demand PGA, PGAD, and the computed return period, TrC,

calculated as illustrated in the previous chapters, for each of the analyzed limit states.

LIMIT STATE PGAc [g] TrC [years]

SLO

SLD

SLV

SLC

PGAD [g]

0.0789

0.0919

0.2359

0.2979

4

5

10

93

0.0345

0.036

0.048

0.110

Table 10 - Data computed from the analysis of all the limit states and in input for the PAM computation.


Finally, by computing the area of the graph shown in Figure 20 it is possible to find the PAM coefficient,

which result equal to 10.68%. Then by using Table 7 it can be found that, according to the PAM coefficient,

the structure is in seismic risk class G.

3.7.3 RESULT: SEISMIC RISK CLASS.

As prescribed by the standard, the worst case obtained between class risk from the IS-V coefficient and

from the PAM coefficient, is the seismic risk class of the structure.

Finally, it is possible to state that the class risk of the structure obtained using the non-linear time history

analysis is G, as shown in Figure 21.

33



Figure 21 - Seismic risk class of the case study non-linear static analysis.

3.8 SEISMIC RISK CLASSIFICATION OF THE CASE STUDY:NON-LINEAR TIME HISTORY ANALYSIS.

The same classification can be performed using the analysis of the non-linear time history response of the

structure subjected to artificial or natural earthquakes according to the code NTC2018 (3.2.3.6).

Figure 22 - Accelerogram time history profile according to NTC2018.

Figure 23 - Ground acceleration, velocity and displacement obtained from the response spectrum.


Indeed, as it has been done with the non-linear static analysis, different earthquakes response spectra

have been chosen according to the selected limit states and the hypothetical location of the building (Reg-

gio Emilia) as stated in 3.6.

Using the design spectra, was derived the corresponding artificial accelerograms through the commercial

software SeismoArtif.

The accelerogram have been shaped according to the prescription of the standard with scale factor equal

to 1, thus with maximum acceleration for at least 10 s, with a first increasing profile and a subsequent de-

crease, as it can be seen from Figure 22.

Figure 24 - Response spectrum obtained from the SLV accelerogram time history, compared to the target response spectrum.

Figure 25 - Response spectrum obtained from the time histories accelerograms of all the limit states.

35



The obtained time histories, as for example the one obtained for the SLV case in Figure 23, are used to

calculate again the response spectrum to be compared with the target response spectrum profile in order

to not exceed the defined bounds of acceptance and in Figure 24 are shown the acceleration, velocity and

displacement spectrum obtained.

The same procedure has been done for all the time histories obtained for all the limit states as shown in

Figure 25.

The idea in this case is to perform the non-linear time history analysis of the building subjected to each of

the calculated accelerograms and perform at each time step the verifications prescribed by the code for

each limit state as it has been done for the Pushover analysis, but in a direct way instead of an inverse one.

Figure 26 - Flowchart of the process adopted for the non-linear time history verification of the structure.

However, as it is reported also in the standard code, the procedure has to be repeated for each limit state

for at least 3 different time histories obtained from the same target response spectrum, since the obtained

accelerogram from the same target spectrum is random, thus it is prescribed to compute the mean of the

obtained results for each limit state.

The data reported in the following to show the adopted procedure correspond only to the most demanding

of the 3 tested time histories.

Regarding the estimation of the PGA that makes the structural elements overtake the state limits prescri-

bed by the code, this has been estimated following the steps that are illustrated in Figure 26.


The PGA computation is done by taking into account the fact that the structure has a certain dynamic re-

sponse, thus it is mainly influenced by acceleration peaks reached before the failing instant.

In the following are reported the obtained results for each limit state.

3.8.1 OPERATIONAL LIMIT STATE (SLO).

As it has been performed for the Pushover analysis, also in the case of the non-linear time history analysis

the inter-story drifts have to be analyzed from the simulations performed on the model of the structure

without the presence of the masonry infills (Figure 14).

Figure 27 - (a) Inter-story drifts measured from the simulation of the non-linear time history compared to the limit state; (b) detail of the simulation.

Figure 28 - PGA analysis for the operational limit state (SLO): red dot represents the identified PGA.

In Figure 27 (a), Figure 27 (b) the inter-story drifts time histories are reported together with the correspon-

ding limit state fixed at the strictest threshold, thus limiting the maximum inter-story drift to two-third of

0,002 times the floor height.

