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Advantage 1. Greatly save construction time. Construction is not affected by the season 2. Increase the use area of buildings, reduce construction waste and environmental pollution 3. Building materials can be reused, stimulating the development of other new building materials industries 4. Good seismic performance, easy to transform, flexible and convenient in use, bringing comfort and so on 5. High strength, lightweight, high safety and wealth of components, and lower building cost

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Steel Building Case Study For Challenges and Solutions

Steel Building Case Study for Challenges and Solutions reveals the dominance of steel structures due to their superior attributes, such as unparalleled strength, long-lasting durability, earthquake resistance, and unlimited design possibilities.

In recent years, steel structure buildings have occupied most of the market share in construction with their unique advantages, such as high strength, durability, earthquake resistance, and design flexibility. However, in the face of these wonderfully designed and individual buildings, engineers and architects must face various challenges and problems: structural design feasibility, resistance to natural disasters, sustainability, safety, maintenance, and the application of innovative technologies. To cope with these challenges, mature technology and experience are needed, and innovative ideas, tenacity, and a responsible attitude are needed.

Table of Contents

Question 1: Structural design and maintaining stability

Challenge: The structural design of steel structure buildings and maintaining their stability are essential and complex tasks. Only when the design is reasonable and the strength of the structure is ensured can the safety of the building be guaranteed. Since steel structure buildings have long spans and high heights, it is quite a challenge to ensure the stability of the building under any circumstances.

Solution: Use steel with reasonable properties. Especially for multi-story or high-rise super high-rise buildings, high-strength performance steel is one of the main methods to ensure the stability of the building. At the same time, designers must use advanced calculation and analysis tools to reasonably analyze and optimize the structure and conduct experimental simulations and tests to ensure the stability of the building under various external forces.

Steel Building Case Study: CCTV Headquarters

The China Central Television Headquarters has a unique shape. The two main buildings are connected into one from above, and the architectural shape is highly irregular. It even looks tilted from the outside, giving people the first impression of being “extremely unsafe.” The complex and difficult challenges the unique shape will bring to design and construction can be seen.

Solution : The structure looks tilted from the outside, but the core is vertical during the design. The designer used high-strength steel, and the suspended parts dispersed the stress through steel trusses, external keels, and diagonal tie rods to ensure the stability of the building structure. Stability. This is one of the successful cases of steel structure buildings overcoming their stability when designing and constructing super high-rise buildings.

Question 2: Wind and earthquake resistance

Challenge : Any building needs to have good wind and earthquake resistance. Wind and earthquakes easily affect High-rise steel structures due to their significant height and weight. Therefore, it is tough to ensure the safety of steel structure buildings under extreme climate conditions.

Solution : Dampers are an artifact to solve wind resistance problems in high-rise buildings and skyscrapers! The damper is typically a giant sphere weighing hundreds of tons that sits atop tall buildings to dampen vibrations caused by wind in the building. Another type is wind tunnel model testing, which can more accurately determine the impact of load on the structure, thereby providing designers with load analysis and reasonable design. In addition, advanced technologies in earthquake engineering and various anti-seismic measures can ensure buildings’ earthquake resistance and stability.

Steel Building Case Study: Canton Tower

Canton Tower is an iconic super high-rise building with a height of 600 meters, making it the tallest tower in China. Canton Tower, also known as Xiaomanyao, subverts the design principles of steel structure buildings that are thin at the top and thick at the bottom, with a downward center of gravity and symmetrical structure. The entire Canton Tower is significant at the top, small at the bottom, thin in the middle, and thick at the top. It is a massive challenge for design and construction.

Solution : Scientists designed a 12-meter-high model of the Canton Tower to scale and tested it by applying various external forces to optimize the design. A damper can be used as a fire water tank, preventing wind and undertaking fire-fighting tasks in the event of a fire.

Question 3: Environmental protection and sustainability

Challenge : Steel structure materials will produce a large amount of pollutants during the production process. Waste gas, wastewater, waste residue, etc., significantly impact the environment. The construction industry’s pursuit of green environmental protection and sustainability is an essential goal.

Solution : Improve steel production technology, strictly implement environmental protection management systems, and develop and use renewable resources and recycled steel applications. Extend the service life of steel structures.

Steel Building Case Study: The Sustainable Energy Center Building of the University of Nottingham

The Sustainable Energy Center Building of the University of Nottingham Ningbo, China, adopts the concept of “increasing revenue and reducing expenditure” to couple the application of low-carbon technologies to achieve near-zero carbon emissions in building operations. The building envelope adopts a double-layer curtain wall structure to improve the thermal insulation capacity of the glass curtain wall, effectively improve the indoor environment and reduce noise; it insists on giving priority to natural ventilation and energy conservation; it makes full use of solar photovoltaic and photothermal energy; and adopts ground source heat pump technology.

Question 4: Maintenance and Durability

Challenge : Due to the metallic properties of steel, steel structure buildings are highly susceptible to corrosion and aging caused by environmental influences. Regular maintenance can maintain its performance and appearance and extend the life of the building.

Solution : Reduce environmental impact by applying anti-corrosion measures, regular inspection, and maintenance.

Steel Building Case Study: Eiffel Tower

The world-famous Eiffel Tower has a life expectancy of 25 years, but it still stood 130 years ago. The main reason is that the tower is regularly maintained and repainted with high-quality anti-corrosion paint every seven years for maintenance. The Eiffel Tower demonstrates successful practices in steel building maintenance and durability.

In conclusion

The design and construction of steel buildings is a complex and challenging task. But people have been breaking all kinds of impossibilities, constantly carrying out technological innovation and reform, and creating fantastic steel structure buildings. Human beings are good at accepting challenges and providing various solutions, making seemingly impossible things a reality, and shaping the development trend of future architecture!

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Steel Frames: Design Studio Case Studies

The Design Studio Case Studies are presented so that the student may learn by analyzing precedent buildings that employ structural steel aesthetics and creative applications. The three buildings presented in this module have won AISC IDEAS Awards. They represent a wide variety of scales, materials, and tectonic expressions. The projects presented include a 7,500 S.F. house in Houston, TX; a 37,000 S.F. river park comlpex along the Mississippi River; and a 30,000 S.F. complex at Iowa State University that includes a conservatory and butterfly house. (2006) Download Steel Frames CR (137 MB) Steel Frames TR (72 MB) Steel Frames RG (118 MB) Steel Frames LC (75 MB)

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Failure case studies : steel structures

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Description

Creators/contributors, contents/summary.

• Preface Acknowledgments West Gate Bridge Collapse, 1970 University of Washington Stadium Collapse, 1987 Damage to Steel Moment-Resisting Frames during the Northridge Earthquake, 1994 Colorado State Route 470 Overpass Collapse, 2004 Pittsburgh Convention Center Expansion Joint Failure, 2007 I-35W Bridge Collapse, 2007 Elliot Lake Algo Centre Mall Collapse, 2012 Skagit River Bridge Collapse, 2013 Index.
• (source: Nielsen Book Data)

Design of Warren Truss Steel Footbridge (+PDF)

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This case study covers the following aspects:

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1. Introduction

2. Footbridge Design Specifications and Challenges

3. Eurocode Requirements

4. Case Study - Warren Truss Footbridge

1.Introduction

A footbridge or a pedestrian bridge has mainly a purpose that allows people to walk over the bridge. The aesthetic considering harmony with the surrounding environment is an important factor in this type of bridge. Since that, the shape of the bridge is getting slender and aesthetic. And also the footbridge generally has a narrow carriageway and lightweight itself. Those characteristics make a high possibility happen the vibration on the bridge. Especially, if the frequency of walking is equal to the natural frequency of the bridge, it makes resonance phenomena. This resonance phenomenon causes a higher amplitude of vibration, which can influence the safety of pedestrians.

2. Footbridge Design Specifics and Challenges

Let’s have a look at what makes footbridge design different from a road and rail bridge and what challenges the designer might have to face when designing a footbridge. In footbridge design, aesthetics and structure robustness could be one of the key points. At the same time, the designer needs to pay attention to the stability and the vibration of the bridge . It doesn’t mean unique to footbridges but those specific points can be encountered frequently when designers design a footbridge.

