Influence of Column–Base Connections on Seismic Behavior of Single-Story Steel Buildings

Abstract

This study focuses on assessing the seismic performance of existing single-story steel buildings used as industrial buildings. This research aims to provide a systematic procedure for evaluating the seismic response of a single-story strategic building and properly accounting for the behavior of the column–base joints. Through meticulous data collection, advanced numerical modeling, and pushover analyses, this study highlights the significant impact of column–base joint behavior on the overall seismic performance of industrial buildings. The findings reveal that while single-story steel buildings show a satisfactory seismic performance in terms of lateral resistance and stiffness in the longitudinal direction, deficiencies in the joint design can strongly impact the performance in the transversal direction. This study emphasizes the necessity of incorporating joint flexibility into numerical analyses to accurately assess structural behavior. In conclusion, a precise assessment of the base joints provides insights for informing retrofitting strategies.

Full text

Citation: Prota, A.; Tartaglia, R.;
Landolfo, R. Influence of Column–
Base Connections on Seismic Behavior
of Single-Story Steel Buildings.
Buildings 2024,14, 3606. https://
doi.org/10.3390/buildings14113606
Academic Editor: Harry Far
Received: 21 October 2024
Revised: 8 November 2024
Accepted: 11 November 2024
Published: 13 November 2024
Copyright: © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Article
Influence of Column–Base Connections on Seismic Behavior of
Single-Story Steel Buildings
Alessandro Prota 1, Roberto Tartaglia 2,* and Raffaele Landolfo 1
1Department of Structures for Engineering and Architecture, University of Naples Federico II,
Via Forno Vecchio, 80134 Naples, Italy; alessandro.prota@unina.it (A.P.); landolfo@unina.it (R.L.)
2Department of Engineering (DING), University of Sannio, Piazza Roma, 82100 Benevento, Italy
*Correspondence: rotartaglia@unisannio.it
Abstract: This study focuses on assessing the seismic performance of existing single-story steel
buildings used as industrial buildings. This research aims to provide a systematic procedure for
evaluating the seismic response of a single-story strategic building and properly accounting for
the behavior of the column–base joints. Through meticulous data collection, advanced numerical
modeling, and pushover analyses, this study highlights the significant impact of column–base joint
behavior on the overall seismic performance of industrial buildings. The findings reveal that while
single-story steel buildings show a satisfactory seismic performance in terms of lateral resistance
and stiffness in the longitudinal direction, deficiencies in the joint design can strongly impact the
performance in the transversal direction. This study emphasizes the necessity of incorporating joint
flexibility into numerical analyses to accurately assess structural behavior. In conclusion, a precise
assessment of the base joints provides insights for informing retrofitting strategies.
Keywords: existing building; seismic assessment; steel structures; column–base joints; finite element
analysis
1. Introduction
This study examines the seismic performance of six existing single-story non-residential
steel buildings located in Italy and situated in various seismic zones. In Italy, steel struc-
tures became increasingly popular in the second half of the 20th century, primarily due
to their ability to span large distances without the need for complex technological solu-
tions [
1
]. This advantage was particularly important in an era when there was a growing
demand for open, flexible spaces in industrial and commercial buildings, as well as in
infrastructure projects. Steel provided a practical solution to these needs by enabling long
spans and large, uninterrupted spaces, which were difficult to achieve with traditional
materials. Non-residential single-story steel buildings comprise a significant portion of the
Italian building stock; while their primary application has been industrial [
2
,
3
], single-story
designs are also suitable for various other purposes. The primary issues that can lead to
severe damage in such structures following seismic events are related to the evolution
of the seismic classification and the development of regulations concerning the design
criteria over time. Most of the Italian building stock consists of buildings designed only to
withstand gravity loads [
1
]; only after the Molise earthquake in 2003 was the entire Italian
territory classified as an earthquake-prone region. Moreover, the seismic performance of
steel structures heavily depends on the details of their connections. In the past, the lack of
a differentiation between ductile and brittle mechanisms in connection designs resulted in
vulnerabilities [
4
]. Connections designed without considering capacity design principles
are more likely to fail under seismic loads; therefore, assessing these details is a critical
component of evaluating overall seismic performance.
This evaluation is particularly important for single-story steel buildings, which usu-
ally combine different lateral-force-resisting systems: braced frames in the longitudinal
Buildings 2024,14, 3606. https://doi.org/10.3390/buildings14113606 https://www.mdpi.com/journal/buildings

Buildings 2024,14, 3606 2 of 21
direction and moment-resisting frames for the main steel frames, offering flexibility in the
design and accommodating openings like doors and windows. Conventional analyses often
assume either perfectly rigid or nominally pinned connections concerning the column–base
connections of the main steel frames, simplifying the implementation and design proce-
dures. However, these assumptions may need revision since most real-world joints transmit
limited moments and undergo significant deformations under loads. Thus, incorporating
joint flexibility into numerical analyses is necessary to assess the true behavior of a frame.
The aim of this work is to compare the seismic performance of the investigated single-
story steel buildings by offering a schematic procedure for a code-compliant assessment. It
emphasizes the importance of the original design typology and the effect of the column–
base joint behavior, considering both the ideal fully rigid or pinned conditions and the
real behavior obtained from a code-conforming simulated joint design. In the first part
of the paper, six case studies located in different parts of Italy, representative of different
main steel frame configurations and designed in different time periods, are presented. The
procedure for obtaining information about the structural material properties and the main
features of the column–base connection is then described. Following this data collection
phase, refined numerical models that use component-based finite element methods are
developed to define the moment–rotation response of the column–base joints. Then, global
3D non-linear numerical models of the selected case studies are developed, incorporating
the previously mentioned column–base joint behaviors through the calibration of non-linear
links. Pushover analyses are carried out to assess the seismic performance of these models.
Finally, based on the results of the analysis, local seismic reinforcement interventions
are presented.
2. Existing Strategic Single-Story Buildings
2.1. General Description
Six existing single-story non-residential steel buildings, located in different parts of
Italy (IT), were selected as case studies (see Figure 1). The investigated buildings were
considered strategic structures because they are involved in industries with activities that
pose particular risks. These buildings are located in six different Italian provinces: Brescia
(BS), Bologna (BO), Viterbo (VT), Chieti (CH), Palermo (PA), and Reggio Calabria (RC).
Buildings 2024, 14, x FOR PEER REVIEW 2 of 22
This evaluation is particularly important for single-story steel buildings, which
usually combine different lateral-force-resisting systems: braced frames in the
longitudinal direction and moment-resisting frames for the main steel frames, offering
flexibility in the design and accommodating openings like doors and windows.
Conventional analyses often assume either perfectly rigid or nominally pinned
connections concerning the column–base connections of the main steel frames,
simplifying the implementation and design procedures. However, these assumptions may
need revision since most real-world joints transmit limited moments and undergo
significant deformations under loads. Thus, incorporating joint flexibility into numerical
analyses is necessary to assess the true behavior of a frame.
The aim of this work is to compare the seismic performance of the investigated single-
story steel buildings by offering a schematic procedure for a code-compliant assessment.
It emphasizes the importance of the original design typology and the effect of the column–
base joint behavior, considering both the ideal fully rigid or pinned conditions and the
real behavior obtained from a code-conforming simulated joint design. In the first part of
the paper, six case studies located in different parts of Italy, representative of different
main steel frame configurations and designed in different time periods, are presented. The
procedure for obtaining information about the structural material properties and the main
features of the column–base connection is then described. Following this data collection
phase, refined numerical models that use component-based finite element methods are
developed to define the moment–rotation response of the column–base joints. Then,
global 3D non-linear numerical models of the selected case studies are developed,
incorporating the previously mentioned column–base joint behaviors through the
calibration of non-linear links. Pushover analyses are carried out to assess the seismic
performance of these models. Finally, based on the results of the analysis, local seismic
reinforcement interventions are presented.
2. Existing Strategic Single-Story Buildings
2.1. General Description
Six existing single-story non-residential steel buildings, located in different parts of
Italy (IT), were selected as case studies (see Figure 1). The investigated buildings were
considered strategic structures because they are involved in industries with activities that
pose particular risks. These buildings are located in six different Italian provinces: Brescia
(BS), Bologna (BO), Viterbo (VT), Chieti (CH), Palermo (PA), and Reggio Calabria (RC).
Figure 1. Location of the selected case studies.
Figure 1. Location of the selected case studies.
A proper nomenclature was introduced in order to uniquely identify the investigated
single-story steel buildings:
•The structural material: steel (S).
•
The building’s location: through the abbreviation of the Italian provinces where the
buildings are located (i.e., if located in Bologna, (BO)).

