Seismic Retrofitting of Existing Industrial Steel Buildings: A Case-Study

Abstract

Industrial single-storey buildings are the most diffuse typology of steel construction located in Italy. Most of these existing buildings were erected prior to the enforcement of adequate seismic provisions; hence, crucial attention is paid nowadays to the design of low-impact retrofit interventions which can restore a proper structural performance without interrupting productive activities. Within this framework, an existing industrial single-storey steel building located in Nusco (Italy) is selected in this paper as a case-study. The structure, which features moment resisting (MR) truss frames in both directions, is highly deformable and presents undersized MR bolted connections. Structural performance of the case-study was assessed by means of both global and local refined numerical analyses. As expected, the inadequate performance of connections, which fail due to brittle mechanisms, detrimentally affects the global response of the structure both in terms of lateral stiffness and resistance. This effect was accounted for in global analyses by means of properly calibrated non-linear links. Thus, both local and global retrofit interventions were designed and numerically investigated. Namely, lower chord connections were strengthened by means of rib stiffeners and additional rows of M20 10.9 bolts, whereas concentrically braced frames (CBFs) were placed on both directions’ facades. Designed interventions proved to be effective for the full structural retrofitting against both seismic and wind actions without limiting building accessibility.

Full text

Citation: Tartaglia, R.; Milone, A.;
Prota, A.; Landolfo, R. Seismic
Retrofitting of Existing Industrial
Steel Buildings: A Case-Study.
Materials 2022,15, 3276. https://
doi.org/10.3390/ma15093276
Academic Editor: Karim Benzarti
Received: 11 March 2022
Accepted: 29 April 2022
Published: 3 May 2022
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materials
Article
Seismic Retrofitting of Existing Industrial Steel Buildings: A
Case-Study
Roberto Tartaglia , Aldo Milone, Alessandro Prota and Raffaele Landolfo *
Department of Structures for Engineering and Architecture, University of Naples Federico II,
Via Forno Vecchio 36, 80134 Naples, Italy; roberto.tartaglia@unina.it (R.T.); aldo.milone@unina.it (A.M.);
alessandro.prota@unina.it (A.P.)
*Correspondence: landolfo@unina.it
Abstract:
Industrial single-storey buildings are the most diffuse typology of steel construction
located in Italy. Most of these existing buildings were erected prior to the enforcement of adequate
seismic provisions; hence, crucial attention is paid nowadays to the design of low-impact retrofit
interventions which can restore a proper structural performance without interrupting productive
activities. Within this framework, an existing industrial single-storey steel building located in Nusco
(Italy) is selected in this paper as a case-study. The structure, which features moment resisting (MR)
truss frames in both directions, is highly deformable and presents undersized MR bolted connections.
Structural performance of the case-study was assessed by means of both global and local refined
numerical analyses. As expected, the inadequate performance of connections, which fail due to brittle
mechanisms, detrimentally affects the global response of the structure both in terms of lateral stiffness
and resistance. This effect was accounted for in global analyses by means of properly calibrated
non-linear links. Thus, both local and global retrofit interventions were designed and numerically
investigated. Namely, lower chord connections were strengthened by means of rib stiffeners and
additional rows of M20 10.9 bolts, whereas concentrically braced frames (CBFs) were placed on both
directions’ facades. Designed interventions proved to be effective for the full structural retrofitting
against both seismic and wind actions without limiting building accessibility.
Keywords: existing structures; steel constructions; seismic retrofitting; finite element analyses
1. Introduction
Industrial single-storey buildings represent the majority of existing steel constructions
located in Italy [
1
]. This kind of structural type mainly spread during the second half of the
20th century due to its capability of covering relatively large spans without recurring to
complex technological solutions, and with affordable costs [2].
Hence, most Italian industrial steel buildings realised between the 1980s–1990s were
designed in compliance with the CNR 10,011 [
3
] code, and, in particular, the vertical
and the wind actions were accounted for as prescribed by CS.LL.PP. n. 56 and n. 140,
respectively [4,5]
. Only in 1986, the document Decreto Ministeriale 24 January 1986 [
6
]
introduced the equivalent static forces to account for the seismic action. However, this code
did not provide adequate instructions to ensure a satisfactory seismic performance, since it
does not provide adequate prescription for the design of the local detailing. For instance,
in the design of connections, no distinctions were made between ductile and brittle mecha-
nisms. Moreover, as highlighted by [
7
,
8
], the lack of prescriptions for joints characterization
often led to non-conservative design assumptions (e.g., in case of base connections).
Inadequate technical practices were also fostered by the common idea that seismic
action could not govern design choices for industrial single-storey buildings, owing to their
relatively low mass with respect to enclosed surfaces [
2
], similarly with what was observed
for moment-resisting frames equipped with truss beams [9,10].
Materials 2022,15, 3276. https://doi.org/10.3390/ma15093276 https://www.mdpi.com/journal/materials

Materials 2022,15, 3276 2 of 23
However, the occurrence of multiple seismic events, e.g., Friuli (1976), L’Aquila (2009), and
Emilia (2012) earthquakes, proved the incorrectness of this belief, as several industrial buildings
reported moderate-to-severe damages, with some relevant cases of global collapse also [11].
Differently from residential buildings, an important aspect that should be accounted
for when dealing with industrial constructions is represented by indirect costs, i.e., ex-
penses due to interruption of the productive activities for long time [
12
]. Namely, on most
occasions, seismic damage to Italian industrial steel buildings consisted of local failures of
connections, claddings, and/or roofing [
7
], though a few notable cases of global collapse
occurred as well [13].
In light of these events, the interest in assessing and enhancing the seismic performance
of steel structures [
14
–
18
] and, in particular, the industrial single-storey buildings has
quickly developed up to present time. In particular, crucial attention is currently paid to the
design of low-impact retrofitting interventions which simultaneously minimise time needed
to resume productive activities and effectively prevent not only structural damage, but also
damage on industrial machineries [
19
]. It is worth reporting that some contributions aiming
at investigating the efficiency of low-impact retrofitting strategies on industrial buildings
are already available in the literature. Formisano et al. [
19
] investigated the efficiency of
global retrofitting interventions on an industrial steel structure located in Italy. The authors
proved the effectiveness of concentrically braced frames (CBFs) with both X-shaped and
portal (i.e., double Y-shaped) configurations in enhancing both strength and stiffness of
the structure without preventing building accessibility. Hirde et al. [
20
] inspected the
effectiveness of two retrofit strategies for a damaged industrial steel building located in
India. Namely, a first low-impact seismic enhancement was achieved by welding new angle
profiles to existing structural members (i.e., back-to-back). The authors investigated a more
invasive solution involving the introduction of new truss beams below the existing load-
bearing gables. Although being highly effective in improving both resistance and lateral
stiffness of the structure, it should be remarked that this intervention was only feasible
since no requirements about the minimum net height of the industrial building had to be
fulfilled. Finally, Bournas et al. [
21
] analysed damages in industrial buildings (both with
steel and precast RC structure) affected by the Emilia earthquake. On the basis of detected
criticalities, the authors suggested that local interventions on beam-to-column joints and
claddings connections could highly improve the performance of industrial buildings in
seismic zones. The authors also highlighted the current absence of normative guidelines
for the design and check of this kind of intervention.
Within this framework, the aim of this work is to design and check the effectiveness of
low-impact retrofit interventions to increase the industrial building capacity against lateral
action, without interrupting the building functionality. Indeed, this work is part of a wider
Italian research project (Reluis WP5 [
22
]) aiming at verifying the validity of low-impact
strategies for the seismic retrofitting of existing non-code-conforming buildings.
For this purpose, an existing single-storey steel building located in Nusco (Italy)
is selected as a case-study; the structure was designed and erected during the 90 s in
compliance with normative provisions enforced at the time [3].
Preliminary Finite Element Analyses (FEAs) on the selected case-study showed how
the existing structure is rather deformable in both the principal directions, and unable to
properly resist seismic actions. Therefore, both local and global retrofitting interventions
were designed and verified by means of refined numerical models.
Indeed, one of the main aims of this paper is to underline the importance of the
local behaviour of the steel joints in the assessment of existing structures, and how their
performance should be accounted for also in the global analyses, since they could affect not
only the local resistance, but also the lateral stiffness of the whole structure.
The paper is mainly divided into five sections: in the first part, the main features of
the investigated case-study are presented. Concept and design procedures for low-impact
seismic retrofit interventions are discussed in the second section, whereas in the third part,
the main finite element (FE) modelling assumptions are summarised. The global and local

Materials 2022,15, 3276 3 of 23
seismic performance of the existing structure is presented in the fourth section, and finally,
the efficiency of designed retrofit solutions is discussed in the last part.
1.1. General Description of the Structure of the Selected Case-Study
The selected case-study is a single-storey industrial steel building that serves as a
warehouse for an adjacent building in which aluminium products are manufactured. The
dynamic response of the investigated structure, which was built later with respect to the
production unit (i.e., between 1992 and 1999), was decoupled from the main building by
means of a seismic joint.
Original design report and drawings, as well as on-site surveys, allowed the complete
characterization of geometrical features of the selected building (see Figure 1).
Materials 2022, 15, x FOR PEER REVIEW 3 of 24
The paper is mainly divided into five sections: in the first part, the main features of
the investigated case-study are presented. Concept and design procedures for low-impact
seismic retrofit interventions are discussed in the second section, whereas in the third part,
the main finite element (FE) modelling assumptions are summarised. The global and local
seismic performance of the existing structure is presented in the fourth section, and
finally, the efficiency of designed retrofit solutions is discussed in the last part.
1.1. General Description of the Structure of the Selected Case-Study
The selected case-study is a single-storey industrial steel building that serves as a
warehouse for an adjacent building in which aluminium products are manufactured. The
dynamic response of the investigated structure, which was built later with respect to the
production unit (i.e., between 1992 and 1999), was decoupled from the main building by
means of a seismic joint.
Original design report and drawings, as well as on-site surveys, allowed the
complete characterization of geometrical features of the selected building (see Figure 1).
Figure 1. Geometrical features of the selected building according to the original design report.
The structure has a rectangular plan extending for 55.5 m in the longitudinal
direction, and for 36 m in the transversal one; the total height of the building is equal to
12.7 m (see Figure 2).
Truss frames are used in X- and Y-directions to resist both gravity loads and
horizontal actions. Both top and bottom chords are connected to the supporting columns,
which are continuous in correspondence of the connections, thus creating a moment-
resisting frame. Namely, three moment-resisting frames (MRFs) were placed in both X-
and Y-directions, spaced out by intermediate connecting trusses (see Figure 2).
Columns belonging to MRFs were made by means of welded hollow members; on
the contrary, hot-rolled profiles (i.e., IPE 360 and HE 300B) were adopted for the claddings
support system. Notably, all hollow columns are oriented with their strong axis being
parallel to the Y-direction.
Coupled angle members having different cross-sections were adopted for seismic-
resistant trusses, whereas both single and coupled angles were used for connecting
trusses.
The truss members are connected to each other and with columns by means of gusset
plates placed within the gaps of back-to-back profiles, which are, in turn, bolted (in X-
direction) or welded (in Y-direction) to column ends. Base connections were realised with
extended stiffened plates in both directions.
Figure 1. Geometrical features of the selected building according to the original design report.
The structure has a rectangular plan extending for 55.5 m in the longitudinal direction,
and for 36 m in the transversal one; the total height of the building is equal to 12.7 m
(see Figure 2).
Truss frames are used in X- and Y-directions to resist both gravity loads and horizontal
actions. Both top and bottom chords are connected to the supporting columns, which are
continuous in correspondence of the connections, thus creating a moment-resisting frame.
Namely, three moment-resisting frames (MRFs) were placed in both X- and Y-directions,
spaced out by intermediate connecting trusses (see Figure 2).
Columns belonging to MRFs were made by means of welded hollow members; on
the contrary, hot-rolled profiles (i.e., IPE 360 and HE 300B) were adopted for the claddings
support system. Notably, all hollow columns are oriented with their strong axis being
parallel to the Y-direction.
Coupled angle members having different cross-sections were adopted for seismic-
resistant trusses, whereas both single and coupled angles were used for connecting trusses.
The truss members are connected to each other and with columns by means of gusset
plates placed within the gaps of back-to-back profiles, which are, in turn, bolted (in X-
direction) or welded (in Y-direction) to column ends. Base connections were realised with
extended stiffened plates in both directions.

