Limit State Design

In this paper, evaluation of torsional stiffness in beam and slab bridge deck elements is presented. A beam and slab bridge decks structurally behave as a grillage. A grillage has an efficient transverse load distribution due to transverse asymmetric load. In the case of bridge deck without transverse beams in the span, transverse load distribution depends on the torsional stiffness of longitudinal beams, transverse beams over the. supports and deck slab. The results of load testing conducted on series of bridges in Croatia is compared with results obtained on different numerical grillage models in which torsional stiffness of main structural elements was varied. Five different numerical models for each tested bridge is used. To evaluate torsional stiffness of main structural elements of the bridge the transverse distribution coefficients are introduced. The design value of the coefficients of torsional stiffness reduction for verification of the serviceability limit state (SLS), wi...

This paper presents an experimental study on damage assessment of reinforced concrete (RC) beams subjected to incremental cyclic loading. During testing acoustic emissions (AEs) were recorded. The analysis of the AE released was carried out by using parameters relaxation ratio, load ratio and calm ratio. Digital image correlation (DIC) technique and tracking with available MATLAB program were used to measure the displacement and surface strains in concrete. Earlier researchers classified the damage in RC beams using Kaiser effect, crack mouth opening displacement and proposed a standard. In general (or in practical situations), multiple cracks occur in reinforced concrete beams. In the present study damage assessment in RC beams was studied according to different limit states specified by the code of practice IS-456:2000 and AE technique. Based on the two ratios namely load ratio and calm ratio and when the deflection reached approximately 85% of the maximum allowable deflection it was observed that the RC beams were heavily damaged. The combination of AE and DIC techniques has the potential to provide the state of damage in RC structures.

This work deals with the evaluation of the design criteria and security check (Ultimate Limit State -ULS) of the American (ACI-440.2R, 2017) and European (FIB Model Code, 2010) standards of reinforced concrete structures strengthened with Carbon Fiber Reinforced Polymers (CFRP), by the technique of Externally Bonded Reinforcement (EBR). It is intended to evaluate if, for a given database of 64 experimental tests of beams and slabs, the obtained results respect the safety conditions according to the mentioned standards, to increase the efficiency of this reinforcement technique and to lead to the establishment of regulatory design criteria in Brazil. Results show a conservative match among experimental and theoretical values calculated according to the two guidelines and it is concluded that a future regulation in Brazil on this subject should be based on the FIB Model Code.

The beam-column connection is the main element in frame
structures, ensuring the integrity and stability of the building. Cyclic lateral
loads, in particular earthquakes, cause serious damage to frame joints. The shear forces generated damage the integrity of the beam-column connection. The recommendations in the literature for the determination of these forces is based on an approximate static calculation. There are also empirical formulas or capacitive calculation applied in current codes. All these methods are not based on slender static formulas guaranteeing unambiguous answers for the magnitude of the shear force arising from the action of a specific load. The involvement of the concrete section of the beam is neglected. In the search for accurate values for the shear force at the joint, with the possibility of avoiding the listed drawbacks, a number of analytical solutions have been carried out for beams under the action of different types of loads taking into account the shape of the beam cross-section and the characteristics of the construction materials. In this paper, the derived formulae will be applied to investigate the contribution to the shear force of various parameters involved in the expressions. Experimental investigations indicate a significant contribution of concrete strength to the shear force value. Numerical
solutions for a cantilever beam will confirm the experimental observations, and will prove a change in shear force by 13 to 15% when using high-strength concretes. The differences in shear force by the types of loads vary from 1-3%, and the change in the cross-section of the reinforcing bars - from 1-3%.__________________________________________________________________________________Citation Albena Doicheva 2026 IOP Conf. Ser.: Mater. Sci. Eng. 1349 012001DOI 10.1088/1757-899X/1349/1/012001

