Progressive Collapse Assessment and Retrofit of a Multistory Steel Braced Office Building

The progressive collapse of the building structures due to abnormal loads has attracted global attention in recent years. Many studies in the literature have been dedicated to the analysis and design procedures for progressive collapse resistance, and several technological solutions have been developed for progressive collapse retrofit. However, many studies are based on simple models and their validity and possibility to generalize the research results to current practice are rather limited. Moreover, there are still not many case studies developed based on full-scale real buildings. The present paper contributes to filling this gap by investigating the robustness of a quite complex real case study, namely a steel braced frame building erected in the early ‘60 s in Naples-Italy to house the Civil Engineering Authority. To this aim, different column removal scenarios have been considered and both nonlinear static and dynamic analyses have been carried out. The results have highlighted that the simple braced frames are susceptible to progressive collapse due to the weak brace connections. However, joint strengthening is not a viable solution, because it would prevent the full functionality of this strategic building during the implementation of the progressive collapse retrofit. As an alternative, an outrigger-belt truss system has been developed that applies the concept of Vierendeel truss system to redistribute the loads due to the column removal. The effectiveness of the proposed retrofit strategy to improve the progressive collapse resistance of the building has been verified through nonlinear dynamic analyses, proving its feasibility for practical applications.


Background
The collapse of the World Trade Center has attracted worldwide attention to the vulnerability of the building structures to accidental loading inducing progressive collapse. Generally, the building structures are designed for normal loads such as dead and live loads, earthquakes, snow, wind, and so on. As a consequence, under certain circumstances, extreme loading conditions (such as fire, impact, blast, material defects, construction errors, ad so on) may cause the failure of structural load-bearing elements, thus activating the progressive collapse of the building. To avoid global catastrophic scenarios, after the failure of a critical member or connection, the acting loads should be redistributed on adjacent structural members, using different load redistribution mechanisms, namely alternate load path, tie force, tensile catenary, compressive arching, as well as Vierendeel actions (Byfield & Paramasivam, 2007;Guo et al., 2013;Ferraioli et al., 2014Ferraioli et al., , 2016Ferraioli et al., , 2018Ferraioli et al., , 2019aZha et al., 2010;Qiao et al., 2020;Lu et al., 2018). If properly accounted for in the design, such mechanisms enable the structure to guarantee life protection by avoiding global collapse. The catenary action under large deformations is the capacity of the elements that are intended to support the load in flexure (typically beams) to resist vertical loads through the formation of a catenary-like mechanism that depends on the tensile stiffness and strength of the anchorages. The Vierendeel action in multi-story frames is produced by the additional moment due to the double-curvature deformation of the beam and corresponding load redistribution through shear forces. In the latest years, many papers have been devoted to investigating the mechanisms activated by the different structural resisting systems (i.e., steel frames, reinforced concrete (RC) structures, and bridges) to prevent the spreading of collapse (Alashker et al., 2010;Miyachi et al., 2012;Sadek et al., 2008). At the same time, the progressive collapse behavior has been found deeply affected by the structural configuration. This is usually related to the joint behavior which, in turn, depends on the structural layout, generally resulting in rigid joints in moment-resisting frames and nominally pinned beam-tocolumn joints in braced frames. In particular, multi-story steel buildings show different behaviors depending on both structural system and connection features (Dinu et al., 2017;Wang et al., 2016;Yang & Tan, 2013;Zhong et al., 2017). In this context, several papers on the subject have shown the importance of bracing systems and connections for progressive collapse resistance. The ductility and energy dissipation capacity of concentric braces may be increased by inserting an energy-dissipator element in the braces. Many studies have been presented in the literature using steel rings made of steel pipes as an energy dissipator in concentric braces (Andalib et al., , 2018Bazzaz et al., 2012Bazzaz et al., , 2014Bazzaz et al., , 2015aBazzaz et al., , 2015b. Jeyarajan et al. (2015a) investigated a three-dimensional 10-story steel building with different lateral bracing systems showing that the simply braced steel frames are more vulnerable to progressive collapse compared to moment-resisting frames due to weak columnto-beam joints. Khandelwal et al. (2009) investigated the progressive collapse resistance of 10-story steel buildings with concentrically or eccentrically bracing systems and observed that the latter brace configuration is less vulnerable to progressive collapse. Despite their ductility, the sheartab connections proved ineffective in resisting progressive collapse. Fu (2010) showed that the cross-bracing lateral resistance system is less vulnerable to progressive collapse under the one-column removal scenario. Kim et al. (2011) investigated the progressive collapse potential of various braced frames including diagonal braces, X-type, V-type, inverted-V (chevron)-type, K-braces, and knee braces. Asgarian and Rezvani (2012) applied a new algorithm for progressive collapse analysis of two concentrically braced frames with different numbers and locations of braced bays. Sun et al. (2012) investigated the mechanisms of progressive collapse under different fire conditions of steel momentresisting frames retrofitted with different bracing systems. Jiang et al. (2014) developed a parametric study to find the fire-induced progressive collapse mechanisms of steel frames under various fire scenarios and restraining conditions. Rezvani and Asgarian (2014) investigated the effect of the seismic detailing on the progressive collapse capacity of seismically designed concentrically braced frame buildings. Rezvani et al. (2017) investigated the effect of inverted-V bracing on enhancing the resistance of steel MRFs subjected to the loss of an exterior column in their first story. Lately, Naji et al. (2019) studied the behavior of concentrically and eccentrically braced frames by analyzing a 10-story steel moment frame under a progressive collapse scenario.