The aesthetic structure design of the footbridge is quite often developed in close cooperation with an architect. Architects have their ideas about the appearance and the visual impact of the bridge. Therefore, the shape of bridges might involve unusual or complicated geometry. The footbridge design allows for various selections of materials, so designers need to understand the properties and behavior of materials such as timber, aluminum, or glass.

In terms of structure robustness, when designers design footbridges, probably they want a footbridge to be lightweight. So, a footbridge is often designed as a slender airy structure. At the same time, we have to ensure that they have sufficient stiffness and strength to maintain their stability including wind effects and accidental situations. Therefore, a critical load combination may be different from those common at road bridges.

The stability is also related to dynamic response and vibration. It is not the main issue for a majority of short and medium-span road bridges, but it is an important factor in the design of footbridges. If the structure has a low natural frequency, it might lead to unstable lateral response and loss of stability. Also, it might lead to vibration which may cause discomfort to users.

3. Footbridge Design Specifications and Challenges

The Eurocode proposes various requirements regarding footbridge design. Requirements for the footbridge design can be found in:

• EN 1991-2:2003, Section 5
• EN 1991-1-4, Section 8.2
• EN 1991-1-7, Section 4.3
• EN 1992 (Concrete)
• EN 1993 (Steel)
• EN 1994 (Composite)
• EN 1996 (Timber)

Footbridges are subjected to different types of live loads. The same limit state principles apply to footbridges.

Static load models for the footbridges are made up of four elementary components called uniformly distributed load, concentrated load, service vehicle, and horizontal forces. These loads are combined into groups of loads. It is a similar concept as with road traffic.

The accidental loads are covered partially in the traffic loading code, EN 1991-2 and it also covered partially in the accidental actions, EN 1991-1-7. Since accidental loads can have fatal consequences, and strengthening the structure to resist them would be uneconomical so we need to take measures to avoid them. Therefore, collision forces on piers of footbridges are reduced because the piers are usually protected by barriers. Collision forces on the deck can be avoided through this accident load if we provide sufficient clearance which is in the UK and Ireland 5.7 meters. Furthermore, for the accidental presence of a vehicle on the bridge can be avoided if a permanent barrier is installed which prevents access of vehicles on the bridge.

Dynamic Loads can be found in section 5.7, EN 1991-2. Now, we will look at what differentiates footbridges from normal road bridges of short and medium span bridge that have the application of dynamic loads. There are two key points which we need to pay attention to:

The first key point is the natural frequency of the structure. Because if any of the natural frequencies are identical to the frequency due to dynamic forces applied to the structure, there is a risk of resonance which may lead to unacceptable vibration or even loss of stability.

The second key point is to pay attention to vibrations. The vibration from normal pedestrian traffic should not cause discomfort to users so that is why the code specifies a limit defined as an acceleration limit. Dynamic effects of walking pedestrians can be represented by a periodic force, and this force will have a typical frequency of between one and three hertz. In the horizontal direction, the effects of walking pedestrians would have a frequency between 0.5 and 1.5 hertz, and if there’s a group of joggers crossing the bridge, that may induce forces with a frequency of about three hertz; so we can see that this range says from 0.5 to 3 hertz would be a critical spectrum. Furthermore, if any of the natural frequencies of the structure is within this spectrum, there is a risk of issues related to the vibration or stability so specific models and detailed criteria on how to fulfill it and how to achieve that the structure is stable. They are defined in a nation annex or other national application document.

For the UK and Ireland, Eurocode 1 specifies the maximum vertical deck acceleration which has a limiting serviceability value in the range between 0.5 and 2 m/s 2 . The exact limit value is calculated based on a formula in the code and it depends on the site usage route redundancy and structure height. Single pedestrian or a pedestrian group load is represented by the application of vertical pulsating force which moves across the span of the bridge. The pulsating force can be calculated via the formula shown in figure 7. The formula has various parameters.

The footbridges for the purpose of dynamic loading are split into four classes depending on the location and usage. The dynamic force is applied, and also we should know that the pedestrian speed crossing. It is also defined which helps us to define the duration of dynamic loading.

The other aspect of dynamic loading would be loading crowded conditions so if a bridge is located in the city center or close to a stadium, it may get into the crowded state instead of using a point single force pulsating and moving across the bridge. The dynamic loading is modeled by a vertical pulsating distributed load.

That helps us to assess the possible vibration issue and the other requirement regarding the natural frequencies. If there are no significant lateral modes with frequencies below 1.5 hertz. We may assume that the structure is stable. It means there is no risk of lateral instability. If any of the critical frequencies are lower than 1.5 hertz then there are additional checks to perform or to introduce some dumping devices or we may redesign the structure.

Apart from the dynamic effects of pedestrians, in certain situations, we may need to investigate the dynamic effects of wind loading. The Eurocode dealing with the wind loading also provides general guidance. It says that dynamic magnification effects due to vertical response can be ignored if fundamental frequencies in bending and torsion are greater than 1 hertz or we may need to fulfill alternative conditions, taking into account that generally we want to avoid frequencies below 1.5 or even 3 hertz. It means that for most bridges where we fulfill the condition for the pedestrian dynamic load. We are fulfilling the condition for the wind loading as well. But for the long span or special structures, it is something which needs to be taken into account.

4. Case Study – Warren Truss Footbridge

The bridge of the case study has a span of 50 meters, a clear internal width of 3 meters, and a maximum structure depth in the mid-span of 4.2 meters. Both top and bottom chords of the truss are curved in the gentle radius to improve the appearance although in this particular case the aesthetics weren’t the governing factor for the design because of the rural location of the bridge with a low flow of pedestrians. The design of this footbridge was actually developed as a result of a value engineering exercise or a value engineering proposal because the original structure was a two spans slab beam bridge. We proposed a single-span structure to avoid placing support in the center median of the motorway.

And the truss works well for this arrangement. We can focus on how this particle structure or generally truss can be generated in midas Civil. How we can generate a model in relation to what we discussed in the Eurocode requirements for dynamic response and natural frequencies. We will look into stability and dynamic response and again how this can be performed in midas Civil. Then global static analysis member verification and the generation of the design report.

4.1 Model generation – Geometry

A model can be defined by using functions related to modeling manually. midas Civil provides various options to model. The user can use the ‘Truss Wizard’ function to model truss shape elements directly. If there is a CAD file, it can be imported to midas Civil.

4.2 Model generation – Structure’s properties

The member sections and material properties are selected in the database of midas Civil. The user doesn’t need to define additional properties if there is desired property in the database. The bearings of the bridge are modeled via the Elastic Links function.

In the bridge model, dummy beam elements are created to apply pedestrian dynamic loads. In order to perform the dynamic analysis in midas Civil, the user needs to set some options regarding the mass of a structure. Those options are called ‘Convert Self-weight into Masses’ and ‘Loads to Masses’.

4.3 Stability and Dynamic Response

There are two key parts. One is the analysis to obtain a natural frequency and the other is the dynamic analysis to obtain a dynamic response. To investigate the natural frequencies of the structure in midas Civil, the user need to turn the ‘Eigenvalue Analysis Control’ function. Here, we can select the analysis type, the number of frequencies, and so on. 

The output from the eigenvalue analysis can be either numerical like in this example. For each mode, we can see the actual frequency. For example, the mode 1 in the figure has a frequency of 1.68 which is actually close to 1.5 hertz but we can notice that it is vibrating in the longitudinal axis of the bridge for the modal participation masses. So it is not critical. The second mode has a frequency of 2.53 hertz and it’s vibrating in the y-axis so it is a lateral transverse vibration. And the third mode has 3.47 in the z-axis so it is an actual vertical vibration.

