Serviceability Limit State Criteria Research Articles

Serviceability Limit State Assessment of Semi-Submersible Floating Wind Turbines

Abstract The design of a floating wind turbine (FWT) should satisfy the serviceability limit state (SLS) requirement for an efficient and safe operation throughout the entire work life. The SLS requirements are introduced by the owner/developer of the wind turbine facility to achieve serviceability (production of power) or an efficient operation of the facility or a “first step” towards ensuring safety. Currently, there is limited information about SLS requirements in design standards. This study deals with an assessment of current methods, criteria, and procedure for the SLS design check with an emphasis on tilt/pitch and nacelle accelerations in view of power production and its fluctuations. Moreover, other criteria, on the borderline between serviceability and safety criteria, e.g., relating to clearance, are briefly discussed. The criteria relating to power production are illustrated in a case study with a 10-MW semi-submersible FWT considered for an offshore site in the Northern North Sea. Simplified static/dynamic analysis methods for use in the global design phase and high fidelity integrated, dynamic analysis methods for detailed design in terms of serviceability are presented, discussed, and applied in the case study. A good understanding of wind turbine dynamic performance associated with serviceability is essential to facilitate design decision-making. The relative contribution of wind and wave loads to the different SLS criteria is investigated. Finally, the main conclusions are summarized. In lieu of the current state of the art regarding SLS requirements for FWTs, we hope that this study provides a basis for improving design standards and guiding research and engineering practice for the semi-submersible floater design of FWTs.

Design of cross-laminated timber (CLT) floors for human-induced vibrations

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 take into account different factors. In order to get a better description of the actual behaviour of floor structure, certain classifications of floors based on vibration serviceability performance were introduced in design methods.

Elastic shakedown limit of a steel lattice girder

This paper presents a solution for the problem concerning the behaviour of a steel lattice girder subjected to dynamic load pulses. The theory of shakedown is used in the analysis. It is assumed that such loads cause a non-elastic response which includes dissipation of energy causing deformations and residual forces developed in the structural members of the girder. At a certain intensity of these forces, the girder can react to subsequent load pulses without further dissipation of energy, behaving in the elastic region after shakedown. This condition is referred to as adaptation of the structure to assumed cyclic loading. Elastic shakedown limit is determined through a direct analysis of the girder's dynamic behaviour, i.e. by checking if energy dissipation decreases with loading cycles. This gives the number of load applications after which no further increase of the energy dissipation is observed. The existing permanent deformations persist and residual forces remain in the same state. The analysis takes into account the possibility that compressed members can buckle which may result in non-elastic, longitudinal and transverse vibrations of these members. Non-linear geometry of members is taken into account. Then a perfectly elastic-viscoplastic model of the material is used. The main goal is to determine the state of the non-elastic movements of the girder joints and the residual internal forces developed in the girder members after each load application. The values obtained in this way serve as the basis for describing the next loading cycle. It is possible to use the approach presented in the paper to evaluate the effects of accidental loads. Then it is checked whether a small number of repetitions of accidental load would result in exceeding the serviceability limit state criteria of the maximum permanent deformation or displacement and/or strain amplitudes. If so, the magnitude of accidental load is greater than the elastic shakedown limit. Some examples are given to illustrate the application of the theory of shakedown.

Numerical Investigation on Shear Deflection of Steel Welded I Sections with Varying Span to Depth Ratios

Deflection of the steel I-sections is an important phenomenon that needs to be taken into account to ensure that the serviceability limit state criteria of the Australian Standards are met. The method that is widely used to calculate the deflection of steel I-sections is by the use of existing formulae that only accommodate the bending stiffness of the beams. A numerical investigation is performed in this study to find the contribution of shear effects in the final deflection of the Welded-Beams (WB) and Welded-Columns (WC). The numerical analyses were carried out in SAP2000 and numerical model was first validated using the experimental results of welded plate girders. The model was then used to analyse simply supported WB and WC sections under uniformly distributed load (UDL) with varying span lengths. The results of the numerical analyses are reported in this study which compare the mid-span deflection values from the simply supported deflection formula with the numerical model deflection values. The data acquired from the numerical analyses were used to establish a span to depth ratio for WB and WC sections below which the shear deflection becomes significant. The analysis of the results obtained from the numerical investigation suggests that a predication error begins to emerge in the result that is acquired from flexure deflection formulae at a certain span-depth ratio.

Reliability analysis of offshore wind turbine foundations under lateral cyclic loading

Abstract. The design of foundations for offshore wind turbines (OWTs) requires the assessment of long-term performance of the soil–structure interaction (SSI), which is subjected to many cyclic loadings. In terms of serviceability limit state (SLS), it has to be ensured that the load on the foundation does not exceed the operational tolerance prescribed by the wind turbine manufacturer throughout its lifetime. This work aims at developing a probabilistic approach along with a reliability framework with emphasis on verifying the SLS criterion in terms of maximum allowable rotation during an extreme cyclic loading event. This reliability framework allows the quantification of uncertainties in soil properties and the constitutive soil model for cyclic loadings and extreme environmental conditions and verifies that the foundation design meets a specific target reliability level. A 3D finite-element (FE) model is used to predict the long-term response of the SSI, accounting for the accumulation of permanent cyclic strain experienced by the soil. The proposed framework was employed for the design of a large-diameter monopile supporting a 10 MW offshore wind turbine.

