Ultimate Limit State Research Articles

Experimental and analytical investigation on eccentric performance of circular CFST columns jacketed by concrete-filled square tube

This paper presents an experimental and analytical investigation of the eccentric behaviour of circular CFST columns strengthened by a square steel tube and sandwiched concrete jackets. The main parameters include the eccentricity, strength of sandwiched concrete, and thickness of the outer steel tube. The failure modes, load-axial displacement curves, load-lateral deflection curves, and longitudinal strain distributions are presented. The effects of these parameters on the ultimate strength, ductility index, and lateral deflection are discussed in detail. Based on the longitudinal strain results obtained from the experiment and basic hypotheses, the possible positions of the neutral axis in the column section at the ultimate limit state were analysed, and three failure patterns of the specimens were determined. Analytical formulas corresponding to each failure pattern were derived to calculate the eccentric load-bearing capacity of the strengthened columns based on the limit equilibrium theory. Finally, a simplified formula was proposed to serve as the basis for future designs and applications.

Stability analysis of heavy machinery moving on weak subsoil. 3D FEM model vs. analytical models

In this paper, the authors present an extension of the scope of the previously conducted research to the full three-dimensional computer simulation (using the finite element method), which takes into account the interaction between: heavy caterpillar tracks system – working platform – weak subsoil. The article presents a computer model considering two caterpillars, resting on elastic-plastic sub-soil, with standard Mohr-Coulomb yield conditions, allowing for computer simulation of the behavior of the system up to achievement of ultimate limit state. The results of the above model are treated as the reference for a simplified Analytical Models of estimating the limit state, which might be used in design procedures. In turn, these Analytical Models are enhancements of previously presented one. The most important results concluding form the Analytical Model are simple interaction formulas, in the space of moments acting on the machine-subsoil system, limiting a domain of safety in given soil conditions.

Resistance Factor Spectra for the Ultimate Limit State of the National Building Code of Canada

Over the years, structural engineering codes and specifications in Canada and elsewhere have moved from an allowable stress design (ASD) approach to a load and resistance factor design (LRFD) philosophy. LRFD methodology takes better account of the inherent variability in both loading and resistance by providing different factors of safety for loads of distinct natures with regard to their probability of overload, frequency of occurrences and changes in point of application. The method also results in safer structures because it considers the behavior at collapse. While resistance factors for traditional construction materials based on LRFD in the National Building Code (NBC) of Canada are available, they cannot be used for non-conventional ones. This is because the resistance of such materials due to various load effects has unique bias factors (λR) and coefficients of variation (VR), which greatly impact their reliability index (β). In this study, relationships between the resistance factor ϕ and critical load effects from the NBC load combinations at ultimate limit states are developed for a wide range of resistance bias factors and coefficients of variation. The relationships are presented in the form of charts that are useful for researchers and code-writing professionals who have expertise in the various fields of structural engineering but lack proper background in reliability theory. The developed spectra showed that for the same ϕ, β increases with an increase in the live-to-dead load (L/D) ratio until it reaches 1; thereafter, the shape of the relationship will depend on the statistics of the resistance as well as on the magnitude of ϕ. For a small ϕ and VR, β will keep increasing with an increase in the L/D ratio from 1 until 3, albeit at a lesser rate. For L/D > 3, the relationship between the critical β and applied load is just about constant. This finding is also true for load combinations involving snow and wind. Application of the method is illustrated by a practical example involving the shear strength of a corrugated web steel beam.

Rapid Visual Screening Feature Importance for Seismic Vulnerability Ranking via Machine Learning and SHAP Values

Structures inevitably suffer damage after an earthquake, with severity ranging from minimal damage of nonstructural elements to partial or even total collapse, possibly with loss of human lives. Thus, it is essential for engineers to understand the crucial factors that drive a structure towards suffering higher degrees of damage in order for preventative measures to be taken. In the present study, we focus on three well-known damage thresholds: the Collapse Limit State, Ultimate Limit State, and Serviceability Limit State. We analyze the features obtained via Rapid Visual Screening to determine whether or not a given structure crosses these thresholds. To this end, we use machine learning to perform binary classification for each damage threshold, and use explainability to quantify the effect of each parameter via SHAP values (SHapley Additive exPlanations). The quantitative results that we obtain demonstrate the potential applicability of ML methods for recalibrating the computation of structural vulnerability indices using data from recent earthquakes.