Retrofit Strategies Against Progressive Collapse
The existing buildings may not have the necessary properties to withstand abnormal loadings that are generally not considered in conventional structural design. At the same time, the seismic design provisions may not be effective to protect the structure from collapse to an extent disproportionate to the original cause.
Nevertheless, the existing steel buildings are sometimes in the need to be properly retrofitted to increase their progressive collapse resisting capacity. Although several retrofit strategies for mitigating the progressive collapse of buildings have been proposed in the literature, they have not attracted much attention since in most cases they are neither economical nor suitable for practical implementation. In general, there are some alternative strategies to improve the robustness of steel multistory buildings. In the past, many studies have shown that the resistance of the fin-plate joints is not sufficient to resist the tensile force due to the large beam deflection. This is the reason why simple braced frames with fin-plate pinned joints have been found more vulnerable to progressive collapse when compared to frames with rigid column-to-beam joints. Thus, a strategy for progressive collapse mitigation could be to improve the column-to-beam joints and, if possible, convert the nominally pinned joints into moment joints. Jeyarajan et al., (2015bJeyarajan et al., ( , 2015c showed that using modified fin-plate or end-plate column-to-beam joints allows for increasing the joint rigidity and axial tension resistance compared to conventional fin-plate joints. For this reason, they proposed to strengthen the column-to-beam fin-plate joints to achieve rigid (or at least semi-rigid) connections. Nevertheless, this solution is too much expensive and time-consuming to be implemented in current practice, which is why alternative retrofit strategies have been investigated in the literature (Rezvani et al., 2017;Wijesundara et al., 2018). Liu (2010) proposed novel retrofitting schemes for strengthening simple joints of existing steel-framed structures, ensuring the full development of catenary action. As an alternative, the risk of progressive collapse of buildings can be reduced by strengthening structural members or using pre-stressed steel cables. Galal and El-Sawy (2010) investigated the performance enhancement obtained with three retrofit strategies, namely increasing the strength of the beams, increasing the stiffness of the beams, and increasing both strength and stiffness of the beams. Zha et al. (2010) analyzed the progressive collapse behavior of a 1 3 steel-concrete composite structure retrofitted by using prestressed steel cables and increasing the crack resistance of concrete at the column-to-beam joint. Adding steel braces may be an appropriate and economical strategy to enhance the progressive collapse resistance of steel-framed buildings with a structural system having high stiffness and strength. Many studies have highlighted that vertical bracing systems can play an important role in increasing both stiffness and strength and redistributing the loads under column removal conditions. Mohamed (2009) observed that adding bracing systems can divert some of the high forces generated by the removed column. Chen et al. (2012) investigated the strengthening effect of horizontal steel braces on the progressive collapse resistance of steel moment frames. Choi and Chang (2009) proposed two collapse prevention methods, namely reinforcement of members of truss structures and X-bracing of frame structures. Fu (2010) showed that reducing the column spacing or adding a cross-bracing lateral resisting system are both effective ways of enhancing the progressive collapse resistance. As an alternative, even the Vierendeel action may contribute to enhancing the robustness against progressive collapse. A Vierendeel truss system at certain floor levels may be obtained by converting the pinned beam-to-column joints into rigid moment connections. In this context, the outrigger-belt truss system, which is one of the commonly used lateral load resisting systems for tall buildings, may become a redundant structural system in an accidental loading scenario. An additional cross-type truss using tie-cables at the outrigger-belt truss level can further increase the progressive collapse resistance. Schachter et al. (2015) presented a case study of the retrofit of a 5-story concrete structure where the floor slabs are suspended to a new steel girder located above the roof. The existing columns and supplemental tie rods are used as hangers that transfer the load to the new girder.

Objective
Most of the above-recalled papers are based on simple bidimensional models and their applicability in the current practice is questionable. In addition, just a few studies dealing with applications to full-scale real buildings are available in the literature. The present work attempts to close this gap of knowledge by presenting a case study referring to a steel braced frame office building erected in the early '60 s in Naples-Italy. At first, the paper investigates the robustness of the existing building under different column removal scenarios and discusses the effect of the brace connections in simple braced frames. To this aim, nonlinear static and dynamic alternative path analyses are performed for checking the potential for progressive collapse. Then, an outrigger-belt truss system is proposed to enhance the progressive collapse resisting capacity of the building. In the end, the structural beneficial effects of the retrofit strategy on mitigating the progressive collapse of the building are evaluated and discussed.