From Figure 27, it can be seen that the inter-story drifts of the 3^rdfloor and the 2^nd floor, exceed the limit

state at time 5.4 seconds due to the change of section of the main structural elements between the first

(a) (b)

37



two inter-stories and the last two.

In Figure 28 it is graphically reported the computation of the PGA that makes the structure overtake the

limit state, approximately equal to 0,0584g. The demand PGA, instead, is 0,1043g.

3.8.2 DAMAGE LIMIT STATE (SLD).

Exactly the same procedure adopted for the operational limit state (SLO) is adopted also for the damage

limit state (SLD) and in Figure 29 the inter-story drifts time histories are reported with the limit state thre-

sholds, that have been changed with respect to the operational limit state (SLO), increasing the value to

0.002 times the height of the story.

(a) (b)Figure 29 - (a) Inter-story drifts measured from the simulation of the non-linear time history compared to the limit state;

(b) detail of the simulation.

Figure 30 - PGA analysis for the damage limit state (SLD): red dot represents the identified PGA.

From Figure 29, it can be seen that the inter-story drift of the 3rdfloor, exceeds the limit state at time 7.82

seconds due to the change of section of the main structural elements between the first two inter-stories

and the last two. In Figure 30 it is reported the PGA computation that makes the structure overtake the

limit state at approximately 0,06855g. The demand PGA, instead, is 0,1253g.


3.8.3 LIFE SAFEGUARD LIMIT STATE (SLV).

The same check that has been previously explained for the Pushover analysis can be applied in this case,

always by verifying the main relations:

(MEyd/MRyd)α+ (MEzd/MRzd)

α ≤ 1

and

VRd ≥ VEd

Indeed, as for the previous cases, the artificial accelerogram related to the analyzed limit state has been

applied. However, while for the previous cases only the inter-story drifts had to be verified, this time the

verification becomes more computationally intensive especially in terms of amount of data.

Figure 31 - Failed elements with respect to the life safeguard limit state.

All the bending moments, torsion, shear and axial load for each element of the structure and respectively in

5 different sections of the element have to be studied at each time step and the verification, that has been

previously mentioned, applied at each time step.

This means that for a structure such as the one in analysis the verification is performed on the bending mo-

ment and shear for 600 points at each time step. This is done in order to precisely understand the instant

where the structure fails and in which element, while usually also an envelope technique could be applied,

taking into account only the maximum and the minimum value of the stresses applied to the structural ele-

ment in analysis during the whole time history.

Thanks to this methodology it has been found that the first elements to fail are the beams respectively

nominated ‘81’ and ‘93’ and that are shown in Figure 31.It is interesting to evaluate the time history of the bending moment M3 to which the element 81 is subjected

compared to the resisting bending moment computed in that time instant (since it is a function of the axial

39



(a) (b)Figure 32 - (a) bending moment M3 applied to the beam element ‘81’ compared to the resisting bending moment computed at the same

step; (b) V2 shear load compared to the resisting shear load of the section computed at the same step.

Figure 33 - Ground acceleration for the selected limit state and selection of the PGA that cause the structure failure: red dot represents the identified PGA.

load). As it can be seen from Figure 32 (a) the bending moment overtakes the threshold at instant 1.17 se-

conds and almost the same applies for the shear load, that overtakes the resisting shear load at time 1.19

seconds as it can be seen from Figure 32 (b).

Then the PGA for which the failing mode is reached has to be selected according to the rule presented

before and in this case it can be easily understood the reason of this methodology, since at the moment

of fracture the ground acceleration is much lower compared to higher peaks where the structure did not

show problems.

Thus, the obtained PGA is of 0,0747g and can be seen in Figure 33. The demand PGA instead is 0,2974g.


3.8.4 COLLAPSE LIMIT STATE (SLC).

Regarding the collapse limit state analyzed thanks to the use of the non-linear time history, the procedure

is not straight forward, because the code covers more in detail the non-linear static analysis, but not this

type of analysis, probably because not commonly used.

Indeed, based on the NTC2018 code and on the concept of energy dissipation which the collapse limit state

(SLC) focus on, the following procedure is proposed:

1. Select the response spectrum of the structure for the collapse limit state (SLC) and compute the

related accelerogram.