This state-of-the-art review provides a critical overview of advances in multilayer concrete slab technology by systematically exploring three interconnected performance pillars: structural integrity, vibration serviceability, and acoustic insulation. The development of these composite systems is inherently complex due to the conflicting performance requirements and hence inevitable trade-offs; most notably, the role of stiff shear connectors as acoustic and vibration bridges. The basis for the analysis is a systematic survey of the literature for studies published between 2014 and 2025. Experimental evidence shows that composite action, and in particular connector behavior, significantly enhances bending stiffness and load-carrying capacity against monolithic construction; substantial gaps remain regarding stress redistribution, combined states of stress, and impact-related behavior. Vibration serviceability, which controls occupant comfort, is governed by natural frequency but also acceleration response, damping, mode shapes, and boundary conditions; simplified frequency limits such as those in Eurocode 5 shall hence be interpreted with regard to human perceptual response. Acoustic performance, in particular impact sound insulation, is often neglected within structurally oriented studies, despite bare slabs frequently failing to meet regulatory limits; hence, separation strategies, such as floating floors, are required, although these may conflict with rigid structural connections. The review points out a need for system-level multidisciplinary research, innovative connector solutions, validated multiphysics models, and holistic design frameworks in order to achieve an optimum balance between strength, comfort, and sustainability in high-performance building systems.

This work presents the vulnerability assessment of two churches at the state of Colima by means of 3D rigid block models, using a limit analysis approach. The paper contains a description of the buildings and the damage they suffered during the 2003 earthquake. The 3D models were elaborated on the basis of macroblocks defined according to the damage observed after the earthquake and also, taking into account the typical failure mechanisms in churches reported in the literature. The limit analyses were carried out with a software already tested and validated elsewhere. The results show that the limit analysis approach with rigid block models is a valuable tool for the identification of critical failure mechanisms, their associated failure multipliers and, in a global fashion, for the vulnerability assessment of historical churches. The results also indicate that empirical methods provide a good estimation of the vulnerability level of this buildings type.

The paper reports the results of a collapse test performed on a 6 m span timber-concrete composite beam with glued re-bar connection. The beam was first ramp loaded to failure, then some push-out tests were performed on specimens cut from the end of the beam in order to fully characterise the connection. During the tests all relevant quantities such as deflections, slips and strains were monitored. The experimental results are compared with those carried out using a FE numerical software and the analytical procedure proposed by Ceccotti according to the Eurocode 5 (EC5). An overall good correspondence was found, as long as realistic properties of the connection such as those obtained through push-out tests are used. Conversely the approximate formulas suggested by the EC5 for evaluating the connection properties are too conservative. Their use may lead to too stiff and strong connections, with possible undesirable brittle failure of the whole composite beam.

Limit-state design methodologies for serviceability of foundations are an important area under development. Due to various sources of uncertainty, settlement analysis models and the soil or rock properties required for settlement analysis may be in error; hence any settlement estimate is a random variable. To develop limit-state design codes for largediameter bored piles, analysis methods for estimating the settlement of large-diameter bored piles need to be carefully calibrated. This paper aims at calibrating four analysis methods for bored piles in soils (Vesic's elastic method, Mayne and Harris's analytical solution, O'Neill and Reese's load-transfer method, and a method based on load-transfer curves established in this paper based on Hong Kong data) and three methods for bored piles socketed in rocks (Vesic's method, Kulhawy and Carter's method, and a load-transfer method using the correlations established in this paper based on Hong Kong data). For rock-socketed piles, two methods for estimating the rock deformation modulus are further studied: One based on a correlation with rock quality designation and the other based on a correlation with rock mass rating. These analysis models have been calibrated at the working load level using 36 cases of static loading tests on large-diameter bored piles in Hong Kong with complete soil and rock information. The eŠects of construction on pile settlement have also been included.

The development of limit-state design codes for large-diameter bored piles requires a careful calibration of existing design methods. Due to various sources of uncertainty in understanding the geology and construction details, estimation of design loads, and design analysis models and their parameters, the estimated pile capacity values from several design methods for large-diameter bored piles vary widely and the corresponding reliability levels are not clearly known. This paper aims at evaluating the performance of six design methods for bored piles in soils and four design methods for bored piles socketed in rocks based on a database of 62 full-scale load tests on large-diameter bored piles in Hong Kong. These methods include a descriptive method, the b-method, and several empirical correlations with blow count from the standard penetration test or unconˆned compressive strength of rock. The capability of these design methods to estimate individual resistance components and the total capacity is calibrated separately. Construction eŠects, particularly the use of permanent liners, pile-shaft grouting, and the time delay between the end of pile excavation and pile concreting, are explicitly considered. The performance of each design method is indicated by the ˆrst and second moments of the model bias factor, which can be used as a basis for developing partial factors for limit state design.

