Serviceability Limit State Research Articles

Analysing Flexural Response in RC Beams: A Closed-Form Solution Designer Perspective from Detailed to Simplified Modelling

This paper presents a detailed analytical approach for the bending analysis of reinforced concrete beams, integrating both structural mechanics principles and Eurocode 2 provisions. The general analytical expressions derived for the curvature were applied for the transverse displacement analysis of a simply supported reinforced concrete beam under four-point loading, focusing on key limit states: the initiation of cracking, the yielding of tensile reinforcement and the compressive failure of concrete. The displacement’s results were validated through experimental testing, showing a high degree of accuracy in the elastic and crack propagation phases. Deviations in the yielding phase were attributed to the conservative material assumptions within the Eurocode 2 framework, though the analytical model remained reliable overall. To streamline the computational process for more complex structures, a simplified model utilising a non-linear rotational spring was further developed. This model effectively captures the influence of cracking with significantly reduced computational effort, making it suitable for serviceability limit state analyses in complex loading scenarios, such as seismic impacts. The results demonstrate that combining detailed analytical methods with this simplified model provides an efficient and practical solution for the analysis of reinforced concrete beams, balancing precision with computational efficiency.

Global Sensitivity Analysis and Surrogate Models for Evaluation of Limit States in Steel Truss Structures

This article presents the global sensitivity analysis of the serviceability limit state of a steel truss using Monte Carlo simulations. The focus is on the probabilistic assessment of deflection, with failure probability defined as the likelihood of exceeding the deflection limit. Deflection is computed using the beam finite element method. A surrogate model is introduced to reduce computational costs. By integrating the surrogate and original models, significant CPU cost reductions are achieved. Furthermore, classical Sobol sensitivity analysis is used to examine the model outputs and analyze the significance of member loading and stiffness on the deflection. This study advances the use of surrogate models in global sensitivity analysis, enhancing computational efficiency and the understanding of interactions between input variables in the reliability assessment of steel truss structures.

Mechanically Stabilized Earth Wall Reliability Analysis Using Response Surface Methodology, ANN, ANFIS and Multi-objective Genetic Algorithm

Considering uncertainty in the analysis of geotechnical structures is a necessary condition for optimal and robust design. An alternative method for studying the reliability of a mechanically reinforced earth wall in granular soil is used to account for these uncertainties more rigorously. This allows for the inclusion of various uncertainties in a mathematical risk formulation based on random variables. The deterministic model is a benchmark taken from the literature used in a numerical simulation to determine the maximum horizontal displacement of the wall. In this case, the serviceability limit state is considered, allowing the wall's actual behavior to be described. ANOVA was used to identify the most influential parameters on the system's response. As uncorrelated random variables, only the parameters (E, φ and γ) were considered. The mathematical model serving as the limit state function was numerically predictedby three methods, response surface methodology (RSM), artificial neural network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS), and their predictive capacities were then compared. The results showed that the ANN model outperformed the RSM and ANFIS models regarding prediction. ANN models and multi-objective genetic algorithm (MOGA) are used to optimize the Hasofer-Lind reliability index. The analysis is then carried out by taking into account the various types of functions of parameter distributions, which allowed us to better appreciate the effects of the uncertainties and identify the set of parameters with a high incidence.

Bearing Performance of a Helical Pile for Offshore Photovoltaic under Horizontal Cyclic Loading

For an offshore photovoltaic helical pile foundation, significant horizontal cyclic loading is imposed by wind and waves. To study a fixed offshore PV helical pile’s horizontal cyclic bearing performance, a numerical model of the helical pile under horizontal cyclic loading was established using an elastic–plastic boundary interface constitutive model of the clay soil. This model was compared with a monopile of the same diameter under similar conditions. The study examined the effects of horizontal cyclic loading amplitude, period, and vertical loads on the horizontal cyclic bearing performance. The results show that under horizontal monotonic loading, the bearing capacities of a helical pile and monopile in a serviceability limit state are quite similar. However, as the amplitude of horizontal cyclic loading increases, soil stiffness deteriorates significantly, leading to greater horizontal displacement accumulation for both types of piles. The helical pile’s bearing capacity under horizontal cyclic loadings is approximately 60% of that under monotonic loading. With shorter cyclic loading periods, horizontal displacement accumulates rapidly in the initial stage and stabilizes over a shorter duration. In contrast, longer cyclic loading periods lead to slower initial displacement accumulation, but the total accumulated displacement at stabilization is greater. When vertical loads are applied, the helical pile exhibits more stable horizontal cyclic bearing performance than the monopile.