Buildings 2024,14, 3606 3 of 21
Therefore, the building located in Bologna is hereafter indicated as S-BO.
All the investigated case studies are characterized by a regular rectangular plan, with
a plan extension ranging from 1184 m2(for S-BS) to 450 m2(for S-CH).
Typically, in the construction of single-story steel buildings, an external cladding
envelope is employed. This envelope is often upheld by secondary steel members with
relatively short spans, which, in turn, rely on the primary steel structure for support. In
particular, the investigated buildings present three different configurations with respect
to the main steel frames (see Figure 2): (a) rigid portal frames (RPFs), (b) rigid truss
frames (RTFs), and (c) pinned truss frames (PTFs). RPFs are characterized by a rigid joint
(a moment-resistant connection) between the ends of the roof beams and the columns;
meanwhile, in RTFs, the attainment of rigid frames involves the connection of both the
top and bottom chords to the supporting columns. Finally, PTFs are characterized by a
pinned connection between the ends of the roof beams and the columns, providing energy
dissipation mainly at the bases of the columns.
Buildings 2024, 14, x FOR PEER REVIEW 3 of 22
A proper nomenclature was introduced in order to uniquely identify the investigated
single-story steel buildings:
• The structural material: steel (S).
• The building’s location: through the abbreviation of the Italian provinces where the
buildings are located (i.e., if located in Bologna, (BO)).
Therefore, the building located in Bologna is hereafter indicated as S-BO.
All the investigated case studies are characterized by a regular rectangular plan, with
a plan extension ranging from 1184 m
2
(for S-BS) to 450 m
2
(for S-CH).
Typically, in the construction of single-story steel buildings, an external cladding
envelope is employed. This envelope is often upheld by secondary steel members with
relatively short spans, which, in turn, rely on the primary steel structure for support. In
particular, the investigated buildings present three different configurations with respect
to the main steel frames (see Figure 2): (a) rigid portal frames (RPFs), (b) rigid truss frames
(RTFs), and (c) pinned truss frames (PTFs). RPFs are characterized by a rigid joint (a
moment-resistant connection) between the ends of the roof beams and the columns;
meanwhile, in RTFs, the aainment of rigid frames involves the connection of both the
top and boom chords to the supporting columns. Finally, PTFs are characterized by a
pinned connection between the ends of the roof beams and the columns, providing energy
dissipation mainly at the bases of the columns.
(a) (b) (c)
Figure 2. Main steel frame configuration: (a) RPF (S-VT); (b) RTF (-BO); and (c) PTF (S-CH).
The main steel frames provide lateral stiffness and resistance in the transverse
direction (Dir. X), while in the longitudinal direction (Dir. Y), for all the investigated case
studies, concentrically braced frames (CBFs) were adopted as the lateral-force-resisting
systems (LFRS). As typical for non-residential steel single-story buildings, cross bracing
spanning both in the longitudinal and transverse directions is employed to provide the
roof diaphragm’s action. Table 1 summarizes the main geometrical features and structural
schemes of the examined existing buildings.
Table 1. Case studies: main features.
ID
Label
Dir. X Width
L
x
(m)
Dir. Y Width
L
y
(m)
Plan Extension
A (m
2
)
Headroom
H (m)
Dir. X
LFRS
Dir. Y
LFRS
N° Transverse
Frame
S-BS 37 32 1184 6.7 RTF CBF 8
S-VT 30 32 960 10 RPF CBF 6
S-BO 35 30 1050 7 RTF CBF 7
S-CH 15 30 450 7 PTF CBF 7
S-PA 22 30 660 7.4 PTF CBF 8
S-RC 35 30 1050 7.8 RTF CBF 7
2.2. Information on As-Built Existing Buildings
The investigated buildings were erected within a time range that spans from 1972 to
1992. The construction periods allow us to identify the design typology adopted for the
case studies based on the code in force at the time of construction [5–10] (see Table 2).
Thus, until the beginning of the 1970s, two different design approaches were adopted in
Italy: gravity load (GL) and obsolete seismic (OS) design. In the case of GL design, seismic
action was totally neglected; in conjunction, the CNR guidelines [11,12] were widely used
Figure 2. Main steel frame configuration: (a) RPF (S-VT); (b) RTF (-BO); and (c) PTF (S-CH).
The main steel frames provide lateral stiffness and resistance in the transverse di-
rection (Dir. X), while in the longitudinal direction (Dir. Y), for all the investigated case
studies, concentrically braced frames (CBFs) were adopted as the lateral-force-resisting
systems (LFRS). As typical for non-residential steel single-story buildings, cross bracing
spanning both in the longitudinal and transverse directions is employed to provide the
roof diaphragm’s action. Table 1summarizes the main geometrical features and structural
schemes of the examined existing buildings.
Table 1. Case studies: main features.
ID
Label
Dir. X Width
Lx(m)
Dir. Y Width
Ly(m)
Plan Extension
A (m2)
Headroom
H (m)
Dir. X
LFRS
Dir. Y
LFRS
N◦Transverse
Frame
S-BS 37 32 1184 6.7 RTF CBF 8
S-VT 30 32 960 10 RPF CBF 6
S-BO 35 30 1050 7 RTF CBF 7
S-CH 15 30 450 7 PTF CBF 7
S-PA 22 30 660 7.4 PTF CBF 8
S-RC 35 30 1050 7.8 RTF CBF 7
2.2. Information on As-Built Existing Buildings
The investigated buildings were erected within a time range that spans from 1972
to 1992. The construction periods allow us to identify the design typology adopted for
the case studies based on the code in force at the time of construction [
5
–
10
] (see Table 2).
Thus, until the beginning of the 1970s, two different design approaches were adopted
in Italy: gravity load (GL) and obsolete seismic (OS) design. In the case of GL design,
seismic action was totally neglected; in conjunction, the CNR guidelines [
11
,
12
] were
widely used by Italian steel designers. These guidelines required the action of wind to be
taken into account by applying equivalent pressures to structures based on a site’s location.
Subsequently, considering a structure’s geometry, these pressures were converted into
equivalent horizontal and vertical forces acting on the structure.

Buildings 2024,14, 3606 4 of 21
Table 2. Case studies: design approach and reference design codes.
ID
Label Design Year Design
Approach
Reference
Design Code
Reference
Seismic Code
S-BS 1980 GL [6] -
S-VT 1990 GL [8] -
S-BO 1993 GL [8] -
S-CH 1995 GL [8] -
S-PA 1975 OS [5] [9]
S-RC 1985 OS [7] [10]
Contrariwise, the OS approach was based on considering seismic action as an equiv-
alent static horizontal force proportional to the seismic weight of the structure, defined
in accordance with the old Italian regulations [
9
,
10
]. However, it should be noticed that
the OS approach was adopted just for buildings located in the sites classified as within
seismic zones at that time period. Indeed, only one-quarter of the country was classified
as a seismic-prone region before the 1980s, whereas only after the “Puglia and Molise”
earthquake was (2002) a new seismic classification, considering four different seismic zones
and including the entire national territory, applied.
As concerns structural identification, the information about the overall dimensions
and cross-sectional properties of the steel members contained in the original design reports
and drawings turned out to be incomplete or unreliable, as is common in dealing with
these types of existing structures. Therefore, the missing information was collected through
a survey of the building and a campaign of in situ measurements.
Permanent non-structural loads considered were the cladding weight (0.15 kN/m
2
)
and, at the roof level, an additional insulation board (0.05 kN/m
2
) and ballast (1.0 kN/m
2
).
Maintenance loads (0.50 kN/m
2
), snow loads (q
s,k
), and equivalent static wind loads (q
w,k
)
were considered as variable loads [13,14].
2.3. Material Properties
The material properties were obtained according to the usual constructive practice at
the time of construction (see Table 2), as suggested by the Italian code
provisions [13,14]
,
or by referring to the codes in force at that time, as indicated in EN 1998-3 [
15
]. Recently,
in 2021, Di Lorenzo et al. [
16
] proposed a methodology for identifying existing metal
carpentry structures. It requires as input data only the functional destination and the
exposure or importance of the construction [
13
], as well as the design year of the investi-
gated building. Therefore, according to [
16
], for steel buildings erected between 1961 and
1990, the steel grade Fe360, which corresponds to steel grade S235 according to UNI EN
10025 [
17
], can be assumed. However, with this procedure, the properties referred to as the
nominal/guaranteed values (e.g., the minimum values for current materials), as required
by the product standards, may differ, significantly even, from the mean values typically
used in the assessment of existing buildings.
In order to overcome this issue, it is possible to refer to the research carried out by da
Silva et al. [
18
]. In particular, the authors, based on a database comprising 837 coupon tests
derived from various sources, provide an average value for the yield strength (f
y,m
) of S235
equal to 310 MPa, with a coefficient of variation (C.o.V.) equal to 0.10. Moreover, considering
a Knowledge Level “KL2”, as result of the amount and quality of the information collected
on the existing structures [
13
–
15
], a confidence factor (CF) equal to 1.20 is selected to take
account of material variability.
Thus, a yield strength value (f
y
) equal to 260 Mpa was used in the calculation of the
steel members’ capacity.
2.4. Locations and Seismic Hazards
It is possible to classify the six sites as a function of the value of the maximum hor-
izontal acceleration on rigid ground, which has a 10% probability of being exceeded in