Figure 16: Result table of the eigenvalue analysis

For the assessment of the dynamic response, we want to prove that the vertical deck acceleration is within the limits set in the code so that any vibration is not causing any discomfort to the users. The general principles are to calculate values of pulsating force at defined time increments and to apply the force onto series of nodes along the bridge span. midas Civil provides several functions regarding the time history analysis. The procedure to apply the time history load case in midas Civil:

1. Create a time history load case.

2. Generate a time history function.

3. Apply dynamic nodal loads on the structure.

In the time history load case function, the user can specify the duration of the load, time increments, and damping. And to define a time history function, the user can input values directly. In this case, bridge designed, walking load is only applied because it’s in a rural condition and there wasn’t a requirement for joggers. If we have a structure in an urban environment or a specific requirement, we might need to define two load functions for walking and jogging.

Figure 18: Time History Load Case and Functions 

And then, this pulsating force defined in the time history function is applied to selected nodes on the structures via the Dynamic Nodal Loads function.

After the analysis, we can review the acceleration, forces, or displacements at any point in graphical form or numerical form. But the problem is if our time increments are hundreds per second. It means a lot of numbers to review. So it is not practical to look at results in this way. There is a function in midas Civil to allow the user to create an envelope of results for any selected point on the structure. The figure shows the dynamic acceleration results of the warren truss footbridge. The peak acceleration is 0.036 m/s 2 is much smaller than the limiting value in the code, 0.5 m/s 2 . It is due to the low pedestrian loading. The peak acceleration is close to the middle of the time period. It says that the maximum acceleration would be at time 16 seconds and the minimum acceleration would be 14 seconds. It makes sense because the pedestrian is right in the middle of the bridge so it has the greatest effect on the vibration.  

4.4 Global Static Analysis

The global static analysis is performed the same way as any other structure. Deformation, reactions, stress results, and force diagrams have been checked. Review of deformation is usually the first step after analysis to verify the correct behavior of the model. And we can decide whether pre-chamber is necessary or not through checking deflection from permanent loads.

Figure 23: Member stress results

4.5 Member Verification

Member verification is defined as a set of checks and it is the most time-consuming. Even in-house prepared design spreadsheets save time but we still need to identify critical members and manually transfer results from the structural model. midas Civil has a set of member design features to simplify this task.

midas Civil provides steel design features for Eurocode 3, section 6. There are 3 ways to obtain verification results. Results table as shown figure 25 shows the design results for the selected members. These results can be checked as a graphic view or text format.

Figure 25: Member force results

Figure 26: Member force results

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Martin has over 15 years of experience in structural bridge design and is a Chartered Engineer at Barry Transportation. He has worked mostly with concrete bridges, but also worked on a number of steel and composite structures over the course of his career. Some of his most notable projects include the D3 Motorway, R48 Expressway, and I/11 in the Czech Republic, D3 Motorway in Slovakia, A5 Nothern Ireland, and Aa737 in the UK, and M3 Motorway, N9/N10, and M17/M18 in Ireland. 

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Topics MIDAS CIVIL Bridge Design Eurocode Case Study Steel Bridges Accidental Loads

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Failure Case Studies: Steel Structures

Prepared by the Education Committee of the Forensic Engineering Division of the American Society of Civil Engineers, this book provides case studies of failures observed in steel structures between 1970 and 2013. Designed to promote learning from failures by disseminating information regarding previous failure cases, each case study is comprised of a summary description of a documented civil engineering failure followed by lessons learned from the failure and references for further study. Case studies include West Gate bridge collapse, University of Washington stadium collapse, Damage to steel moment resisting frames during the Northridge Earthquake, Colorado State Route 470 overpass collapse, Pittsburgh Convention Center expansion joint failure, I-35W bridge collapse, Elliot Lake Algo mall collapse, and Skagit River Bridge collapse. This book supplies a summary of the published findings from eight steel structure failure investigations and a valuable collection of references that can be used by civil engineering students and practicing engineers to improve their failure literacy. Engineering professors and students can use these case studies as the basis for class discussions, a starting point for further research, and a reminder that learning from past failures can avoid similar failures in the future and lead to improved engineering practices. Practicing engineers can use the book as a continuing education resource to improve their practice and to avoid similar failures.

• Record URL: https://doi.org/10.1061/9780784415306
• Find a library where document is available. Order URL: http://worldcat.org/isbn/9780784482209
• © 2019 American Society of Civil Engineers.

American Society of Civil Engineers

• Publication Date: 2019-8
• Media Type: Web

Subject/Index Terms

• TRT Terms: Bridges ; Case studies ; Civil engineering ; Collapse ; Expansion joints ; Failure analysis ; Overpasses ; Steel structures ; Structural analysis
• Subject Areas: Bridges and other structures; Highways; Maintenance and Preservation; Materials;

Filing Info

• Accession Number: 01730622
• Record Type: Publication
• ISBN: 9780784482209
• Files: TRIS, ASCE
• Created Date: Feb 7 2020 9:39AM

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Case studies on residential buildings using steel

Publication 328.

Document Status

Civil & Structural Supplement

Publication

Provides information on using steel for residential buildings with details obtained from 12 case studies of recent projects, covering issues of efficiency, adaptability and high quality. This document aims to meet the constraints of construction in inner city locations as well as the demands of the multi-storey residential sector. It encompasses a wide range of steel technologies, including a 'mix' of technologies to achieve optimised design and better value in steel. The steel technologies covered by the case studies are: Light Steel Framing Modular Construction Slimdek and Slimflor Composite Construction.

Lawson, R. M.

Case studies included: 1. Glasgow miles better for Slimdek. 2. High quality apartments using Slimdek at Portishead Marina. 3. Slimdek proves its colours at Harlequin court, Covent Garden. 4. Britain's tallest residential/commercial development in Manchester. 5. Leeds Nuffield hospital uses steel-intensive construction. 6. World's largest modular/steel framed building in Manchester. 7. Raines court creates affordable housing in North London. 8. Six-storey housing using light steel framing and bathroom modules. 9. Twenty-storey tower block is transformed using light steel framing. 10. Quality apartments using new Metframe flooring system. 11. Major affordable private housing project underway in Basingstoke. 12. Light steel framing for Heathrow hotel.

• Steel building systems/frame
• Building structure
• Building types
• Housing/residential facilities
• Building systems/frame

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With over 30 years experience, the Steel Construction Institute provide technical expertise and best practice to the steel construction sector.

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

Associated data.

The data used in this study to support presented findings are included within the article.

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

1. Introduction

Industrial single-storey buildings represent the majority of existing steel constructions located in Italy [ 1 ]. This kind of structural type mainly spread during the second half of the 20th century due to its capability of covering relatively large spans without recurring to complex technological solutions, and with affordable costs [ 2 ].

Hence, most Italian industrial steel buildings realised between the 1980s–1990s were designed in compliance with the CNR 10,011 [ 3 ] code, and, in particular, the vertical and the wind actions were accounted for as prescribed by CS.LL.PP. n. 56 and n. 140, respectively [ 4 , 5 ]. Only in 1986, the document Decreto Ministeriale 24 January 1986 [ 6 ] introduced the equivalent static forces to account for the seismic action. However, this code did not provide adequate instructions to ensure a satisfactory seismic performance, since it does not provide adequate prescription for the design of the local detailing. For instance, in the design of connections, no distinctions were made between ductile and brittle mechanisms. Moreover, as highlighted by [ 7 , 8 ], the lack of prescriptions for joints characterization often led to non-conservative design assumptions (e.g., in case of base connections).

Inadequate technical practices were also fostered by the common idea that seismic action could not govern design choices for industrial single-storey buildings, owing to their relatively low mass with respect to enclosed surfaces [ 2 ], similarly with what was observed for moment-resisting frames equipped with truss beams [ 9 , 10 ].

However, the occurrence of multiple seismic events, e.g., Friuli (1976), L’Aquila (2009), and Emilia (2012) earthquakes, proved the incorrectness of this belief, as several industrial buildings reported moderate-to-severe damages, with some relevant cases of global collapse also [ 11 ].

Differently from residential buildings, an important aspect that should be accounted for when dealing with industrial constructions is represented by indirect costs, i.e., expenses due to interruption of the productive activities for long time [ 12 ]. Namely, on most occasions, seismic damage to Italian industrial steel buildings consisted of local failures of connections, claddings, and/or roofing [ 7 ], though a few notable cases of global collapse occurred as well [ 13 ].