Building System Description
The steel structure under consideration currently houses the local Civil Engineering Authority of the Naples District and was intended to extend the original building dating back to the late '40 s (Fig. 1). The existing structure was becoming quite inadequate for the fastly increasing building development of the city in the postwar years. A fully bolted, steel-based solution was chosen to speed up the erection procedure while reducing at the same time the load on foundations. A special system of pile foundation was adopted to reach the underlying tuff bearing layer (Fig. 2). Special attention, in terms of both structural detailing and planning of constructional stages, was paid to the interaction between the new and the existing building, which had to be kept operational throughout the works for the erection of the new structure. To simplify the construction stages, with a minimum disturbance to the office employees, a system of steel columns passing through the existing floor decks was studied, piercing holes of at least 30 × 30 cm of space (Fig. 3). The building is an eight-story construction characterized by a V-shaped plan, as shown in Fig. 4, in which three main bodies can be identified (namely A, B, and C). According to a practice commonly shared at the time of

Building Structural Details
The floors are made according to the traditional scheme of steel purlins and cold-formed trapezoidal sheeting integrated by an upper concrete cast. Horizontal braces are arranged just below the floor to link together adjacent beams structurally (Fig. 4). The bracing of the mainframes is obtained with concentric bracing systems (Fig. 5) arranged in both longitudinal and transverse directions. The braces in the transverse direction are of two types. The first type (namely bracing system (A) in Fig. 5) is composed of two members arranged in the side spans. Their cross-section was kept constant, for construction uniformity, along with the whole height of the building. The diagonal braces are compressed due to the gravity loads and, therefore, double coupled profiles were used. The second type (namely bracing system (B) in Fig. 5) has the static scheme of reticular arches with three hinges.
The same static scheme was used for bracing in the longitudinal direction (namely bracing system (C) in Fig. 5). In the longitudinal direction, the steel columns are interrupted while the beams are continuous in the joint. The structure relies predominantly on bolted joints, with some connections obtained by field-welding. Some details of the connections are shown in Fig. 6. All connections, either welded or bolted, were designed to withstand gravity and wind loads only and may be considered pinned. As a consequence, they have a satisfying capability to fully accommodate the large rotations that arise when the column is removed. However, they are not able to withstand the high tensile stresses due to the catenary action. Shortly, the following cross-sections and materials were considered.

Preliminary Analysis
At present, the building is in satisfactory condition, with no major degradation detectable. In addition, both the lightness and effectiveness of the steel structure helped the building to withstand the severe earthquake of 1980 without significant damage. No seismic action was considered in the design since the building was designed for gravity and wind loads only. Under such loading conditions, a preliminary analysis has shown that the structure fully complies with the building regulation in force at the time of construction. Nevertheless, some minor issues have been pointed out concerning compliance with the provisions of the current Italian building code (NTC, 2018) for vertical loads whereas, some major issues can be identified that concern the seismic loads. Specifically, the braces are undersized and, hence, the bracing system does not provide sufficient lateral resistance due to the buckling of the braces. The geometry and structural details of the building were partially known from some information about the original design and construction of the building (Travaglini & De Miranda, 1962). This information was integrated by a direct visual survey. The model of the structure was implemented through the simulated design procedure introduced in the current Italian Code (NTC, 2018) for the assessment and retrofitting of existing buildings. This means that the design code, seismic classification, and practice rules at the time of construction (dating back to the late '40 s) were considered. Therefore, the method of allowable stresses in force in Italy at that time was used for the simulated design

Numerical Modeling
After a column is suddenly removed due to abnormal loads, different mechanisms are mobilized to transfer loads to the superstructure and avoid collapse: Vierendel action, catenary action, columns acting as hangers, and tensile membrane action in slabs. In the case study, the connection of the corrugated sheet was considered not capable of transferring tensile stresses from the floor slab to the beams. Thus, the load redistribution through the floor slabs was neglected for the sake of conservativeness. The building model structure was implemented in SAP2000 (2019) computer program (Fig. 7). The geometry, structural details, and material properties were derived from the original construction drawings integrated by the direct visual survey. Two types of beam-to-column joints were identified. In the frames on the perimeter of the building, the beams are continuous in the joint, while the steel columns are interrupted and bolted with end-plate splice connections (Fig. 6b-c). Therefore, these connections were considered full-rigid and full-strength and not explicitly modeled since the plastic hinges form at the ends of each member, not in connections. The other beam-to-column joints are simple shear tab connections that may be classified as partially restrained simple connections (flexible). The expected flexural strength, defined as the smallest flexural strength among all the failure modes (i.e., bolt shear failure, weld failure, plate flexure failure, and so on), is very low. Thus, these beam-to-column shear tab connections were considered nominally pinned. Both material and geometric nonlinearities (i.e., P-delta and large displacements effects) were considered in the analysis. To this aim, a suitable plastic hinge model was used for beams, columns, and braces. For beams and columns, the plastic hinges were defined based on the moment-curvature relationship of the section under combined bending and normal force. For braces, the axial force-deformation relationship was considered. The concentrated plastic hinges properties (i.e., nonlinear modeling parameters and acceptance criteria) were calculated based on ASCE 41-13 (2014). The strength degradation was neglected since the acceptable plastic rotation angle of the steel members is always within the first post-yield linear branch of the moment-rotation curve (i.e., before the strength degradation). Finally, it should be observed that, in general, it would be desirable that the numerical model is validated against experimental results. Ambient vibration tests (AVTs) and subsequent dynamic identification have been extensively applied in the literature for calibrating finite element models (FEM) of structures from their modal response. This FEM tuning procedure has shown to be effective in structures of different types such as buildings (Skolnik et al. 2006, Ferraioli, 2015, bridges (Jaishi et al. 2005), and towers (Gentile et al. 2007, Ferraioli et al., 2017. However, the model tuning based on experimental data aims to calibrate a linear elastic model of the structure to be used for seismic analysis and design. On the contrary, in the case study, the building model structure is used for progressive collapse assessment and retrofit. The corresponding disproportionate collapse analysis is based on the alternate path method where a critical structural member, typically a column, is removed and the ability of the structure to bridge over the missing element is investigated. In this scenario, the progressive collapse behavior of the building has little or nothing to do with the linear elastic model of the structure calibrated against modal experimental results. In general, the progressive collapse response after a column removal comprises an initial linear elastic phase followed by significant geometric (large displacements) and material (plasticity) nonlinearities and, finally, a catenary phase, which is developed only if the inelastic deformations are large enough to make possible a transition from flexural to tensile catenary resistance (Ferraioli, 2019b). The linear elastic phase depends on the first vertical mode shape of the damaged structure (i.e., the structure with the column removed) and not on the flexural and torsional mode shapes of the entire building. The subsequent plastic and catenary action stages depend on the complex mechanisms that are mobilized to resist collapse: Vierendel action, compressive arching in beams and floor slabs, tensile catenary actions, membrane action in structural slabs, and, finally, vertical load-bearing elements acting as hangers. These mechanisms are related to geometric and material nonlinearities. Their validation cannot be performed using the results of non-destructive experimental tests on the undamaged structure, but it would require destructive full-scale tests on the structure subjected to column removal scenarios.