Buildings 2024,14, 3606 5 of 21
50 years (a
g
). The a
g
values are, 0.144 g, 0.149 g, 0.164 g, 0.165 g, 0.172 g, and 0.270 g for
Viterbo (VT), Brescia (BS), Bologna (BO), Chieti (CH), Palermo (PA), and Reggio Calabria
(RC), respectively. The seismic actions on buildings were evaluated in relation to a ref-
erence period (V
R
), which was obtained for each type of construction by multiplying its
nominal design life (V
N
) by the utilization coefficient (C
U
). Given the strategic nature of
the investigated structures, a value of 2.0 was adopted for the utilization coefficient, as
reported by the Italian code provisions [
13
]. Therefore, assuming V
N
is equal to 50 years,
a reference period of 100 years was selected for the evaluation of the seismic action. A
plain topography (topography class “T1”) and a medium soil class (stratigraphy class
“C”) were assumed according to the geotechnical classification provided by the original
design report for the six industrial buildings [
13
,
19
]. The European and Italian codes [
13
,
19
]
outline multiple limit states (LSs) to ensure structural safety against seismic forces. Among
these, the Damage Limitation (DL) LS and the Significant Damage (SD) LS are particularly
pertinent for existing structures. To determine the seismic action associated with each of
the limit states considered, it is possible to refer to the following expression:
TR=−VR/ln1−PVR(1)
where T
R
is the mean return period of the seismic action employed, and P
VR
is the ex-
ceedance probability in V
R
, selected in accordance with [
13
]. In particular, a P
VR
equal to
63% and 10% was assumed for the DL and SD limit states, respectively [
13
]. Therefore,
earthquakes with T
R
equal to 101 and 949 years were considered for the DL and SD limit
states, respectively. Figure 3depicts the elastic response spectra for the four selected sites
at TRvalues corresponding to the investigated limit states.
Buildings 2024, 14, x FOR PEER REVIEW 5 of 22
2.4. Locations and Seismic Hazards
It is possible to classify the six sites as a function of the value of the maximum hori-
zontal acceleration on rigid ground, which has a 10% probability of being exceeded in 50
years (ag). The ag values are, 0.144 g, 0.149 g, 0.164 g, 0.165 g, 0.172 g, and 0.270 g for Viterbo
(VT), Brescia (BS), Bologna (BO), Chieti (CH), Palermo (PA), and Reggio Calabria (RC),
respectively. The seismic actions on buildings were evaluated in relation to a reference
period (VR), which was obtained for each type of construction by multiplying its nominal
design life (VN) by the utilization coefficient (CU). Given the strategic nature of the inves-
tigated structures, a value of 2.0 was adopted for the utilization coefficient, as reported by
the Italian code provisions [13]. Therefore, assuming VN is equal to 50 years, a reference
period of 100 years was selected for the evaluation of the seismic action. A plain topogra-
phy (topography class “T1”) and a medium soil class (stratigraphy class “C”) were as-
sumed according to the geotechnical classification provided by the original design report
for the six industrial buildings [13,19]. The European and Italian codes [13,19] outline mul-
tiple limit states (LSs) to ensure structural safety against seismic forces. Among these, the
Damage Limitation (DL) LS and the Significant Damage (SD) LS are particularly pertinent
for existing structures. To determine the seismic action associated with each of the limit
states considered, it is possible to refer to the following expression:
T=−V
/(ln (1 − P
) (1)
where TR is the mean return period of the seismic action employed, and PVR is the exceed-
ance probability in VR, selected in accordance with [13]. In particular, a PVR equal to 63%
and 10% was assumed for the DL and SD limit states, respectively [13]. Therefore, earth-
quakes with TR equal to 101 and 949 years were considered for the DL and SD limit states,
respectively. Figure 3 depicts the elastic response spectra for the four selected sites at TR
values corresponding to the investigated limit states.
(a) (b) (c)
(d) (e) (f)
Figure 3. Elastic response spectra: (a) Brescia (BS); (b) Viterbo (VT); (c) Bologna (BO); (d) Chieti
(CH); (e) Palermo (PA); and (f) Reggio Calabria (RC).
0.0
2.0
4.0
6.0
8.0
10.0
12.0
0.01.02.03.04.0
S
a
[m/s
2
]
T [s]
SD LS (T
R
: 949y)
DL LS (T
R
: 101y)
0.0
2.0
4.0
6.0
8.0
10.0
12.0
0.0 1.0 2.0 3.0 4.0
SD LS (TR: 949y)
DL LS (TR: 101y)
Sa[m/s2]
T [s]
0.0
2.0
4.0
6.0
8.0
10.0
12.0
0.01.02.03.04.0
S
a
[m/s
2
]
T [s]
SD LS (T
R
: 949y)
DL LS (T
R
: 101y)
0.0
2.0
4.0
6.0
8.0
10.0
12.0
0.0 1.0 2.0 3.0 4.0
S
a
[m/s
2
]
T [s]
SD LS (T
R
: 949y)
DL LS (T
R
: 101y)
0.0
2.0
4.0
6.0
8.0
10.0
12.0
0.01.02.03.04.0
S
a
[m/s
2
]
T [s]
SD LS (T
R
: 949y)
DL LS (T
R
: 101y)
0.0
2.0
4.0
6.0
8.0
10.0
12.0
0.0 1.0 2.0 3.0 4.0
S
a
[m/s
2
]
T [s]
SD LS (T
R
: 949y)
DL LS (T
R
: 101y)
Figure 3. Elastic response spectra: (a) Brescia (BS); (b) Viterbo (VT); (c) Bologna (BO); (d) Chieti (CH);
(e) Palermo (PA); and (f) Reggio Calabria (RC).
2.5. Simulated Design of the Column–Base Connections
The performance of the base connections plays a central role in the definition of single-
story structures; however, in many cases, neither within the design report nor during the

Buildings 2024,14, 3606 6 of 21
visual survey is it possible to detect the details of the column–base joints. This issue is
particularly relevant in the assessment of existing steel structures, in which the connections
were designed just considering resistance checks, neglecting any capacity design and
ductility requirements. Indeed, as reported in many post-earthquake steel building damage
evaluations [
20
,
21
], several column–base connections designed following previous design
practices and guidelines did not perform satisfactorily. Indeed, a common engineering
practice is to assume column–base joints are ideally pinned or fully rigid; however, the
assumption of a full-strength rigid joint is only an approximation of the real behavior. In
reality, most joints can be classified as semi-rigid and partial-strength according to the
EN1993-1-8 [
22
] classification. This additional flexibility, if ignored, can lead to significant
errors in the evaluation of the structural response.
Within this framework, one of the primary objectives of this study is to compare the
seismic response of the investigated industrial buildings considering two different joints
configurations—(a) the “ideal” configuration, either fully rigid (I-F) or pinned (I-P), and
(b) the “real” (R) configuration—by designing the base connection based on the regulatory
requirements and technical procedures adopted at the time of construction.
Evaluations of the “real” joint behavior were made following a code-consistent simu-
lated design approach in which, following the same procedure adopted by designers at the
time, resistance checks were carried out in order to identify the main characteristics of the
joint components (i.e., steel plate thickness, number of anchor rods, and anchor rod diame-
ter). To support the simulated design, it was possible to refer to the CNR guidelines [
11
,
12
]
and to the technical manual provided by D. Danieli and F. De Miranda in 1971 [
23
], in which
construction practices related to non-residential single-story steel buildings are reported.
In particular, according to [
23
], a 2D model was considered as a calculation model for the
bending (M
j,Ed
) and shear (V
j,Ed
) at the base, in which for buildings designed according to
the OS approach, the maximum value between the effect of the equivalent static seismic
force (F
E
) and wind (F
w
) force was considered in the design. Meanwhile, for a building
designed according to the GL approach, F
w
was considered as the horizontal design load.
Moreover, a plate thickness ranging from 15 mm to 20 mm was typically considered for
the steel base plates, and for moment-resisting column–base joints, vertical stiffeners were
required according to engineering practice [23].
S-PA and S-RC were designed according to OS design (see Table 2); however, due to
the different construction periods, distinct seismic code guidelines were implemented for
the design of these two industrial buildings. Indeed, from 1935 to 1975, Italy was divided
into two seismic categories (I and II), plus a non-seismic zone in which buildings were
designed accounting for gravity loads only. Seismic loads were applied as the equivalent
lateral forces proportional to the building’s seismic mass equal to W
Tot
/g. W
Tot
includes
the permanent load plus 1/3 of the variable loads. So, the design lateral force for S-PA
could be calculated as follows:
FE=C·WTot (2)
where C was equal to 0.10 and 0.07 for seismic categories I and II, respectively. Then, F
E
was uniformly distributed across the different floors [9].
DM 03/03/1975 [
10
] introduced some basic earthquake engineering concepts into Italy
for the first time, which remained unchanged until as late as 2003: (i) an innovative system
for categorizing seismic zones; (ii) a site amplification effect; and (iii) the implementation
of modal analysis (in lieu of equivalent static analysis), along with a design spectrum, as a
methodology for earthquake-resistant building design. In particular, the horizontal force
for S-RC could be evaluated as follows:
FE=C·R·I·WTot (3)
where R was a coefficient that took into account the dynamic effects that could be fixed as
equal to 1 for the sake of safety. Instead, coefficient I ck an “importance factor” that was
set to greater than 1 for structures destined to manage emergencies after an earthquake.

Buildings 2024,14, 3606 7 of 21
Furthermore, this force was not uniformly distributed across the different floors but rather
with a reverse triangular distribution [
10
]. Then, the seismic force was divided among the
different LFRSs in the direction investigated (FE,i).
The equivalent horizontal force considered in the simulated design and the values
of the bending moment (M
j
), shear (V
j
), and axial force (N
j
) at the column–base joints are
depicted in Table 3for the six buildings investigated.
Table 3. Simulated design: column–base joint actions.
Case Study ID FwFE,i MjVjNj
- [kN] [kN] [kNm] [kN] [kN]
S-BO 24 - 44 12 146
S-CH 24 / 102 12 67
S-BS 38 / 70 19 183
S-VT 150 / 559 91 368
S-RC 55 47 120 28 164
S-PA 29 15 106 15 96
Connections were designed just considering resistance checks, making assumptions
about the base plate rigid elements and evaluating the action distributions on the bolts
and/or welds. This presumption of rigidity allowed for the stress/strain characteristics of
the anchor bolts and the concrete to be represented through an elastic model. The utilization
of an elastic stress/strain model enabled the application of a linear analysis in ascertaining
the compressive stress within the concrete beneath the plate, the tensile forces exerted on
the anchor bolts, and the internal bending moments used to determine the thickness of
the plate.
The main features of the designed column–base connections are depicted in Figure 4,
in which it can be observed that with the exception of S-PA only, European wide flange
columns were used for all the investigated structures. For S-PA, the column of the main
frame was a built-up column composed of two UPN 180 profiles spaced 500 mm apart,
connected by two steel plates with a thickness of 10 mm, which joined the flanges of the
two UPN profiles.
Buildings 2024, 14, x FOR PEER REVIEW 8 of 22
Figure 4. Main frames’ column–base connection details.
3. Numerical Modeling Assumptions
3.1. Moment–Rotation Responses of the Column–Base Joints
The component method is an analytical approach, reported within EN 1993-1-8 [22],
for assessing steel joint behavior. This method involves conceptualizing a joint as an
assembly of distinct components, each contributing to the overall response of the joint. It
should be noticed that these codified regulations are formulated assuming base plates are
used without stiffeners. Nonetheless, numerous existing structures were historically
designed using base plates featuring stiffeners because there were instances where local
practices may have encouraged designers to persist in utilizing them. Moreover, it should
be noticed that EC3 assumes constant eccentricity of the axial force, implying that an
increase in the bending moment corresponds proportionally to an increase in the axial
force. However, it therefore becomes crucial to assess the response of a connection in the
context of a non-proportional loading path, such as a constant axial force combined with
varying bending moments, as seen in assessing responses to escalating seismic loads.
The finite element method (FEM) represents a viable alternative to the component
method that is able to overcome all the limits mentioned and provide a good prediction
of a joint’s performance; however, this method may be not suitable in terms of the
modeling complexity and the computational time for field engineering. Therefore, in this
study, an alternative method defined as a component-based finite element model
(CBFEM) was adopted to define the moment–rotation response of the designed joints. The
CBFEM is an approach that combines aspects of both the component method and the finite
element method. It integrates the advantages of the component method’s simplicity into
analyzing joint behavior with the finite element method’s ability to handle complex
geometries and material behaviors.
The CBFEM breaks down a joint or connection into distinct components, similar to
the component method, but it utilizes finite element techniques to analyze these
individual components. Each component is modeled using finite elements, allowing for a
more detailed and accurate representation of their behavior under various loads and
conditions. By employing finite elements to model the components within a joint, the
CBFEM enables a comprehensive analysis of complex connections, considering factors
such as non-linear material behavior, geometric intricacies, and local variations in stiffness
Figure 4. Main frames’ column–base connection details.