Materials 2022,15, 3276 4 of 23
Materials 2022, 15, x FOR PEER REVIEW 4 of 24
According to the original design report, S235 grade steel was used for all members
and plates, whereas 6.8 strength class bolts were adopted for the connections.
Figure 2. Geometrical features of the selected case-study and disposition of resisting systems in both
directions.
In light of the retrieved information, the highest level of knowledge (“KL3”—
exhaustive knowledge) was attained for the selected case-study according to Italian
provisions for existing buildings [23,24]. Hence, characteristic values of material
properties were used for seismic analyses accounting for no reduction (i.e., a partial safety
factor FC = 1 is assumed in [23,24] for KL3).
1.2. Description of Investigated Connections
The main geometrical features of moment-resisting connections between truss
members and columns are depicted in Figure 3. Owing to the constant orientation of all
hollow columns, two different joint configurations were adopted in the X- and Y-
direction.
A T-shaped 20 mm gusset plate is used to connect both the upper chord and the
diagonal to the column (see Figure 3a) in the X-direction. Seven staggered M24 bolts are
used for the upper coupled angles (2-Ls 150 mm × 150 mm × 14 mm), whereas four in-line
M24 bolts are adopted for the coupled diagonals (2-Ls 90 mm × 90 mm × 9 mm). The gusset
plate terminates with an end-plate, which is, in turn, bolted to the column flange (350 mm
× 20 mm, welded to two 460 mm × 8 mm webs) by means of seven rows of M24 bolts.
Moreover, the connection is further stiffened by means of two trapezoidal 20 mm ribs,
placed at the base of the gusset plate.
Contrariwise, a simpler configuration is adopted for the lower connection. Indeed,
coupled members of the lower chord (2-Ls 120 mm × 120 mm × 13 mm) are connected with
a single row of M18 bolts to a 20 mm saddle plate, which is welded to the column flange.
Slightly different solutions were adopted in the Y-direction due to the presence of the
column web. Namely, the upper 20 mm gusset plate is directly welded to the web, which
is locally stiffened by means of two 20 mm continuity plates (CPs).
Notably, the same kind and number of bolts used in the X-direction are adopted to
connect the diagonal (2-Ls 130 mm × 130 mm × 16 mm) to the gusset plate, in spite of the
XY Z
36.0 m
6.0 m
55.5 m
27.7 m
1
2.7 m
X-direction Truss Moment Resisting Frames
Y-direction Truss Moment Resisting Frames
Connecting Trusses
27.7 m
6.0 m
6.0 m
6.0 m
6.0 m
6.0 m
Figure 2.
Geometrical features of the selected case-study and disposition of resisting systems in
both directions.
According to the original design report, S235 grade steel was used for all members
and plates, whereas 6.8 strength class bolts were adopted for the connections.
In light of the retrieved information, the highest level of knowledge (“KL3”—exhaustive
knowledge) was attained for the selected case-study according to Italian provisions for
existing buildings [
23
,
24
]. Hence, characteristic values of material properties were used for
seismic analyses accounting for no reduction (i.e., a partial safety factor FC = 1 is assumed
in [23,24] for KL3).
1.2. Description of Investigated Connections
The main geometrical features of moment-resisting connections between truss mem-
bers and columns are depicted in Figure 3. Owing to the constant orientation of all hollow
columns, two different joint configurations were adopted in the X- and Y-direction.
A T-shaped 20 mm gusset plate is used to connect both the upper chord and the
diagonal to the column (see Figure 3a) in the X-direction. Seven staggered M24 bolts are
used for the upper coupled angles (2-Ls 150 mm
×
150 mm
×
14 mm), whereas four in-line
M24 bolts are adopted for the coupled diagonals (2-Ls 90 mm
×
90 mm
×
9 mm). The
gusset plate terminates with an end-plate, which is, in turn, bolted to the column flange
(350 mm
×
20 mm, welded to two 460 mm
×
8 mm webs) by means of seven rows of M24
bolts. Moreover, the connection is further stiffened by means of two trapezoidal 20 mm
ribs, placed at the base of the gusset plate.
Contrariwise, a simpler configuration is adopted for the lower connection. Indeed,
coupled members of the lower chord (2-Ls 120 mm
×
120 mm
×
13 mm) are connected with
a single row of M18 bolts to a 20 mm saddle plate, which is welded to the column flange.
Slightly different solutions were adopted in the Y-direction due to the presence of the
column web. Namely, the upper 20 mm gusset plate is directly welded to the web, which is
locally stiffened by means of two 20 mm continuity plates (CPs).

Materials 2022,15, 3276 5 of 23
Materials 2022, 15, x FOR PEER REVIEW 5 of 24
different profiles employed, whereas only six M24 staggered bolts are used in this case to
connect the upper chord (2-Ls 200 mm × 200 mm × 20 mm). Finally, the lower connection
is almost identical to the X-direction one, aside from the 20 mm saddle plate being welded
to both column web and flanges. Moreover, in this case, a single row of M18 bolts is used
to connect coupled profiles of the lower chord to the saddle (2-Ls 180 mm × 180 mm × 18
mm).
(a)
(b)
Figure 3. Details of truss-to-column connections adopted for MRFs: (a) X-direction and (b) Y-
direction.
Y
XZ
Coupled Upper Chord
(2 Ls 150×150×14 mm)
Coupled Diagonal
(2 Ls 90×90×9 mm)
Coupled Lower Chord
(2 Ls 120×120×13 mm)
Welded Hollow Column
(2 350×20 mm + 2 460×8 mm)
4 M24 6.8 Bolts
Saddle Plate
t = 20 mm
2 M18 6.8 Bolts
7 M24 6.8 Bolts
7×2 M18 6.8 Bolts
XY Z
Coupled Diagonal
(2 Ls 130×130×16 mm)
Coupled Upper Chord
(2 Ls 200×200×20 mm)
Coupled Lower Chord
(2 Ls 180×180×18 mm)
Welded Hollow Column
(2 350×20 mm + 2 460×8 mm)
Saddle Plate
t = 20 mm
2 M18 6.8 Bolts
Gusset Plate
t = 20 mm
C
ontinuit
y
Plates
t = 20 mm
4 M24 6.8 Bolts
6 M24 6.8 Bolts
Figure 3.
Details of truss-to-column connections adopted for MRFs: (
a
) X-direction and
(b) Y-direction.

Materials 2022,15, 3276 6 of 23
Notably, the same kind and number of bolts used in the X-direction are adopted to
connect the diagonal (2-Ls 130 mm
×
130 mm
×
16 mm) to the gusset plate, in spite of the
different profiles employed, whereas only six M24 staggered bolts are used in this case to
connect the upper chord (2-Ls 200 mm
×
200 mm
×
20 mm). Finally, the lower connection
is almost identical to the X-direction one, aside from the 20 mm saddle plate being welded
to both column web and flanges. Moreover, in this case, a single row of M18 bolts is used to
connect coupled profiles of the lower chord to the saddle (2-Ls 180 mm
×
180 mm
×
18 mm).
2. Design Philosophy of Retrofit Interventions
The selected case-study shows poor seismic behaviour due to excessive lateral de-
formability and inadequacy of adopted structural details. Indeed, the preliminary analyses
performed on a simplified model resulted in a very large first vibration period (T
1
= 2.08 s,
flexural mode in the Y-direction) and torsional deformability. Moreover, the moment-
resisting (MR) joints in both X- and Y-directions showed local shortages in terms of elastic
stiffness, resistance, and ductility, as will be shown in the next Sections.
The existing structural lateral deformability was checked in case of both seismic and
wind actions at service limit sates (SLS) in accordance with the limitations provided by
EN1998:1 [
25
] and EN1993:1-1 [
26
], respectively. Namely, for the seismic Damage Limitation
(DL, return period of 50 years) limit state, a maximum lateral displacement capacity equal
to 1/200 (0.5%) of the building height was assumed in compliance with EN1998:1 [
25
].
Contrariwise, wind loads, which were defined considering a rare load combination, were
checked in terms of maximum lateral displacements at the top of the columns. For this
purpose, a maximum displacement capacity equal to 1/300 of the column’s height was
considered in compliance with EN1993:1-1 [26] prescriptions.
Both local and global retrofit interventions had to be designed for the investigated
case-study; among the different possibilities [
27
–
30
], non-invasive retrofit interventions
were conceived and designed in order to achieve a satisfactory seismic performance of the
building without interrupting the productive activities.
Therefore, as will be presented in the next Section, concentric braced frames (CBFs)
were introduced on the external perimeter of the existing building; moreover, the local
performance of the MR joints was investigated by means of FEAs, and retrofit interventions
were properly designed.
2.1. Design of Global Retrofitting Interventions
The design of global strengthening for the selected case-study was performed aiming
at a full retrofit against seismic actions and wind loads.
Thus, the interventions were designed based on combined results from global and
local FEAs. A first global assessment of the existing structure behaviour was conducted by
means of static non-linear analyses; hence, pushover curves were simplified according to
the N2 method [
31
], which allows deriving bi-linear equivalent force-displacement curves.
Thus, the smooth pushover curves were converted into equivalent curves by equating
the ultimate displacements (i.e., displacements corresponding to 80% of the maximum
base shear measured on the degrading branch of the curves) and the areas underneath
the force-displacement curves. According to EN1998:3—Annex B [
31
] prescriptions, the
bi-linear pushover curves were interrupted when the maximum allowable plastic rotation
was reached in the most stressed plastic hinge.
The structural capacity was compared with the seismic demand at significant damage
(SD) limit state (LS), transposing the bi-linear curves into an Accelerations–Displacements
Response Spectrum (ADRS) domain. Therefore, the seismic demand on the structure, i.e.,
the so-called “performance point” (PP), was conventionally derived (see Figure 4, red
hollow circle).