2. Extract using the FEM the last floor displacement and the related base shear from the resulting

non-linear time history.

3. Compute the linear relation between base shear and roof displacement in the first few cycles of

oscillation of the structure where the hypothesis of linearity is still valid.

Figure 34 - (a) Roof displacement measured in case of collapse limit state; (b) Structure base shear.

Figure 35 - (a) Base shear and roof displacement trend in the first instants of the simulation where the linear hypothesis is valid; (b) Roof displacement vs. Base shear reaction.

(a) (b)

(a) (b)

41



4. Compute the total energy that the structure should have absorbed in a linear manner by conside-

ring proportional the relation between roof displacement and base shear.

This is shown in Figure 36 (a) and computed as the integral in time of the base reaction times the

ground displacement. Instead the output energy, equal to the total input energy minus the dissipated

energy is computed as the integral in time of the roof displacement times the base shear.

Thanks to the total input energy into the structure, it is possible to evaluate the maximum demand

base shear that the structure should have seen during the simulation if the structure would have re-

mained linear during all the steps, see Figure 36 (b).

Figure 36 - (a) Computation of the total energy in input and in output; (b) Displacement and base shear reaction of the structure if it would have had only linear response.

5. Check the maximum value of the base shear reached during the time history analysis RMax;

6. Consider the ultimate base shear as the one for which the maximum resistance of the structure is

reduced by a factor of 15%:

RMax 85% = 85% RMax

(a) (b)

Figure 37 - Force-displacement curve.


7. Find the ultimate roof displacement, du, as the maximum displacement reached during the collapse

limit state analysis (SLC) and the displacement of the structure for which the first yielding occurs, dy,

by using the diagram constructed from the previous stages and shown in Figure 37.

8. Check if the demand in terms of ductility factor, computed according to the Guidelines of the

NTC2018 (chapter 7.3.4.2), is bigger or smaller than the capacity ductility factor, respectively compu-

ted as prescribed by the NTC2018 (chapter 4.1.2.3.4.2):

μd= RD/RMax 85% ductility factor demand

μC= du/dy ductility factor capacity

9. If the ductility demand is smaller than the ductile capacity of the structure, the collapse limit state

(SLC) is verified, while if this is not the case, follow this approach iteratively to identify which is the

demand that satisfies the maximum absorbable energy by the structure:

A) The main hypothesis is that the base shear is mainly due to the ground acceleration times

the total building mass while the parameters characteristic of the structure remain unchanged:

RMax 85%, du and dy.

B) Thus, it is possible to proportionally decrease the ground acceleration, without changing its

frequency content, and the base shear should decrease proportionally in order to maintain the

proportions used in point 4, with the hypothesis of linear behavior.

C) Compute the ductility factor demand and the ductility factor capacity and check their diffe-

rence.

D) Repeat points b and c until the ductility factor demand is equal to the ductility factor capacity.

E) Get the PGA capacity as the maximum value reached by the ground acceleration in all the

time history.

This procedure is simply based on the fact that the ductile capacity of the structure cannot change since is

based on the area covered by the curvature-moment diagram or the force-displacement diagram.

Thus, the demand is progressively reduced, according to the basic hypothesis, in order to decrease the

energy given in input to the structure, in such a way that it can be compared to the PGA reached by the

accelerogram.

This methodology has been applied on the non-linear time history of the structure and in the following the

obtained results are reported. Indeed, the procedure has been explained by using data directly coming from

the non-linear time history analysis of this case study and the related images have been shown respectively

in those figures.

The obtained capacity PGA in this case is 0,2320g and the related figure obtained in correspondence of

demand equal to the capacity is shown in Figure 38 (b). The demand PGA is instead 0,3693g.

43



Figure 38 - (a) Decrease of the demand that implies the decrease of the value RD; (b) Obtained decreased demand.

3.9 SEISMIC RISK CLASSIFICATION: NON-LINEAR TIME HISTORY RESULTS.

3.9.1 RESULTS: IS-V.

For the computation of the IS-V coefficient it is only needed the result obtained from the analysis of the

life safeguard limit state, where it has been possible to obtain a capacity PGA, PGAC, of 0.0747g while the

demand PGA, PGAD, is of 0.2974g. Thus, by using the relation:

IS-V = PGAC / PGAD

an IS-V coefficient of 25.11% is obtained, which, according to Table 5, corresponds to seismic risk class E.