In light of these events, the interest in assessing and enhancing the seismic performance of steel structures [ 14 , 15 , 16 , 17 , 18 ] and, in particular, the industrial single-storey buildings has quickly developed up to present time. In particular, crucial attention is currently paid to the design of low-impact retrofitting interventions which simultaneously minimise time needed to resume productive activities and effectively prevent not only structural damage, but also damage on industrial machineries [ 19 ]. It is worth reporting that some contributions aiming at investigating the efficiency of low-impact retrofitting strategies on industrial buildings are already available in the literature. Formisano et al. [ 19 ] investigated the efficiency of global retrofitting interventions on an industrial steel structure located in Italy. The authors proved the effectiveness of concentrically braced frames (CBFs) with both X-shaped and portal (i.e., double Y-shaped) configurations in enhancing both strength and stiffness of the structure without preventing building accessibility. Hirde et al. [ 20 ] inspected the effectiveness of two retrofit strategies for a damaged industrial steel building located in India. Namely, a first low-impact seismic enhancement was achieved by welding new angle profiles to existing structural members (i.e., back-to-back). The authors investigated a more invasive solution involving the introduction of new truss beams below the existing load-bearing gables. Although being highly effective in improving both resistance and lateral stiffness of the structure, it should be remarked that this intervention was only feasible since no requirements about the minimum net height of the industrial building had to be fulfilled. Finally, Bournas et al. [ 21 ] analysed damages in industrial buildings (both with steel and precast RC structure) affected by the Emilia earthquake. On the basis of detected criticalities, the authors suggested that local interventions on beam-to-column joints and claddings connections could highly improve the performance of industrial buildings in seismic zones. The authors also highlighted the current absence of normative guidelines for the design and check of this kind of intervention.

Within this framework, the aim of this work is to design and check the effectiveness of low-impact retrofit interventions to increase the industrial building capacity against lateral action, without interrupting the building functionality. Indeed, this work is part of a wider Italian research project (Reluis WP5 [ 22 ]) aiming at verifying the validity of low-impact strategies for the seismic retrofitting of existing non-code-conforming buildings.

For this purpose, an existing single-storey steel building located in Nusco (Italy) is selected as a case-study; the structure was designed and erected during the 90 s in compliance with normative provisions enforced at the time [ 3 ].

Preliminary Finite Element Analyses (FEAs) on the selected case-study showed how the existing structure is rather deformable in both the principal directions, and unable to properly resist seismic actions. Therefore, both local and global retrofitting interventions were designed and verified by means of refined numerical models.

Indeed, one of the main aims of this paper is to underline the importance of the local behaviour of the steel joints in the assessment of existing structures, and how their performance should be accounted for also in the global analyses, since they could affect not only the local resistance, but also the lateral stiffness of the whole structure.

The paper is mainly divided into five sections: in the first part, the main features of the investigated case-study are presented. Concept and design procedures for low-impact seismic retrofit interventions are discussed in the second section, whereas in the third part, the main finite element (FE) modelling assumptions are summarised. The global and local seismic performance of the existing structure is presented in the fourth section, and finally, the efficiency of designed retrofit solutions is discussed in the last part.

1.1. General Description of the Structure of the Selected Case-Study

The selected case-study is a single-storey industrial steel building that serves as a warehouse for an adjacent building in which aluminium products are manufactured. The dynamic response of the investigated structure, which was built later with respect to the production unit (i.e., between 1992 and 1999), was decoupled from the main building by means of a seismic joint.

Original design report and drawings, as well as on-site surveys, allowed the complete characterization of geometrical features of the selected building (see Figure 1 ).

Geometrical features of the selected building according to the original design report.

The structure has a rectangular plan extending for 55.5 m in the longitudinal direction, and for 36 m in the transversal one; the total height of the building is equal to 12.7 m (see Figure 2 ).

Geometrical features of the selected case-study and disposition of resisting systems in both directions.

Truss frames are used in X- and Y-directions to resist both gravity loads and horizontal actions. Both top and bottom chords are connected to the supporting columns, which are continuous in correspondence of the connections, thus creating a moment-resisting frame. Namely, three moment-resisting frames (MRFs) were placed in both X- and Y-directions, spaced out by intermediate connecting trusses (see Figure 2 ).

Columns belonging to MRFs were made by means of welded hollow members; on the contrary, hot-rolled profiles (i.e., IPE 360 and HE 300B) were adopted for the claddings support system. Notably, all hollow columns are oriented with their strong axis being parallel to the Y-direction.

Coupled angle members having different cross-sections were adopted for seismic-resistant trusses, whereas both single and coupled angles were used for connecting trusses.

The truss members are connected to each other and with columns by means of gusset plates placed within the gaps of back-to-back profiles, which are, in turn, bolted (in X-direction) or welded (in Y-direction) to column ends. Base connections were realised with extended stiffened plates in both directions.

According to the original design report, S235 grade steel was used for all members and plates, whereas 6.8 strength class bolts were adopted for the connections.

In light of the retrieved information, the highest level of knowledge (“KL3”—exhaustive knowledge) was attained for the selected case-study according to Italian provisions for existing buildings [ 23 , 24 ]. Hence, characteristic values of material properties were used for seismic analyses accounting for no reduction (i.e., a partial safety factor FC = 1 is assumed in [ 23 , 24 ] for KL3).

1.2. Description of Investigated Connections

The main geometrical features of moment-resisting connections between truss members and columns are depicted in Figure 3 . Owing to the constant orientation of all hollow columns, two different joint configurations were adopted in the X- and Y-direction.

Details of truss-to-column connections adopted for MRFs: ( a ) X-direction and ( b ) Y-direction.

A T-shaped 20 mm gusset plate is used to connect both the upper chord and the diagonal to the column (see Figure 3 a) in the X-direction. Seven staggered M24 bolts are used for the upper coupled angles (2-Ls 150 mm × 150 mm × 14 mm), whereas four in-line M24 bolts are adopted for the coupled diagonals (2-Ls 90 mm × 90 mm × 9 mm). The gusset plate terminates with an end-plate, which is, in turn, bolted to the column flange (350 mm × 20 mm, welded to two 460 mm × 8 mm webs) by means of seven rows of M24 bolts. Moreover, the connection is further stiffened by means of two trapezoidal 20 mm ribs, placed at the base of the gusset plate.

Contrariwise, a simpler configuration is adopted for the lower connection. Indeed, coupled members of the lower chord (2-Ls 120 mm × 120 mm × 13 mm) are connected with a single row of M18 bolts to a 20 mm saddle plate, which is welded to the column flange.

Slightly different solutions were adopted in the Y-direction due to the presence of the column web. Namely, the upper 20 mm gusset plate is directly welded to the web, which is locally stiffened by means of two 20 mm continuity plates (CPs).

Notably, the same kind and number of bolts used in the X-direction are adopted to connect the diagonal (2-Ls 130 mm × 130 mm × 16 mm) to the gusset plate, in spite of the different profiles employed, whereas only six M24 staggered bolts are used in this case to connect the upper chord (2-Ls 200 mm × 200 mm × 20 mm). Finally, the lower connection is almost identical to the X-direction one, aside from the 20 mm saddle plate being welded to both column web and flanges. Moreover, in this case, a single row of M18 bolts is used to connect coupled profiles of the lower chord to the saddle (2-Ls 180 mm × 180 mm × 18 mm).

2. Design Philosophy of Retrofit Interventions

The selected case-study shows poor seismic behaviour due to excessive lateral deformability and inadequacy of adopted structural details. Indeed, the preliminary analyses performed on a simplified model resulted in a very large first vibration period (T 1 = 2.08 s, flexural mode in the Y-direction) and torsional deformability. Moreover, the moment-resisting (MR) joints in both X- and Y-directions showed local shortages in terms of elastic stiffness, resistance, and ductility, as will be shown in the next Sections.