Materials 2022,15, 3276 7 of 23
Materials 2022, 15, x FOR PEER REVIEW 7 of 24
Figure 4. Graphical interpretation in ADRS domain for the design procedure of global retrofitting
interventions.
This procedure allows to assess the structural ductile capacity, disregarding brittle
failure mechanisms (e.g., brittle bolts’ shear failure) that should be subsequently assessed.
The second step involved the assessment of the local behaviour of the MR joints; in
particular, as introduced in Section 3, a shortage was observed in the bottom part of the
external MR joints. The real joints’ behaviour was investigated by means of both an
analytical method and a refined finite element model; finally, its behaviour was accounted
for in a new set of global analyses by introducing non-linear links in correspondence of
the MR joints.
The global retrofit intervention was ensured increasing the existing structure lateral
stiffness and resistance; thus, the required stiffness increment was derived assuming the
occurrence of ductile failure of the structure at the intersection with elastic response
spectrum (ERS) as follows:
∆𝐾 =𝑀 ∙𝑆
,𝑆,
𝑆, −𝐾
 (1)
where ΔKCBFs is the minimum lateral stiffness increment to be provided by new CBFs; MTOT
is the total seismic mass of the structure; Sa,ERS(δCd,SD) is the spectral pseudo-acceleration
derived from the ERS for a spectral displacement equal to the δCd,SD, i.e., the spectral
displacement corresponding to ductile failure of the existing structure; and Kex is the
lateral stiffness of the existing structure.
Fulfilment of Equation (1) ensures that PP is compatible with the seismic response of
the retrofitted structure provided that brittle failures are prevented. This additional
requirement was achieved by means of local retrofit interventions, which will be
discussed in detail in the following subsection.
The retrofit intervention was designed not only to satisfy seismic requirements, but
also to verify the structural deformability against wind loads. Therefore, the minimum
increase of lateral stiffness also accounted for lateral deformation limits introduced by
EN1993:1-1 [26]. Namely, according to [26], maximum lateral displacements due to the
wind loads should be smaller than 1/300 of the element’s length.
In order to account for both seismic and wind lateral stiffness requirements, Equation
(1) becomes:
∆𝐾 =𝑀𝑎𝑥
(∆𝐾;∆𝐾
)
∆𝐾 =𝑀𝑎𝑥(
𝑀 ∙𝑆
,𝑆,
𝑆, −𝐾
; 300 𝐹,
𝐻−𝐾
) (2)
With Fw,Ed being the design wind action acting in a given direction, and Hc being the
height of welded hollow columns.
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Spectral Pseudo-Accelerations Sa[m/s2]
Spectral Displacement Sd[m]
Existing Structure
Retrofitted Structure
Elastic Response Spectrum
Brittle Failure
Ductile Failure
Performance Point
Brittle Failure Prevention
(Local Interventions)
δD,SD
δCd,SD
δCb,SD
Stiffness & Resistance Increment
(Global Interventions)
Figure 4.
Graphical interpretation in ADRS domain for the design procedure of global
retrofitting interventions.
This procedure allows to assess the structural ductile capacity, disregarding brittle fail-
ure mechanisms (e.g., brittle bolts’ shear failure) that should be subsequently assessed. The
second step involved the assessment of the local behaviour of the MR joints; in particular,
as introduced in Section 3, a shortage was observed in the bottom part of the external MR
joints. The real joints’ behaviour was investigated by means of both an analytical method
and a refined finite element model; finally, its behaviour was accounted for in a new set of
global analyses by introducing non-linear links in correspondence of the MR joints.
The global retrofit intervention was ensured increasing the existing structure lateral
stiffness and resistance; thus, the required stiffness increment was derived assuming
the occurrence of ductile failure of the structure at the intersection with elastic response
spectrum (ERS) as follows:
∆KCBFs =MTOT ·Sa,E RS (Sd,DF )
Sd,DF
−Kex (1)
where
∆
K
CBFs
is the minimum lateral stiffness increment to be provided by new CBFs; M
TOT
is the total seismic mass of the structure; S
a,ERS
(
δCd,SD
) is the spectral pseudo-acceleration
derived from the ERS for a spectral displacement equal to the
δCd,SD
, i.e., the spectral
displacement corresponding to ductile failure of the existing structure; and K
ex
is the lateral
stiffness of the existing structure.
Fulfilment of Equation (1) ensures that PP is compatible with the seismic response
of the retrofitted structure provided that brittle failures are prevented. This additional
requirement was achieved by means of local retrofit interventions, which will be discussed
in detail in the following subsection.
The retrofit intervention was designed not only to satisfy seismic requirements, but
also to verify the structural deformability against wind loads. Therefore, the minimum
increase of lateral stiffness also accounted for lateral deformation limits introduced by
EN1993:1-1 [
26
]. Namely, according to [
26
], maximum lateral displacements due to the
wind loads should be smaller than 1/300 of the element’s length.
In order to account for both seismic and wind lateral stiffness requirements,
Equation (1) becomes:
∆KCBF =Max (∆KCBF−s;∆KCB F−w)
∆KCBF =Max(MTOT ·Sa,E RS (Sd,DF )
Sd,DF −Kex ;300 Fw,Ed
Hc−Kex )(2)
With F
w,Ed
being the design wind action acting in a given direction, and H
c
being the
height of welded hollow columns.

Materials 2022,15, 3276 8 of 23
It should be remarked that design criteria provided by Equations (1) and (2) hold true
under the assumption of an in-plane rigid storey, which was granted by the presence of
roof braces.
Finally, after determining minimum cross sections of braces accordingly, resistance
and stability checks were performed on new CBFs for gravity, seismic, and wind load
combinations as follows:
N−
Ed,g,i≤Nb,Rd,i(3)
N−
Ed,E,i≤Nb,Rd,i∪N+
Ed,E,i≤Npl,Rd,i(4)
N−
Ed,w,i≤Nb,Rd,i∪N+
Ed,w,i≤Npl,Rd,i(5)
where N
Ed,g,i
,N
Ed,E,i
,N
Ed,w,i
are the design axial forces in new CBF members due to gravity,
seismic, and wind actions, respectively, whereas N
b,Rd,i
,N
pl,Rd,i
are the design buckling and
plastic resistances of the same members, respectively. For the sake of clarity, in Equations
(3)–(5), the superscript “
−
” is related to compressive axial forces, whereas the superscript
“+” is adopted for tensile axial forces.
Four X-shaped CBFs were placed along the Y-direction, according to design criteria
reported in Equations (2)–(5), and CHS profiles (193.7 mm
×
10 mm) were adopted. On
the other hand, to minimise the footprint of new resisting systems, and to guarantee the
passage of industrial machines as forklifts, two portal CBFs placed beside the facades were
conceived in the X-direction. For this purpose, CHS profiles (244.5 mm
×
20 mm and
244.5 mm
×
16 mm) were properly selected according to the design criterion provided
by Equation (1), and, hence, checked in terms of stability and resistance according to
Equations (3)–(5) (see Figure 5).
Materials 2022, 15, x FOR PEER REVIEW 8 of 24
It should be remarked that design criteria provided by Equations (1) and (2) hold true
under the assumption of an in-plane rigid storey, which was granted by the presence of
roof braces.
Finally, after determining minimum cross sections of braces accordingly, resistance
and stability checks were performed on new CBFs for gravity, seismic, and wind load
combinations as follows:
𝑁,,
≤𝑁
,, (3)
𝑁,,
≤𝑁
,, ∪ 𝑁
,,
≤𝑁
,, (4)
𝑁,,
≤𝑁
,, ∪ 𝑁
,,
≤𝑁
,, (5)
where NEd,g,i, NEd,E,i, NEd,w,i are the design axial forces in new CBF members due to gravity,
seismic, and wind actions, respectively, whereas Nb,Rd,i, Npl,Rd,i are the design buckling and
plastic resistances of the same members, respectively. For the sake of clarity, in Equations
(3–5), the superscript “−” is related to compressive axial forces, whereas the superscript
“+” is adopted for tensile axial forces.
Four X-shaped CBFs were placed along the Y-direction, according to design criteria
reported in Equations (2)–(5), and CHS profiles (193.7 mm × 10 mm) were adopted. On
the other hand, to minimise the footprint of new resisting systems, and to guarantee the
passage of industrial machines as forklifts, two portal CBFs placed beside the facades were
conceived in the X-direction. For this purpose, CHS profiles (244.5 mm × 20 mm and 244.5
mm × 16 mm) were properly selected according to the design criterion provided by
Equation (1), and, hence, checked in terms of stability and resistance according to
Equations (3–5) (see Figure 5).
Figure 5. Description of adopted global retrofitting interventions.
It should be noted that the CBFs in both directions were designed in compliance with
the last draft of the prEN1998-1-2 [32], currently under revision. According to [32], in the
design of X-CBF, both tension and compression members of bracing systems should be
considered in structural analysis, at the price of checking the possible occurrence of global
instability phenomena under design compressive forces. This approach allowed a more
appropriate evaluation of the actual lateral stiffness of the retrofitted building with respect
to the only-tension members’ approach. However, the introduction of CBFs on the
36.0 m
6.0 m
6.0 m
6.0 m
6.0 m
6.0 m
6.0 m
XY Z
55.5 m
27.7 m
12.7 m
Portal-shaped new CBFs
X-shaped new CBFs
Existing Structure
27.7 m
CHS
244.5×20 mm
CHS
244.5×16 mm
CHS
193.7×10 mm
CHS
244.5×20 mm
Figure 5. Description of adopted global retrofitting interventions.
It should be noted that the CBFs in both directions were designed in compliance with
the last draft of the prEN1998-1-2 [
32
], currently under revision. According to [
32
], in the
design of X-CBF, both tension and compression members of bracing systems should be
considered in structural analysis, at the price of checking the possible occurrence of global
instability phenomena under design compressive forces. This approach allowed a more
appropriate evaluation of the actual lateral stiffness of the retrofitted building with respect
to the only-tension members’ approach. However, the introduction of CBFs on the external
perimeter of the existing structure implies an increase of the actions transferred to the

Materials 2022,15, 3276 9 of 23
foundation system; moreover, it should be noted that this type of intervention enables to
increase both the lateral stiffness and the resistance of the existing structure, but it does not
allow to increase its ultimate displacement capacity.
2.2. Design of Local Retrofitting Solutions
The design of local retrofitting solutions was performed in order to prevent local
and premature brittle failures. For this purpose, multiple local collapse mechanisms were
considered for MR truss connections in both directions (see Figure 6a), namely:
Materials 2022, 15, x FOR PEER REVIEW 9 of 24
external perimeter of the existing structure implies an increase of the actions transferred
to the foundation system; moreover, it should be noted that this type of intervention
enables to increase both the lateral stiffness and the resistance of the existing structure,
but it does not allow to increase its ultimate displacement capacity.
2.2. Design of Local Retrofitting Solutions
The design of local retrofitting solutions was performed in order to prevent local and
premature brittle failures. For this purpose, multiple local collapse mechanisms were
considered for MR truss connections in both directions (see Figure 6a), namely:
• Bolted connections shear resistance Fcon,Rd,i (due to bolt shearing, plate bearing, or net-
area failure depending on the i-th connection configuration);
• Truss members axial resistance Ntruss,Rd,i (due to yielding in tension or buckling in
compression depending on the considered i-th truss member);
• Column web panel (CWP) resistance Vcwp,Rd,i (due to web shearing or column
hinging);
• Upper connection resistance for other local mechanisms Fup,Rd,i (due to T-stub opening
in X-direction or web punching in Y-direction).
(a)
(b) (c)
Figure 6. Considered failure mechanisms in MR truss connections for the design of local retrofitting
interventions and assumed schemes for the estimation of resistance (a): column hinging (b) and web
punching (c).
The design resistance of bolted connections was evaluated according to prescriptions
from EN1993:1-8 [33], whereas usual formulations provided by EN1993:1-1 [26] were used
to calculate the axial resistance of truss members and shear resistance of the column.
Connection Shear Resistance
Lower Chord Resistance
Column Web Panel Resistance
T-Stub Mechanism
Connection Shear Resistance
Diagonal Resistance
Web Punching Resistance
Connection Shear Resistance
Upper Chord Resistance
H
c
d
F
Ed,E
M
pl,Rd,i
M
pl,Rd,i
V
cwp,Rd,i
V
cwp,Rd,i
h
gp
b
w
t
w
Cylindric Plastic Hinge
Figure 6.
Considered failure mechanisms in MR truss connections for the design of local retrofitting
interventions and assumed schemes for the estimation of resistance (
a
): column hinging (
b
) and
web punching (c).
•
Bolted connections shear resistance F
con,Rd,i
(due to bolt shearing, plate bearing, or
net-area failure depending on the i-th connection configuration);
•
Truss members axial resistance N
truss,Rd,i
(due to yielding in tension or buckling in
compression depending on the considered i-th truss member);
•
Column web panel (CWP) resistance V
cwp,Rd,i
(due to web shearing or column hinging);
•
Upper connection resistance for other local mechanisms F
up,Rd,i
(due to T-stub opening
in X-direction or web punching in Y-direction).
The design resistance of bolted connections was evaluated according to prescriptions
from EN1993:1-8 [
33
], whereas usual formulations provided by EN1993:1-1 [
26
] were used
to calculate the axial resistance of truss members and shear resistance of the column.
With regards to the column hinging mechanism, the equivalent resistance of the
column was assumed equal to the shear force transmitted by the hollow profile in corre-