Acceptance Criteria
The internal actions on the beam-to-column connections due to the column removal differ significantly from the design conditions. The tensile axial forces in the beams gradually increase, while the bending moment decreases. The load-displacement behavior is dominated by the response at the large rather than small deformation stage and the transition from flexural to catenary action mechanism occurs. In this situation, the beams resist the vertical loads by developing a string-like mechanism through a new alternative equilibrium path under large displacements and rotations (Ferraioli et al., 2014). The connections play a critical role since an alternative load path could be mobilized only if the beam-column connections have enough rotational capacity to sustain the abnormal extra-loads developed following the removal of a critical vertical load-bearing element. Practically, the tensile capacity of the beam-to-column connections controls the mobilization of catenary action and, hence, the failure mode. Previous research papers highlighted that the simple connections can fail before the development of tensile catenary action since both high tensile axial force and large rotations are not explicitly accounted for in the design procedures (Ferraioli, 2021). In this paper, the rotation capacity of these connections was checked using the GSA(2016) and UFC (2016) acceptance criteria for nonlinear modeling of steel frame connections. Finally, the progressive collapse induces high tensile axial forces in the brace connections. This situation differs significantly from the design conditions leading to a brittle failure of the brace connections. This brittle failure mode was checked a posteriori by evaluating the corresponding applied load.

Analysis Procedures
The initiating events of progressive collapse are generally associated with dynamic phenomena, such as explosion, impact, or sudden failure of a key structural member. However, in this paper, the progressive collapse analysis was carried out using a threat-independent approach based on the alternate path method. In this approach, a critical element, typically a column, is instantaneously removed and the ability of the structure to bridge over the missing element is investigated. Four different column removal scenarios were considered in the analysis (Fig. 8). The locations of the removed column were selected to better represent the different progressive collapse behaviors and mechanisms: S1) Corner column condition; S2) Short side column condition; S3) Long side column condition; S4) Internal column condition. The analysis ignores the dynamic effects due to abnormal loads of very short duration. Practically, the analysis is developed under the hypothesis that the strain rates are in the seismic loading range, i.e., rather low, which justifies neglecting the strain rate effects in the analysis model. On the other side, progressive collapse is a dynamic and nonlinear phenomenon and, thus, both the dynamic effects and the material and geometric nonlinearities should be accounted for. Therefore, the nonlinear dynamic procedure (NDP) should be used to provide accurate descriptions of the more important characteristics of the progressive collapse behavior. However, the implementation of NDP in current practice is time-consuming and computationally demanding. This is the reason why the current design guidelines for progressive collapse resistance (GSA, 2016; UFC, 2016) allow using simplified methods such as the linear static procedure (LSP) and the nonlinear static procedure (NSP).