Buildings 2024,14, 3606 8 of 21
3. Numerical Modeling Assumptions
3.1. Moment–Rotation Responses of the Column–Base Joints
The component method is an analytical approach, reported within EN 1993-1-8 [
22
],
for assessing steel joint behavior. This method involves conceptualizing a joint as an
assembly of distinct components, each contributing to the overall response of the joint.
It should be noticed that these codified regulations are formulated assuming base plates
are used without stiffeners. Nonetheless, numerous existing structures were historically
designed using base plates featuring stiffeners because there were instances where local
practices may have encouraged designers to persist in utilizing them. Moreover, it should
be noticed that EC3 assumes constant eccentricity of the axial force, implying that an
increase in the bending moment corresponds proportionally to an increase in the axial force.
However, it therefore becomes crucial to assess the response of a connection in the context
of a non-proportional loading path, such as a constant axial force combined with varying
bending moments, as seen in assessing responses to escalating seismic loads.
The finite element method (FEM) represents a viable alternative to the component
method that is able to overcome all the limits mentioned and provide a good prediction of
a joint’s performance; however, this method may be not suitable in terms of the modeling
complexity and the computational time for field engineering. Therefore, in this study,
an alternative method defined as a component-based finite element model (CBFEM) was
adopted to define the moment–rotation response of the designed joints. The CBFEM is
an approach that combines aspects of both the component method and the finite element
method. It integrates the advantages of the component method’s simplicity into analyzing
joint behavior with the finite element method’s ability to handle complex geometries and
material behaviors.
The CBFEM breaks down a joint or connection into distinct components, similar to the
component method, but it utilizes finite element techniques to analyze these individual
components. Each component is modeled using finite elements, allowing for a more
detailed and accurate representation of their behavior under various loads and conditions.
By employing finite elements to model the components within a joint, the CBFEM enables
a comprehensive analysis of complex connections, considering factors such as non-linear
material behavior, geometric intricacies, and local variations in stiffness and strength. In
2023, Della Corte et al. [
24
] presented findings from analyses aimed at characterizing the
behavior of steel column–base connections with stiffened plates. Their study demonstrated
that analyses conducted using the CBFEM yielded results comparable to more detailed
FE models. The designed column–base joints were modeled using IDEA StatiCa software
Version 24 [
25
] due to its specialized focus on steel connections, utilizing the CBFEM to
efficiently model complex connections with accuracy. IDEA StatiCa employs shell elements
to represent the plates and specifically designed spring elements to simulate the behavior
of the anchor bolts.
Therefore, 3D models of all of the investigated joints were built starting from the
information summarized in Figure 5, assuming the anchor length was equal to 8 times the
bolt diameter, which is the minimum length value prescribed by [
22
]. With respect to the
concrete foundation block, its length was assumed to be equal to the depth of the anchor
bolts, and the plan dimensions were set as large enough to avoid any effect of the concrete
block borders on the compression resistance below the base plate.
A bilinear elastic–perfectly plastic stress/strain curve was assumed for the steel plates
considering the yield strength as described in the previous section and a nominal maximum
total strain equal to 0.05 [22].
Figure 5depicts the moment–rotation response curves for all of the column–base
connections investigated.

Buildings 2024,14, 3606 9 of 21
Buildings 2024, 14, x FOR PEER REVIEW 9 of 22
and strength. In 2023, Della Corte et al. [24] presented findings from analyses aimed at
characterizing the behavior of steel column–base connections with stiffened plates. Their
study demonstrated that analyses conducted using the CBFEM yielded results
comparable to more detailed FE models. The designed column–base joints were modeled
using IDEA StatiCa software Version 24 [25] due to its specialized focus on steel
connections, utilizing the CBFEM to efficiently model complex connections with accuracy.
IDEA StatiCa employs shell elements to represent the plates and specifically designed
spring elements to simulate the behavior of the anchor bolts.
Therefore, 3D models of all of the investigated joints were built starting from the
information summarized in Figure 5, assuming the anchor length was equal to 8 times the
bolt diameter, which is the minimum length value prescribed by [22]. With respect to the
concrete foundation block, its length was assumed to be equal to the depth of the anchor
bolts, and the plan dimensions were set as large enough to avoid any effect of the concrete
block borders on the compression resistance below the base plate.
A bilinear elastic–perfectly plastic stress/strain curve was assumed for the steel plates
considering the yield strength as described in the previous section and a nominal
maximum total strain equal to 0.05 [22].
Figure 5 depicts the moment–rotation response curves for all of the column–base
connections investigated.
(a) (b)
(c) (d)
Buildings 2024, 14, x FOR PEER REVIEW 10 of 22
(e) (f)
Figure 5. Moment–rotation column–base joint response curves: (a) S-BO; (b) S-CH; (c) S-BS; (d) S-
VT; (e) S-RC; and (f) S-PA.
All of the joints investigated show an intermediate rotational stiffness (S
j
) between
that of a fixed (S
j,rig
) and a hinged (S
j,pin
) node and can be classified as partial rigid
connections. In the same manner, comparing the joints’ flexural capacity with respect to
the plastic capacity of the columns (M
c,Rd
), it can be observed that in none of the cases
investigated, the joints show full-strength behavior; consequently, all of the joints
investigated could be classified as semi-rigid and partial-strength connections in
accordance with EN1993-1-8.
3.2. Assumptions of Global Finite Element Models
For the six case studies, three different sets of 3D global finite element models (FEMs)
were developed in the SAP2000 environment [26] to assess the influence of the base joints
on the overall behavior in the transverse direction. The aim was to evaluate how changes
in the stiffness and strength of the base joints impacted the global structural response.
Therefore, for each model configuration, the effects of the base joints’ characteristics on
the buildings’ lateral performance were identified.
The first set of models was developed to assess the overall structural response while
disregarding the specifics of the column–base connections, considering rigid and full-
strength connections (I-R). It utilized frame elements for the beams, columns, and
diagonals, representing them along the centroidal axes of the steel profiles. Due to the
presence of in-plane bracing systems, a diaphragm constraint was applied at the roof level.
In the PTF and RTF structures, local releases were applied to modeling the truss element
connections, acting as internal hinges. To maintain flexural continuity in both the lower
and upper chords, no releases were applied to these elements. The self-weight of the
beams, columns, and diagonal elements was considered a dead load (G) within the model.
Accounting for non-structural elements involved considering equivalent area loads: a
uniform load of g
2k,r
= 1.2 kN/m
2
for the roofing system and a unitary weight of g
2k,c
= 0.15
kN/m
2
for lightweight claddings. Snow and roof maintenance live loads were included as
per the Italian regulatory provisions [13].
The non-linear behavior of the steel elements was simulated using a concentrated
plasticity model, placing the plastic hinges at the ends of the bending elements and in the
middle of the bracing elements. The parameters adopted for the definition of the plastic
hinges are in line with the guidelines set by the American Society of Civil Engineers [27].
The second set of global models mirrored the first, except for the introduction of non-
linear links placed at the column–base connections (R). These links were designed to
numerically characterize the behavior at the column–base joints. The plasticity model
used was based on hysteretic behavior proposed by Wen [28]; it characterized the
Figure 5. Moment–rotation column–base joint response curves: (a) S-BO; (b) S-CH; (c) S-BS; (d) S-VT;
(e) S-RC; and (f) S-PA.
All of the joints investigated show an intermediate rotational stiffness (S
j
) between that
of a fixed (S
j,rig
) and a hinged (S
j,pin
) node and can be classified as partial rigid connections.
In the same manner, comparing the joints’ flexural capacity with respect to the plastic
capacity of the columns (M
c,Rd
), it can be observed that in none of the cases investigated,
the joints show full-strength behavior; consequently, all of the joints investigated could be
classified as semi-rigid and partial-strength connections in accordance with EN1993-1-8.

Buildings 2024,14, 3606 10 of 21
3.2. Assumptions of Global Finite Element Models
For the six case studies, three different sets of 3D global finite element models (FEMs)
were developed in the SAP2000 environment [26] to assess the influence of the base joints
on the overall behavior in the transverse direction. The aim was to evaluate how changes
in the stiffness and strength of the base joints impacted the global structural response.
Therefore, for each model configuration, the effects of the base joints’ characteristics on the
buildings’ lateral performance were identified.
The first set of models was developed to assess the overall structural response while
disregarding the specifics of the column–base connections, considering rigid and full-
strength connections (I-R). It utilized frame elements for the beams, columns, and diagonals,
representing them along the centroidal axes of the steel profiles. Due to the presence of
in-plane bracing systems, a diaphragm constraint was applied at the roof level. In the PTF
and RTF structures, local releases were applied to modeling the truss element connections,
acting as internal hinges. To maintain flexural continuity in both the lower and upper
chords, no releases were applied to these elements. The self-weight of the beams, columns,
and diagonal elements was considered a dead load (G) within the model. Accounting for
non-structural elements involved considering equivalent area loads: a uniform load of
g
2k,r
= 1.2 kN/m
2
for the roofing system and a unitary weight of g
2k,c
= 0.15 kN/m
2
for
lightweight claddings. Snow and roof maintenance live loads were included as per the
Italian regulatory provisions [13].
The non-linear behavior of the steel elements was simulated using a concentrated
plasticity model, placing the plastic hinges at the ends of the bending elements and in the
middle of the bracing elements. The parameters adopted for the definition of the plastic
hinges are in line with the guidelines set by the American Society of Civil Engineers [27].
The second set of global models mirrored the first, except for the introduction of
non-linear links placed at the column–base connections (R). These links were designed to
numerically characterize the behavior at the column–base joints. The plasticity model used
was based on hysteretic behavior proposed by Wen [
28
]; it characterized the material’s
behavior by considering parameters that influence its stiffness, strength, and energy dissi-
pation capabilities during cyclic loading and unloading cycles. Wen’s model is valuable
for simulating the plastic deformation and energy dissipation in structural elements under
various loading conditions.
Calibration of these links was performed based on outcomes derived from local FEAs
(see Figure 6). Table 4showcases the parameters obtained from the last iteration of the
models’ calibration, where k is the elastic spring constant, yield is the yield moment, ratio
is the specified ratio of post-yield stiffness to elastic stiffness (k), and exp is an exponent
greater than or equal to unity (usually ranging from 1 to 20). Larger values of this exponent
increase the sharpness of the yielding [26].
The third set of global models, developed for the RPF and RTF buildings, was identical
to the first, with the exception that the base connection was considered to be pinned (I-P).
Since a pinned base does not provide moment resistance, the system relies on the rigid
connections at the beam-to-column joints, allowing the frame to act as a whole in resisting
lateral forces.
Table 4. Parameters obtained from the last iteration of Wen’s model calibration.
ID Yield k exp Ratio
- (kNm) (kNm/rad) - -
S-BS 47 71,000 5.0 0.24
S-VT 510 340,000 11.0 0.155
S-BO 30 57,000 2.8 0.18
S-CH 68 60,000 9.0 0.21
S-PA 78 85,750 8.0 0.18
S-RC 50 66,000 2.0 0.335