ABSTRACT: The study and analysis of metocean data is essential in predicting future environmental conditions. In relation with design nearshore structure for of seaweed cultivation, this study focuses on the collection and analysis of metocean data of potential sites in Malaysia so as to prevent under-designing and over-designing of the structure. The study investigates the metocean environment for the spatial design and monitoring of a seaweed aquaculture farm at monsoons proton East Coastal region.

This study focuses on the influential factors that enhance the reliability and versatility of structure throughout the life span. The factors are considered on the basis of the need for assessment of state of –art- structural analysis and design. Through investigation the researcher found that there are two most influential factors are repeatedly influencing the life of structure. The two factors are structural elements and loading patterns. Structural elements are identified on the basis of structure height, span, bays, percentage of shear wall, ratio of structural and non- structural panels to total number of panels and type of frame. The loading pattern investigated on the serviceability limit of structural components.

Cross-laminated timber (CLT) is an innovative engineering wood product made by gluing layers of solid timber boards placed in an orthogonally alternating orientation to the neighbouring layers. CLT panels provide an efficient solution for floors in single and multi-storey buildings. Due to their light weight and often long-span, the design of these floors is generally governed by serviceability limit state criteria, that is, deflection or vibration limits. Vibrations induced by dynamic actions, such as people walking and their everyday activities, cannot result in structural failure but may cause discomfort to occupants if vibrations are not properly controlled. This paper gives an overview of some available methods for the vibration serviceability design of residential CLT floors. Differences between these methods are discussed through the consideration of criteria and their limit values. Although some criteria are common to certain methods, it may happen that the same criteria tak...

All Eurocodes are currently under a critical review, while the work for a second generation of codes are about to start in 2015. For the geotechnical design EN 1997-1 is facing high demands for harmonization and simplification of the present code. The paper presents some proposals for improving the code regarding ultimate limit state (ULS) design. The goal is to make the code better in accounting for uncertainties involved in the design and possible consequences of an ultimate limit state. When applying a material factor approach (MFA), the partial safety factors are suggested to depend on both the uncertainty of the material and the consequence of failure. Such an approach is well suited for slope stability analysis. However, the authors suggest that also the uncertainties involved with loads should be placed on the material factors. For retaining wall design and load factor approach (LFA) is suggested in addition to MFA similar to present Design Approach (DA) 1 in the Eurocode. This approach gave the most consistent design for all cases in a comprehensive study preformed. Some modifications are though suggested also for DA1 to make the design simpler and even more consistent.

This paper provides reliability analysis and outlines its possible use in landslide analysis. The study site comprises steep slopes composed of alternating clay, sand and silty layers, at Lake Balaton (Hungary). Using the Slide2 version of the Rocscience software, we were able to detect deep circular slip surfaces that has a lower probability than the one obtained from Plaxis and Geo5 software modelling. The calculated safety factors are between 1.27 and 1.4, which only partly satisfy the requirements of Eurocode 7. These results were obtained with probabilistic calculation using Latin-Hypercube method and Janbu simplification.

In designing foundation, there are three fundamental requirements namely: ultimate limit state (ULS), serviceability limit state (SLS), and economics. Generally, the ULS and SLS are the focus of the design process, while the cost factors are not explicitly considered. This paper deals with the three requirements with the minimum construction cost as the controlling objective. A wide range of sand density conditions are considered, while the typical ULS and SLS design checks available in the literature are employed. The optimization tool used is the Solver add-in function available in MS-Excel™. The effects of different construction cost structures in four Indonesia's provinces are examined in this paper. The purpose of this research is to be able in designing the shallow foundation with 3 aspects consideration at once, namely ULS, SLS and economic. On the other hand, this research is to analyse the sensitivity's factor which influence the design, namely work unit price, soil...