(a) (b)

3.9.2 RESULTS: PAM.

As it has been done for the non-linear static analysis, the PAM coefficient has been computed and in Table 11 are reported the capacity PGA, PGAC, the demand PGA, PGAD, and the computed return period, TrC,

calculated as illustrated in the previous chapters, for each of the analyzed limit states.


SLO

SLD

SLV

SLC

PGAD [g]

0.1043

0.1253

0.2974

0.3693

7

11

16

314

0.0584

0.0685

0.0747

0.2320





which result equal to 5,482%. Then, by using Table 7, it can be found that, according to the PAM coefficient,

the structure is in seismic risk class F.


As prescribed by the code, the worst case between the obtained class risk with the IS-V coefficient and

with the PAM coefficient, is the seismic risk class of the structure. Finally, it is possible to state that the

class risk of the structure obtained using the non-linear time history analysis is F.

Figure 40 - seismic risk class obtained for the case study using the non-linear dynamic time history analysis.

45



4. SEISMIC PERFORMANCE IMPROVEMENT: ISAAC DEVICE.

The ISAAC system is a smart active technology for the seismic protection of existing buildings that requires

the external installation of modular devices on the top floor of the structure.

The system allows to reach a significant improvement of dynamic performance of the building by decrea-

sing its amplitude of oscillation during an earthquake. In practice, this is reached thanks to the delivery of

huge amounts of forces on the roof of the building through the installed devices. These are controlled by a

central computer that record the motion of the building thanks to accelerometric sensors and in real-time

computes the amount of forces that need to be delivered by the devices.

In order to evaluate the improvements obtainable thanks to the use of this solution, the same techniques

prescribed by the code NTC2018, and previously used on the selected case study, have been applied in the

following for the evaluation of the seismic risk class improvement reached by the structure equipped with

this technology.

4.1 ISAAC DEVICE MODELLING AND SIMULATION.

In order to simulate the installation of the devices and to test the performances obtainable in a real-time

application, it has been created a complex co-simulator that integrate two different software: SAP2000

and Matlab. Indeed, the first one is used to simulate a non-linear time history response of the structure

subjected both to ground motion and force of the seismic protection system, while the second one to simu-

late the control logic and the behavior of the devices in delivering the force requested by the control logic.

Figure 41 - Co-simulator used for the analysis of the ISAAC system and the non-linear structure interaction.


The working principle is simply illustrated in Figure 41: at each step the non-linear time history is processed

by the FEM software, then the output is read by the Matlab code and exactly as it would happen in reality,

the control algorithm computes the forces that need to be delivered to the structure for the next step by

reading the motion of the structure only in the points where the sensors are applied.

Then the computed forces are applied to the real structure and the cycle repeats continuously.

The forces delivered by the seismic protection system have been considered as equally distributed on

the top of the 8 columns of the structure, thus simulating the adoption of a frame fixed to the floor of the

structure where 1 main device is installed, or 8 smaller devices directly fixed one per each column.

Moreover, to test the behavior of the last inter-story in response to the application of these forces, the same

tests have been repeated by considering the forces as applied only on the top of the two main central

columns obtaining no particular differences with respect to the base case, and for this reason these other

results have not been reported here.

4.2 IDENTIFICATION AND CONTROL OF THE STRUCTURE.

In order to tune the control algorithm parameters, a linear modal model is obtained with an automatic Expe-

rimental Modal Analysis (EMA) procedure, periodically running when the structure is not seismically excited.

This is practically implemented by exciting the structure in the control direction with a force sweep signal

with frequencies ranging from 0 to 20Hz and 1kN magnitude, generated by the device itself, and recording

the resulting absolute accelerations in the same excited direction (through accelerometers for an actual

building, while in the adopted numerical model also displacements and velocities are available), at each

floor of the building.

These results are automatically processed by an EMA algorithm to get modal parameters, shapes and

participation factors. These are used to build the simplified linear model of the structure.

Figure 42 - Comparison between simplified linear model from simulated EMA and full nonlinear model in terms of roof displacements due to the same ground acceleration time history.

47



The goodness of fit of the linear model can be appreciated (especially for small displacements) by compa-

ring its response to the ground acceleration time history (see Figure 33) used for SLV evaluation with the

one of the full nonlinear model. This comparison is shown in Figure 42 for roof displacements.