Materials 2022,15, 3276 10 of 23
spondence of the formation of two plastic hinges, i.e., at the column base and alongside the
lower chord connection (see Figure 6b):
Vcw p,Rd,i=2Mpl ,Rd,i
(Hc−d)(column hinging)(6)
where M
pl,Rd,i
is the plastic bending resistance of the column with respect to the i-th
inflection axis, and dis the distance between centroids of the upper and the lower chord.
The T-stub opening mechanism in the X-direction was modelled according to provi-
sions from [
26
], accounting for all possible failure modes (i.e., mode 1—pure plate yielding,
mode 2—plate yielding + bolts tension failure, mode 3—pure bolts tension failure).
With regards to web punching in the Y-direction, the resistance was estimated regard-
ing the column web segment within the two CPs as a doubly-restrained plate subjected to
a line load simulating the gusset plate contact force (see Figure 6c):
Fup,Rd,i=2t2
whgp fy
bw
(column web punching)(7)
with t
w
and b
w
being the column web thickness and width, respectively, and h
gp
being the
gusset plate height.
The design of local retrofitting interventions was, hence, performed in order to achieve
the hierarchy between ductile and brittle mechanisms for each considered connection.
Namely, undesirable failure modes, such as bolts shearing, bolts tension failure, trusses net-
area failure, or T-stub mode 3 collapse, were prevented by introducing new strengthening
elements and/or improving existing connections with the aid of new high-strength bolts.
From analytical calculations, lower chord connections in both the X- and Y-direction
resulted in the weakest component for existing MR truss joints, with a shear capacity equal
to 183 kN. The corresponding maximum base shear V
b,R
, which can be approximately
estimated using the a simplified structural scheme (i.e., similar to the one in Figure 6b),
resulted equal to 74 kN.
Hence, local retrofit solutions were designed in order to obtain a stronger connection
with a shear resistance larger than the axial capacity of the connected truss elements.
Therefore, the retrofit solution involving the introduction of four 150 mm
×
10 mm rib
stiffeners was conceived for both directions, in order to: (i) increase connection stiffness,
and (ii) increase the number of shear plans (from one to two). High-strength 10.9 pre-loaded
M20 bolts were used in place of existing bolts. Moreover, new
Φ
21 holes were drilled in
lower chord profiles to place two additional bolt rows in both directions (see Figure 7).
The shear resistance of new connection results equal to 2 times the buckling resistance
of the trusses element in the X-direction (2262 kN and 888 kN, respectively), whereas it
results slightly higher than the buckling resistance of the trusses element in the Y-direction
(2262 kN and 2222 kN, respectively).
Materials 2022, 15, x FOR PEER REVIEW 10 of 24
With regards to the column hinging mechanism, the equivalent resistance of the
column was assumed equal to the shear force transmitted by the hollow profile in
correspondence of the formation of two plastic hinges, i.e., at the column base and
alongside the lower chord connection (see Figure 6b):
𝑉,, =2𝑀,,
(𝐻−𝑑) (𝑐𝑜𝑙𝑢𝑚𝑛 ℎ𝑖𝑛𝑔𝑖𝑛𝑔) (7)
where Mpl,Rd,i is the plastic bending resistance of the column with respect to the i-th
inflection axis, and d is the distance between centroids of the upper and the lower chord.
The T-stub opening mechanism in the X-direction was modelled according to
provisions from [26], accounting for all possible failure modes (i.e., mode 1—pure plate
yielding, mode 2—plate yielding + bolts tension failure, mode 3—pure bolts tension
failure).
With regards to web punching in the Y-direction, the resistance was estimated
regarding the column web segment within the two CPs as a doubly-restrained plate
subjected to a line load simulating the gusset plate contact force (see Figure 6c):
𝐹,, =2𝑡
ℎ
𝑓

𝑏 (𝑐𝑜𝑙𝑢𝑚𝑛 𝑤𝑒𝑏 𝑝𝑢𝑛𝑐ℎ𝑖𝑛𝑔) (8)
with tw and bw being the column web thickness and width, respectively, and hgp being the
gusset plate height.
The design of local retrofitting interventions was, hence, performed in order to
achieve the hierarchy between ductile and brittle mechanisms for each considered
connection. Namely, undesirable failure modes, such as bolts shearing, bolts tension
failure, trusses net-area failure, or T-stub mode 3 collapse, were prevented by introducing
new strengthening elements and/or improving existing connections with the aid of new
high-strength bolts.
From analytical calculations, lower chord connections in both the X- and Y-direction
resulted in the weakest component for existing MR truss joints, with a shear capacity equal
to 183 kN. The corresponding maximum base shear Vb,R, which can be approximately
estimated using the a simplified structural scheme (i.e., similar to the one in Figure 6b),
resulted equal to 74 kN.
Hence, local retrofit solutions were designed in order to obtain a stronger connection
with a shear resistance larger than the axial capacity of the connected truss elements.
Therefore, the retrofit solution involving the introduction of four 150 mm × 10 mm rib
stiffeners was conceived for both directions, in order to: (i) increase connection stiffness,
and (ii) increase the number of shear plans (from one to two). High-strength 10.9 pre-
loaded M20 bolts were used in place of existing bolts. Moreover, new Φ21 holes were
drilled in lower chord profiles to place two additional bolt rows in both directions (see
Figure 7). The shear resistance of new connection results equal to 2 times the buckling
resistance of the trusses element in the X-direction (2262 kN and 888 kN, respectively),
whereas it results slightly higher than the buckling resistance of the trusses element in the
Y-direction (2262 kN and 2222 kN, respectively).
(a) (b)
400×20 mm
Rib Stiffeners
Filler Plate
10.9 M20 Bolts
XY Z
400×20 mm
Rib Stiffeners
Filler Plate
10.9 M20 Bolts
Y
XZ
Figure 7. Local retrofit solutions on MR joints in both X- (a) and Y-directions (b).

Materials 2022,15, 3276 11 of 23
3. Main Modelling Assumptions
3.1. Global Modelling of the Structure
Two global finite element models (FEMs) of the entire structure were developed us-
ing Seismostruct 2022 [
34
] (see Figure 8). The first model was built in order to perform
the global structural assessment of the industrial building disregarding the presence of
the connections; thus, wire elements were adopted for beams and columns, modelled in
correspondence of centroidal axes of steel profiles. The presence of horizontal X-braces,
which ensure in-plane rigidity of the roof, was accounted for by means of a diaphragm con-
straint. Foundations and relative base connections were modelled by means of equivalent
restraints; namely, the extended stiffened base plates allowed to model column-foundation
connections as fixed restraints in both the X- and Y-direction. Connections among truss
elements, which can be regarded as internal hinges, were modelled by means of local
releases. In order to correctly account for the flexural continuity of both lower and upper
chords, no releases were introduced in such elements.
Materials 2022, 15, x FOR PEER REVIEW 12 of 24
(a) (b)
Figure 8. Global model main features: (a) Existing and (b) Retrofitted structure.
3.2. Local Modelling of the Truss MR Joints
Refined FEMs of truss MR joints were developed using ABAQUS 6.13 [36]. FEAs
were performed considering a sub-assemblage of the whole structure, which is obtained
by extracting the truss in correspondence of the inflection point of axial force diagrams in
the chords under horizontal actions, i.e., at the chord midspan. Structural continuity was,
hence, restored by means of proper boundary conditions (see Figure 9a).
(a)
(b)
Figure 9. Local FEMs main features: (a) Abaqus local Modelling and (b) Sesimostruct local Model-
ling (Sub-assemblies).
In order to simulate the structural response of the truss MR frame under lateral loads,
both monotonic and cyclic horizontal displacement histories were applied at the chord
ends. Namely, a peak ISD equal to 6% was reached in monotonic FEAs, whereas AISC 341
loading protocol [37] was used for cyclic analyses, with a maximum ISD equal to 4%.
In order to balance computational effort with analyses accuracy, only the upper end
of the column, the connections, and the ends of truss members were modelled by means
of solid elements, whereas wire elements were adopted for all other parts. Therefore, rigid
MPC constraints were introduced at the interface among wire and solid instances.
Experimental tests were not conducted on the investigated MR truss joints; therefore,
the numerical modelling assumptions were set consistently with the ones adopted by the
authors in previous research [38,39], and validated against experimental tests on beam-
to-column steel joints. In particular, all solid parts were discretised using C3D8R solid
Figure 8. Global model main features: (a) Existing and (b) Retrofitted structure.
Non-linear behaviour of the investigated members was accounted for by the intro-
duction of lumped plastic hinges, which were defined according to prescriptions from
ASCE-13 [
35
]. Namely, N-M
x
-M
y
plastic hinges were adopted for the columns, i.e., at the
base and in correspondence of the lower chord connection, in order to account for flexural
response of hollow columns in both directions in presence of axial forces. On the other
hand, non-symmetric axial hinges were introduced in truss elements to model both steel
yielding in tension and possible global instability phenomena in compression.
The second global model was formally identical to the previous one, with the only
exception of non-linear links, which were placed in correspondence of truss-to-column
intersections to account for the local response of bolted connections. As will be shown in
the next Section, the behaviour of links was calibrated against the results of local FEAs.
According to the original design report, the yielding strength f
y
of existing members
was set equal to 235 N/mm
2
, whereas European S355 steel grade (f
y
= 355 N/mm
2
) was
used for retrofitting interventions.
The presence of non-structural elements was accounted by means of equivalent area
loads. Namely, a uniform load g
2k,r
= 1.6 kN/m
2
was assumed for the roofing system
(i.e., composed by steel sheeting + isolating layer + ballast), whereas a unitary weight
g
2k,c
= 0.1 kN/m
2
was considered for lightweight claddings. Moreover, live loads due to
snow (q
sk
) and roof maintenance (q
rm
) were also introduced according to Italian normative
provisions in force [
23
,
24
]. In particular, q
sk
= 3.1 kN/m
2
was considered, owing to the high
altitude of the construction site (≈1000 m a.s.l.), whereas qrm was set equal to 0.5 kN/m2.
Static non-linear analyses (SNLAs) were performed on global FEMs according to
prescriptions from EN1998:3 [
31
]. Namely, a maximum inter-storey drift (ISD) equal to 6%
was imposed in both directions, assuming the roof centre of masses as the control point.