The existing structural lateral deformability was checked in case of both seismic and wind actions at service limit sates (SLS) in accordance with the limitations provided by EN1998:1 [ 25 ] and EN1993:1-1 [ 26 ], respectively. Namely, for the seismic Damage Limitation (DL, return period of 50 years) limit state, a maximum lateral displacement capacity equal to 1/200 (0.5%) of the building height was assumed in compliance with EN1998:1 [ 25 ]. Contrariwise, wind loads, which were defined considering a rare load combination, were checked in terms of maximum lateral displacements at the top of the columns. For this purpose, a maximum displacement capacity equal to 1/300 of the column’s height was considered in compliance with EN1993:1-1 [ 26 ] prescriptions.

Both local and global retrofit interventions had to be designed for the investigated case-study; among the different possibilities [ 27 , 28 , 29 , 30 ], non-invasive retrofit interventions were conceived and designed in order to achieve a satisfactory seismic performance of the building without interrupting the productive activities.

Therefore, as will be presented in the next Section, concentric braced frames (CBFs) were introduced on the external perimeter of the existing building; moreover, the local performance of the MR joints was investigated by means of FEAs, and retrofit interventions were properly designed.

2.1. Design of Global Retrofitting Interventions

The design of global strengthening for the selected case-study was performed aiming at a full retrofit against seismic actions and wind loads.

Thus, the interventions were designed based on combined results from global and local FEAs. A first global assessment of the existing structure behaviour was conducted by means of static non-linear analyses; hence, pushover curves were simplified according to the N2 method [ 31 ], which allows deriving bi-linear equivalent force-displacement curves. Thus, the smooth pushover curves were converted into equivalent curves by equating the ultimate displacements (i.e., displacements corresponding to 80% of the maximum base shear measured on the degrading branch of the curves) and the areas underneath the force-displacement curves. According to EN1998:3—Annex B [ 31 ] prescriptions, the bi-linear pushover curves were interrupted when the maximum allowable plastic rotation was reached in the most stressed plastic hinge.

The structural capacity was compared with the seismic demand at significant damage (SD) limit state (LS), transposing the bi-linear curves into an Accelerations–Displacements Response Spectrum (ADRS) domain. Therefore, the seismic demand on the structure, i.e., the so-called “performance point” (PP), was conventionally derived (see Figure 4 , red hollow circle).

Graphical interpretation in ADRS domain for the design procedure of global retrofitting interventions.

This procedure allows to assess the structural ductile capacity, disregarding brittle failure mechanisms (e.g., brittle bolts’ shear failure) that should be subsequently assessed. The second step involved the assessment of the local behaviour of the MR joints; in particular, as introduced in Section 3 , a shortage was observed in the bottom part of the external MR joints. The real joints’ behaviour was investigated by means of both an analytical method and a refined finite element model; finally, its behaviour was accounted for in a new set of global analyses by introducing non-linear links in correspondence of the MR joints.

The global retrofit intervention was ensured increasing the existing structure lateral stiffness and resistance; thus, the required stiffness increment was derived assuming the occurrence of ductile failure of the structure at the intersection with elastic response spectrum (ERS) as follows:

where Δ K CBFs is the minimum lateral stiffness increment to be provided by new CBFs; M TOT is the total seismic mass of the structure; S a,ERS ( δ Cd,SD ) is the spectral pseudo-acceleration derived from the ERS for a spectral displacement equal to the δ Cd,SD , i.e., the spectral displacement corresponding to ductile failure of the existing structure; and K ex is the lateral stiffness of the existing structure.

Fulfilment of Equation (1) ensures that PP is compatible with the seismic response of the retrofitted structure provided that brittle failures are prevented. This additional requirement was achieved by means of local retrofit interventions, which will be discussed in detail in the following subsection.

The retrofit intervention was designed not only to satisfy seismic requirements, but also to verify the structural deformability against wind loads. Therefore, the minimum increase of lateral stiffness also accounted for lateral deformation limits introduced by EN1993:1-1 [ 26 ]. Namely, according to [ 26 ], maximum lateral displacements due to the wind loads should be smaller than 1/300 of the element’s length.

In order to account for both seismic and wind lateral stiffness requirements, Equation (1) becomes:

With F w,Ed being the design wind action acting in a given direction, and H c being the height of welded hollow columns.

It should be remarked that design criteria provided by Equations (1) and (2) hold true under the assumption of an in-plane rigid storey, which was granted by the presence of roof braces.

Finally, after determining minimum cross sections of braces accordingly, resistance and stability checks were performed on new CBFs for gravity, seismic, and wind load combinations as follows:

where N Ed,g,i , N Ed,E,i , N Ed,w,i are the design axial forces in new CBF members due to gravity, seismic, and wind actions, respectively, whereas N b,Rd,i , N pl,Rd,i are the design buckling and plastic resistances of the same members, respectively. For the sake of clarity, in Equations (3)–(5), the superscript “−” is related to compressive axial forces, whereas the superscript “+” is adopted for tensile axial forces.

Four X-shaped CBFs were placed along the Y-direction, according to design criteria reported in Equations (2)–(5), and CHS profiles (193.7 mm × 10 mm) were adopted. On the other hand, to minimise the footprint of new resisting systems, and to guarantee the passage of industrial machines as forklifts, two portal CBFs placed beside the facades were conceived in the X-direction. For this purpose, CHS profiles (244.5 mm × 20 mm and 244.5 mm × 16 mm) were properly selected according to the design criterion provided by Equation (1), and, hence, checked in terms of stability and resistance according to Equations (3)–(5) (see Figure 5 ).

Description of adopted global retrofitting interventions.

It should be noted that the CBFs in both directions were designed in compliance with the last draft of the prEN1998-1-2 [ 32 ], currently under revision. According to [ 32 ], in the design of X-CBF, both tension and compression members of bracing systems should be considered in structural analysis, at the price of checking the possible occurrence of global instability phenomena under design compressive forces. This approach allowed a more appropriate evaluation of the actual lateral stiffness of the retrofitted building with respect to the only-tension members’ approach. However, the introduction of CBFs on the external perimeter of the existing structure implies an increase of the actions transferred to the foundation system; moreover, it should be noted that this type of intervention enables to increase both the lateral stiffness and the resistance of the existing structure, but it does not allow to increase its ultimate displacement capacity.

2.2. Design of Local Retrofitting Solutions

The design of local retrofitting solutions was performed in order to prevent local and premature brittle failures. For this purpose, multiple local collapse mechanisms were considered for MR truss connections in both directions (see Figure 6 a), namely:

Considered failure mechanisms in MR truss connections for the design of local retrofitting interventions and assumed schemes for the estimation of resistance ( a ): column hinging ( b ) and web punching ( c ).

• Bolted connections shear resistance F con,Rd,i (due to bolt shearing, plate bearing, or net-area failure depending on the i -th connection configuration);
• Truss members axial resistance N truss,Rd,i (due to yielding in tension or buckling in compression depending on the considered i -th truss member);
• Column web panel (CWP) resistance V cwp,Rd,i (due to web shearing or column hinging);
• Upper connection resistance for other local mechanisms F up,Rd,i (due to T-stub opening in X-direction or web punching in Y-direction).

The design resistance of bolted connections was evaluated according to prescriptions from EN1993:1-8 [ 33 ], whereas usual formulations provided by EN1993:1-1 [ 26 ] were used to calculate the axial resistance of truss members and shear resistance of the column.

With regards to the column hinging mechanism, the equivalent resistance of the column was assumed equal to the shear force transmitted by the hollow profile in correspondence of the formation of two plastic hinges, i.e., at the column base and alongside the lower chord connection (see Figure 6 b):

where M pl,Rd,i is the plastic bending resistance of the column with respect to the i -th inflection axis, and d is the distance between centroids of the upper and the lower chord.

The T-stub opening mechanism in the X-direction was modelled according to provisions from [ 26 ], accounting for all possible failure modes (i.e., mode 1—pure plate yielding, mode 2—plate yielding + bolts tension failure, mode 3—pure bolts tension failure).

With regards to web punching in the Y-direction, the resistance was estimated regarding the column web segment within the two CPs as a doubly-restrained plate subjected to a line load simulating the gusset plate contact force (see Figure 6 c):

with t w and b w being the column web thickness and width, respectively, and h gp being the gusset plate height.