Buildings 2024,14, 3606 11 of 21
Buildings 2024, 14, x FOR PEER REVIEW 11 of 22
material’s behavior by considering parameters that influence its stiffness, strength, and
energy dissipation capabilities during cyclic loading and unloading cycles. Wen’s model
is valuable for simulating the plastic deformation and energy dissipation in structural
elements under various loading conditions.
Calibration of these links was performed based on outcomes derived from local FEAs
(see Figure 6). Table 4 showcases the parameters obtained from the last iteration of the
models’ calibration, where k is the elastic spring constant, yield is the yield moment, ratio
is the specified ratio of post-yield stiffness to elastic stiffness (k), and exp is an exponent
greater than or equal to unity (usually ranging fro m 1 to 2 0). Lar ger values of this e xponen t
increase the sharpness of the yielding [26].
The third set of global models, developed for the RPF and RTF buildings, was
identical to the first, with the exception that the base connection was considered to be
pinned (I-P). Since a pinned base does not provide moment resistance, the system relies
on the rigid connections at the beam-to-column joints, allowing the frame to act as a whole
in resisting lateral forces.
(a) (b) (c)
(d) (e) (f)
Figure 6. Non-linear link calibrations: (a) S-BO; (b) S-CH; (c) S-BS; (d) S-VT; (e) S-RC; and (f) S-PA.
Table 4. Parameters obtained from the last iteration of Wen’s model calibration.
ID Yield k exp Ratio
- (kNm) (kNm/rad) - -
S-BS 47 71,000 5.0 0.24
S-VT 510 340,000 11.0 0.155
S-BO 30 57,000 2.8 0.18
S-CH 68 60,000 9.0 0.21
S-PA 78 85,750 8.0 0.18
S-RC 50 66,000 2.0 0.335
0
20
40
60
80
100
0.00% 0.20% 0.40%
NLINK
FEA
φ[rad]
M [kNm]
0
50
100
150
200
0.00% 0.20% 0.40% 0.60%
NLINK
FEA
φ[rad]
M [kNm]
0
20
40
60
80
100
120
140
0.00% 0.20% 0.40%
φ[rad]
M [kNm]
NLINK
FEA
0
100
200
300
400
500
600
700
0.00% 0.20% 0.40% 0.60%
φ[rad]
M [kNm]
NLINK
FEA
0
20
40
60
80
100
120
140
0.00% 0.20% 0.40% 0.60%
φ[rad]
M [kNm]
NLINK
FEA
0
20
40
60
80
100
120
0.00% 0.20% 0.40%
φ[rad]
M [kNm]
NLINK
FEA
Figure 6. Non-linear link calibrations: (a) S-BO; (b) S-CH; (c) S-BS; (d) S-VT; (e) S-RC; and (f) S-PA.
4. Seismic Assessment of the Investigated Existing Buildings
4.1. Seismic Assessment Through Non-Linear Static Analysis
In compliance with both Italian and European standards [
13
–
15
], static non-linear
(pushover) analyses were performed to evaluate the seismic performance of the structures
studied, following a displacement-based approach. Various performance criteria were
assessed in both the transverse and longitudinal directions for the limit states investigated.
In the longitudinal direction, where the lateral-force-resisting systems (LFRSs) were
tension-only concentrically braced frames (CBFs), for the SD LS, the displacement demand
(d
Ed-SD
) was compared to the roof displacement corresponding to the local failure of the
diagonals in tension (d
Rd-SD
). Moreover, for the SD LS, it was required that the ratio
between the displacement at the top of the column and the column height (story drift) be
limited to less than 0.015 (dRd-SD-1.5%), as specified by [29].
In the transverse direction, d
Ed-SD
had to be less than the roof displacement (d
Rd-SD
)
corresponding to the rotational capacity of the flexural elements (
θRd,SD
), as defined in [
27
].
Additionally, the story drift was mandated to be less than 2% (d
Rd-SD-2.0%
) following the
guidelines for MRF structures [
29
]. Furthermore, an additional local performance criterion
was introduced for the second set of global models (the “R” configuration), focusing on the
potential brittle failure of the column–base connections. For the Significant Damage (SD)
limit state, the displacement demand (d
Ed-SD
) was compared with the roof displacement
at the point of local failure in a column–base connection (d
Rd-brit
). Indeed, the calibrated
non-linear link allowed us to quantify the bending moment demand in the joint (M
j,Ed
)
during the analyses up to failure (Mj,Ed > Mj,Rd).
With respect to the DL limit state, limiting the inter-story drift to less than 0.005
(corresponding roof displacement: d
Rd-DL-0.5%
) and preventing yielding in the lateral-
force-resisting members (d
Rd-DL
) were critical considerations. Local failures pertaining to
chord-to-column connections or diagonal connections were not within the scope of this
study. The influence of these local components on comprehensive seismic assessments was
already discussed by the authors in a prior publication [30].

Buildings 2024,14, 3606 12 of 21
4.2. Results of Pushover Analyses in the Longitudinal Direction
Figure 7illustrates the pushover curves derived for the six industrial buildings in-
vestigated in the longitudinal direction, accompanied by the capacity point, as defined
by the aforementioned performance criteria. It is important to note that the modeling
assumptions for the three sets of global models (i.e., I-R, R, and I-P) only concerned the
behavior of the column–base joints in the transversal LFRSs. These assumptions do not
affect the behavior in the longitudinal direction, and therefore, no significant differences
were observed between the three model sets in this direction.
Buildings 2024, 14, x FOR PEER REVIEW 12 of 22
4. Seismic Assessment of the Investigated Existing Buildings
4.1. Seismic Assessment Through Non-Linear Static Analysis
In compliance with both Italian and European standards [13–15], static non-linear
(pushover) analyses were performed to evaluate the seismic performance of the structures
studied, following a displacement-based approach. Various performance criteria were
assessed in both the transverse and longitudinal directions for the limit states investigated.
In the longitudinal direction, where the lateral-force-resisting systems (LFRSs) were
tension-only concentrically braced frames (CBFs), for the SD LS, the displacement
demand (dEd-SD) was compared to the roof displacement corresponding to the local failure
of the diagonals in tension (dRd-SD). Moreover, for the SD LS, it was required that the ratio
between the displacement at the top of the column and the column height (story drift) be
limited to less than 0.015 (dRd-SD-1.5%), as specified by [29].
In the transverse direction, dEd-SD had to be less than the roof displacement (dRd-SD)
corresponding to the rotational capacity of the flexural elements (θRd,SD), as defined in [27].
Additionally, the story drift was mandated to be less than 2% (dRd-SD-2.0%) following the
guidelines for MRF structures [29]. Furthermore, an additional local performance criterion
was introduced for the second set of global models (the “R” configuration), focusing on
the potential brile failure of the column–base connections. For the Significant Damage
(SD) limit state, the displacement demand (dEd-SD) was compared with the roof
displacement at the point of local failure in a column–base connection (dRd-brit). Indeed, the
calibrated non-linear link allowed us to quantify the bending moment demand in the joint
(Mj,Ed) during the analyses up to failure (Mj,Ed > Mj,Rd).
With respect to the DL limit state, limiting the inter-story drift to less than 0.005
(corresponding roof displacement: dRd-DL-0.5%) and preventing yielding in the lateral-force-
resisting members (dRd-DL) were critical considerations. Local failures pertaining to chord-
to-column connections or diagonal connections were not within the scope of this study.
The influence of these local components on comprehensive seismic assessments was
already discussed by the authors in a prior publication [30].
4.2. Results of Pushover Analyses in the Longitudinal Direction
Figure 7 illustrates the pushover curves derived for the six industrial buildings
investigated in the longitudinal direction, accompanied by the capacity point, as defined
by the aforementioned performance criteria. It is important to note that the modeling
assumptions for the three sets of global models (i.e., I-R, R, and I-P) only concerned the
behavior of the column–base joints in the transversal LFRSs. These assumptions do not
affect the behavior in the longitudinal direction, and therefore, no significant differences
were observed between the three model sets in this direction.
(a) (b) (c)
0
200
400
600
800
0.00 0.05 0.10
Displacement [m]
Base Shear [kN]
d
Rd-DL-0.5%
d
Rd-DL
d
Rd-SD
d
Rd-SD-1.5%
0
50
100
150
200
250
300
350
0.00 0.10 0.20
Displacement [m]
Base Shear [kN]
d
Rd-DL-0.5%
d
Rd-DL
d
Rd-SD
d
Rd-SD-1.5%
Displacement [m]
Base Shear [kN]
0
500
1000
1500
2000
2500
3000
3500
0.00 0.02 0.04 0.06
d
Rd-DL-0.5%
d
Rd-DL
d
Rd-SD
d
Rd-SD-1.5%
Buildings 2024, 14, x FOR PEER REVIEW 13 of 22
(d) (e) (f)
Figure 7. Pushover curves: (a) S-BO; (b) S-CH; (c) S-BS; (d) S-VT; (e) S-RC; and (f) S-PA.
As can be seen from Figure 7, the capacity of these structures in the DL state is
constrained by local criteria regarding excessive deformation of the diagonals. The same
consideration applies to the SD limit state, with the exception of S-CH, where the ultimate
deformation of the diagonal occurs at an inter-story drift greater than 1.5%.
The idealized elastic–perfectly plastic base shear– roof displacement response was
derived in compliance with [13,14,31] and subsequently depicted within the Acceleration–
Displacement Response Spectrum (ADRS) framework with the demand spectrum in the
DL and SD limit states. The displacement demands corresponding to the SD and DL limit
states (dEd-SD and dEd-DL, respectively) were computed according to [32] and compared with
the displacement capacity (dRd-SD, dRd-SD-1.5%, dRd-DL, and dRd-DL-0.5%) of the as-built structures.
To derive the “capacity spectrum” for a specific capacity point, it is necessary to
identify the elastic displacement capacity beginning from the corresponding inelastic
displacement. This process involves employing the equal displacement rule, adapted for
short-period systems as per the modifications outlined in [32]. The safety indexes, defined
as the ratio of the PGA of the capacity spectrum (PGAC) to the PGA of the elastic demand
spectrum (PGAD) for the limit states investigated, are summarized in Tables 5 and 6.
Table 5. Longitudinal direction safety check for the SD LS.
Case Study SD LS
ID PGAD-SD PGAC-SD Ratio PGAC-SD-1.5% Ratio
- [m/s2] [m/s2] - [m/s2] -
S-BO 2.9 4.1 1.4 5.7 2.0
S-CH 2.9 6.3 2.2 6.0 2.1
S-BS 2.6 5.4 2.1 4.0 1.6
S-VT 2.6 4.6 1.8 / /
S-RC 4.1 12.4 3.0 / /
S-PA 3.0 8.6 2.8 9.0 3.0
0
200
400
600
800
1000
0.00 0.05 0.10
d
Rd-DL-0.5%
d
Rd-DL
d
Rd-SD
d
Rd-SD-1.5%
Displacement [m]
Base Shear [kN]
0
500
1000
1500
2000
2500
0.00 0.05 0.10
Displacement [m]
Base Shear [kN]
dRd-DL-0.5%
dRd-DL
dRd-SD
dRd-SD-1.5%
0
100
200
300
400
500
600
700
0 0.1 0.2 0.3 0.4
Displacement [m]
Base Shear [kN]
d
Rd-DL-0.5%
d
Rd-DL
d
Rd-SD
d
Rd-SD-1.5%
Figure 7. Pushover curves: (a) S-BO; (b) S-CH; (c) S-BS; (d) S-VT; (e) S-RC; and (f) S-PA.
As can be seen from Figure 7, the capacity of these structures in the DL state is
constrained by local criteria regarding excessive deformation of the diagonals. The same
consideration applies to the SD limit state, with the exception of S-CH, where the ultimate
deformation of the diagonal occurs at an inter-story drift greater than 1.5%.
The idealized elastic–perfectly plastic base shear–roof displacement response was
derived in compliance with [
13
,
14
,
31
] and subsequently depicted within the Acceleration–
Displacement Response Spectrum (ADRS) framework with the demand spectrum in the
DL and SD limit states. The displacement demands corresponding to the SD and DL limit
states (d
Ed-SD
and d
Ed-DL
, respectively) were computed according to [
32
] and compared
with the displacement capacity (d
Rd-SD
, d
Rd-SD-1.5%
, d
Rd-DL
, and d
Rd-DL-0.5%
) of the as-
built structures.
To derive the “capacity spectrum” for a specific capacity point, it is necessary to
identify the elastic displacement capacity beginning from the corresponding inelastic
displacement. This process involves employing the equal displacement rule, adapted for
short-period systems as per the modifications outlined in [
32
]. The safety indexes, defined
as the ratio of the PGA of the capacity spectrum (PGA
C
) to the PGA of the elastic demand
spectrum (PGAD) for the limit states investigated, are summarized in Tables 5and 6.