Materials 2022,15, 3276 12 of 23
3.2. Local Modelling of the Truss MR Joints
Refined FEMs of truss MR joints were developed using ABAQUS 6.13 [
36
]. FEAs
were performed considering a sub-assemblage of the whole structure, which is obtained
by extracting the truss in correspondence of the inflection point of axial force diagrams in
the chords under horizontal actions, i.e., at the chord midspan. Structural continuity was,
hence, restored by means of proper boundary conditions (see Figure 9a).
Materials 2022, 15, x FOR PEER REVIEW 12 of 24
(a) (b)
Figure 8. Global model main features: (a) Existing and (b) Retrofitted structure.
3.2. Local Modelling of the Truss MR Joints
Refined FEMs of truss MR joints were developed using ABAQUS 6.13 [36]. FEAs
were performed considering a sub-assemblage of the whole structure, which is obtained
by extracting the truss in correspondence of the inflection point of axial force diagrams in
the chords under horizontal actions, i.e., at the chord midspan. Structural continuity was,
hence, restored by means of proper boundary conditions (see Figure 9a).
(a)
(b)
Figure 9. Local FEMs main features: (a) Abaqus local Modelling and (b) Sesimostruct local
Modelling (Sub-assemblies).
In order to simulate the structural response of the truss MR frame under lateral loads,
both monotonic and cyclic horizontal displacement histories were applied at the chord
ends. Namely, a peak ISD equal to 6% was reached in monotonic FEAs, whereas AISC 341
loading protocol [37] was used for cyclic analyses, with a maximum ISD equal to 4%.
In order to balance computational effort with analyses accuracy, only the upper end
of the column, the connections, and the ends of truss members were modelled by means
of solid elements, whereas wire elements were adopted for all other parts. Therefore, rigid
MPC constraints were introduced at the interface among wire and solid instances.
Experimental tests were not conducted on the investigated MR truss joints; therefore,
the numerical modelling assumptions were set consistently with the ones adopted by the
authors in previous research [38,39], and validated against experimental tests on beam-
to-column steel joints. In particular, all solid parts were discretised using C3D8R solid
element type (i.e., 8-node linear brick, reduced integration), whereas B31 beam elements
(i.e., 2-node linear beams) were adopted for wire parts. The mesh density was defined on
the basis of results from sensitivity analyses reported in [40,41]. In particular, a mesh size
equal to 20 mm was set for beams and columns, whereas bolts and plates were discretised
by means of a 5 mm mesh, with at least two elements through the thickness.
The Von Mises criterion was used to model steel yielding, and both kinematic and
isotropic hardening were accounted for by means of material parameters provided by
[42].
In compliance with global FEMs, yielding strength of existing profiles and plates was
set equal to 235 N/mm
2
, whereas yielding f
yb
and ultimate tensile strength f
tb
of 6.8 class
bolts were assumed equal to 480 and 600 N/mm
2
, respectively. With regards to stiffening
elements, f
y
= 355 N/mm
2
was considered. Moreover, 10.9 class high-strength bolts were
adopted for the seismic retrofit (f
yb
= 900 N/mm
2
, f
tb
= 1000 N/mm
2
).
Figure 9.
Local FEMs main features: (
a
) Abaqus local Modelling and (
b
) Sesimostruct local Modelling
(Sub-assemblies).
In order to simulate the structural response of the truss MR frame under lateral loads,
both monotonic and cyclic horizontal displacement histories were applied at the chord
ends. Namely, a peak ISD equal to 6% was reached in monotonic FEAs, whereas AISC 341
loading protocol [37] was used for cyclic analyses, with a maximum ISD equal to 4%.
In order to balance computational effort with analyses accuracy, only the upper end of
the column, the connections, and the ends of truss members were modelled by means of
solid elements, whereas wire elements were adopted for all other parts. Therefore, rigid
MPC constraints were introduced at the interface among wire and solid instances.
Experimental tests were not conducted on the investigated MR truss joints; therefore,
the numerical modelling assumptions were set consistently with the ones adopted by the
authors in previous research [
38
,
39
], and validated against experimental tests on beam-
to-column steel joints. In particular, all solid parts were discretised using C3D8R solid
element type (i.e., 8-node linear brick, reduced integration), whereas B31 beam elements
(i.e., 2-node linear beams) were adopted for wire parts. The mesh density was defined on
the basis of results from sensitivity analyses reported in [
40
,
41
]. In particular, a mesh size
equal to 20 mm was set for beams and columns, whereas bolts and plates were discretised
by means of a 5 mm mesh, with at least two elements through the thickness.
The Von Mises criterion was used to model steel yielding, and both kinematic and
isotropic hardening were accounted for by means of material parameters provided by [
42
].
In compliance with global FEMs, yielding strength of existing profiles and plates was
set equal to 235 N/mm
2
, whereas yielding f
yb
and ultimate tensile strength f
tb
of 6.8 class
bolts were assumed equal to 480 and 600 N/mm
2
, respectively. With regards to stiffening
elements, f
y
= 355 N/mm
2
was considered. Moreover, 10.9 class high-strength bolts were
adopted for the seismic retrofit (fyb = 900 N/mm2,ftb = 1000 N/mm2).
Bolt clamping was simulated by means of the “Bolt Load” command. In order to
account for the long service life and the absence of a controlled pre-loading, a low clamping
stress equal to 0.35 f
tb
was considered for existing bolts. Contrariwise, a clamping stress
equal to 0.7 f
tb
was adopted for new high-strength bolts according to provisions from
EN1993:1-8 [33].

Materials 2022,15, 3276 13 of 23
“Surface-to-Surface” interactions were introduced to model contact among the ele-
ments. Namely, a “Hard contact” formulation was used for normal contact behaviour,
whereas a “Penalty” formulation was considered for tangential behaviour, with the friction
coefficient being equal to 0.3. Finally, continuity among welded parts was modelled by
means of “Tie” constraints.
As anticipated, the local FEAs results will be directly accounted for in the global
analyses of the whole industrial building by the introduction of non-linear links placed
in lower part of the MR truss joints. Figure 9b depicts the local Seismostruct [
34
] model
having the same geometrical and mechanical features of the ABAQUS model, adopted for
the calibration of the non-linear links.
A multilinear curve [
34
] was adopted for modelling the non-linear links behaviour
under both monotonic and cyclic actions.
4. Performance of the Existing Structure
4.1. Global Assessment
The existing building is located in Nusco (Italy), with a peak ground acceleration
(PGA) equal to 0.238 g; a soil topography class “T1” and the stratigraphy class “C” were
used according to geotechnical considerations drawn from the original design report.
According to both Italian and European codes [
23
–
25
], the seismic performance of the
existing building at significant damage (SD) limit state (LS) was investigated by means of
static non-linear (pushover) analyses (SNLA) (see Figure 10a).
Materials 2022, 15, x FOR PEER REVIEW 13 of 24
Bolt clamping was simulated by means of the “Bolt Load” command. In order to
account for the long service life and the absence of a controlled pre-loading, a low
clamping stress equal to 0.35 ftb was considered for existing bolts. Contrariwise, a clamping
stress equal to 0.7 ftb was adopted for new high-strength bolts according to provisions from
EN1993:1-8 [33].
“Surface-to-Surface” interactions were introduced to model contact among the
elements. Namely, a “Hard contact” formulation was used for normal contact behaviour,
whereas a “Penalty” formulation was considered for tangential behaviour, with the
friction coefficient being equal to 0.3. Finally, continuity among welded parts was
modelled by means of “Tie” constraints.
As anticipated, the local FEAs results will be directly accounted for in the global
analyses of the whole industrial building by the introduction of non-linear links placed in
lower part of the MR truss joints. Figure 9b depicts the local Seismostruct [34] model
having the same geometrical and mechanical features of the ABAQUS model, adopted for
the calibration of the non-linear links.
A multilinear curve [34] was adopted for modelling the non-linear links behaviour
under both monotonic and cyclic actions.
4. Performance of the Existing Structure
4.1. Global Assessment
The existing building is located in Nusco (Italy), with a peak ground acceleration
(PGA) equal to 0.238 g; a soil topography class “T1” and the stratigraphy class “C” were
used according to geotechnical considerations drawn from the original design report.
According to both Italian and European codes [23–25], the seismic performance of
the existing building at significant damage (SD) limit state (LS) was investigated by means
of static non-linear (pushover) analyses (SNLA) (see Figure 10a).
(a) (b)
Figure 10. Static non-linear analyses (SLNA) of the existing building in both X- and Y-directions: (a)
pushover curves and (b) ADRS domain checks.
The pushover curves were approximated with equivalent elastic-plastic bi-linear
curves, which were imported in the ADRS plan in conjunction with elastic response
spectrum (ERS), defined through site-dependent seismic hazard maps adopted by Italian
provisions [20] (see Figure 10b).
The displacement demand at the SD limit state (δD,SD) was compared against the
brittle (δCb,SD) and ductile (δCd,SD) displacement capacity according to N2 method. In
particular, for the investigated case-study, the brittle failure corresponds to the collapse
of shear connections between the trusses and the column, whereas the ductile failure is
governed by the central column that reaches its maximum rotation capacity.
The structural performances were checked also in terms of deformability against the
seismic and wind actions. The seismic action was taken into account checking the Damage
Limitation (DL) limit state for which the displacement demand (δD,DL) was defined as done
0
500
1000
1500
2000
0.00 0.20 0.40 0.60
Base Shear [kN]
Displacement [m]
SNLA - X - Direction - As-Built
N2 - X - Direction - As-Built
SNLA - Y - Direction - As-Built
N2 - Y - Direction - As-Built
Brittle Failure
Ductile Failure
Existing
Existing
Existing
Existing
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
0.00 0.10 0.20 0.30
Spectral Pseudo-Acceleration S
e
[m/s
2
]
Spectral Displacement S
d
[m]
ERS
N2 - X-Direction -
N2 - Y-Direction -
Brittle Failure
Ductile Failure
PP
Existing
Existing
Figure 10.
Static non-linear analyses (SLNA) of the existing building in both X- and Y-directions:
(a) pushover curves and (b) ADRS domain checks.
The pushover curves were approximated with equivalent elastic-plastic bi-linear
curves, which were imported in the ADRS plan in conjunction with elastic response
spectrum (ERS), defined through site-dependent seismic hazard maps adopted by Italian
provisions [20] (see Figure 10b).
The displacement demand at the SD limit state (
δD,SD
) was compared against the
brittle (
δCb,SD
) and ductile (
δCd,SD
) displacement capacity according to N2 method. In
particular, for the investigated case-study, the brittle failure corresponds to the collapse
of shear connections between the trusses and the column, whereas the ductile failure is
governed by the central column that reaches its maximum rotation capacity.
The structural performances were checked also in terms of deformability against the
seismic and wind actions. The seismic action was taken into account checking the Damage
Limitation (DL) limit state for which the displacement demand (
δD,DL
) was defined as
done for the SD limit state, whereas the displacement capacity was assumed as 0.5% of
the total height of the building (
δC,DL
). On the other hand, wind action is represented by
a simplified set of pressures according to the Italian code requirements [
20
,
21
]. Thus, the
lateral displacements at the top of the columns were monitored and compared against
horizontal displacement limits.