Calculating shear lag in steel-concrete composite beams under combined compression and bending

Long and complex composite steel-concrete structures are becoming common, requiring a deep understanding of the effects induced by the simultaneous action of axial forces and bending. In fact, the axial force generated, for instance, by cable inclination in cable-supported structures can modify the stress distribution within the elements compared to bending scenarios, thereby necessitating a revision of the effective width to be utilized. Nonetheless, current design codes, including Eurocode specifications and others, lack provisions for addressing the combined effects of axial force and bending, as they are exclusively tailored for bending. This limitation can introduce design complexities, necessitating the implementation of intricate Finite Element (FE) models, which impose substantial computational loads and design efforts. The methodology proposed in this paper overcomes these challenges allowing to assess the stress distribution and resistance of composite deck at Serviceability Limit State (SLS) and Ultimate Limit States (ULS) by leveraging results obtained from standard beam models typically used by structural designers or practitioners. A comprehensive parametric analysis using nonlinear finite element models is performed to validate the developed methodology. A comparison with the Eurocode 4 formulations highlights that the proposed method provides superior accuracy in estimating peak stress in concrete slabs under combined compression and bending. Additionally, it facilitates straightforward verification at the ULS in compliance with Eurocode requirements.

RC dapped-end beams with various reinforcement layouts: An experimental investigation

Reinforced Concrete (RC) discontinuity regions (D-regions), such as dapped ends, can represent vulnerable zones in existing RC structures since they can exhibit a brittle failure mechanism. In common design practice, the ultimate strength of D-regions is assessed through Strut and Tie (S&T) models. Current design codes recommend two resistant mechanisms for dapped ends but do not provide information about the identification of steel bars involved in the resistant mechanism when the reinforcement is formed by distributed bars. An experimental campaign on dapped-end beams with various reinforcement layouts, including configurations without diagonal bars or with one or multiple layers of diagonal bars, has been carried out at the Structures and Material Testing Laboratory of the Department of Civil and Environmental Engineering in Florence. Results allow for identifying the influence of different reinforcement layouts on the crack pattern at the Service Limit State (SLS) and on the post-peak response. Both the strain on bars and the crack opening displacements are investigated until failure. The work highlights that layouts with distributed diagonal bars reduce the crack widths at the SLS compared to other configurations, increase the ductility, and allow for the timely detection of damaged dapped ends during in situ inspections.

Experimental and numerical investigation of flexural behavior of precast tunnel segments with hybrid reinforcement

Precast concrete segments reinforced with a combination of steel fibers and conventional rebar (RC-SFRC) have gained prominence in the mechanized construction of tunnels in recent years due to the advantages offered by this hybrid reinforcement solution in enhancing the mechanical behavior of these structural members. This research aims to understand better the flexural behavior of RC-SFRC tunnel segments proposed to replace conventional reinforcement in São Paulo Metro Line 5. An experimental program and numerical analyses using a multiscale model were conducted to predict the post-cracking parameters of SFRC through three-point bending tests according to EN14651 and assess the flexural behavior of full-scale tunnel segments. In both scenarios, 2D multiscale numerical models with discrete and explicit representations of the reinforcements were applied. The comparison of numerical and experimental results in terms of crack width, mean crack spacing, deflection, and the ultimate and service loads derived from design predictions demonstrate that the proposed RC-SFRC reinforcement represents an advantageous alternative, significantly enhancing the performance of the segments for both serviceability and ultimate limit states. Furthermore, the responses show that the adopted numerical strategy is promising and can be consolidated as a tool for optimizing the design process.