The design of local retrofitting interventions was, hence, performed in order to achieve the hierarchy between ductile and brittle mechanisms for each considered connection. Namely, undesirable failure modes, such as bolts shearing, bolts tension failure, trusses net-area failure, or T-stub mode 3 collapse, were prevented by introducing new strengthening elements and/or improving existing connections with the aid of new high-strength bolts.

From analytical calculations, lower chord connections in both the X- and Y-direction resulted in the weakest component for existing MR truss joints, with a shear capacity equal to 183 kN. The corresponding maximum base shear V b,R , which can be approximately estimated using the a simplified structural scheme (i.e., similar to the one in Figure 6 b), resulted equal to 74 kN.

Hence, local retrofit solutions were designed in order to obtain a stronger connection with a shear resistance larger than the axial capacity of the connected truss elements. Therefore, the retrofit solution involving the introduction of four 150 mm × 10 mm rib stiffeners was conceived for both directions, in order to: (i) increase connection stiffness, and (ii) increase the number of shear plans (from one to two). High-strength 10.9 pre-loaded M20 bolts were used in place of existing bolts. Moreover, new Φ 21 holes were drilled in lower chord profiles to place two additional bolt rows in both directions (see Figure 7 ). The shear resistance of new connection results equal to 2 times the buckling resistance of the trusses element in the X-direction (2262 kN and 888 kN, respectively), whereas it results slightly higher than the buckling resistance of the trusses element in the Y-direction (2262 kN and 2222 kN, respectively).

Local retrofit solutions on MR joints in both X- ( a ) and Y-directions ( b ).

3. Main Modelling Assumptions

3.1. global modelling of the structure.

Two global finite element models (FEMs) of the entire structure were developed using Seismostruct 2022 [ 34 ] (see Figure 8 ). The first model was built in order to perform the global structural assessment of the industrial building disregarding the presence of the connections; thus, wire elements were adopted for beams and columns, modelled in correspondence of centroidal axes of steel profiles. The presence of horizontal X-braces, which ensure in-plane rigidity of the roof, was accounted for by means of a diaphragm constraint. Foundations and relative base connections were modelled by means of equivalent restraints; namely, the extended stiffened base plates allowed to model column-foundation connections as fixed restraints in both the X- and Y-direction. Connections among truss elements, which can be regarded as internal hinges, were modelled by means of local releases. In order to correctly account for the flexural continuity of both lower and upper chords, no releases were introduced in such elements.

Global model main features: ( a ) Existing and ( b ) Retrofitted structure.

Non-linear behaviour of the investigated members was accounted for by the introduction of lumped plastic hinges, which were defined according to prescriptions from ASCE-13 [ 35 ]. Namely, N-M x -M y plastic hinges were adopted for the columns, i.e., at the base and in correspondence of the lower chord connection, in order to account for flexural response of hollow columns in both directions in presence of axial forces. On the other hand, non-symmetric axial hinges were introduced in truss elements to model both steel yielding in tension and possible global instability phenomena in compression.

The second global model was formally identical to the previous one, with the only exception of non-linear links, which were placed in correspondence of truss-to-column intersections to account for the local response of bolted connections. As will be shown in the next Section, the behaviour of links was calibrated against the results of local FEAs.

According to the original design report, the yielding strength f y of existing members was set equal to 235 N/mm 2 , whereas European S355 steel grade ( f y = 355 N/mm 2 ) was used for retrofitting interventions.

The presence of non-structural elements was accounted by means of equivalent area loads. Namely, a uniform load g 2 k , r = 1.6 kN/m 2 was assumed for the roofing system (i.e., composed by steel sheeting + isolating layer + ballast), whereas a unitary weight g 2 k , c = 0.1 kN/m 2 was considered for lightweight claddings. Moreover, live loads due to snow ( q sk ) and roof maintenance ( q rm ) were also introduced according to Italian normative provisions in force [ 23 , 24 ]. In particular, q sk = 3.1 kN/m 2 was considered, owing to the high altitude of the construction site (≈1000 m a.s.l.), whereas q rm was set equal to 0.5 kN/m 2 .

Static non-linear analyses (SNLAs) were performed on global FEMs according to prescriptions from EN1998:3 [ 31 ]. Namely, a maximum inter-storey drift (ISD) equal to 6% was imposed in both directions, assuming the roof centre of masses as the control point.

3.2. Local Modelling of the Truss MR Joints

Refined FEMs of truss MR joints were developed using ABAQUS 6.13 [ 36 ]. FEAs were performed considering a sub-assemblage of the whole structure, which is obtained by extracting the truss in correspondence of the inflection point of axial force diagrams in the chords under horizontal actions, i.e., at the chord midspan. Structural continuity was, hence, restored by means of proper boundary conditions (see Figure 9 a).

Local FEMs main features: ( a ) Abaqus local Modelling and ( b ) Sesimostruct local Modelling (Sub-assemblies).

In order to simulate the structural response of the truss MR frame under lateral loads, both monotonic and cyclic horizontal displacement histories were applied at the chord ends. Namely, a peak ISD equal to 6% was reached in monotonic FEAs, whereas AISC 341 loading protocol [ 37 ] was used for cyclic analyses, with a maximum ISD equal to 4%.

In order to balance computational effort with analyses accuracy, only the upper end of the column, the connections, and the ends of truss members were modelled by means of solid elements, whereas wire elements were adopted for all other parts. Therefore, rigid MPC constraints were introduced at the interface among wire and solid instances.

Experimental tests were not conducted on the investigated MR truss joints; therefore, the numerical modelling assumptions were set consistently with the ones adopted by the authors in previous research [ 38 , 39 ], and validated against experimental tests on beam-to-column steel joints. In particular, all solid parts were discretised using C3D8R solid element type (i.e., 8-node linear brick, reduced integration), whereas B31 beam elements (i.e., 2-node linear beams) were adopted for wire parts. The mesh density was defined on the basis of results from sensitivity analyses reported in [ 40 , 41 ]. In particular, a mesh size equal to 20 mm was set for beams and columns, whereas bolts and plates were discretised by means of a 5 mm mesh, with at least two elements through the thickness.

The Von Mises criterion was used to model steel yielding, and both kinematic and isotropic hardening were accounted for by means of material parameters provided by [ 42 ].

In compliance with global FEMs, yielding strength of existing profiles and plates was set equal to 235 N/mm 2 , whereas yielding f yb and ultimate tensile strength f tb of 6.8 class bolts were assumed equal to 480 and 600 N/mm 2 , respectively. With regards to stiffening elements, f y = 355 N/mm 2 was considered. Moreover, 10.9 class high-strength bolts were adopted for the seismic retrofit ( f yb = 900 N/mm 2 , f tb = 1000 N/mm 2 ).

Bolt clamping was simulated by means of the “Bolt Load” command. In order to account for the long service life and the absence of a controlled pre-loading, a low clamping stress equal to 0.35 f tb was considered for existing bolts. Contrariwise, a clamping stress equal to 0.7 f tb was adopted for new high-strength bolts according to provisions from EN1993:1-8 [ 33 ].

“Surface-to-Surface” interactions were introduced to model contact among the elements. Namely, a “Hard contact” formulation was used for normal contact behaviour, whereas a “Penalty” formulation was considered for tangential behaviour, with the friction coefficient being equal to 0.3. Finally, continuity among welded parts was modelled by means of “Tie” constraints.

As anticipated, the local FEAs results will be directly accounted for in the global analyses of the whole industrial building by the introduction of non-linear links placed in lower part of the MR truss joints. Figure 9 b depicts the local Seismostruct [ 34 ] model having the same geometrical and mechanical features of the ABAQUS model, adopted for the calibration of the non-linear links.

A multilinear curve [ 34 ] was adopted for modelling the non-linear links behaviour under both monotonic and cyclic actions.

4. Performance of the Existing Structure

4.1. global assessment.

The existing building is located in Nusco (Italy), with a peak ground acceleration (PGA) equal to 0.238 g; a soil topography class “T1” and the stratigraphy class “C” were used according to geotechnical considerations drawn from the original design report.

According to both Italian and European codes [ 23 , 24 , 25 ], the seismic performance of the existing building at significant damage (SD) limit state (LS) was investigated by means of static non-linear (pushover) analyses (SNLA) (see Figure 10 a).