Materials 2022,15, 3276 14 of 23
The analysis results are summarised in Table 1, where the structural lateral displace-
ments at SD, DL, and in case of wind actions were pointed out and compared against the
corresponding displacement capacity.
Table 1. Seismic and wind checks for the existing structure in terms of displacements.
Dir. Significant Damage
(SD) Damage Limitation (DL) Wind Action
δD,SD δCb,SD δCd,SD
δCb,SD
δDd,SD
δD,DL δC,DL δC,DL
/
δD,DL δDδCδC
δD
(-) (m) (m) (m) (-) (m) (m) (-) (m) (m) (-)
X 0.14 0.12 0.03 0.21 0.043 0.063 1.45 0.05 0.04 0.87
Y 0.23 0.30 0.10 0.43 0.059 0.063 1.05 0.13 0.04 0.32
As it can be observed, the existing structure does not meet the required performance
in terms of resistance and deformability when subjected to both seismic and wind actions.
4.2. Local Assesment
Figure 11 depicts the results of local analyses performed on both MR truss joints
in terms of base shear-displacement curves, Von Mises stresses (MISES), and equivalent
plastic strains (PEEQ). It can be noticed that the local seismic performance of truss joints in
the X- and Y-direction is poor, owing to premature failure of lower chord connections in
both cases; namely, existing M18 bolts (having a strength class equal to 6.8) fail in shear for
rather low values of ISD (1–2%).
Such undesirable failure mechanisms sensibly affect the cyclic performance of connec-
tions, which exhibits a significant pinching effect in both directions (see Figure 11a,b).
As expected, the ultimate displacement capacity of local assemblies under cyclic
loadings is lower than the related capacity under monotonic lateral actions due to cyclic
degradation of bolts. Moreover, since the same number and kind of bolts are used in both
directions to connect lower chords (i.e., two M18 6.8 bolts), the peak base shear in both
directions is basically identical (≈80 kN, +7% with respect to analytical calculations).
Contrariwise, a significant difference can be noticed in terms of both elastic stiffness
and ultimate displacements, with the X-direction assembly being more rigid and having a
displacement capacity which is about half of the related capacity in the Y-direction.
This outcome clearly depends on the difference in lateral stiffness of truss frames
located in the two orthogonal directions. Indeed, the X-direction truss frame is the most
rigid resisting system, owing to the favourable orientation of the hollow column (i.e.,
inflected about its strong axis).
Therefore, considerably higher actions are transferred by the bolts for the same value
of ISD, resulting in a premature exceedance of the connection shear resistance.
Notably, the monotonic local behaviour of Y-direction MR connections is asymmetric
with respect to deflections orientation (see Figure 11b, dashed curves). Indeed, though the
Y-direction truss quickly fails for hogging deflections, the base shear transmitted in case of
sagging deflections keeps increasing even for rather high values of ISD.
This depends on a secondary mechanism in which the lower chord in compression
transfers axial forces by direct contact with the column web after bolts have exceeded
their elastic range. On the contrary, contact load-bearing does not trigger in lower chord
connection in the X-direction, due to the larger extension of the saddle plate, since bolt
fracture occurs prior to chord-to-column contact.
With respect to local mechanisms in upper connections, PEEQ distribution in the
X-direction
(i.e., on the T-stub gusset plate) under sagging deflections confirms the activa-
tion of mode 2 failure, as foreseen with analytical models provided by EN1993:1-8 [
33
] (see
Section 3.2). Indeed, PEEQ are spread among both the gusset and the bolts, resulting in a
satisfying local ductility as mode 3 collapse is prevented (see Figure 11c).

Materials 2022,15, 3276 15 of 23
Materials 2022, 15, x FOR PEER REVIEW 15 of 24
Table 1. Seismic and wind checks for the existing structure in terms of displacements.
Dir. Significant Damage
(SD) Damage Limitation (DL) Wind Action
δ
D,SD
δ
Cb,SD
δ
Cd,SD
𝛿,
𝛿
,
 δ
D,DL
δ
C,DL
δ
C,DL
/δ
D,DL
δ
D
δ
C
𝛿
𝛿
(-) (m) (m) (m) (-) (m) (m) (-) (m) (m) (-)
X 0.14 0.12 0.03 0.21 0.043 0.063 1.45 0.05 0.04 0.87
Y 0.23 0.30 0.10 0.43 0.059 0.063 1.05 0.13 0.04 0.32
As it can be observed, the existing structure does not meet the required performance
in terms of resistance and deformability when subjected to both seismic and wind actions.
4.2. Local Assesment
Figure 11 depicts the results of local analyses performed on both MR truss joints in
terms of base shear-displacement curves, Von Mises stresses (MISES), and equivalent
plastic strains (PEEQ). It can be noticed that the local seismic performance of truss joints
in the X- and Y-direction is poor, owing to premature failure of lower chord connections
in both cases; namely, existing M18 bolts (having a strength class equal to 6.8) fail in shear
for rather low values of ISD (1–2%).
(a) (b)
(c)
−150
−100
−50
0
50
100
150
−0.5 −0.3 −0.1 0.1 0.3 0.5
Force [kN]
Displacement [m]
Monotonic
Cyclic
Existing
Y-Direction
V
b,R
= 74.3 kN
V
b,R
= 74.3 kN
−150
−100
−50
0
50
100
150
−0.5 −0.3 −0.1 0.1 0.3 0.5
Force [kN]
Displacement [m]
Monotonic
Cyclic
Existing
X-Direction
Vb,R = 74.3 kN
Vb,R = 74.3 kN
Materials 2022, 15, x FOR PEER REVIEW 16 of 24
(d)
Figure 11. Local performance of existing MR truss connections in terms of base shear vs. displace-
ment curves and distributions of MISES and PEEQ. (a) Base Shear vs. Displacements (X); (b) Base
Shear—Displacements (Y); (c) Von Mises and PEEQ distribution of MR truss in X direction under
hogging actions; (d) Von Mises and PEEQ distribution of MR truss in Y direction under hogging
actions.
Such undesirable failure mechanisms sensibly affect the cyclic performance of con-
nections, which exhibits a significant pinching effect in both directions (see Figure 11a,b).
As expected, the ultimate displacement capacity of local assemblies under cyclic
loadings is lower than the related capacity under monotonic lateral actions due to cyclic
degradation of bolts. Moreover, since the same number and kind of bolts are used in both
directions to connect lower chords (i.e., two M18 6.8 bolts), the peak base shear in both
directions is basically identical (≈80 kN, +7% with respect to analytical calculations).
Contrariwise, a significant difference can be noticed in terms of both elastic stiffness
and ultimate displacements, with the X-direction assembly being more rigid and having
a displacement capacity which is about half of the related capacity in the Y-direction.
This outcome clearly depends on the difference in lateral stiffness of truss frames
located in the two orthogonal directions. Indeed, the X-direction truss frame is the most
rigid resisting system, owing to the favourable orientation of the hollow column (i.e., in-
flected about its strong axis).
Therefore, considerably higher actions are transferred by the bolts for the same value
of ISD, resulting in a premature exceedance of the connection shear resistance.
Notably, the monotonic local behaviour of Y-direction MR connections is asymmetric
with respect to deflections orientation (see Figure 11b, dashed curves). Indeed, though the
Y-direction truss quickly fails for hogging deflections, the base shear transmitted in case
of sagging deflections keeps increasing even for rather high values of ISD.
This depends on a secondary mechanism in which the lower chord in compression
transfers axial forces by direct contact with the column web after bolts have exceeded their
elastic range. On the contrary, contact load-bearing does not trigger in lower chord con-
nection in the X-direction, due to the larger extension of the saddle plate, since bolt frac-
ture occurs prior to chord-to-column contact.
With respect to local mechanisms in upper connections, PEEQ distribution in the X-
direction (i.e., on the T-stub gusset plate) under sagging deflections confirms the activa-
tion of mode 2 failure, as foreseen with analytical models provided by EN1993:1-8 [33]
(see Section 3.2). Indeed, PEEQ are spread among both the gusset and the bolts, resulting
in a satisfying local ductility as mode 3 collapse is prevented (see Figure 11c).
Therefore, the analytical approach allows to adequately predict the shear resistance
of the connections, but it is not able to account for the local mechanisms and the different
stiffness of the two joints. Therefore, in order to account these aspects within the global
Figure 11.
Local performance of existing MR truss connections in terms of base shear vs. displacement
curves and distributions of MISES and PEEQ. (
a
) Base Shear vs. Displacements (X); (
b
) Base Shear—
Displacements (Y); (
c
) Von Mises and PEEQ distribution of MR truss in X direction under hogging
actions; (d) Von Mises and PEEQ distribution of MR truss in Y direction under hogging actions.
Therefore, the analytical approach allows to adequately predict the shear resistance of the
connections, but it is not able to account for the local mechanisms and the different stiffness
of the two joints. Therefore, in order to account these aspects within the global model of the
structure, non-linear links, properly calibrated against local FEAs results, were introduced.
Results of the calibration procedure are reported in Figure 12 in terms of base shear
force vs. imposed displacements. It can be observed that non-linear links are perfectly able