Analysis and Design of Box Culvert for Durability against Varying Thickness of Cushion

Abstract: This study presents the structural analysis of a reinforced concrete (RCC) box culvert with dimensions 1m x 2m x 1.5m, subjected to varying cushion loadings of 0.770m, 1.010m, and 1.200m, using STAAD.Pro software. The analysis focuses on both Ultimate Limit State (ULS) and Serviceability Limit State (SLS) criteria to ensure the structural integrity and durability of the culvert. For ULS, load combinations include dead load, live load, earth pressure, and cushion load, assessing the culvert's capacity to withstand maximum expected loads without failure. The study evaluates bending moments, shear forces, and ensures that the flexural and shear strengths of the culvert are within permissible limits. Results indicate that even under the highest cushion loading, the culvert design remains robust with appropriate reinforcement. For SLS, the analysis incorporates quasipermanent load combinations to evaluate deflections and crack widths, ensuring the structure's functionality and aesthetic durability under normal service conditions. Deflections and crack widths for all cushion depths were found to be within acceptable limits, demonstrating the culvert's ability to maintain serviceability and resist long-term degradation. Overall, the analysis confirms that the RCC box culvert, when designed according to the principles of ULS and SLS, achieves a balance between safety, functionality, and durability, ensuring reliable performance over its service life.

Assessment of cantilevered curtain wall system supported by tension rods for an enclosed circular building

Curtain wall systems have undergone significant advancements to meet the evolving architectural requirements and achieve aesthetic appeal and functionality in buildings worldwide. These non-structural enclosures, typically constructed with lightweight materials like glass or metal panels, contribute to the visual appeal of high-rise structures while providing numerous benefits, such as ample natural light and unobstructed views. The current paper focuses on analyzing and designing a cantilevered curtain wall system supported by tension rods for the auditorium façade at a simulation centre. The curtain wall surrounds the entire primary structure of the building, which has a circular layout. The study uses numerical modeling with the Robot software to analyze stresses and deflections in the glass, tension rods, mullions, and transoms while considering a wind load of 1.6 kPa. According to the findings, tempered laminated glass that is 19.52 mm thick satisfies the Ultimate Limit States (ULS) and Serviceability Limit States (SLS). Under the limit states, the Technal system (FM169) reinforced with steel tubes can transfer the design loads. The steel framing system that supports the tension rods and transfers the load of the curtain wall to the main structure is likewise considered safe. The structural integrity of the curtain wall is ensured by the prescribed requirements for the connections, which include a 5 mm fillet weld with a throat thickness of 3.5 mm, 20 mm diameter tension rod (Kin long system), and 8 mm thick MS plates with channel brackets. This research expands the practical application of cantilevered curtain wall systems of buildings with enclosed circular layouts.

Timber-timber composite (TTC) joints made of short-supply chain beech: Push-out tests of inclined screw connectors

This paper presents the results of experimental investigations on six-layered, homogeneous glulam beams made of Italian short supply chain beech (Fagus sylvatica L.). At first, the beams were produced and mechanically characterized for bending, then, they were employed to realize timber-timber composite joints and tested under quasi-static monotonic loading. The test configurations were adopted to reproduce connections used in timber-to-timber composite structures for applications in new constructions. Outcomes in terms of connection stiffness, strength, static ductility and failure modes are presented and discussed. Moreover, the experimental stiffness were used to carry out analytical verification at the serviceability and ultimate limit states to extend the validity of the proposed screw and specimen’s configurations.

Using Machine Learning Algorithms to Develop a Predictive Model for Computing the Maximum Deflection of Horizontally Curved Steel I-Beams

Horizontally curved steel I-beams exhibit a complicated mechanical response as they experience a combination of bending, shear, and torsion, which varies based on the geometry of the beam at hand. The behaviour of these beams is therefore quite difficult to predict, as they can fail due to either flexure, shear, torsion, lateral torsional buckling, or a combination of these types of failure. This therefore necessitates the usage of complicated nonlinear analyses in order to accurately model their behaviour. Currently, little guidance is provided by international design standards in consideration of the serviceability limit states of horizontally curved steel I-beams. In this research, an experimentally validated dataset was created and was used to train numerous machine learning (ML) algorithms for predicting the midspan deflection at failure as well as the failure load of numerous horizontally curved steel I-beams. According to the experimental and numerical investigation, the deep artificial neural network model was found to be the most accurate when used to predict the validation dataset, where a mean absolute error of 6.4 mm (16.20%) was observed. This accuracy far surpassed that of Castigliano’s second theorem, where the mean absolute error was found to be equal to 49.84 mm (126%). The deep artificial neural network was also capable of estimating the failure load with a mean absolute error of 30.43 kN (22.42%). This predictive model, which is the first of its kind in the international literature, can be used by professional engineers for the design of curved steel I-beams since it is currently the most accurate model ever developed.