Safety assessment of an existing bridge deck subject to different damage scenarios through the global safety format ECOV

The assessment of existing reinforced concrete structures, especially bridges and viaducts, nowadays is one of the most relevant aspects for engineers. In fact, due to the old age of a large part of the infrastructure assets and the deteriorating conditions affecting the structural elements, their safety with respect to the ultimate limit states may be compromised. In this perspective, the assessment by means of global safety formats employing non-linear finite element analyses can be an extremely useful tool. In this context, the study proposes to relate the safety level to the damage through 3D global non-linear numerical analyses. Specifically, the assessment of an existing prestressed reinforced concrete bridge deck is carried out by means of the global safety format denoted as “Estimation of Coefficient of Variation” (ECOV) assuming different damage scenarios. In fact, the safety of the structure is initially assessed with respect to the ultimate limit state in its undamaged condition. Subsequently, different damage scenarios, derived from the inspections, are numerically studied. For each damage scenario, the safety of the deck is evaluated with respect to the ultimate limit state relating the safety loss to the damage level. Finally, damage thresholds for this type of structure are defined on specific static parameters.

Design and testing of a self-centering friction damper-brace for compression ultimate limit state: Inelastic buckling

This paper investigates the design procedures and experimental testing of a low-damage brace equipped self-centering friction-based connection named Resilient Slip friction Joint (RSFJ). The brace energy dissipation and restoring force is provided by the damper component. Previous studies have shown that the damper ultimate compression strength might be jeopardized due to damper rotational flexibility, which might lead to premature elastic buckling of the brace. To address the issue, a concept of telescopic tubes was introduced to be put in parallel to the damper(s). The design of the telescopic tube requires a thorough framework that considers different possible failure loads and the collapse modes, so that the brace ultimate strength can be accurately estimated. Such a process tends to be more complex than the conventional Concentrically Braced Frames (CBFs), due to the non-continuity(ies) appearing as damper installation which may lead to possible plastic hinge formation in different locations of the brace. This study aims to employ second-order plastic analysis for the design of the damper-brace assembly. The proposed method is, is then validated with current international codes’ procedure and also with destructive tests on the self-centring brace specimens. Finally, the seismic design considerations including the design of the connections and protected members are discussed in this paper. The current procedure could also be recruited for other new emerging damper-braces as well.

Design of flexural strengthening based on fib Bulletin 90

This paper presents the analysis of intermediate and end debonding failure in slab strengthened using carbon tapes (Carbon Fiber Reinforced Polymer). The calculations are based on the more accurate method in the latest fib Bulletin 90. Consideration of additional effects based on three conditions: basic bond, bond friction and member curvature in the intermediate crack debonding analysis give the ratios ΔFf Ed/ΔFf Rd from 0.01 to 0.11, depending on the cross-section. For comparison in the simplified analysis of the ratio, MEd/MRd is equal 0.76. It is clearly visible the methods requiring more computational effort give lower values of element effort and allows the design to be more economical. As the strengthening fulfills the ultimate limit state, it does not meet the serviceability limit state.

Resistance factors for reliability based-design of geogrid reinforced soil foundations against ultimate and serviceability limit state

In the recent decades, the use of geosynthetics to improve the overall soil’s bearing capacity and settlement behavior under shallow foundations has become a major topic. Despite several studies that have been carried out on Reinforced Soil Foundations (RSF), no design specifications have been set to design RSF against the Ultimate and Serviceability Limit State (ULS and SLS) in any of the established codes. This paper presents the development of resistance factors based on the Load and Resistance Factor design (LRFD) approach against the ULS and SLS for strip footing resting on C−ϕ soils. The resistance factors are developed using a spreadsheet-based reliability model based on the First Order Reliability Method (FORM) to be consistent with the ASCE-7 load factors. The resistance factors are calibrated at a targeted probability failure (Pf) of 0.13499% and 0.00317% for ULS and 2.27%, for SLS. A Finite Element Model (FEM) is developed to validate three analytical solutions to establish the reliability model. The FEM results showed an agreement with the analytical solutions. For ULS the developed resistance factors at Pf= 0.13499% ranged from 0.33 to 0.9 assuming lognormally distributed variables and 0.25 to 0.89 assuming normally distributed variables. The resistance factors against SLS at Pf= 2.27%. ranged from 0.39 to 0.85 considering lognormally distributed variables and 0.35 to 0.83 considering normally distributed variables.