Materials 2022,15, 3276 16 of 23
to reproduce the local behaviour of the MR joints in term of elastic stiffness, resistance, and
ultimate displacement capacity.
Materials 2022, 15, x FOR PEER REVIEW 17 of 24
stiffness of the two joints. Therefore, in order to account these aspects within the global
model of the structure, non-linear links, properly calibrated against local FEAs results,
were introduced.
Results of the calibration procedure are reported in Figure 12 in terms of base shear
force vs. imposed displacements. It can be observed that non-linear links are perfectly able
to reproduce the local behaviour of the MR joints in term of elastic stiffness, resistance,
and ultimate displacement capacity.
(a) (b)
Figure 12. Calibration of the non-linear links of the existing MR connections under: (a) hogging and
(b) sagging moment.
The local behaviour of MR truss joints affects the global behaviour of the entire
structure. Indeed, a lateral stiffness reduction due to lower connection shortage can be
noticed (see Table 2). This effect can be mostly appreciated in the X-direction (−6.7% with
respect to the first set of global FEAs), i.e., the one in which stiffer frames are located.
Hence, lower connection acts as an additional source of deformability in series with steel
profiles; therefore, its effect becomes relevant in case of more rigid assemblies.
Contrariwise, this effect is basically negligible in the Y-direction, i.e., for most deformable
trusses.
Table 2. Results for the existing structure in terms of elastic stiffness evaluated accounting
for/disregarding the local connection performance.
Dir. Model Elastic Stiffness Variation
- - Without Links
kN/m
With Links
kN/m -
X Global 16,121.3 15,042.0 −6.7%
Sub-assembly 1147.7 1178.1 −18.6%
Y Global 6214.7 6195.2 −0.2%
Sub-assembly 444.5 442.8 −0.5%
As expected, the introduction of the non-linear links has a large influence on the local
model behaviour, i.e., a variation of 18.6%. Contrariwise, the performance of the global
structure is less affected by the presence of the link, as depicted in Table 2, in terms of
elastic stiffness. This result mainly depends on the number of the connections where the
non-links were introduced with respect to the total amount of joints.
On the other hand, the introduction of non-linear links actually changes seismic
demand on the construction, as PP is evaluated based on the lateral elastic stiffness of the
structure. Global behaviour of the existing structure accounting for connection
performance is summarised in Figure 13 in terms of pushover curves and in the ADRS
domain. For the sake of clarity, in the following, smooth pushover curves are labelled as
“SNLA”, whereas bi-linear equivalent curves derived according to the N2 method are la-
belled as “N2”.
0
20
40
60
80
100
120
0 0.1 0.2 0.3 0.4
Base Shear [kN]
Displacement [m]
Global - As-Built - X
Local - As-Built - X
Global - As-Built - Y
Local - As-Built - Y
Existing - X
Existing - X
Existing - Y
Existing - Y
0
20
40
60
80
100
120
0 0.1 0.2 0.3 0.4
Base Shear [kN]
Displacement [m]
Global - As-Built - X
Local - As-Built - X
Global - As-Built - Y
Local - As-Built - Y
Existing - X
Existing - X
Existing - Y
Existing - Y
Figure 12.
Calibration of the non-linear links of the existing MR connections under: (
a
) hogging and
(b) sagging moment.
The local behaviour of MR truss joints affects the global behaviour of the entire
structure. Indeed, a lateral stiffness reduction due to lower connection shortage can be
noticed (see Table 2). This effect can be mostly appreciated in the X-direction (
−
6.7% with
respect to the first set of global FEAs), i.e., the one in which stiffer frames are located. Hence,
lower connection acts as an additional source of deformability in series with steel profiles;
therefore, its effect becomes relevant in case of more rigid assemblies. Contrariwise, this
effect is basically negligible in the Y-direction, i.e., for most deformable trusses.
Table 2.
Results for the existing structure in terms of elastic stiffness evaluated accounting
for/disregarding the local connection performance.
Dir. Model Elastic Stiffness Variation
- - Without Links
kN/m
With Links
kN/m -
XGlobal 16,121.3 15,042.0 −6.7%
Sub-assembly 1147.7 1178.1 −18.6%
YGlobal 6214.7 6195.2 −0.2%
Sub-assembly 444.5 442.8 −0.5%
As expected, the introduction of the non-linear links has a large influence on the local
model behaviour, i.e., a variation of 18.6%. Contrariwise, the performance of the global
structure is less affected by the presence of the link, as depicted in Table 2, in terms of
elastic stiffness. This result mainly depends on the number of the connections where the
non-links were introduced with respect to the total amount of joints.
On the other hand, the introduction of non-linear links actually changes seismic
demand on the construction, as PP is evaluated based on the lateral elastic stiffness of the
structure. Global behaviour of the existing structure accounting for connection performance
is summarised in Figure 13 in terms of pushover curves and in the ADRS domain. For the
sake of clarity, in the following, smooth pushover curves are labelled as “SNLA”, whereas
bi-linear equivalent curves derived according to the N2 method are labelled as “N2”.
The existing structure does not attain a satisfying seismic performance either in the X-
or Y-direction due to brittle failure of connections. Nevertheless, significant differences can
be noticed with respect to the structural behaviour in the two directions, namely:
In the X-direction, the seismic behaviour is inadequate, not only owing to local con-
nection failures, but also in terms of global stiffness and resistance. Indeed, if local failures
were prevented (i.e., by means of local retrofit interventions), the structure would still
exhibit an insufficient displacement capacity (see Figure 13b, black circle), i.e., lower than
the corresponding demand defined by PP (Figure 13b, red circle);

Materials 2022,15, 3276 17 of 23
Materials 2022, 15, x FOR PEER REVIEW 18 of 24
(a) (b)
(c) (d)
Figure 13. Global performance of existing structure in terms of pushover curves and ADRS domain
checks according to EN1998:3 [31] provisions: (a) Pushover curves in X-direction, (b) ADRS domain
checks in X-direction, (c) Pushover curves in Y-direction, (d) ADRS domain checks in Y-direction.
The existing structure does not attain a satisfying seismic performance either in the
X- or Y-direction due to brittle failure of connections. Nevertheless, significant differences
can be noticed with respect to the structural behaviour in the two directions, namely:
• In the X-direction, the seismic behaviour is inadequate, not only owing to local
connection failures, but also in terms of global stiffness and resistance. Indeed, if local
failures were prevented (i.e., by means of local retrofit interventions), the structure
would still exhibit an insufficient displacement capacity (see Figure 13b, black circle),
i.e., lower than the corresponding demand defined by PP (Figure 13b, red circle);
• In the Y-direction, seismic checks in the ADRS domain are not fulfilled, only due to
the brittle failure of lower chord connections. Indeed, PP is attained for a spectral
displacement lower than the corresponding ultimate displacement (see Figure 13d).
Therefore, the disposition of new CBFs for global seismic enhancement was actually
required only in the X-direction. Nevertheless, as expected, the existing structure results
as highly deformable in the Y-direction. Therefore, CBFs should still be installed in this
direction to fulfil deformability requirements for wind loads (see Equation (2)). Namely,
the maximum lateral deflection of hollow columns in the Y-direction is equal to 0.13 m
(see Table 1); hence, a stiffness increase equal to about 2 times Kext should be provided by
new bracings.
5. Performance of the Retrofitted Structure
The seismic performance of the retrofitted structure is, hence, reported both in terms
of local response of enhanced MR truss connections and global performance of the
retrofitted structure. Local behaviour of the two MR joints is depicted in Figure 14 in terms
of base shear-displacement curves and distribution of Von Mises stresses (MISES) and
equivalent plastic strains (PEEQ).
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0.00 0.10 0.20 0.30 0.40 0.50
Base Shear V
b
[kN]
Displacement [m]
SNLA - X - Direction - As-Built
N2 - X - Direction - As-Built
Brittle Failure
Ductile Failure
Existing
Existing
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Spectral Pseudo-Acceleration S
a
[m/s
2
]
Spectral Displacement S
d
[m]
ERS
N2 - X - Direction - As-Built
Brittle Failure
Ductile Failure
PP
Existing
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0.00 0.10 0.20 0.30 0.40 0.50
Base Shear Vb[kN]
Dis
p
lacement
[
m
]
SNLA - Y - Direction -As-Built
N2 - Y - Direction -As-Built
Brittle Failure
Ductile Failure
Existing
Existing
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Spectral Pseudo-Acceleration S
a
[m/s
2
]
Spectral Displacement S
d
[m]
ERS
N2 - Y - Direction - As-Built
Brittle Failure
Ductile Failure
PP
Existing
Figure 13.
Global performance of existing structure in terms of pushover curves and ADRS domain
checks according to EN1998:3 [
31
] provisions: (
a
) Pushover curves in X-direction, (
b
) ADRS domain
checks in X-direction, (c) Pushover curves in Y-direction, (d) ADRS domain checks in Y-direction.
In the Y-direction, seismic checks in the ADRS domain are not fulfilled, only due to the
brittle failure of lower chord connections. Indeed, PP is attained for a spectral displacement
lower than the corresponding ultimate displacement (see Figure 13d).
Therefore, the disposition of new CBFs for global seismic enhancement was actually
required only in the X-direction. Nevertheless, as expected, the existing structure results as
highly deformable in the Y-direction. Therefore, CBFs should still be installed in this direction
to fulfil deformability requirements for wind loads (see Equation (2)). Namely, the maximum
lateral deflection of hollow columns in the Y-direction is equal to 0.13 m (see Table 1); hence, a
stiffness increase equal to about 2 times Kext should be provided by new bracings.
5. Performance of the Retrofitted Structure
The seismic performance of the retrofitted structure is, hence, reported both in terms of
local response of enhanced MR truss connections and global performance of the retrofitted
structure. Local behaviour of the two MR joints is depicted in Figure 14 in terms of base
shear-displacement curves and distribution of Von Mises stresses (MISES) and equivalent
plastic strains (PEEQ).
The retrofit intervention allows to effectively achieve satisfying seismic behaviour,
as ductile mechanisms (i.e., column hinging) are promoted in place of brittle connection
failures. Indeed, plastic strains are concentrated in hollow profiles at both the column base
and lower chord intersection, whereas retrofitted connections always remain in their elastic
range (see Figure 14c–f). The cyclic behaviour of both directions’ MR connections is posi-
tively affected by this condition, as hysteretic loops are sensibly wide and stable, allowing
an efficient dissipation of seismic energy through the activation of plastic deformations
within the columns.

Materials 2022,15, 3276 18 of 23
Materials 2022, 15, x FOR PEER REVIEW 19 of 24
(a) (b)
(c)
(d)
(e)
−150
−100
−50
0
50
100
150
−0.5 −0.3 −0.1 0.1 0.3 0.5
Force [kN]
Displacements [m]
Monotonic
Cyclic
Retrofitted
Y-Direction
−300
−200
−100
0
100
200
300
−0.5 −0.3 −0.1 0.1 0.3 0.5
Force [kN]
Displacements [m]
Monotonic
Cyclic
Retrofitted
X-Direction
Materials 2022, 15, x FOR PEER REVIEW 20 of 24
(f)
Figure 14. Local performance of retrofit interventions in terms of base shear vs. displacement curves
and distributions of MISES and PEEQ. (a) Base Shear vs. Displacements (X); (b) Base Shear vs. Dis-
placements (Y); (c,d) Von Mises and PEEQ distribution of MR truss in X direction under hogging
and sagging actions; (e,f) Von Mises and PEEQ distribution of MR truss in Y direction under hog-
ging and sagging actions.
The retrofit intervention allows to effectively achieve satisfying seismic behaviour,
as ductile mechanisms (i.e., column hinging) are promoted in place of brittle connection
failures. Indeed, plastic strains are concentrated in hollow profiles at both the column base
and lower chord intersection, whereas retrofitted connections always remain in their elas-
tic range (see Figure 14c–f). The cyclic behaviour of both directions’ MR connections is
positively affected by this condition, as hysteretic loops are sensibly wide and stable, al-
lowing an efficient dissipation of seismic energy through the activation of plastic defor-
mations within the columns.
It can also be noticed that there are some minor differences in terms of non-linear
behaviour among monotonic and cyclic local FEAs. This outcome depends on cyclic hard-
ening of the column base material, which results in higher transmitted shear force for
smaller values of ISD with respect to monotonic conditions.
As done for the existing joints, the local performance of the MR joints was accounted
for in the global analyses by means of properly calibrated non-linear links. Figure 15 de-
picts a very good agreement in terms of elastic stiffness, maximum resistance, and ulti-
mate capacity between the FE results and the non-linear link behaviour. It should be ob-
served that, due to the strengthening interventions, the MR joints have symmetric behav-
iour; this is the reason why, in Figure 15, only the response under sagging moment in both
X and Y directions is depicted.
Figure 15. Results of the calibration procedure for retrofitted connections.
Global behaviour of the retrofitted structure is summarised in Figure 16 in terms of
pushover curves and in the ADRS domain.
0
40
80
120
160
200
240
00.20.40.6
Base Shear [kN]
Displacement [m]
Global - Retrofitted - X
Local - Retrofitted - X
Global - Retrofitted - Y
Local - Retrofitted - Y
Figure 14.
Local performance of retrofit interventions in terms of base shear vs. displacement curves
and distributions of MISES and PEEQ. (
a
) Base Shear vs. Displacements (X); (
b
) Base Shear vs.
Displacements (Y); (
c
,
d
) Von Mises and PEEQ distribution of MR truss in X direction under hogging
and sagging actions; (
e
,
f
) Von Mises and PEEQ distribution of MR truss in Y direction under hogging
and sagging actions.