Fig. 7
View of the structural model

Nonlinear Static Procedure (NSP)
The nonlinear static procedure is based on a displacementcontrolled nonlinear static analysis (also known as "pushdown analysis") where the vertical displacement in the location of the removed column is gradually increased and the corresponding equivalent load is evaluated. This allows plotting the so-called pushdown curve, which relates the resulting force to the vertical displacement in the location of the removed column. To approximately compensate for the dynamic effects, a dynamic increase factor (namely Ω N ) is applied to the gravity loads in the bays of the removed column. According to GSA, 2016GSA, (2016, the following load combinations were considered in the analysis: where the load combination of Eq. 1a was applied in the bays immediately adjacent to the removed column, while the load combination of Eq. 1b was applied in the other bays. In Eq. 1, G N is the gravity load, D is the dead load and L is the live load. The dynamic increase factor Ω N was evaluated using the following formula first proposed by Ruth et al. (2006) and McKay et al. (2012) and then included in both GSA (2016) and UFC (2016): where θ pra is the prescribed maximum acceptable plastic hinge rotation angle and θ y is the yield rotation angle.
(1) In Eq. 2, θ pra /θ y is defined as the smallest ratio among the structural members that contribute to progressive collapse resistance (i.e., primary elements, components, or connections). This formula is based on the hypothesis that the controlling structural member has reached its maximum allowable plastic hinge rotation capacity. As highlighted in other studies (Ferraioli, 2019b(Ferraioli, , 2019c, this hypothesis tends to underestimate Ω N for structures that experience a modest level of nonlinearity. On the other side, the hypothesis of a monotonic decreasing of Ω N with ductility is no longer valid when the catenary action is fully developed. In this case, Eq. 2 significantly underestimates Ω N and, thus, it is not conservative.

Nonlinear Dynamic Procedure (NDP)
The nonlinear dynamic analysis was carried out as follows. At first, the load combination of Eq. 1b is applied to the undamaged structure (i.e., structure before the column removal), and the corresponding internal forces in the tobe-removed column (i.e., axial force P, shear force V, and bending moment M) are calculated. Then, the load combination of Eq. 1b and the reaction forces (i.e., − P, − V, and − M) are both applied to the damaged structure (i.e., structure after the column removal). The loads were applied linearly in a time of 1 s to avoid resonance with the first vertical mode shape of the damaged structure. Then, they were kept unchanged for 9 s to reach a stable condition. This loading condition gives the deformed shape at the beginning of the column removal. Finally, the reaction forces are abruptly removed during a time of 10 ms to reproduce the sudden column loss. The nonlinear dynamic analysis was carried out using a modal damping ratio of 2% for the first two vertical mode shapes. It is worth mentioning that this is a conservative value of the damping ratio. In fact, in steel structures, the damping ratio can be 2% to 4% depending upon the construction and joint conditions. A damping ratio of 2% is appropriate for steel structures with welded joints. For bolted joints, the damping ratio is higher since they can experience greater slip than welded joints.

NSP vs NDP-Dynamic Increase Factor
It should be highlighted that, in general, the nonlinear static (pushdown) procedure underestimates the progressive collapse response. This is the reason why a dynamic increase factor (Ω N ) is generally applied in the bays of the removed column. To highlight this effect, Fig. 9 shows a typical pushdown curve corresponding to the load combination of Eq. 1b (i.e., unamplified gravity loads). In general, this curve comprises three phases: a linear elastic phase, a plastic phase, and, finally, a catenary phase. As aforementioned, the last phase due to the catenary action is developed only if the plastic deformation capacity of the structure is large enough to make possible a transition from the flexural resistance to the tensile catenary resistance (Ferraioli, 2019b). The same Fig. 9 shows the IDA (Incremental Dynamic Analysis) envelope curve, which consists of a plot of the load factor versus the corresponding peak vertical displacement. The magnitude of the load factor (LF) in the load combination LFx(1.2D + 0.5L) is gradually increased, and the corresponding peak vertical displacement in the location of the removed column is calculated using the nonlinear dynamic procedure (NDP). In general, the pushdown curve under unamplified gravity loads provides lower displacement than NDP at the same load factor (LF) (Fig. 9). Consequently, a dynamic increase factor (Ω N ) should be applied in the bays directly affected by the removed column to approximately compensate for the dynamic effects. This can be usefully represented through a two-step pushdown analysis (Ferraioli, 2019a). In the first step (namely Push 1 in Fig. 9) the load combination LFx(1.2D + 0.5L) is applied corresponding to the unamplified gravity loads of Eq. 1b. In Fig. 9, Point 1 corresponds to the total vertical load (i.e., LF = 1). In the second step (namely Push 2 in Fig. 9) the load combination (Ω N -1)xLFx(1.2D + 0.5L) is applied in the bays directly affected by the column removal. This gives an increment in displacement (from Point 1 to Point 2 in Fig. 9) at a constant gravity load corresponding to a load factor LF = 1. In general, the formulation of Eq. 2 for the dynamic increase factor is conservative. Therefore, the NSP overestimates the vertical displacement obtained from NDP and, thus, Point 2 is on the right side of the IDA curve (Fig. 9).