The obtained linear model is used to optimally and robustly tune the parameters of control algorithm.

This has been designed aiming at minimizing inter-story drifts magnitudes, which are known to be strictly

linked to structural damage initiation and growth.

A schematic representation of the algorithm idea is given in Figure 43 : inter-story drifts are computed at

every instant from accelerometers data and then processed by the controller, which actuates the device in

such a way that the resulting force minimizes the drifts magnitudes.

Figure 43 - Schematic representation of the control algorithm idea: the control aim is to minimize inter-story drifts Δxi, i=1,2,3,4, thus the force to be exerted by the device is computed with this objective.

4.3 SEISMIC RISK CLASS IMPROVEMENT EVALUATION:NON-LINEAR TIME HISTORY ANALYSIS.

The same procedures illustrated for the analysis of the non-linear time history of the non-controlled structu-

re, has been adopted for the analysis of the structure equipped with the ISAAC technology and the results

will be briefly reported in the following for each of the limit states (SLO, SLD, SLV, SLC).

These will be used to evaluate the seismic risk class of the structure equipped with the installed devices

and to determine the improvement obtainable in this typical case.

It is important to underline that all the accelerograms used in the case of the non-controlled structure eva-

luation, has been used also in this case, this has been done to make highly comparable the time histories

of the two simulated conditions of the structure and thus to potentially evaluate at each time instant the

reduction of the internal stresses, inter-story drifts and other key parameters.

Also for the controlled structure, all the three time histories have been tested, but only the results corre-

sponding to the most demanding one have been reported here.


4.3.1 OPERATIONAL LIMIT STATE.

The device results to be particularly effective in reducing the amplitude of oscillation of the structure in the

operational limit state (SLO) as it can be seen from Figure 48 (a) where is reported the comparison betwe-

en the controlled and non-controlled structure. In Figure 48 (b) are reported the inter-story drifts and the

corresponding limit states, fixed at the strictest threshold, thus limiting the maximum inter-story to two-third

of 0,002 times the floor height.

(a) (b)Figure 44 - (a) I; (b) D.

Figure 45 - PGA analysis for the operational limit state (SLO): red dot represents the identified PGA.

As it can be seen, the inter-story drifts of all the floors do not exceed the limits imposed for the operational

limit state (SLO). For this reason, the capacity PGA results to be equal to the demand PGA of 0,1043g.

49



4.3.2 DAMAGE LIMIT STATE.

Exactly the same procedure adopted for the operational limit state (SLO), is adopted for the damage limit

state (SLD) and in Figure 46 (a) is possible to see the huge improvement obtainable also in this case by

comparing the non-controlled and the controlled structure. Moreover, in Figure 46 (b) are reported the in-

ter-story drifts and the limit state thresholds that have been changed with respect to the operational limit

state (SLO), increasing the value to 0.002 times the height of the story.

(a) (b)Figure 46 - (a) Inter-story drifts measured from the simulation of the non-linear time history compared to the limit state;

(b) detail of the simulation.

Figure 47 - PGA analysis for the damage limit state (SLD): red dot represents the identified PGA.

As it can be seen, all the inter-story drifts remain within the limit state thresholds, making the capacity PGA

be equal to the demand PGA of 0,1253g.


4.3.3 LIFE SAFEGUARD LIMIT STATE.

In this case the accelerogram related to the life safeguard limit state (SLV) has been selected.

In Figure 48 (a) it is reported the total control action delivered by the device on the roof of the structure

and in Figure 48 (b) the first inter-story drift displacements, verified to be a key parameter in leading to

structure failure.

(a) (b)Figure 48 - (a) Control force delivered to the structure for the control; (b) Ground floor inter-story drift simulated for the whole-time history.

As it has been done for the non-controlled structure time history analysis, all the bending moments, torsion,

shear and axial load in each element of the structure and respectively in 5 different sections of the element

have been studied at each time step and the verification of the shear load and bending moment verified.

This showed that the first element to fail, exactly as for the non-controlled case, are the frame elements ‘81’

and ‘93’, the same beams that have been underlined in Figure 31.

(a) (b)Figure 49 - (a) Bending moment M3 in the failed beam ‘81’; (b) Shear load V2 in the failed beam ‘81’.