Static non-linear analyses (SLNA) of the existing building in both X- and Y-directions: ( a ) pushover curves and ( b ) ADRS domain checks.

The pushover curves were approximated with equivalent elastic-plastic bi-linear curves, which were imported in the ADRS plan in conjunction with elastic response spectrum (ERS), defined through site-dependent seismic hazard maps adopted by Italian provisions [ 20 ] (see Figure 10 b).

The displacement demand at the SD limit state ( δ D,SD ) was compared against the brittle ( δ Cb,SD ) and ductile ( δ Cd,SD ) displacement capacity according to N2 method. In particular, for the investigated case-study, the brittle failure corresponds to the collapse of shear connections between the trusses and the column, whereas the ductile failure is governed by the central column that reaches its maximum rotation capacity.

The structural performances were checked also in terms of deformability against the seismic and wind actions. The seismic action was taken into account checking the Damage Limitation (DL) limit state for which the displacement demand ( δ D,DL ) was defined as done for the SD limit state, whereas the displacement capacity was assumed as 0.5% of the total height of the building ( δ C,DL ). On the other hand, wind action is represented by a simplified set of pressures according to the Italian code requirements [ 20 , 21 ]. Thus, the lateral displacements at the top of the columns were monitored and compared against horizontal displacement limits.

The analysis results are summarised in Table 1 , where the structural lateral displacements at SD, DL, and in case of wind actions were pointed out and compared against the corresponding displacement capacity.

Seismic and wind checks for the existing structure in terms of displacements.

As it can be observed, the existing structure does not meet the required performance in terms of resistance and deformability when subjected to both seismic and wind actions.

4.2. Local Assesment

Figure 11 depicts the results of local analyses performed on both MR truss joints in terms of base shear-displacement curves, Von Mises stresses (MISES), and equivalent plastic strains (PEEQ). It can be noticed that the local seismic performance of truss joints in the X- and Y-direction is poor, owing to premature failure of lower chord connections in both cases; namely, existing M18 bolts (having a strength class equal to 6.8) fail in shear for rather low values of ISD (1–2%).

Local performance of existing MR truss connections in terms of base shear vs. displacement curves and distributions of MISES and PEEQ. ( a ) Base Shear vs. Displacements (X); ( b ) Base Shear—Displacements (Y); ( c ) Von Mises and PEEQ distribution of MR truss in X direction under hogging actions; ( d ) Von Mises and PEEQ distribution of MR truss in Y direction under hogging actions.

Such undesirable failure mechanisms sensibly affect the cyclic performance of connections, which exhibits a significant pinching effect in both directions (see Figure 11 a,b).

As expected, the ultimate displacement capacity of local assemblies under cyclic loadings is lower than the related capacity under monotonic lateral actions due to cyclic degradation of bolts. Moreover, since the same number and kind of bolts are used in both directions to connect lower chords (i.e., two M18 6.8 bolts), the peak base shear in both directions is basically identical (≈80 kN, +7% with respect to analytical calculations).

Contrariwise, a significant difference can be noticed in terms of both elastic stiffness and ultimate displacements, with the X-direction assembly being more rigid and having a displacement capacity which is about half of the related capacity in the Y-direction.

This outcome clearly depends on the difference in lateral stiffness of truss frames located in the two orthogonal directions. Indeed, the X-direction truss frame is the most rigid resisting system, owing to the favourable orientation of the hollow column (i.e., inflected about its strong axis).

Therefore, considerably higher actions are transferred by the bolts for the same value of ISD, resulting in a premature exceedance of the connection shear resistance.

Notably, the monotonic local behaviour of Y-direction MR connections is asymmetric with respect to deflections orientation (see Figure 11 b, dashed curves). Indeed, though the Y-direction truss quickly fails for hogging deflections, the base shear transmitted in case of sagging deflections keeps increasing even for rather high values of ISD.

This depends on a secondary mechanism in which the lower chord in compression transfers axial forces by direct contact with the column web after bolts have exceeded their elastic range. On the contrary, contact load-bearing does not trigger in lower chord connection in the X-direction, due to the larger extension of the saddle plate, since bolt fracture occurs prior to chord-to-column contact.

With respect to local mechanisms in upper connections, PEEQ distribution in the X-direction (i.e., on the T-stub gusset plate) under sagging deflections confirms the activation of mode 2 failure, as foreseen with analytical models provided by EN1993:1-8 [ 33 ] (see Section 3.2 ). Indeed, PEEQ are spread among both the gusset and the bolts, resulting in a satisfying local ductility as mode 3 collapse is prevented (see Figure 11 c).

Therefore, the analytical approach allows to adequately predict the shear resistance of the connections, but it is not able to account for the local mechanisms and the different stiffness of the two joints. Therefore, in order to account these aspects within the global model of the structure, non-linear links, properly calibrated against local FEAs results, were introduced.

Results of the calibration procedure are reported in Figure 12 in terms of base shear force vs. imposed displacements. It can be observed that non-linear links are perfectly able to reproduce the local behaviour of the MR joints in term of elastic stiffness, resistance, and ultimate displacement capacity.

Calibration of the non-linear links of the existing MR connections under: ( a ) hogging and ( b ) sagging moment.

The local behaviour of MR truss joints affects the global behaviour of the entire structure. Indeed, a lateral stiffness reduction due to lower connection shortage can be noticed (see Table 2 ). This effect can be mostly appreciated in the X-direction (−6.7% with respect to the first set of global FEAs), i.e., the one in which stiffer frames are located. Hence, lower connection acts as an additional source of deformability in series with steel profiles; therefore, its effect becomes relevant in case of more rigid assemblies. Contrariwise, this effect is basically negligible in the Y-direction, i.e., for most deformable trusses.

Results for the existing structure in terms of elastic stiffness evaluated accounting for/disregarding the local connection performance.

As expected, the introduction of the non-linear links has a large influence on the local model behaviour, i.e., a variation of 18.6%. Contrariwise, the performance of the global structure is less affected by the presence of the link, as depicted in Table 2 , in terms of elastic stiffness. This result mainly depends on the number of the connections where the non-links were introduced with respect to the total amount of joints.

On the other hand, the introduction of non-linear links actually changes seismic demand on the construction, as PP is evaluated based on the lateral elastic stiffness of the structure. Global behaviour of the existing structure accounting for connection performance is summarised in Figure 13 in terms of pushover curves and in the ADRS domain. For the sake of clarity, in the following, smooth pushover curves are labelled as “SNLA”, whereas bi-linear equivalent curves derived according to the N2 method are labelled as “N2”.

Global performance of existing structure in terms of pushover curves and ADRS domain checks according to EN1998:3 [ 31 ] provisions: ( a ) Pushover curves in X-direction, ( b ) ADRS domain checks in X-direction, ( c ) Pushover curves in Y-direction, ( d ) ADRS domain checks in Y-direction.

The existing structure does not attain a satisfying seismic performance either in the X- or Y-direction due to brittle failure of connections. Nevertheless, significant differences can be noticed with respect to the structural behaviour in the two directions, namely:

In the X-direction, the seismic behaviour is inadequate, not only owing to local connection failures, but also in terms of global stiffness and resistance. Indeed, if local failures were prevented (i.e., by means of local retrofit interventions), the structure would still exhibit an insufficient displacement capacity (see Figure 13 b, black circle), i.e., lower than the corresponding demand defined by PP ( Figure 13 b, red circle);

In the Y-direction, seismic checks in the ADRS domain are not fulfilled, only due to the brittle failure of lower chord connections. Indeed, PP is attained for a spectral displacement lower than the corresponding ultimate displacement (see Figure 13 d).

Therefore, the disposition of new CBFs for global seismic enhancement was actually required only in the X-direction. Nevertheless, as expected, the existing structure results as highly deformable in the Y-direction. Therefore, CBFs should still be installed in this direction to fulfil deformability requirements for wind loads (see Equation (2)). Namely, the maximum lateral deflection of hollow columns in the Y-direction is equal to 0.13 m (see Table 1 ); hence, a stiffness increase equal to about 2 times K ext should be provided by new bracings.