A discussion of a paper with the aforementioned title by Ahammed and Melchers, published in this journal (Volume 120, Number 6, November/December 1994), is presented. Discusser Prevost begins by suggesting that the authors confirm that the material of the pipes addressed is steel. He then moves on to discuss the two types of loadings separately, assuming steel pipes only are considered. Discusser Prevost also states that elastic limit is not a criterion of failure but a permanent feature. He concludes by pointing out that the paper lacks a discussion on jointing systems. Discussion is followed by closure from the authors.

According to modern design codes, such as the Eurocode 7, also Soil Retaining structures should be designed according to Ultimate Limit State analysis, see . From an economic point of view, the design of the lining, i.e. the thickness and reinforcement of it, would be optimal if the loading during construction is less critical than the loading during service life, i.e. to the overburden loading. If necessary one could take measures to prevent that any loading during construction becomes critical compared to the overburden loading. If this can be achieved, the structural design would be limited to establishing the overburden pressures, and calculating equilibrium between lining strength and overburden. For optimisation one could use Probabilistic theory and Risk Analytic techniques to establish a sufficient distance between actual loading and design parameters to get the most economic lining thickness and reinforcement. In order to evaluate our present situation with respect to lining design, some observations from engineering practice are discussed: the first, from the construction of the 2 nd Heinenoord tunnel, where the damage to the lining during construction was above average; the second from the construction of the Green Hart tunnel where measurements show, that flexibility of the tube and the influence of interaction between structure and underground can also lead to critical loading conditions for the lining. Finally the analyses and observations are generalized and some conclusions with respect to lining design are drawn.

This paper presents the structural reliability appraisal of timber concrete composite floor designed in line with Eurocode 5 (2004) and Eurocode 2, (2004). Limit state expressions for timber concrete composite floor subdued to tension, bending, tension and bending, shear and compression were generated and their entailed reliability degrees were assessed. The basic variables associated with the design are considered to be random variables with their properties espoused from the previous studies. Reliability analysis was performed using reliability mothed i.e. first order reliability method (FORM) owing to assess the safety levels of the composite floor structural elements by considering six different modes of failure. The analysis comprised of different selected species of softwood, hard wood and glue laminated timber whose strength class were obtained from BS EN 338, 2008 and concrete of strength class C30 from Eurocode 2. The results obtained disclosed that safety indices decrease ...

This paper presents the results of safety assessment of timber columns laminated with aluminium using the First Order Reliability Methods. Three failure modes were considered in the studies: bending failure, buckling failure, and flexural buckling failure modes. The results show that the column is safer for compression failure mode which has safety index values of 4.3 and 9.68 for imposed load and dead-to-live load parameters respectively without laminates, and progressive safety indices of up to 12.4 and 20.87 respectively for columns with laminates of 20mm thickness. The study showed that the most critical failure mode for the column is the flexural buckling mode. It is therefore deduced that from the results of the critical failure mode, laminate thickness of 10mm should be used to withstand any variation in load ratios of 0.6, 0.8 and 1.0 and a maximum imposed load of 15kN be used to ensure a safe column design.

A numerical approach to the reliability analysis of reinforced and prestressed concrete structures is presented. The problem is formulated in terms of the probabilistic safety factor and the structural reliability is evaluated by Monte Carlo simulation. The cumulative distribution of the safety factor associated with each limit state is derived and a reliability index is evaluated. The proposed procedure is applied to reliability analysis of an existing prestressed concrete arch bridge.

The existing tables giving “m and y” values, used i n the Taylor Forge method for bolted flange connections calculation, have remained unchanged through years. Some gasket types do not appear in these tables and no r eference is made to a Tightness Class associated to these value s. Th need for an update of the exiting tables has been r aised by the supplier of French codes (CODAP® [1] and CODETI® [2 ]). A survey about the recommended values of “m and y” and their associated expected leakage rates for the gasket types available on the market has been performed. T he wide discrepancy in the test procedures and the gasket p arameter values showed the need for the development of a com mon test procedure. The new test procedure giving tables of “m and y” v alues depending on the tightness class is presented here. Th application of this procedure on several gasket typ es, lead to the publication of new tables for “m and y” values, in the last French codes revision. NOMENCLATURE A Paramet...