51



The verification on the bending moment M3 and on the shear load V2 can be seen respectively in Figure 49 (a) and Figure 49 (b) (the resisting bending moment and the resisting shear load are obviously changing

with the axial load of the element, but for sake of simplicity, here are illustrated as constants for all the time

history and computed with the axial load measured at the instant of failure).

So, it is proved that the moment of failure of the structure element is delayed to 2.09 seconds, compared

to the non-controlled case where the failure of the first element happened at 1.19 seconds. Indeed, it is

possible to clearly see a reduction up to the 25% of the bending moment and up to the 18.5% of the shear

load before the failure of the element happens. This is a clear demonstration of the dynamic improvements

obtainable by the adoption of this technology.

(a) (b)Figure 50 - (a) Bending moment M3 of the controlled structure compared to the non-controlled; (b) Shear load V2 of the controlled

structure compared to the non-controlled

Finally, it has been possible to compute the capacity PGA as it has been done for the non-controlled case,

and in Figure 51 it is shown the same acceleration time history used for the non-controlled case.

Figure 51 - Red dot represent the PGA of capacity of the structure, blue line is the accelerogram used for the life safeguard limit state (SLV).

Thus, it is possible to say that the capacity PGA of the controlled structure is equal to the value of 0.2382

g. Instead, the demand PGA, as for the non-controlled case, is of 0.2974g.


4.3.4 COLLAPSE LIMIT STATE.

Regarding the analysis of the collapse limit state, it is important to underline some key points that characte-

rize the adoption of the ISAAC technology for the seismic risk class improvement.

From Figure 52 (a) is it possible to see the comparison between the shear base reaction of the non-con-

trolled structure and of the controlled structure. Indeed, one of the key features of the technology is that

the base shear of the structure is reduced (in this case of 30.37%) and, consequently, also the input energy

since the ground displacement does not change (see Figure 52 (b)). So, the adoption of the system can

be compared to a decrease in the demand of ductility to the structure in the analysis of the collapse limit

state (SLC).

(a) (b)Figure 52 - (a) Comparison of the base shear reaction force between the controlled and non-controlled case; (b) Comparison of the total input energy in the construction between the controlled and non-controlled case.

Figure 53 - Force-displacement curve: difference in terms of input energy into the structure.

However, the characteristics of the structure regarding its material, ductility etc. have not been changed

since no intervention has been done on the structure if not just installing the devices on the roof, potentially

increasing the mass of the structure only of 1.37%, thus the main ductility parameters: RMax 85%, du and dy

have been kept constant w.r.t. the non-controlled structure.

The only changed parameter, due to the control interaction with the structure is the stiffness, as can be

verified from Figure 54.

53



Figure 54 - (a) Roof displacement and base shear in the first few cycle; (b) Roof displacement vs. Base shear.

In Figure 53 it is possible to see the difference and, consequently, the improvement obtainable also in ter-

ms of collapse limit state (SLC) analysis, since the demand of the controlled structure with the term RD is

already decreased by the adoption of the control.

Figure 55 - Diagram obtained in the case of a demand PGA equal to the capacity PGA.

Thus, the collapse limit state can now be evaluated has it has been done for the non-controlled structure

by comparing the ductility factors μc and μd. These values are respectively of 2.76 and 3.99, therefore the

same procedure adopted before to scale the demand to find the capacity PGA has to be adopted.

Thanks to this strategy, the diagram illustrated in Figure 55 is obtained and also the capacity PGA, which is

of 0.2771g, while the demand is the same reported for the non-controlled case, 0.3693g.

It is important to specify that also in this case, as for the other Limit State evaluations, a saturation of the

actuators force has been simulated, thus obtaining as overall profile of force in input to the structure the

one illustrated in Figure 56 (b). In Figure 56 (a), instead, the inter-story drift reduction at ground floor can

be appreciated.

(a) (b)


Figure 56 - (a) Ground floor inter-story drift; (b) Control force with saturation.

As it can be seen from Figure 56 (a), the uncontrolled structure results to be not so stable, ending up in

a soft-story collapse mechanism, that, instead, the controlled structure has been able to avoid completely.

This behavior can be clearly seen from the image taken in SAP2000 (see Figure 57) of the last step of

analysis of the structure and by keeping the same scale factor of the deformed shape visualization.