Materials 2022,15, 3276 19 of 23
It can also be noticed that there are some minor differences in terms of non-linear
behaviour among monotonic and cyclic local FEAs. This outcome depends on cyclic
hardening of the column base material, which results in higher transmitted shear force for
smaller values of ISD with respect to monotonic conditions.
As done for the existing joints, the local performance of the MR joints was accounted
for in the global analyses by means of properly calibrated non-linear links. Figure 15 depicts
a very good agreement in terms of elastic stiffness, maximum resistance, and ultimate
capacity between the FE results and the non-linear link behaviour. It should be observed
that, due to the strengthening interventions, the MR joints have symmetric behaviour; this
is the reason why, in Figure 15, only the response under sagging moment in both X and Y
directions is depicted.
Materials 2022, 15, x FOR PEER REVIEW 20 of 24
(f)
Figure 14. Local performance of retrofit interventions in terms of base shear vs. displacement curves
and distributions of MISES and PEEQ. (a) Base Shear vs. Displacements (X); (b) Base Shear vs.
Displacements (Y); (c,d) Von Mises and PEEQ distribution of MR truss in X direction under hogging
and sagging actions; (e,f) Von Mises and PEEQ distribution of MR truss in Y direction under
hogging and sagging actions.
The retrofit intervention allows to effectively achieve satisfying seismic behaviour,
as ductile mechanisms (i.e., column hinging) are promoted in place of brittle connection
failures. Indeed, plastic strains are concentrated in hollow profiles at both the column base
and lower chord intersection, whereas retrofitted connections always remain in their
elastic range (see Figure 14c–f). The cyclic behaviour of both directions’ MR connections
is positively affected by this condition, as hysteretic loops are sensibly wide and stable,
allowing an efficient dissipation of seismic energy through the activation of plastic
deformations within the columns.
It can also be noticed that there are some minor differences in terms of non-linear
behaviour among monotonic and cyclic local FEAs. This outcome depends on cyclic
hardening of the column base material, which results in higher transmitted shear force for
smaller values of ISD with respect to monotonic conditions.
As done for the existing joints, the local performance of the MR joints was accounted
for in the global analyses by means of properly calibrated non-linear links. Figure 15
depicts a very good agreement in terms of elastic stiffness, maximum resistance, and
ultimate capacity between the FE results and the non-linear link behaviour. It should be
observed that, due to the strengthening interventions, the MR joints have symmetric
behaviour; this is the reason why, in Figure 15, only the response under sagging moment
in both X and Y directions is depicted.
Figure 15. Results of the calibration procedure for retrofitted connections.
Global behaviour of the retrofitted structure is summarised in Figure 16 in terms of
pushover curves and in the ADRS domain.
0
40
80
120
160
200
240
00.20.40.6
Base Shear [kN]
Displacement [m]
Global - Retrofitted - X
Local - Retrofitted - X
Global - Retrofitted - Y
Local - Retrofitted - Y
Figure 15. Results of the calibration procedure for retrofitted connections.
Global behaviour of the retrofitted structure is summarised in Figure 16 in terms of
pushover curves and in the ADRS domain.
The strengthening interventions allow to strongly increase the elastic stiffness and
resistance of the existing structure up to a complete seismic retrofit. Moreover, lateral
deformability checks for wind action are fulfilled with a significant safety margin (
δC
/
δD
is equal to 4 and 5.7 in X- and Y-direction, respectively—see Table 3). Indeed, with re-
gards to the Y-direction, minimum cross-sections deriving from stiffness requirements (see
Equation (2)
) were enlarged to avoid global buckling of braces under gravity loads (see
Equation (3)). Contrariwise, lateral deformability requirements for wind actions resulted as
fulfilled in the X-direction due to the predominance of seismic action.
The pushover curves in both X- and Y-directions were stopped in correspondence
of the ductile failure mechanism due to the diagonals in compression, which reach their
maximum inelastic deformation capacity, defined as reported in [
31
]. Contrariwise, all the
MR joints remain in their elastic range.

Materials 2022,15, 3276 20 of 23
Materials 2022, 15, x FOR PEER REVIEW 21 of 24
(a) (b)
(c) (d)
Figure 16. Global performance of existing structure in terms of pushover curves ((a) and (c) in X and
Y directions respectively) and ADRS domain checks according to EN1998:3 [31] provisions ((b) and
(d) in X and Y directions respectively).
The strengthening interventions allow to strongly increase the elastic stiffness and
resistance of the existing structure up to a complete seismic retrofit. Moreover, lateral
deformability checks for wind action are fulfilled with a significant safety margin (δC/δD is
equal to 4 and 5.7 in X- and Y-direction, respectively—see Table 3). Indeed, with regards
to the Y-direction, minimum cross-sections deriving from stiffness requirements (see
Equation (2)) were enlarged to avoid global buckling of braces under gravity loads (see
Equation (3)). Contrariwise, lateral deformability requirements for wind actions resulted
as fulfilled in the X-direction due to the predominance of seismic action.
Table 3. Seismic and wind checks for the retrofitted structure in terms of displacements.
Dir. Conf. Significant Damage
(SD) Wind Action
δD,SD δCb,SD δCd,SD δC,SD/δDd,SD δD δC δC/δD,
- - m m m - m m -
X As Built 0.15 0.05 0.12 0.33 0.06 0.04 0.66
Y 0.23 0.19 0.31 0.61 0.16 0.04 0.25
X Retrofitted 0.06 - 0.09 1.5 0.01 0.04 4
Y 0.05 - 0.11 2.2 0.007 0.04 5.7
The pushover curves in both X- and Y-directions were stopped in correspondence of
the ductile failure mechanism due to the diagonals in compression, which reach their
0
1000
2000
3000
4000
5000
6000
7000
0.00 0.10 0.20 0.30 0.40 0.50
Base Shear V
b
[kN]
Displacement [m]
SNLA - X - Direction - Retrofitted
N2 - X - Direction - Retrofitted
SNLA - X - Direction - As-Built
N2 - X - Direction - As-Built
Ductile Failure
Brittle Failure
Existing
Existing
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Spectral Pseudo-Acceleration S
a
[m/s
2
]
Spectral Displacement S
d
[m]
ERS
N2 - X - Direction - Retrofitted
N2 - X - Direction - As-Built
Brittle Failure
Ductile Failure
PP
Existing
0
1000
2000
3000
4000
5000
6000
7000
0.00 0.10 0.20 0.30 0.40 0.50
Base Shear V
b
[kN]
Displacement [m]
SNLA - Y - Direction - Retrofitted
N2 - Y - Direction - Retrofitted
SNLA - Y - Direction -As-Built
N2 - Y - Direction -As-Built
Ductile Failure
Brittle Failure
Existing
Existing
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Spectral Pseudo-Acceleration S
a
[m/s
2
]
Spectral Displacement S
d
[m]
ERS
N2 - Y - Direction - S2
N2 - Y - Direction - As-Built
Brittle Failure
Ductile Failure
PP
Existing
Retrofitted
Figure 16.
Global performance of existing structure in terms of pushover curves ((
a
,
c
) in X and Y
directions respectively) and ADRS domain checks according to EN1998:3 [
31
] provisions ((
b
,
d
) in X
and Y directions respectively).
Table 3. Seismic and wind checks for the retrofitted structure in terms of displacements.
Dir. Conf. Significant Damage
(SD) Wind Action
δD,SD δCb,SD δCd,SD δC,SD
/
δDd,SD δDδCδC/δD
- - m m m - m m -
XAs Built 0.15 0.05 0.12 0.33 0.06 0.04 0.66
Y 0.23 0.19 0.31 0.61 0.16 0.04 0.25
XRetrofitted 0.06 - 0.09 1.5 0.01 0.04 4
Y 0.05 - 0.11 2.2 0.007 0.04 5.7
6. Conclusions
In the present paper, the effectiveness of low-impact seismic retrofitting interventions
was investigated by means of global and local numerical analyses on a case-study of an
existing industrial single-storey steel building located in Italy.
Particular attention was paid to the local failure modes and their influence on the
global structural analyses; thus, refined numerical models were built to investigate the
local MR truss joints behaviour. Their performances were successively accounted for in the
global structural analyses by the introduction of non-linear links properly calibrated on the
obtained FEAs results.
The investigated structure shows both local and global shortages; from the results of
numerical analyses, the following conclusions can be pointed out:
•
The investigated existing structure is very deformable in both the principal directions;
showing excessive deflections under wind actions;

Materials 2022,15, 3276 21 of 23
•
The global structural behaviour is highly influenced by local deficiencies. Indeed,
brittle failures always anticipate more ductile mechanisms, and lateral deformability
is worsened by the lower stiffness of connections;
•
The local seismic performance of MR truss joints in both the X- and Y-direction is
poor due to premature failure of bolted connection among lower chords and hollow
columns, for rather small values of ISD (1–2%);
•
The hysteretic behaviour of joints is significantly affected by a pinching effect exhibited
in both the principal directions;
•
The introduced non-linear links are able to perfectly reproduce the local joint behaviour
in term of elastic stiffness, resistance, and ultimate displacement, allowing to account
for the real joint performance also in global FEAs;
•
The real joint stiffness, evaluated by means of refined FEAs, and accounted for in the
global analyses by the introduction of non-linear links, influences the whole structural
behaviour, and should be properly accounted for in the existing structural assessment.
The global resistance and stiffness of the structure were increased by means of new
CBFs in both directions, whereas the local performance of MR joints was enhanced by the
introduction of 400 mm ×20 mm rib stiffeners and new rows of 10.9 M18 bolts.
From the numerical analyses results, the following conclusive remarks can be drawn:
•
The design procedure adopted for the retrofitting of MR joints results in a very ductile
mechanism under both monotonic and cyclic loads; the joints behave in elastic range
up to 4% of rotation. For high rotations, the failure mode is governed by plastic
deformations within the column and some local plasticity within the trusses and
plates, whereas the bolts remain in elastic range;
•
The global seismic performance of the retrofitted structure is positively influenced by
local interventions that allow to ensure a ductile behaviour to the whole structure up
to the formation of the plastic hinges in the columns;
•
The introduction of the new CBFs in both directions allow to provide a sufficient elastic
stiffness and resistance to the whole structures against both seismic and wind actions;
•The local and global retrofit interventions were designed to not interrupt the produc-
tive activities within the building, and to minimise the impact on the working spaces.
Thus, the CBFs were designed to be placed on the external façade of the building, and
their shape does not limit either the height or the required spaces for the access of
industrial vehicles and machineries. Contrariwise, the local intervention should be
performed in the inner part of the building, but their installation involves only a small
portion of the entire structure.
Author Contributions:
Conceptualization, R.T., A.M., A.P. and R.L.; Supervision, R.L.; Writing—
original draft, R.T., A.M. and A.P.; Writing—review & editing, R.T., A.M., A.P. and R.L. All authors
have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement:
The data used in this study to support presented findings are included
within the article.
Conflicts of Interest: The authors declare no conflict of interest.
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