5. Performance of the Retrofitted Structure

The seismic performance of the retrofitted structure is, hence, reported both in terms of local response of enhanced MR truss connections and global performance of the retrofitted structure. Local behaviour of the two MR joints is depicted in Figure 14 in terms of base shear-displacement curves and distribution of Von Mises stresses (MISES) and equivalent plastic strains (PEEQ).

Local performance of retrofit interventions in terms of base shear vs. displacement curves and distributions of MISES and PEEQ. ( a ) Base Shear vs. Displacements (X); ( b ) Base Shear vs. Displacements (Y); ( c , d ) Von Mises and PEEQ distribution of MR truss in X direction under hogging and sagging actions; ( e , f ) Von Mises and PEEQ distribution of MR truss in Y direction under hogging and sagging actions.

The retrofit intervention allows to effectively achieve satisfying seismic behaviour, as ductile mechanisms (i.e., column hinging) are promoted in place of brittle connection failures. Indeed, plastic strains are concentrated in hollow profiles at both the column base and lower chord intersection, whereas retrofitted connections always remain in their elastic range (see Figure 14 c–f). The cyclic behaviour of both directions’ MR connections is positively affected by this condition, as hysteretic loops are sensibly wide and stable, allowing an efficient dissipation of seismic energy through the activation of plastic deformations within the columns.

It can also be noticed that there are some minor differences in terms of non-linear behaviour among monotonic and cyclic local FEAs. This outcome depends on cyclic hardening of the column base material, which results in higher transmitted shear force for smaller values of ISD with respect to monotonic conditions.

As done for the existing joints, the local performance of the MR joints was accounted for in the global analyses by means of properly calibrated non-linear links. Figure 15 depicts a very good agreement in terms of elastic stiffness, maximum resistance, and ultimate capacity between the FE results and the non-linear link behaviour. It should be observed that, due to the strengthening interventions, the MR joints have symmetric behaviour; this is the reason why, in Figure 15 , only the response under sagging moment in both X and Y directions is depicted.

Results of the calibration procedure for retrofitted connections.

Global behaviour of the retrofitted structure is summarised in Figure 16 in terms of pushover curves and in the ADRS domain.

Global performance of existing structure in terms of pushover curves (( a , c ) in X and Y directions respectively) and ADRS domain checks according to EN1998:3 [ 31 ] provisions (( b , d ) in X and Y directions respectively).

The strengthening interventions allow to strongly increase the elastic stiffness and resistance of the existing structure up to a complete seismic retrofit. Moreover, lateral deformability checks for wind action are fulfilled with a significant safety margin ( δ C / δ D is equal to 4 and 5.7 in X- and Y-direction, respectively—see Table 3 ). Indeed, with regards to the Y-direction, minimum cross-sections deriving from stiffness requirements (see Equation (2)) were enlarged to avoid global buckling of braces under gravity loads (see Equation (3)). Contrariwise, lateral deformability requirements for wind actions resulted as fulfilled in the X-direction due to the predominance of seismic action.

Seismic and wind checks for the retrofitted structure in terms of displacements.

The pushover curves in both X- and Y-directions were stopped in correspondence of the ductile failure mechanism due to the diagonals in compression, which reach their maximum inelastic deformation capacity, defined as reported in [ 31 ]. Contrariwise, all the MR joints remain in their elastic range.

6. Conclusions

In the present paper, the effectiveness of low-impact seismic retrofitting interventions was investigated by means of global and local numerical analyses on a case-study of an existing industrial single-storey steel building located in Italy.

Particular attention was paid to the local failure modes and their influence on the global structural analyses; thus, refined numerical models were built to investigate the local MR truss joints behaviour. Their performances were successively accounted for in the global structural analyses by the introduction of non-linear links properly calibrated on the obtained FEAs results.

The investigated structure shows both local and global shortages; from the results of numerical analyses, the following conclusions can be pointed out:

• The investigated existing structure is very deformable in both the principal directions; showing excessive deflections under wind actions;
• The global structural behaviour is highly influenced by local deficiencies. Indeed, brittle failures always anticipate more ductile mechanisms, and lateral deformability is worsened by the lower stiffness of connections;
• The local seismic performance of MR truss joints in both the X- and Y-direction is poor due to premature failure of bolted connection among lower chords and hollow columns, for rather small values of ISD (1–2%);
• The hysteretic behaviour of joints is significantly affected by a pinching effect exhibited in both the principal directions;
• The introduced non-linear links are able to perfectly reproduce the local joint behaviour in term of elastic stiffness, resistance, and ultimate displacement, allowing to account for the real joint performance also in global FEAs;
• The real joint stiffness, evaluated by means of refined FEAs, and accounted for in the global analyses by the introduction of non-linear links, influences the whole structural behaviour, and should be properly accounted for in the existing structural assessment.

The global resistance and stiffness of the structure were increased by means of new CBFs in both directions, whereas the local performance of MR joints was enhanced by the introduction of 400 mm × 20 mm rib stiffeners and new rows of 10.9 M18 bolts.

From the numerical analyses results, the following conclusive remarks can be drawn:

• The design procedure adopted for the retrofitting of MR joints results in a very ductile mechanism under both monotonic and cyclic loads; the joints behave in elastic range up to 4% of rotation. For high rotations, the failure mode is governed by plastic deformations within the column and some local plasticity within the trusses and plates, whereas the bolts remain in elastic range;
• The global seismic performance of the retrofitted structure is positively influenced by local interventions that allow to ensure a ductile behaviour to the whole structure up to the formation of the plastic hinges in the columns;
• The introduction of the new CBFs in both directions allow to provide a sufficient elastic stiffness and resistance to the whole structures against both seismic and wind actions;
• The local and global retrofit interventions were designed to not interrupt the productive activities within the building, and to minimise the impact on the working spaces. Thus, the CBFs were designed to be placed on the external façade of the building, and their shape does not limit either the height or the required spaces for the access of industrial vehicles and machineries. Contrariwise, the local intervention should be performed in the inner part of the building, but their installation involves only a small portion of the entire structure.

Funding Statement

This research received no external funding.

Author Contributions

Conceptualization, R.T., A.M., A.P. and R.L.; Supervision, R.L.; Writing—original draft, R.T., A.M. and A.P.; Writing—review & editing, R.T., A.M., A.P. and R.L. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Data availability statement, conflicts of interest.

The authors declare no conflict of interest.

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Experimental study of the mechanical behavior of a steel arch structure used in the main lining of a highway tunnel, 1. introduction, 2. design of laboratory test, 2.1. loading and measuring platform, 2.2. test working conditions, 2.3. steel utilization coefficient, 3. analysis of test results, 3.1. three-bar w-shaped lattice girder, 3.2. four-bar w-shaped lattice girder, 3.3. four-bar double 8-shaped lattice girder, 3.4. i-shaped steel rib, 4. discussion, 5. conclusions, author contributions, data availability statement, conflicts of interest.

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Li, C.; Zhuang, Y.; Lu, Y.; Zheng, G.; Zheng, Y.; Li, W.; Xue, C.; Guo, H.; Fang, Y. Experimental Study of the Mechanical Behavior of a Steel Arch Structure Used in the Main Lining of a Highway Tunnel. Buildings 2024 , 14 , 2571. https://doi.org/10.3390/buildings14082571

Li C, Zhuang Y, Lu Y, Zheng G, Zheng Y, Li W, Xue C, Guo H, Fang Y. Experimental Study of the Mechanical Behavior of a Steel Arch Structure Used in the Main Lining of a Highway Tunnel. Buildings . 2024; 14(8):2571. https://doi.org/10.3390/buildings14082571

Li, Changjun, Yizhou Zhuang, Yuquan Lu, Guoping Zheng, Yunhui Zheng, Wenhao Li, Chenbo Xue, Hongyu Guo, and Yuchao Fang. 2024. "Experimental Study of the Mechanical Behavior of a Steel Arch Structure Used in the Main Lining of a Highway Tunnel" Buildings 14, no. 8: 2571. https://doi.org/10.3390/buildings14082571

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