Bridge Capacity Assessment through LRFR Method and Bridge Seismic Performance Evaluation Using the PBSD Concept: Case Study

In this study, a comprehensive evaluation was conducted of the condition and performance of a concrete arch-type bridge located in close proximity to a fault. Utilizing the LRFR capacity assessment method and seismic performance analysis through the NLTHA process based on the PBSD concept, finite element modeling (FEM) was employed with a focus on construction stage analysis and model updating for calibration to site conditions. The assessment encompassed the determination of the rating factor for structural elements under service and ultimate limit state loading. Performance analysis under seismic loads includes an examination of engineering demand parameters such as concrete and reinforcement strains in columns, subjected to varying seismic hazard levels. Additional scrutiny involves assessing bearing displacement and overturning potential to identify potential damage before column failure. The primary objective of this research was to investigate pertinent and efficient techniques for evaluating bridge capacity and seismic performance. A thorough understanding of these methods is expected to facilitate the identification of suitable solutions to enhance the safety and reliability of bridges in Indonesia.

Verification of ultimate limit state of reinforced concrete walls of rectangular tanks with use “sandwich model” according to abendment of Eurocode

In the paper the calculations of reinforcement area of exemplary reinforced concrete squat silo for coal are presented. The results of classical calculation and calculation executed with use of ”sandwich model” are compared. The last one is recommended in the amendment of EC2-1-1 code. The calculations are preceded with compilation of standard recommendations concerning the dimensioning of concrete membranes, shells and plates

Development of a foam-filled steel web sandwich panel for the rehabilitation of timber floors

Lightweight sandwich panels offer a prominent solution for the rehabilitation of timber floors. This paper addresses the development of a solution capable of continuous production for a foam-filled steel web sandwich panel for floor rehabilitation. The newly designed flooring solution is tested in full-scale quasi-static flexural campaigns. The tests validate the analytical design's compliance with Ultimate limit state (ULS) and Serviceability limit state (SLS) requirements. Furthermore, the flexural behaviour is compared with analytical predictions for thin-walled members according to the effective width method, described in Eurocode 3. Different effective cross-section design assumptions are assessed to allow an accurate prediction of the panel's response.

Safety assessment of existing prestressed reinforced concrete bridge decks through different approaches

AbstractThe assessment of existing reinforced concrete (RC) structures, especially, bridges and viaducts, nowadays is one of the most relevant aspects for infrastructural engineers. Due to the old age of a large part of the railways and roadways assets, their safety, especially, with respect to the Ultimate Limit States (ULS) may result compromised. Safety assessment can be performed following different approaches as well as the most sophisticated methodologies based on the application of safety formats for non‐linear finite element (FE) analyses. This study presents the safety assessment at the ULS of existing prestressed RC bridge decks regarding bending moment and axial force failure mechanism adopting different methodologies. Specifically, the safety assessment will be performed through five different approaches (i.e., Courbon theory, elastic FE analysis, and NLFEAs according to the three global safety formats). The decks are modeled using, first, Courbon theory and then, girder FE model composed only of beam elements. The safety assessment is performed by comparing the design resisting moment and design acting moment in the section of interest, therefore, through a local approach. Within the local approach, design values are calculated using the partial safety factors. Afterwards, the decks are modeled with a 3D non‐linear FE model. Three different global safety formats are implemented within a global approach. The application of the different approaches leads to significantly different conclusions about the safety assessment. The two local approaches are the most conservative, therefore, lead to a lower safety margin. The application of global approaches based on global safety formats leads to a safety margin gain compared to local approaches, with significant variability in terms of safety margin gain depending on the specific global safety format.

Eurocode-compliant system-level reliability analyses of trussed portal frames under climatic loads

Eurocode 3 provides Geometrically and Materially Nonlinear Analysis with Imperfections-method (GMNIA) in which the entire structure can be designed in system-level. In GMNIA, reliability of structural system is verified by using a system safety factor which is obtained in Eurocode 3 based on numerical or experimental capacity test results. Unfortunately, such test results are scarcely published in the literature thus complicating the determination of the factor for a design engineer. In the so-called Direct Design Method, however, system safety factors are provided in advance for the design engineer by system-level reliability studies. This study determines the Eurocode-compliant GMNIA system safety factor for Warren truss portal frames by using the approach of the Direct Design Method. Advanced numerical models are utilized to perform Monte Carlo-simulations for entire structural systems. These simulations provide statistical distributions of system resistances which are employed in the First-Order Reliability Method to derive the system safety factors. Studied structures are made of S700 cold-formed hollow sections. Various system geometries, system configurations and load combinations consisting of snow and wind loads are investigated and a suitable system safety factor is proposed for the ultimate limit state design of Warren truss portal frames. The proposed system safety factor is applied in a practical comparison in which Warren system is designed both by the conventional Eurocode 3 method and GMNIA. This comparison reveals that GMNIA has a remarkable potential to offer reduced material consumption in design compared to the conventional method.