Buildings 2024,14, 3606 13 of 21
Table 5. Longitudinal direction safety check for the SD LS.
Case Study SD LS
ID PGAD-SD PGAC-SD Ratio
PGA
C-SD-1.5% Ratio
-[m/s2] [m/s2]-[m/s2]-
S-BO 2.9 4.1 1.4 5.7 2.0
S-CH 2.9 6.3 2.2 6.0 2.1
S-BS 2.6 5.4 2.1 4.0 1.6
S-VT 2.6 4.6 1.8 //
S-RC 4.1 12.4 3.0 //
S-PA 3.0 8.6 2.8 9.0 3.0
Table 6. Longitudinal direction safety check for the DL LS.
Case Study DL LS
ID PGAD-DL PGAC-DL Ratio
PGA
C-DL-0.5% Ratio
-[m/s2] [m/s2]-[m/s2]-
S-BO 1.3 1.3 1.0 2.1 1.6
S-CH 1.3 1.4 1.1 2.2 1.7
S-BS 1.2 1.9 1.5 6.7 5.5
S-VT 1.2 1.9 1.6 3.1 2.6
S-RC 1.9 5.7 3.0 8.4 4.4
S-PA 1.3 3.1 2.3 3.4 2.6
Based on the findings presented in Tables 5and 6, it is evident that the safety index
assessed in the longitudinal direction exceeded 1.0 across all case studies for the limit states
analyzed. They exhibit adequate stiffness and lateral resistance to seismic action.
4.3. Results of Pushover Analyses in the Transverse Direction
The same procedure as described earlier was employed to perform safety checks in
the transverse direction. Here, the aim was to compare the response of the six industrial
buildings by varying the base constraint conditions, considering an ideal condition (I-R
and/or I-P), and a real condition (R), based on simulated designs and FEAs. In Figure 8,
the pushover curves with their respective capacity points, as previously described, are
depicted. Subsequently, in Tables 7and 8, the safety indices in terms of the ratio between
PGACand PGADare compared.
Unlike the behavior in the longitudinal direction, the curves shown in Figure 8il-
lustrate that the capacity of the analyzed structures in the transverse direction is limited
by excessive lateral deformability. Locally, the members exceed the deformation limit at
inter-story drift values higher than the established thresholds (i.e., 0.5% and 2.0% for DL
and SD, respectively). However, when non-linear column–base joint behavior is explicitly
accounted for, the seismic performance is primarily constrained by brittle failure of the
base connections, particularly with reference to the SD limit state.
The results presented in Tables 7and 8illustrate the significant influence of the base
connections. Specifically, concerning the SD verifications for the I-R configuration, there
are no notable critical issues observed in either the rotational capacity checks of the flexural
elements or those related to the maximum 2% IDR. Conversely, for the I-P configuration,
the structure appears to be considerably more deformable, failing to meet the verifications
regarding the maximum IDR for S-BO and S-RC. On the other hand, the findings for the R
configuration indicate that the resistance capacity appears to be inadequate for the base
connections of S-BO, S-BS, S-RC and S-PA, while due to the partial stiffness of the base
connections, the verifications for the maximum IDR are not met for S-CH. The removal of
the assumption of perfectly rigid base connections significantly impacts the verifications
for the DL LS. In fact, in this scenario, for all case studies except for S-VT, the verifications
are not satisfied when transitioning from the ideal I-R configuration to the real one.

Buildings 2024,14, 3606 14 of 21
Buildings 2024, 14, x FOR PEER REVIEW 14 of 22
Table 6. Longitudinal direction safety check for the DL LS.
Case Study DL LS
ID PGAD-DL PGAC-DL Ratio PGAC-DL-0.5% Ratio
- [m/s2] [m/s2] - [m/s2] -
S-BO 1.3 1.3 1.0 2.1 1.6
S-CH 1.3 1.4 1.1 2.2 1.7
S-BS 1.2 1.9 1.5 6.7 5.5
S-VT 1.2 1.9 1.6 3.1 2.6
S-RC 1.9 5.7 3.0 8.4 4.4
S-PA 1.3 3.1 2.3 3.4 2.6
Based on the findings presented in Tables 5 and 6, it is evident that the safety index
assessed in the longitudinal direction exceeded 1.0 across all case studies for the limit
states analyzed. They exhibit adequate stiffness and lateral resistance to seismic action.
4.3. Results of Pushover Analyses in the Transverse Direction
The same procedure as described earlier was employed to perform safety checks in
the transverse direction. Here, the aim was to compare the response of the six industrial
buildings by varying the base constraint conditions, considering an ideal condition (I-R
and/or I-P), and a real condition (R), based on simulated designs and FEAs. In Figure 8,
the pushover curves with their respective capacity points, as previously described, are
depicted. Subsequently, in Tables 7 and 8, the safety indices in terms of the ratio between
PGAC and PGAD are compared.
(a) (b) (c)
(d) (e) (f)
0
100
200
300
400
500
600
700
800
900
1000
0 0.2 0.4 0.6
R
I-R
I-P
dRd-DL-0.5%
dRd-DL
dRd-SD
dRd-SD-2.0%
dRd-Brit
Base Shear [kN]
Displacement [m]
0
100
200
300
400
500
600
0 0.3 0.6 0.9 1.2
R
I-R
d
Rd-DL-0.5%
d
Rd-DL
d
Rd-SD
d
Rd-SD-2.0%
d
Rd-Brit
Base Shear [kN]
Displacement [m]
0
200
400
600
800
1000
1200
1400
1600
0 0.2 0.4 0.6
Base Shear [kN]
Displacement [m]
R
I-R
I-P
d
Rd-DL-0.5%
d
Rd-DL
d
Rd-SD
d
Rd-SD-2.0%
d
Rd-Brit
0
200
400
600
800
1000
1200
1400
00.20.40.60.8
R
I-R
I-P
d
Rd-DL-0.5%
d
Rd-DL
d
Rd-SD
d
Rd-SD-2.0%
d
Rd-Brit
Base Shear [kN]
Displacement [m]
0
200
400
600
800
1000
1200
1400
00.20.40.60.8
Base Shear [kN]
Displacement [m]
R
I-R
I-P
d
Rd-DL-0.5%
d
Rd-DL
d
Rd-SD
d
Rd-SD-2.0%
d
Rd-Brit
0
200
400
600
800
1000
1200
1400
00.20.40.6
R
I-R
dRd-DL-0.5%
dRd-DL
dRd-SD
dRd-SD-2.0%
dRd-Brit
Base Shear [kN]
Displacement [m]
Figure 8. Pushover curves: (a) S-BO; (b) S-CH; (c) S-BS; (d) S-VT; (e) S-RC; and (f) S-PA.
Table 7. Transverse direction safety checks for the SD LS.
Case Study SD LS
ID PGAD-SD PGAC-SD Ratio
PGA
C-SD-2.0% Ratio PGAC-SD-Brit Ratio
-[m/s2] [m/s2]-[m/s2]-[m/s2]-
S-BO-IR 2.9 5.5 1.9 4.6 1.6 //
S-BO-IP 2.9 5.0 1.7 2.4 0.8 //
S-BO-R 2.9 6.3 2.2 3.9 1.3 1.2 0.4
S-CH-IR 2.9 7.9 2.7 3.3 1.1 //
S-CH-R 2.9 9.6 3.4 2.7 0.9 3.7 1.3
S-BS-IR 2.6 6.5 2.5 5.4 2.1 //
S-BS-IP 2.6 6.4 2.5 2.5 1.0 //
S-BS-R 2.6 8.2 3.2 4.2 1.6 1.6 0.6
S-VT-IR 2.6 13.0 5.1 7.6 3.0 //
S-VT-IP 2.6 8.9 3.5 3.7 1.4 //
S-VT-R 2.6 8.6 3.4 7.0 2.7 6.5 2.5
S-RC-IR 4.1 5.0 1.2 4.9 1.2 //
S-RC-IP 4.1 5.0 1.2 3.0 0.7 //
S-RC-R 4.1 5.8 1.4 4.3 1.0 3.9 0.9
S-PA-IR 3.0 6.4 2.3 6.1 2.1 //
S-PA-R 3.0 8.3 2.7 4.4 1.4 1.8 0.6