Figure 57 - (a) Deformed shape of the non-controlled structure at the final step of analysis; (b) Deformed shape of the controlled structure at the final step of analysis.

(a) (b)

(a) (b)

55



4.4 SEISMIC RISK CLASS IMPROVEMENT EVALUATION: RESULTS.

4.4.1 RESULTS: IS-V.

Exactly as for the non-controlled structure, the computation of the IS-V coefficient only needs the result

obtained from the analysis of the Life Safeguard Limit State, where it has been possible to obtain a capa-

city PGA, PGAC, of 0.2382g while the demand PGA, PGAD, is of 0.2974g. Thus, by using the relation:

IS-V = PGAC / PGAD

an IS-V coefficient of 80,09% is obtained, corresponding, according to Table 5, to seismic risk class A.

4.4.2 RESULTS: PAM.

As it has been done for the non-linear time history analysis of the non-controlled structure, the PAM co-

efficient has been computed and in Table 12 are reported the capacity PGA, PGAC, the demand PGA,

PGAD, and the computed return period, TrC, calculated as illustrated in the previous chapters, for each of

the analyzed limit states.


SLO

SLD

SLV

SLC

PGAD [g]

0.1043

0.1253

0.2974

0.3693

30

50

276

484

0.1043

0.1253

0.2382

0.2771





which result equal to 1,220%. Then, by using Table 7, it can be found that, according to the PAM coefficient,

the structure is in seismic risk class B.


As prescribed by the code, the worst case between the obtained class risk with the IS-V coefficient and

with the PAM coefficient, is the seismic risk class of the structure.

Finally, it is possible to state that the class risk of the structure obtained using the non-linear time history

analysis of the structure equipped with the ISAAC technology is B.

Moreover, it is important to remember that a structure that completely fulfills the requests prescribed by the

code is in class A for the IS-V coefficient and in class B, for the PAM coefficient. This allows to state that in

this case study it has been possible to bring the structure, built according to the standards of the 60s, thus

without design for seismic and dynamic lateral loads, from seismic risk class F to a complete retrofit, without

any local intervention on the structure and simply installing the ISAAC technology on the top of the building.

Figure 59 - Seismic risk class obtained for the case study using the non-linear dynamic time history analysis of the structure equipped with the ISAAC technology and starting from class F.

57



5. ISAAC DEVICE SOLUTION: ADVANTAGES.

In the previous sections it has been demonstrated, according to the Italian standard NTC2018, the complete

retrofit of a structure that can be obtained with the adoption of the ISAAC technology.

The analysis has been performed on a structure as a case study that is a 1:1 scale building model from the

research project “Assessment and Retrofitting of Full-Scale Models of Existing RC frames” of the European

Laboratory for Structural Assessment (ELSA) at Ispra-Italy performed in the mid 2000’s. The main reasons

for the selection of this building is because it represents the typical building design practices of the late

1950’s and 1960’s. This building typology represents a significant fraction of the existing RC buildings in

Italy, one of the target markets for ISAAC seismic protection system.

From the analysis it has been proved that ISAAC seismic protection technology could bring the structure

from a seismic risk class F, to seismic risk class B, thus obtaining almost a complete retrofit of the structure

without any single local reinforcement other than the simple installation of the ISAAC devices on the roof

of the building.

The incredible advantages of this solution could be summarized in:

• No need of eviction of the inhabitants from a building during the works of installation of the ISAAC

devices on the roof of the building.

• Total absence of burdensome works on the structure for the seismic retrofit.

• Non-invasive solution compared to the use of dissipative devices such as velocity-dependent or

displacement-dependent absorbers.

• Full control of the state of the structure thanks to the continuous monitoring of the building using

the installed ISAAC system of seismic protection, that continuously analyze the presence of any ano-

maly in the devices themselves or in the structure.

• Significant decrease in the intervention time.

• Compliance with the Italian code NTC2018 (and Eurocode).

• Applicable solution to common buildings compared to the use of normal passive TMDs.

Figure 60 - ISAAC Device named I-Pro 1, The first smart seismic protection device.

1960's CONCRETE STRUCTURE SEISMIC IMPROVEMENT WITH ISAAC TECHNOLOGY ACCORDING TO NTC 2018.

Technical Report by Eng. A. Bussini, Eng. A. Torti, Eng. M. Cortes.


ISAAC [email protected]

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