Analysis Results
The load-carrying capacity was estimated for both the ductile and brittle failure modes. Specifically, the load-carrying capacity of the ductile failure modes was evaluated based on the nonlinear static (NSP) and dynamic (NDP) procedures. The nonlinear static procedure (pushdown analysis) gives the load-displacement relationship (i.e., pushdown curve) where the applied vertical load is plotted versus the vertical displacement in the location of the removed column. Figure 10 shows the pushdown curves for different column removal scenarios (namely S1, S2, S3, and S4). The capacity of the ductile members was estimated in terms of chord rotation. To this aim, the acceptance criteria for beams, columns, braces, and beam-to-column connections, were verified during the analysis. Figures 11, 12, 13, 14 shows the location and performance level of the plastic hinges at the last step of the pushdown analysis. For the column removal scenarios S1, S3, and S4, one variation in the slope of the pushdown curve is observed in Fig. 10. For the S1 scenario ( Fig. 11), the variation is due to the yielding of the tensile braces. For the S3 scenario (Fig. 13), a combined beam and column mechanism occurs, but beams and columns yield at the same step of the pushdown analysis. Therefore, one only variation in the slope of the pushdown curve is observed (Fig. 10, Scenario S3). In the same way, for the S4 scenario (Fig. 14), some braces and one column yield at the same step of the analysis. For the S2 scenario, two variations in the slope of the pushdown curve occur (Fig. 10). The first one is due to the buckling of compressed braces. The second one is due to the yielding of beams in the bays corresponding to the removed column (Fig. 12). The value of the load factor at the last step of the pushdown analysis is an estimation of the progressive collapse resistance of the building subjected to the column failure. A load factor greater than one means that the gravity loads may be supported by the structure after the column removal. Figure 10 shows that the load factor for the ductile failure modes is lower than one for the column removal scenario S2, while is greater than one for the other scenarios. The nonlinear dynamic procedure (NDP) gives the progressive collapse response of the building after the sudden column removal. Figures 15 shows the vertical displacement time-history in the location of the removed column. During the dynamic analysis, the acceptance criteria in beams, columns, braces, and beamto-column connections were never exceeded. As aforementioned, the NSP approximately compensates for the dynamic effects through the dynamic increase factor Ω N , which is applied in the bays immediately adjacent to the removed column using the load combination of Eq. 1a. Since the formulation of Eq. 2 is generally conservative, the NSP tends to overestimate the vertical displacement in the location of the removed column compared to the NDP. To highlight Fig. 9 Two-step pushdown analysis to evaluate the dynamic increase factor Ω N this effect, Fig. 16 compares the pushdown curves obtained from the NSP under unamplified gravity loads (namely pushdown (Ω N = 1)) and amplified gravity loads (namely pushdown (Ω N )) with the IDA envelope obtained from the NDP. The results show that the pushdown curve obtained using the dynamic increase factor of Eq. 2 (i.e., pushdown (Ω N )) provides a slight overestimate of the vertical displacement compared to the IDA envelope curve. Similar results are obtained for the other column removal scenarios. The load-carrying capacity of the brittle failure modes was evaluated a posteriori based on the results of the NSP. The brittle failure of the brace connections was checked for the different column removal scenarios. Figure 17 shows the weakest location of the bracing connections (i.e., the location where the first fracture occurs). Typically, it is located on the first story of the building where the axial force in the brace is slightly greater than in the other stories. For each column removal scenario, the Load Factor (LF) was evaluated corresponding to the brittle failure of the brace connections. The values obtained are much less than one for all the column removal scenarios (i.e., LF = 0.316 for S1, LF = 0.215 for S2, LF = 0.657 for S3, and LF = 0.456 for S4). It can be concluded that the progressive collapse resistance of the existing building is inadequate and thus upgrading is required.