Buildings 2024,14, 3606 15 of 21
Table 8. Transverse direction safety checks for the DL LS.
Case Study DL LS
ID PGAD-DL PGAC-DL Ratio
PGA
C-DL-0.5% Ratio
-[m/s2] [m/s2]-[m/s2]-
S-BO-IR 1.3 3.5 2.7 1.3 1.0
S-BO-IP 1.3 3.7 2.8 0.7 0.5
S-BO-R 1.3 3.9 3.0 1.1 0.8
S-CH-IR 1.3 5.7 4.4 0.9 0.7
S-CH-R 1.3 6.7 5.2 0.8 0.6
S-BS-IR 1.2 4.0 3.3 1.4 1.2
S-BS-IP 1.2 3.9 3.2 0.7 0.6
S-BS-R 1.2 5.1 4.2 1.1 0.9
S-VT-IR 1.2 4.4 3.6 1.9 1.6
S-VT-IP 1.2 4.5 3.8 1.2 1.0
S-VT-R 1.2 5.0 4.1 1.8 1.5
S-RC-IR 1.9 4.0 2.1 2.1 1.1
S-RC-IP 1.9 4.1 2.2 1.2 0.6
S-RC-R 1.9 4.6 2.4 1.7 0.9
S-PA-IR 1.3 5.3 4.0 2.2 1.6
S-PA-R 1.3 7.2 5.5 1.5 1.1
By analyzing the pushover curves, it is possible to compare the impact of column–base
joint behavior on the overall lateral stiffness of the steel buildings examined. Specifically,
Figure 9illustrates the ratio between the elastic stiffness derived from non-linear static
analyses assuming the ideal fully rigid column–base joint behavior (k
el,I-R
) and the elastic
stiffness from analyses where the moment–rotation behavior of the joints was explicitly
modeled (k
el,R
). The data in Figure 9show that transitioning from the ideal to the actual
joint behavior results in an average decrease in lateral stiffness of 30% for buildings with the
RTF main frame typology, 35% for buildings with the PTF main frame typology, and 12%
for buildings with the RPF main frame typology. These findings highlight the significant
influence that realistic column–base joint behavior has on the structural performance of
steel buildings.
Buildings 2024, 14, x FOR PEER REVIEW 16 of 22
S-CH-R 1.3 6.7 5.2 0.8 0.6
S-BS-IR 1.2 4.0 3.3 1.4 1.2
S-BS-IP 1.2 3.9 3.2 0.7 0.6
S-BS-R 1.2 5.1 4.2 1.1 0.9
S-VT-IR 1.2 4.4 3.6 1.9 1.6
S-VT-IP 1.2 4.5 3.8 1.2 1.0
S-VT-R 1.2 5.0 4.1 1.8 1.5
S-RC-IR 1.9 4.0 2.1 2.1 1.1
S-RC-IP 1.9 4.1 2.2 1.2 0.6
S-RC-R 1.9 4.6 2.4 1.7 0.9
S-PA-IR 1.3 5.3 4.0 2.2 1.6
S-PA-R 1.3 7.2 5.5 1.5 1.1
By analyzing the pushover curves, it is possible to compare the impact of column–
base joint behavior on the overall lateral stiffness of the steel buildings examined.
Specifically, Figure 9 illustrates the ratio between the elastic stiffness derived from non-
linear static analyses assuming the ideal fully rigid column–base joint behavior (kel,I-R) and
the elastic stiffness from analyses where the moment–rotation behavior of the joints was
explicitly modeled (kel,R). The data in Figure 9 show that transitioning from the ideal to
the actual joint behavior results in an average decrease in lateral stiffness of 30% for
buildings with the RTF main frame typology, 35% for buildings with the PTF main frame
typology, and 12% for buildings with the RPF main frame typology. These findings
highlight the significant influence that realistic column–base joint behavior has on the
structural performance of steel buildings.
Figure 9. Effect of the column–base joints on the overall lateral stiffness.
5. Seismic Strengthening Interventions
The pushover analysis results presented in the previous section emphasize the
significant impact of explicitly modeling the column–base connections on the seismic
response of single-story industrial buildings. In particular, for the “R” configuration,
deficiencies were identified both locally in the SD limit state (with brile failure of the
connections) and globally in the DL limit state (overcoming the IDR threshold of 0.5%).
The conventional approach to improving a building’s seismic performance involves
adding lateral-force-resisting systems (LFRSs), such as exoskeletons or bracing systems,
which can be effective but often involve high costs and a greater structural impact [30,33].
Alternatively, enhancing the column–base connections themselves offers a lower-
cost, less intrusive solution. Specifically, stiffening of the column–base assembly with
vertical stiffener plates and the addition of anchor rods can restore both its stiffness and
strength. Studies have shown that improving the base connections can significantly
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
123456
k
el,I-R
k
el,R
I-R configuration
R configuration
Figure 9. Effect of the column–base joints on the overall lateral stiffness.
5. Seismic Strengthening Interventions
The pushover analysis results presented in the previous section emphasize the signifi-
cant impact of explicitly modeling the column–base connections on the seismic response
of single-story industrial buildings. In particular, for the “R” configuration, deficiencies
were identified both locally in the SD limit state (with brittle failure of the connections) and
globally in the DL limit state (overcoming the IDR threshold of 0.5%).

Buildings 2024,14, 3606 16 of 21
The conventional approach to improving a building’s seismic performance involves
adding lateral-force-resisting systems (LFRSs), such as exoskeletons or bracing systems,
which can be effective but often involve high costs and a greater structural impact [30,33].
Alternatively, enhancing the column–base connections themselves offers a lower-cost,
less intrusive solution. Specifically, stiffening of the column–base assembly with vertical
stiffener plates and the addition of anchor rods can restore both its stiffness and strength.
Studies have shown that improving the base connections can significantly improve both
local and global seismic performance [
34
,
35
]. Strengthening these connections can reduce
global deformability and maintain structural integrity under seismic loads. Additional
research supporting this approach [
36
,
37
] demonstrates how targeted local retrofitting
measures can yield significant improvements in the overall structural performance.
In this context, the proposed intervention involves reinforcing the column–base con-
nections by adding vertical stiffener plates to increase the stiffness and anchor rods to
improve the resistance. Strengthening interventions were applied to S-BO, S-BS, S-RC, and
S-PA. However, as indicated in Tables 7and 8, enhancing the column–base performance
in terms of stiffness and resistance was insufficient to meet the code requirements for
S-CH (refer to the I-R configuration in Tables 7and 8). In this case, a global strengthening
intervention is necessary to ensure compliance. The design of such global interventions is
outside the scope of this research.
Figure 10 illustrates the detailed design of the local strengthening interventions.
Buildings 2024, 14, x FOR PEER REVIEW 17 of 22
improve both local and global seismic performance [34,35]. Strengthening these
connections can reduce global deformability and maintain structural integrity under
seismic loads. Additional research supporting this approach [36,37] demonstrates how
targeted local retrofiing measures can yield significant improvements in the overall
structural performance.
In this context, the proposed intervention involves reinforcing the column–base
connections by adding vertical stiffener plates to increase the stiffness and anchor rods to
improve the resistance. Strengthening interventions were applied to S-BO, S-BS, S-RC, and
S-PA. However, as indicated in Tables 7 and 8, enhancing the column–base performance
in terms of stiffness and resistance was insufficient to meet the code requirements for S-
CH (refer to the I-R configuration in Tables 7 and 8). In this case, a global strengthening
intervention is necessary to ensure compliance. The design of such global interventions is
outside the scope of this research.
Figure 10 illustrates the detailed design of the local strengthening interventions.
The performance of the strengthened column–base connections was evaluated by
implementing a 3D component-based finite element model (CBFEM) within the IDEA
StatiCa environment, similar to the approach taken for the as-built connections. This
modeling allowed for a detailed investigation of the connections’ behavior, enabling an
accurate comparison between the as-built and strengthened configurations (see Figure
11).
The expected bending moment demand at the column base was estimated for the I-
R configuration by applying the N2 method to the pushover curve on the ADRS plan. By
identifying the target displacement in the investigated limit state, it was possible to
estimate the internal forces, including the bending moment and shear forces, at the
column bases. This information provides for the design of additional anchor bolts and
stiffeners to ensure that the column–base reinforcements meet the required strength and
deformation capacities under seismic loading [22].
Figure 10. Local strengthening intervention.
Figure 10. Local strengthening intervention.
The performance of the strengthened column–base connections was evaluated by
implementing a 3D component-based finite element model (CBFEM) within the IDEA
StatiCa environment, similar to the approach taken for the as-built connections. This
modeling allowed for a detailed investigation of the connections’ behavior, enabling an
accurate comparison between the as-built and strengthened configurations (see Figure 11).
The expected bending moment demand at the column base was estimated for the
I-R configuration by applying the N2 method to the pushover curve on the ADRS plan.
By identifying the target displacement in the investigated limit state, it was possible to
estimate the internal forces, including the bending moment and shear forces, at the column
bases. This information provides for the design of additional anchor bolts and stiffeners to
ensure that the column–base reinforcements meet the required strength and deformation
capacities under seismic loading [22].