Displacement and damage analysis of earth dams during the 2023 Turkiye earthquake sequence

The earthquake sequence that occurred on 6 February 2023 in Turkiye caused significant damage to various infrastructures including geostructures such as dams. A total of 17 earth dams within a 200-km radius of the earthquake epicenter experienced varying degrees of damage, ranging from minor (∼2 cm) to major (up to ∼150 cm) deformations. As study of these reveals that the damaged dams are located within the closest distance to the fault of less than 30 km, with an average value of ∼12 km. This study specifically focuses on the seismic displacement analysis of the 17 damaged dams, utilizing the sliding block methods. The recorded motion data was analyzed using the kriging technique to estimate the spectral response at the dam sites. Moreover, the recorded ground motions were scaled to the resonant period of the dam site to estimate acceleration time history. The findings reveal that the rigid block analysis can provide an average estimation of seismic displacement with a relative error of less than 44%. The results of the damage analysis indicate that seven dams reached the ultimate limit state and two dams experienced the serviceability limit state. Moreover, the univariate and multivariate fragility functions are developed to estimate seismic probabilistic analysis of earth dams based on the observed data and the limit states. The results show that the selection of a single intensity measure (IM) and a combination of IMs can affect the predicted probability of failure. The findings provide an insight into the resilience assessment of dams and other geosystems during this strong earthquake.

Dependence of Sensitivity Factors on Ratio of Traffic Load to Dead Load

According to modern structural codes, a design is considered to be adequate if the limit states are not exceeded. For the ultimate limit state, the design value of action effect Ed is required to be less or equal than the design value of ultimate resistance Rd. This ensures, according to the Eurocode, a sufficiently low probability of failure expressed as the target reliability index β. Consequently, the distributions of action effect and of resistance need to satisfy the following conditions: PE>Ed≤Φ+αEβ and PR≤Rd≤Φ−αRβ, where αE and αR, with |α| ≤ 1, are the values of the FORM sensitivity factors. The values of the sensitivity factors αE and αR are suggested, according to EN1990, as −0.7 and 0.8, respectively; for the accompanying actions, the sensitivity factor is recommended as 0.28. In this paper, the dependence of the sensitivity factors for traffic live load, dead load, and resistance on the ratio of traffic load to dead load is studied (which is directly proportional to the maximum span of the bridge). Significantly different sensitivity factors for resistance, dead load, and traffic load, other than proposed by the Eurocode, has been calculated for typical ratio of traffic to dead load. It further showed that, if it is assumed that Ed = Rd and the Eurocode partial safety factors are used, a different design point than the starting point, i.e., Ed = Rd, is obtained.

Punching performance of flat slabs with openings accounting for the influence of moment transfer and shear reinforcement

The arrangement of openings adjacent or near to slab-column connections is very common practice in flat slab design due to a number of advantages for technical installations. Such location is however conflicting with the most critical region of the slab, where punching shear failures may develop and typically govern the design at ultimate limit state. This requires in many cases arranging shear reinforcement to enhance the performance of the connections both in terms of resistance and deformation capacity. Such shear reinforcement is in addition particularly useful when unbalanced moments are transferred from the slab to the columns, which is a phenomenon typically detrimental for the punching shear resistance of inner connections. Despite the practical relevance of this case, there is currently no experimental evidence on the response of shear-reinforced slab-column connections with adjacent openings and moment transfer. Design is thus performed on the basis of simplified rules, modifying the resistance of connections without openings. In the present study, a comprehensive test programme addressed at this issue is presented in an effort to improve the current state-of-knowledge. Five slabs representing several practical cases and potential arrangements of shear reinforcement were tested. The experimental results are investigated in detail and compared to codes of practice, highlighting a number of deficiencies of current simplified rules. The phenomena is finally investigated on the basis of the mechanical model of the Critical Shear Crack Theory, showing a general frame for modelling and design of such detail.

Determining Compressed Concrete Element Limit States Based on the Widths and Depths of Cracks Caused by Transverse Deformations.