Retrofit Method
A solution frequently used for the progressive collapse retrofit is based on strengthening the horizontal elements that play a key role in redistributing the gravity loads from the affected bays to the undamaged structural elements. Typically, additional steel plates can be welded at the flanges of the I-shaped beams to enhance their stiffness and strength and, consequently, increase the progressive collapse resistance of the structure. However, in existing buildings, the top flange of the beam is not accessible for welding due to the presence of the composite floor slab, hydraulic or electrical systems, horizontal bracings, and so on. Therefore, additional flange plates or I-shaped sections can be welded only to the bottom flange of the existing beams. Moreover, in the case study, the beam's flexural capacity is rather limited since the steel beam-column connections are simple (flexible) connections. Finally, the poor tensile resistance of the connections prevents the formation of a catenary-like mechanism. Therefore, the beams' retrofit with plates and I-shaped sections would be ineffective. In general, the use of modified beam-to-column and brace connections can be effective in significantly enhancing the progressive collapse resistance of steel frames. However, in the case study, the tensile resistance of the connections is very small and, thus, their strengthening would be uneconomical also because it would prevent the building from being fully operational during the retrofit implementation. This is a dramatically important issue since the case study is a strategic building.
As an alternative, the addition of steel bracings across predefined stories has been often applied in current practice to enhance the progressive collapse resistance of high-rise buildings. However, this retrofit solution inhabits the front of an entire story and this is a not negligible problem for an office building. An alternative method is based on top beams grid systems that hold the column from the top in case of a column loss scenario. However, the case study building has a poor progressive collapse resistance. Therefore, heavy steel cross-sections would be required to increase the vertical stiffness and strength of the building through the flexural action of the top beams grid system. This makes this solution uneconomical and leads to an increase in mass and, consequently, in seismic actions. As an alternative, top gravity truss systems have been proposed in recent years (Freddi et al., 2022) since the trusses can provide significant vertical stiffness and strength with relatively small sections and limited added mass. Moreover, this retrofit method is rapid, low-impact, and reversible, does not significantly affect the seismic behavior of the building, and, finally, keeps most areas of the building fully operational during the retrofit implementation. For these reasons, as a cheaper and more effective alternative, the progressive collapse retrofit design was carried out by adding a new structural system consisting of a steel outrigger mega truss on the top floor of the building (Fig. 18). The sizing of the mega truss members was carried out using simple equilibrium conditions under gravity loads (Fig. 19). Practically, the outrigger-belt truss system was designed to successfully carry all the gravity loads due to the column loss, thus neglecting the load-carrying capacity of the existing building. Structural steel S275 for all steel members (f yk = 275 MPa) and full penetration welded connections were considered in the analysis. This design procedure gave the following cross-sections: CHS 219,1X10 for diagonal struts, CHS 273X10 for vertical webs, and CHS 273X10 for top chords. The retrofit strategy was conceived to create a top truss system designed to resist the column removal with low vertical displacements and tensile catenary actions, thus preventing the failure of the connections. This solution offers the following advantages: • Low weight: the steel lattice structure does not involve a significant increase in the weight of the building and, thus, no additional strengthening interventions on foun- 1 3 dation structures are required. For the same reason, the increase in mass relevant to the seismic response of the structure is of little concern. • Complete reversibility: the truss can be easily removed if necessary. • Simplicity: the system is of simple analysis and calculation and can be implemented with minor disturbance without interrupting the current activity in the building. This turns out to be convenient in constructions devoted to public use. Furthermore, it can be easily hidden or configured in the form of a roof parapet.
• Minimum strengthening required: the retrofit system prevents the onset of alternate stress paths in the bearing structure, as this role is played by the mega truss itself. As a consequence, little if no development of the catenary effect takes place in the structure after the column loss. This minimizes the strengthening required, leading the designer to check just the capacity of the columns and their connections in tension, without any other modification to the structural joints. Likewise, the strengthening of the floors is not required.

Scenario S1
Scenario S2 Scenario S3 Scenario S4 Fig. 17 First failure of the brace connections for different column removal scenarios. Original building. Column removal scenarios S1,S2,S3,S4 • Integrability: thanks to its high stiffness, the outrigger belt truss can be profitably integrated with additional strengthening systems aimed at improving the seismic performance of the building, such as steel braces and RC cores.

Progressive Collapse Assessment
The evaluation of the progressive collapse resistance of the retrofitted building was carried out by using both the nonlinear static and the nonlinear dynamic procedures. The progressive collapse resistance of the retrofitted building is predominantly provided by the outrigger-belt truss system that works elastically. Therefore, the pushdown curve has a linear trend and is not plotted. The corresponding maximum load factors are much greater than one for all the column removal scenarios, showing the effectiveness of the progressive collapse retrofit. The outrigger-belt truss system is also effective in reducing the dynamic response of the structure subjected to the column removal. Figure 15 compares the nonlinear dynamic responses of the original and the retrofitted building. The comparison shows that the retrofit strategy is effective in reducing the vertical displacements above the removed column thus increasing the progressive collapse resistance of the building. The reduction in displacement is 21.0%, 29.7%, 26.9 and 21.2 for the column removal scenarios S1, S2, S3, and S4, respectively. To highlight the final collapse mode for each column removal scenario, Figs. 20,21,22 and 23 show the distribution of the plastic hinges and corresponding performance levels at the last step of the pushdown analysis. It is interesting to compare these figures related to the retrofitted building to the corresponding Figs.11, 12, 13 and 14 related to the original building. For the column removal scenario S1, the collapse of the original building is due to the yielding of the tensile braces in the external bay (Fig. 11). The progressive collapse retrofit using the outrigger-belt truss system completely changes the collapse mode, which is dominated by the brittle failure of the columns adjacent to the removed column (Fig. 20) that become overloaded because of the redistribution of loads after the column removal. For the column removal scenario S2, the collapse of the original building is due to the compression of the Y-shaped brace (Fig. 12), while the collapse of the retrofitted building is dominated by the failure of the compressed columns adjacent to the removed column (Fig. 21) and the tensile columns above the removed column that act as hangers. For the column removal scenario S3, the collapse of the original building is due to the tensile yielding of the Y-shaped brace and the subsequent brittle failure of the compressed columns adjacent to the removed column (Fig. 13). For the retrofitted building, this collapse mode occurs in conjunction with the yielding of the tensile columns above the removed column (Fig. 22). Finally, for the column removal scenario S4, the collapse of the original building is due to the yielding of the Y-shaped braces (Fig. 14). In the retrofitted building, the loads can be redistributed due to the outrigger-belt  truss system. Thus, the usual collapse mode occurs in which the columns adjacent to the removed column yield in compression, and the columns above the removed column yield in tension (Fig. 23). It should be underlined that the existing steel columns play a critical role in all the column removal scenarios. The outrigger-belt truss system redistributes most of the applied loads to the columns adjacent to the removed column. Therefore, these steel columns are subjected to high axial forces and should be considered "force-controlled" since P/P CL > 0.5 (where P CL is the lower-bound axial load capacity). Their plastic hinging marks the beginning of a non-ductile failure mode since these columns have a poor ductility capacity. On the other side, it should be highlighted that, for the column removal scenarios S2, S3, and S4, the columns above the removed column act as hangers from the outrigger-belt truss and, therefore, their plastic hinging occurs in tension. Therefore, the column-to-beam connection plays a critical role since it has only four bolts to hold down the column (Fig. 6b, c). Thus, the tensile failure of this connection should be checked. For this purpose, at first, the software Idea StatiCa (2021) for the local structural analysis of steel joints was used, and the tensile strength of 153 kN was predicted for the original column-to-beam connection. Then, the axial force in the column-to-beam connections was evaluated using the nonlinear static (pushdown) analysis. Figure 24 shows the location of column-to-beam connections where the axial force is greater than the tensile strength (i.e., failure of the column to beam connections). For the S2 and S4 column removal scenarios, the column-to-beam connections of the last three floors of the building should be strengthened, while for the S3 scenario the increase in tensile strength is required only on the top floor. Where required, the strengthening of the columnto-beam connection can be carried out using 12 mm thick S355 steel plates welded to column and beam members and replacing the existing bolts with new bolts M20 10.9 (Fig. 25). This solution significantly increases the tensile strength of the column-to-beam connection (from the initial value of 153 kN to the final value of 320 kN) and allows the connections of the columns above the removed column to carry the high tensile axial forces due to the column loss.