Experimental and analytical investigation of the shear behavior of steel-bamboo composite I-beams with composite connections

In steel-bamboo composite beams, the debonding failure and slip behavior of steel-bamboo pure bonding interfaces at the flanges often lead to premature failure of beams and underutilization of material strengths. Therefore, a novel steel-bamboo composite I-beam with composite connections was presented in this study, in which the pure bonding interfaces at the beam's flanges were reinforced by self-tapping screws (STSs). 13 beams were designed and fabricated with interface type, shear span-to-depth ratio, height-to-thickness ratios of bamboo and steel at the web, and width-to-thickness ratio of steel at the flange as main parameters. Then, shear tests and theoretical analysis were performed to evaluate the beam's shear behavior. The results indicated that the debonding failure and slip behavior of the beams were effectively limited, and the shear resistance, deformation capacity, and ductility were significantly improved. The shear resistance of beams was improved by reducing the shear span-to-depth ratio, height-to-thickness ratios of the bamboo and steel at the web, and steel flange width-to-thickness ratio. Finally, the developed analytical models can be concluded to be used to accurately predict the interfacial shear stress at the beam flanges in the serviceability limit state (SLS) and ultimate shear capacity of the beams.

Performance-based multi-hazard engineering (PB-MH-E): The case of steel buildings under earthquake and wind

Focusing on natural hazards as wind and earthquake, the goal of this work is to understand if interference occurs in the design choices for steel buildings of a certain height, thus determining which design requirement and hazard is predominant, between Ultimate Limit State (ULS) requirements under earthquakes, or comfort of the occupants and the Serviceability Limit State (SLS) of the structure under wind. Thus, in order to compare structural responses, both in linear (i.e., SLSs) and non-linear field (i.e., ULS) a simplified analysis procedure that could be also implemented in Standards and in design practice (so-called SAC-FEMA method, originally introduced in the seismic field by Cornell in the early 2000s and more recently extended to the wind) is adapted, leading to a true optimal Performance-Based Multi-Hazard Design (PB-MH-D) of the structure considering the two hazards. The procedure is applied to two case-study steel buildings, 17 and 60 floor heigh; the approach is shown to efficiently lead to a design solution who consistently tackles with the same level of reliability with the two hazards.

Redundancy and reliability levels of post-tensioned and grouted concrete cross-section in case of tendon failure

Since the 1960 s and 1970 s, the prestressing steel used on post-tensioned concrete (PTC) bridges has been known to be susceptible to stress corrosion cracking (SCC). This can result in brittle rupture of the prestressing steel. Objective of this study is to evaluate the reliability levels achieved with assessment method developed for verifying crack behaviour before failure in cross-section of PTC bridges with cross-section loss of prestressing steel. Additionally, the study aims to investigate of tendon loss on crack before failure behaviour. This paper applies a reliability analysis for methodology based on robustness analysis on crack before failure behaviour in PTC with deteriorating prestressing steel. The analysis involves examining cross-sections with various design criteria. The effects of choices made in designing the PTC structure are analysed and noted to have a significant impact on the safety margin of the structure, while the deterioration of prestressing steel does not significantly decrease the ductility of the cross-section if certain conditions are met. The use of stricter serviceability limit-state (SLS) criteria used in past design results the greater safety margin for the structure in the event of tendon loss, which therefore makes it beneficial for structural redundancy in the ultimate limit state (ULS).