Buildings 2024,14, 3606 17 of 21
Buildings 2024, 14, x FOR PEER REVIEW 18 of 22
(a) (b)
(c) (d)
Figure 11. Moment–rotation response curves for strengthened column–base joints: (a) S-BO; (b) S-
BS; (c) S-RC; and (d) S-PA.
The results shown in Figure 11 demonstrate the effectiveness of the strengthening
interventions applied to the column–base connections. The enhancements provided
notable increases in the moment resistance (M
j,Rd
) of 109%, 73%, 44%, and 118% for S-BO,
S-BS, S-RC, and S-PA, respectively. Additionally, the initial elastic stiffness of the
connections improved significantly, with increases of 160%, 80%, 112%, and 46% for the
same buildings.
To assess the implications of the local strengthening interventions on the global
structural behavior, the column–base joints’ local performance was incorporated into the
global analyses. Therefore, non-linear links, properly calibrated for each intervention,
were introduced into the 3D SAP2000 model to account for these modifications. Non-
linear static analyses were conducted following the same assumptions as those used for
the as-built configuration (R). The safety assessment for the retrofied buildings (R-st) is
summarized in Tables 9 and 10, which present the safety indexes, defined as the ratio of
PGA
C
to PGA
D
for the limit states investigated.
Figure 11. Moment–rotation response curves for strengthened column–base joints: (a) S-BO; (b) S-BS;
(c) S-RC; and (d) S-PA.
The results shown in Figure 11 demonstrate the effectiveness of the strengthening
interventions applied to the column–base connections. The enhancements provided notable
increases in the moment resistance (M
j,Rd
) of 109%, 73%, 44%, and 118% for S-BO, S-BS,
S-RC, and S-PA, respectively. Additionally, the initial elastic stiffness of the connections
improved significantly, with increases of 160%, 80%, 112%, and 46% for the same buildings.
To assess the implications of the local strengthening interventions on the global struc-
tural behavior, the column–base joints’ local performance was incorporated into the global
analyses. Therefore, non-linear links, properly calibrated for each intervention, were in-
troduced into the 3D SAP2000 model to account for these modifications. Non-linear static
analyses were conducted following the same assumptions as those used for the as-built
configuration (R). The safety assessment for the retrofitted buildings (R-st) is summarized
in Tables 9and 10, which present the safety indexes, defined as the ratio of PGA
C
to PGA
D
for the limit states investigated.
Table 9. Transverse direction safety check in the SD LS.
Case Study SD LS
ID PGAD-SD PGAC-SD Ratio
PGA
C-SD-2.0% Ratio PGAC-SD-Brit Ratio
-[m/s2] [m/s2]-[m/s2]-[m/s2]-
S-BO-R-st 2.9 6.6 2.3 4.3 1.5 3.1 1.1
S-BS-R-st 2.6 7.8 3.0 4.5 1.7 2.7 1.0
S-RC-R-st 4.1 6.1 1.5 4.4 1.1 4.5 1.1
S-PA-R-st 3.0 8.4 2.8 5.5 1.8 3.2 1.1

Buildings 2024,14, 3606 18 of 21
Table 10. Transverse direction safety check in the DL LS.
Case Study DL LS
ID PGAD-DL PGAC-DL Ratio
PGA
C-DL-0.5% Ratio
-[m/s2] [m/s2]-[m/s2]-
S-BO-R-st 1.3 3.6 2.8 1.3 1.0
S-BS-R-st 1.2 5.1 4.2 1.2 1.0
S-RC-R-st 1.9 4.5 2.4 2.0 1.1
S-PA-R-st 1.3 7.0 5.4 1.8 1.4
As shown in Tables 9and 10, the local strengthening interventions proposed allowed
all the code requirements to be met in terms of both the local and global performance
criteria for the limit states investigated. Indeed, in all the cases investigated, the seis-
mic performance index exceeded 1, demonstrating the effectiveness of the retrofitting
measures in enhancing the structural response. This approach, often overlooked, could
offer an economical and effective retrofit solution without the need for more extensive
LFRS additions.
6. Conclusions
This research underscores the importance of evaluating the seismic performance of
existing strategic single-story steel buildings situated in Italy, with a particular emphasis
on the nuanced behavior of column–base joints.
The methodology developed presents a systematic approach to assessing code-compliant
seismic performance, taking into account the original design typologies and joint behaviors.
From the results of numerical analyses, the following conclusions can be pointed out:
•
The single-story steel buildings, although they were originally designed to consider
gravity and wind loads only, demonstrate a satisfactory seismic performance in terms
of lateral resistance and stiffness in the longitudinal direction.
•
The absence of capacity design criteria in older regulations results in base nodes
designed solely for resistance checks, categorized as semi-rigid and partial-strength
according to the CBFEM analyses.
•
The non-linear links introduced accurately replicate the local joint behavior in terms
of the moment–rotation response, enabling the consideration of real joint performance
in global 3D FEMs.
•
In the transverse direction, the global structural behavior is heavily impacted by the
base connections’ performance. In most of the cases investigated, the joints show brittle
behavior, mainly governed by the low resistance of the anchors. This local deficiency
consistently precedes both the global structural ductility and the lateral deformability.
•
The local strengthening at the column–base connections proposed offers an econom-
ical and effective retrofitting solution to improve both the local and global seismic
performance. For brittle component failure, the seismic performance index increased
from values between 0.4 and 0.9 to between 1.0 and 1.1. This corresponds to improve-
ments ranging from 22% to 175%, ensuring compliance with the code prescriptions. In
terms of lateral deformability check at DL limit state, the index increased from values
between 0.8 and 1.1 to between 1.0 and 1.4, with improvements ranging from 11%
to 27%.
Finally, the findings of this study are directly applicable to similar Italian single-
story industrial buildings; however, the methodology for local and global assessment
and retrofitting can be applied more broadly to various building types, especially those
originally designed for gravity or wind loads. The approach provides a flexible framework
that can be adapted to other structural configurations, making it relevant for a broader
range of buildings beyond those considered in this study.

Buildings 2024,14, 3606 19 of 21
Author Contributions: Conceptualization, A.P. and R.T.; methodology, A.P. and R.T.; software, A.P.
and R.T.; validation, A.P. and R.T.; formal analysis, A.P. and R.T; investigation, A.P. and R.T; resources,
R.L.; data curation, A.P. and R.T.; writing—original draft preparation, A.P. and R.T; writing—review
and editing, R.T. and R.L.; visualization, A.P.; supervision, R.T. and R.L.; project administration, R.L.
All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Data Availability Statement: The data are contained within the article.
Conflicts of Interest: The authors declare no conflicts of interest.
Nomenclature
List of symbols and acronmys
ADRS Acceleration–Displacement Response Spectrum
agMaximum horizontal acceleration on rigid ground, which has a 10% probability of
being exceeded in 50 years
CSeismic coefficient
CBFEM Component-based finite element model
CBFs Concentrically braced frames
CF Confidence factor
CUUtilization coefficient of a building
dEd-DL Displacement demand in the DL limit state
dEd-SD Displacement demand in the SD limit state
DL Damage Limitation limit state
dRd-DL Roof displacement corresponding to the first yielding of the steel members
dRd-DL-0.5% Roof displacement corresponding a story drift equal to 0.005
dRd-SD Roof displacement corresponding to local failure of the steel members
dRd-SD-1.5% Roof displacement corresponding a story drift equal to 0.015
dRd-SD-2.0% Roof displacement corresponding a story drift equal to 0.02
FEEquivalent static seismic force according to the OS approach
FEM Finite element method
FwEquivalent static wind force
fyMaterial yield strength assumed for a steel member’s capacity (MPa)
fy,m Average value for the steel’s yield strength (MPa)
GDead load (kN)
g2k,c Characteristic permanent load of lightweight claddings per unit area (kN/m2)
g2k,r Characteristic permanent load of the roofing system per unit area (kN/m2)
GL Gravity load
IImportance factor of a building
IDR Inter-story drift ratio
I-P Structural configuration considering pinned column–base joints
I-R Structural configuration considering full-strength rigid column–base joints
kel,I-R
Elastic stiffness derived from non-linear static analyses assuming the ideal fully
rigid column–base joint behavior
kel,R
Elastic stiffness from analyses where the moment–rotation behavior of a joint
is explicitly modeled
KL Knowledge Level
LFRS Lateral-force-resisting system
LS Limit state
Mc,Rd Plastic bending capacity of a column
MjBending moment acting at the column base
Mj,Rd Bending capacity of the column–base joint
NjAxial force acting at the column base
OS Obsolete seismic (design)
PGACPeak ground acceleration of the capacity spectrum
PGADPeak ground acceleration of the elastic demand spectrum
PTFs Pinned truss frames

Buildings 2024,14, 3606 20 of 21
PVR Exceedance probability at VR
RStructural configuration considering the actual moment–rotation response of the
column–base joint
RdDynamic coefficient of a building
RPFs Rigid portal frames
R-st
RTFs Rigid truss frames
S-BO The steel single-story building located in Bologna (BO)
S-BS The steel single-story building located in Brescia (BS)
S-CH The steel single-story building located in Chieti (CH)
SD Significant Damage limit state
SjActual monotonic–moment rotation response of the column–base joint
Sj,pin Upper bound of the moment–rotation response for a pinned column–base joint
Sj,rig Lower bound of the moment–rotation response for the ideal fully rigid
column–base joint
S-PA The steel single-story building located in Palermo (PA)
S-RC The steel single-story building located in Reggio Calabria (RC)
S-VT The steel single-story building located in Viterbo (VT)
TRMean return period of the seismic action employed
VjShear acting at the column base
VNNominal design life of a building
VRReference period
WTot Seismic weight of a building
θRd,SD Rotational capacity of the flexural elements
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