The structural durability of key structural elements of the Benin-Sagamu overhead bypass bridge located at Oluku, Benin City, Edo state, was determined by the use of reliability theory. The bridge dimensions were measured to determine its dead load while manual traffic count was used to estimate the traffic live loads by calculating the Annual Average Daily Traffic and simulating the total number of vehicles that would use the bridge in 120 years similar to methods used in EN 1991-2 (2003). From the traffic survey data, the mean vehicle load was used as the representation of assessment vehicle live load. The assessment vehicle model closest to those in CS 454 was used as the assessment vehicle and its axle loads and dimensions adopted for structural analysis using the influence line theory. Moments from the analysis resulting from dead and live loads represented the bridge strength model. The resistance model of the bridge was derived from concrete strength by Non-Destructive testing and from the section properties. The reliability theory was applied to determine the reliability and probability of failure of the transverse and longitudinal girders of the bridge. The reliability index of the transverse girder and longitudinal girders were 3.9 and 5.2 respectively and compares favorably to target reliabilities of EN 1990 (2002). The reliability theory was found to be efficient in determining the structural durability by the use of manual traffic counts.

This paper presents a discussion on different ways of assessing the safety of concrete structures applying Reliability Analyses. The usual design approach based on the Ultimate Limit States (ULS) is confronted with the Global Resistance Format, as defined infib Model Code 2010. The Global Format considers the several uncertainties present in the structural behaviour through a pre-defined limit state in which one or more loading variables are increased by aλfactor, until a collapse situation is attained. In this evaluation, the variables related to the actions and to the resistances are taken with their average value. The obtained values for theλfactor shall be compatible, in the safety point-of- view, with the β reliability factors corresponding to the required safety levels. A conventional building is analyzed, and the obtained reliability factors corresponding to the two approaches are presented. It is shown that the application of the Global Resistance Format can lead to more eco...

This paper deals with application of nonlinear analysis to study the system's limit state behaviour of cable-tensioned steel structures. The cable tendon is modelled as an equivalent truss element with initial pretensioned force applied either as selfequilibrating axial load or as an equivalent thermal load. The modulus of elasticity of the cable material can be modified to account for the constructional stretch and sagging effects in the cables. Pin-jointed space truss systems are modelled using a plastic-hinge nonlinear formulation, which implicitly satisfies the design specifications for ultimate strength of axially loaded members. Rigid space frame systems are modelled using an elasto-plastic nonlinear frame analysis program. The effectiveness of providing pretensioned cables in improving the limit state behaviour of pin-and rigid-connected space frames is demonstrated through several examples.

Based on realistic modeling of 44 bridges in national bridge inventory using its actual layout and dimensions, a theoretical framework is defined to calculate the tolerable differential settlement limits based on the over-bending moment or over-shear force generated by settlements and the moment or shear capacity of the bridge. First, the derived over-bending moment or over-shear force is validated through literature results. Second, the differential settlement limits of bridges are derived from the bridge strength capacities. Finally, based on the established differential settlement limits, the relationship of bridge differential settlement limits with its span length, number of spans, bridge skew, and the bridge type is discussed and compared with American Association of State Highway and Transportation Officials specification (2010). A statistics-based differential settlement limit criterion is also suggested for steel and prestressed concrete bridges and compared with the field survey results. From the research outcomes, it is concluded that extra caution is needed when implementing the 0.4% differential settlement limits of bridge foundations in American Association of State Highway and Transportation Officials.

Sandwich composites are widely used in various industries such as aeronautical, mechanical, automotive, marine and others. However, most of the existing sandwiches are not suitable and cost effective for applications in civil infrastructure. An innovative fibre composite sandwich panel made of glass fibre reinforced skins and a high strength core material has been developed for building and other structural applications. The behaviour of this new generation sandwich panel has been studied to assist the technical persons and the construction crews in better understanding its properties for an efficient use. If a fibre composite sandwich panel is placed not in the main fibre direction, an adverse effect on its performance may occur. Also, the point load is critical because the load creates stress concentration, which can easily damage the sandwich panel. This paper discusses the initial experimental investigation on this innovative sandwich for its one and two-way spanning floor applications under point loading. Initial investigation has shown that the stiffness of the sandwich is affected by the fibre orientation of the sandwich skins. No much effect has been observed for variation of fixity between slab and joist.