Cantilever piled-wall design criteria in cohesionless soil: a review

Purpose The design of cantilever pile walls (CPWs) presents several common challenges. These challenges include soil variability, groundwater conditions, complex loading conditions, construction considerations, structural integrity, uncertainties in design parameters and construction and monitoring costs. Accordingly, this paper is to provide a detailed literature review on the design criteria of CPWs, specifically in cohesionless soil. This study aims to present a comprehensive overview of the current state of knowledge in this area. Design/methodology/approach The paper uses a literature review approach to gather information on the design criteria of CPWs in cohesionless soil. It covers various aspects such as excavation support systems (ESSs), deformation behavior, design criteria, lateral earth pressure calculation theories, load distribution methods and conventional design approaches. Findings The review identifies and discusses common challenges associated with the design of CPWs in cohesionless soil. It highlights the uncertainties in determining load distribution and the potential for excessive wall deformations. The paper presents various approaches and methodologies proposed by researchers to address these challenges. Originality/value The paper contributes to the field of geotechnical engineering by providing a valuable resource for geotechnical engineers and researchers involved in the design and analysis of CPWs in cohesionless soil. It offers insights into the design criteria, challenges and potential solutions specific to CPWs in cohesionless soil, filling a gap in the existing knowledge base. The paper draws attention to the limitations of existing analytical methods that neglect the serviceability limit state and assume rigid plastic soil behavior, highlighting the need for improved design approaches in this context.

Serviceability limit state of incrementally launched steel bridge I-girders

Bridge girders are subjected to repeated patch loading during incremental launching (i.e. travelling over supports). Plastic deformations are likely to occur in the girder already at the first patch loading. They influence the girder’s structural response and bring about a decrease in the ultimate resistance at subsequent patch loadings. This problem is analysed in the present paper through the serviceability limit state (SLS) of incrementally launched bridge I-girders (ILBGs). The SLS of ILBGs is a current problem since only a few studies, with contrasting conclusions and certain limitations, have been recognised in the literature. Research is limited on plate girders without longitudinal stiffeners made of structural steel. Flat slide-type launching shoes are considered in this paper.The serviceability requirement (repeatable behaviour of ILBGs) and criterion (that effective membrane strains should remain in the elastic range) are adopted from the literature. So, the serviceability resistance is adopted as a load at the start of the effective membrane plastic strains in the girder. In order to propose a practical and simple SLS design procedure, the serviceability resistance is normalised against the ultimate resistance, so a serviceability correction factor (ksls) is defined. The paper presents a parametric numerical analysis of the factor (ksls). A finite element model previously developed and validated by the author is employed to simulate a nonlinear response of patch-loaded girders. The parametric study includes 599 girders. ksls is inversely proportional to the web thickness and directly proportional to the flange thickness and the yield strength of the steel material. The load length, web depth and flange width do not influence ksls. The influence of the spacing between transverse stiffeners on ksls is negligible. Finally, by regression analysis of the results of parametric study, an original and reliable serviceability correction factor is proposed as the main objective of the research. The range when the SLS of ILBGs should be checked is also defined.

Aeolian sand challenges in desert rail infrastructures, overview of Iran’s experience and advancement

The processes of wind erosion and the movement of dunes have destructive effects on the transportation infrastructure with an emphasis on railway lines. Consequently, the construction and maintenance costs of desert railways will increase under the influence of sand sediment movement. In severe conditions, passing trains can also be affected, compromising their safety and comfort. However, the passage of railway infrastructures through desert areas prone to aeolian sand is inevitable. This research discusses the main challenges encountered by railways in Iran's deserts, including two ultimate and serviceability limit states that affect civil works, track superstructure, rolling stock, and signaling systems. It also examines the mitigating measures implemented in Iran based on the source, transport, or deposition areas of sand dunes. Moreover, the performance of Iran's desert railways has been classified based on wind sand activities. According to the distribution map of Iran's railway network, sand accumulation in the main desert lines has been classified into four levels: very severe, severe, moderate, and low. The research also presents the experience of implementing and monitoring the hump slab track system, which has proven to be a sustainable solution for addressing the dune problem with suitable efficiency over a period of six months.