Fig. 25
Column-to-beam connection. a Original building; b retrofitted building 1 3

Conclusions
Although several studies in the literature have been dedicated to the analysis and design procedures for progressive collapse resistance and many technological solutions have been proposed for progressive collapse retrofit, there are still not many case studies developed based on fullscale real buildings. This paper has presented the study on the progressive collapse assessment and retrofit of a steel braced frame office building erected in the early '60 s in Naples (Italy) that still today houses the local Civil Engineering Authority of the Naples District. Different column removal scenarios have been considered and both nonlinear static and dynamic analysis procedures have been implemented. Based on the analyses carried out, the following conclusions can be drawn.
• The progressive collapse assessment of the original building reveals that the nonlinear static procedure slightly overestimates the vertical displacement compared to the nonlinear dynamic procedure. This means that the formulation of the dynamic increase factor proposed by GSA and based on the ductility factor is conservative and succeeds in approximately compensating for the dynamic effects. • The progressive collapse resistance is affected by the bracing system of the original building, which is found to be undersized and inadequate for robustness under different column removal scenarios. The brace connections show a rather brittle failure response. The values of the Load Factor (LF) corresponding to the load-carrying capacity of these brittle failure modes are very low (i.e., LF = 0.316 for S1, LF = 0.215 for S2, LF = 0.657 for S3, and LF = 0.456 for S4). This is due to the low tensile load-bearing capacity of the brace connections that should be upgraded. However, the systematic strengthening of all the brace connections is complicated and economically onerous and would prevent the building from being fully operational during the retrofit implementation. • A top gravity truss system consisting of a steel outrigger mega truss on the top floor of the building has been proposed to improve the progressive collapse performance. This retrofit solution prevents the building from the onset of alternate stress paths in the bearing structure, as this role is played by the mega truss itself. This dramatically reduces the strengthening interventions, leading the designer to check just the capacity of columns and their connections in tension, without any other modification of the structural joints. Likewise, the strengthening of the floors is not required.
• The proposed retrofit system is of simple analysis and design. Moreover, it has low weight. Therefore, the increase in mass relevant to the seismic response of the structure is of little concern, and no additional interventions on foundations are generally required. • Unlike other retrofit strategies, the outrigger-belt truss system preserves the building function and minimizes the indirect costs related to the interruption of building use. This turns out to be convenient in constructions devoted to public use. Moreover, it minimizes the impact on architectural functionality and can be easily hidden or arranged in the form of a roof parapet. • Finally, the proposed retrofit solution is rapid, lowimpact, and reversible since it can be removed and rapidly replaced and can be profitably integrated with additional strengthening systems aimed at improving the seismic performance of the building, such as steel braces and RC cores. • The effectiveness of the retrofit strategy is finally investigated through nonlinear static and dynamic analyses. The maximum load factor in pushover analysis is much greater than one for all the column removal scenarios, showing the improvement in the progressive collapse static performance of the building. The results from nonlinear dynamic analyses show the effectiveness of the outrigger-belt truss system in reducing the dynamic response of the structure. The reduction in vertical displacement above the removed column ranges between 21 and 30%.
Finally, it should be highlighted that two general problems should be addressed when applying the outrigger-belt truss system. First, the top gravity truss redistributes the gravity loads after the colon loss, and this gives additional compressive forces in the adjacent columns that may fail because of buckling. Then, the columns above the removed column act as hangers, and this may cause tensile forces up to the strength of the connections. In the case study building, as well as in three of the selected scenarios, the strengthening of some column-to-beam connections at the upper stories is required to increase the tensile strength from the initial value of 153 kN to the final value of 320 kN.