In the modern theory of compressed concrete elements, the most attention is paid to longitudinal deformations, whereas transverse ones are rarely considered and just within Poisson's coefficient limits (i.e., elastic concrete behavior in the transverse direction). However, transverse deformations significantly develop beyond the limits corresponding to Poisson's coefficient, where they lead to longitudinal crack initiation and development. In-depth experimental and numerical investigations of transverse deformations in the inelastic stage showed that it is necessary to consider crack propagation. The present study proposes simultaneous consideration of longitudinal and transverse deformations, as well as the appearance of cracks and their widths and depths. This allowed us to obtain a complete compressed concrete element behavior pattern at all performance stages in two types of limit states (based on longitudinal and transverse deformations). Consequently, new ultimate limit states by the depth and width of cracks caused by transverse deformations are proposed to be included in modern design practices and codes.

Dynamic Analysis of Three Alternative Mooring Systems for a Semi-Submersible Wind Turbine in Intermediate Water Depth

Abstract Three forms of the mooring system in 60 m water depth are proposed for semi-submersible with partially inclined columns (SPIC) concept floating wind turbine (FWT). One is a simple form with only catenary lines, and the other two are hybrid forms including clump weights. The clumps are attached to the suspended section for Hybrid form1 and the bottom section for Hybrid form2. Hybrid form2 achieves the smallest line length and chain weight. Three alternative proposals can be evaluated through mooring line characteristics, dynamic responses, utilization factors, and simple cost analysis. Hybrid form2 allows for smallest pretension, and largest stiffness and nonlinearity only at large offsets. Under operational conditions, the mean surge for Hybrid form1 and Hybrid form2 is similar, but the fairlead tension is significantly smaller for Hybrid form2. Under the survival condition, the clumps of Hybrid form2 are lifted up and put down, leading to small mean offsets of FWT but large wave-frequency components of line tension. Among the three forms of the mooring system, the Hybrid form2 can limit the FWT to the smallest offset range while also controlling the mean mooring line tension to a level similar to the other two forms. Under normal working conditions and accidental conditions with single line broken, the maximal surge motions of FWT under the restraint of three mooring systems all meet the design requirements. The mooring line strength of the three mooring systems meets the requirements in ultimate limit state (ULS) and accidental limit state (ALS) analyses. Among them, the utilization coefficient of Hybrid form2 is closest to 1, demonstrating its best economic performance.

Probabilistic models of dynamic increase factor (DIF) for reinforced concrete structures: A Bayesian approach

The response of structures under rapidly varying loads can be affected by strain rate sensitivity generally expressed using Dynamic Increase Factor (DIF). Current models for estimating the DIF in Reinforced Concrete (RC) structures are generally deterministic and have restricted applicability due to their dependence on limited experimental data resulting in bias. This paper overcomes these limitations by proposing three probabilistic models that quantify compressive and tensile concrete and steel DIF, accounting for the relevant uncertainties. The proposed models are based on existing deterministic models with the addition of probabilistic correction terms. Bayesian updating is employed to estimate the unknown model parameters using observational data from a large collection of experimental observations. The models incorporate model uncertainties stemming from assumed model form and (potential) missing variables through a model error term. The proposed probabilistic models are used to evaluate the reliability of RC structures under dynamic loads. As an illustration, the proposed probabilistic models are used to estimate the reliability of an example RC column under combined dynamic axial force and moment, and a RC column or beam under dynamic bending moments resulting in cracking. In the two examples, we consider the ACI 318-19 requirements for Ultimate Limit State (ULS) and Serviceability Limit States (SLS). In comparison to deterministic DIF models, the proposed probabilistic models yield enhanced predictive accuracy, presenting a practical and robust approach to assess the structural reliability under impact and blast loads.

Feasibility of outrigger structural system for tall timber buildings: A numerical study

Tall timber buildings are prone to serviceability problems (e.g. lateral displacements and wind-induced accelerations). This article investigates the feasibility of timber outrigger system to build up to 20 storeys using linear elastic finite element analysis and relevant European and international standards such as EN 1990, EN 1991-1-1, EN 1991-1-4, EN 1995-1-1 and ISO 10137. The location of up to two outriggers was optimised based on different serviceability criteria. Various outrigger layouts were investigated, and their stiffness demands were discussed. The efficiency of outrigger structures in reducing lateral displacements and wind-induced accelerations is highlighted. A feasibility study considering serviceability requirements was performed using different basic wind velocities, number of storeys and gravity loads. Although the focus of the article is on serviceability requirements, some ultimate limit state considerations (forces and stresses) were briefly discussed. The results demonstrate the feasibility of building up to 16 storeys under medium to high wind velocities.