Convergence-Related Serviceability Limit States of Segmental Tunnel Rings: Lessons Learned from Structural Analysis of Real-Scale Tests

An extended hybrid method for the analysis of the symmetric structural behavior of segmental tunnel linings is proposed. Their deformations cannot be determined by the traditional hybrid methods when the convergences are close to the serviceability limit states (SLSs). Two real-scale tests are employed for the validation of the proposed method. It involves structural analysis that is based on transfer relations. They represent analytical solutions of the linear theory of thin circular arches, and they contain the symmetric mode of rigid-body displacements. The method is termed hybrid because it is based on two types of input, namely the external loading and experimental data of displacements monitored during the test. It is termed extended because, additionally, the vertical and horizontal convergences are employed to produce more accurate structural deformations than obtained by the traditional hybrid method. The latter is found to be unsuitable for structural analysis after sudden failure has occurred in the vicinity of segmental interfaces. At the respective load steps, the structures were in convergence-related serviceability class C, referring to endangered serviceability. The local failures occurring at these load steps resulted in a rapid increase in the structural deformations and fast attainment of the SLS. If, in convergence-related serviceability class C, local failures at segmental interfaces are detected, the strengthening of the structure is necessary. This cannot be delayed to the attainment of serviceability class D, i.e., to reaching the SLS.

Concept and flexural performance of non-prestressed steel plate-UHPC-NC composite girder bridge

A novel non-prestressed composite girder bridge, incorporating steel plates, ultra-high performance concrete (UHPC), and normal concrete (NC), is proposed for small and medium-span bridges. For the proposed steel plate-UHPC-NC composite bridge, UHPC girders are reinforced with steel plates on the bottom in lieu of part of closely-spaced rebars in the beam. Cast-in-situ NC deck slab is adopted to ensure its transverse integrity and to reduce costs in comparison with UHPC bridge deck. To verify the performance of the proposed novel composite bridge, three types of UHPC-NC composite beams with same reinforcement ratio (reinforced with only rebars, only steel plates, both rebars and steel plates) were first conducted with bending test. The impact of various reinforcement types on the flexural behaviors of UHPC-NC composite specimens was identified, including failure mode, crack distribution pattern, and crack width development. The findings demonstrated that the UHPC girder reinforced with both steel plates and rebars would significantly enhance the crack resistance of UHPC girders during bending in comparison with the other two. In addition, the composite girder reinforced with steel plates and rebars can achieve a nominal stress of 31.41 MPa at the serviceability limit state (with a UHPC crack width of 0.05 mm). The commercial software DIANA is then utilized to numerically simulate the mechanical properties of the proposed composite beam. The deviation between the finite element (FE) results and the experimental load-bearing capacity is within 1.9 %. Parameter analysis demonstrates that the bridge deck's strength has negligible influence on the load-carrying capacity of the proposed composite beam. Finally, a design scenario for a 30 m-span simple-supported bridge is conducted, and the initial cost analysis indicates that the proposed steel plate-UHPC-NC composite girder is 2 % lower than the conventional prestressed concrete T-girder. The proposed non-prestressed steel plate-UHPC-NC bridge presents notable benefits, including cost-effectiveness, strong crack resistance, and the prospect of complete prefabrication, offering a feasible alternative for small and medium-span bridges.

Proposition for the effective moment of inertia to determine the deflection in a composite slab

The objective of this work is to propose a mathematical expression for calculating the effective moment of inertia of a composite slab that utilizes steel formwork incorporated into the concrete, and consequently, to verify the deflection. The analysis of the behavior and strength of composite steel and concrete slabs covers several parameters, such as load-deflection curves, load-end slip curves, and load-steel strain curves. Among these parameters, the load versus deflection curve at the mid-span perform a crucial role in the evaluation and verification of deflection. Regarding the calculation of deflection, generally, the technical standards recommend that the moment of inertia of the composite section be given by the simple average of the moments of inertia of the uncracked and cracked sections. However, experimental investigations have shown that this procedure inadequately characterizes composite slab behavior, resulting in underestimated effective moment of inertia and reduced deflection, especially when subjected to higher loads. Using the results of experimental tests on a composite slab built with a specific steel sheeting carried out at the Structures Laboratory of the Federal University of Minas Gerais, this work evaluated several expressions suggested by technical standards and authors of scientific articles aiming to validate a proposal for determining the moment of effective inertia in composite slabs that adequately represents the behavior load versus deflection during the entire loading phase until collapse. From this evaluation it is possible to recommend the proposed equation for design verification in the case of the service limit state for excessive deformations.