Reliability of Super-T PSC girders at serviceability limit state stresses across all span ranges

Reliability assessment gives useful information on the level of performance or adequacy of design rules. There are five standardized Super-T prestressed concrete (PSC) girder sections widely used for bridges in Australia. The Australian standard (AS 5100) requires serviceability limit state criteria of allowable stresses to be met. However, there is not yet an assessment of the performance achieved by these rules. In this study, all potential strand arrangements (more than 50,000) for all Super-T sections, across all feasible span ranges, are assessed. Ten girder-slab bridge decks are analysed; the critical girder in the deck is designed for all possible strand arrangements. Design adequacy is assessed using the annual reliability index. A system reliability analysis is conducted using Ditlevsen bounds to check that none of the four stress limits are exceeded. Generally, it is found that the Super-T girder designs are adequate for most strand arrangements compliant with AS 5100. Further, the reliability varies significantly depending on the selected span, section and strand arrangement. This work informs designers on the reliability performance of Super-T girders designed to AS 5100 and provides background for future revisions of AS 5100.

Predictive models of ultimate and serviceability performances for underground twin caverns

The construction of a new cavern modifies the state of stresses and displacements in a zone around the existing cavern. For multiple caverns, the size of this influence zone depends on the ground type, the in situ stress, the cavern span and shape, the width of the pillar separating the caverns, and the excavation sequence. Performances of underground twin caverns can be unsatisfactory as a result of either instability (collapse) or excessive displacements. These two distinct failures should be prevented in design. This study simulated the ultimate and serviceability performances of underground twin rock caverns of various sizes and shapes. The global factor of safety is used as the criterion for determining the ultimate limit state and the calculated maximum displacement around the cavern opening is adopted as the serviceability limit state criterion. Based on the results of a series of numerical simulations, simple regression models were developed for estimating the global factor of safety and the maximum displacement, respectively. It was proposed that a proper pillar width can be determined based on the threshold influence factor value. In addition, design charts with regard to the selection of the pillar width for underground twin rock caverns under similar ground conditions were also developed.

Statistical calibration of safety factors for flexural stiffness of composite columns

Composite column design is strongly influenced by the computation of the critical buckling load, which is very sensitive to the effective flexural stiffness (EI) of the column. Because of this, the behaviour of a composite column under lateral loading and its response to deflection is largely determined by the EI of the member. Thus, prediction models used for composite member design should accurately mirror this behaviour. However, EI varies due to several design parameters, and the implementation of high-strength materials, which are not considered by the current composite design codes of practice. The reliability of the design methods from six codes of practice (i.e., AS 5100, AS/NZS 2327, Eurocode 4, AISC 2010, ACI 318, and AIJ) for composite columns is studied in this paper. Also, the reliability of these codes of practice against a serviceability limit state criterion are estimated based on the combined use of the test-based statistical procedure proposed by Johnson and Huang (1997) and Monte Carlo simulations. The composite columns database includes 100 tests of circular concrete-filled tubes, rectangular concrete-filled tubes, and concrete-encased steel composite columns. A summary of the reliability analysis procedure and the evaluated reliability indices are provided. The reasons for the reliability analysis results are discussed to provide useful insight and supporting information for a possible revision of available codes of practice.

Regression models for estimating ultimate and serviceability limit states of underground rock caverns

Performances of underground rock caverns can be unsatisfactory as a result of either instability (collapse) or excessive movements. Collapse refers to ultimate limit state failure, in which the stresses exceed the strength of the rock masses. Failure of the serviceability limit state refers to excessive deformations resulting in difficulties during excavation such as lining placement and reinforcement installation. Both distinct limit states may need to be considered in design. This study used numerical modeling to assess both the ultimate and the serviceability limit states of underground single and twin rock caverns. The global factor of safety is used as the criterion for the ultimate limit state and the calculated percent strain around the cavern opening is adopted as the serviceability limit state criterion. Based on the numerical results, simple regression models were developed for estimating the global factor of safety and the induced percent strain of the single and twin caverns, respectively. Charts for assessing cavern stability for preliminary design use were developed. In addition, the use of the critical strain concept and the elastic and design line methodology to limit the induced strains was discussed.

Load capacity and serviceability conditions for footbridges made of fibre-reinforced polymer laminates

The contribution is focused on derivation of the Ultimate Limit State (ULS) and Serviceability Limit State (SLS) design criteria for footbridges built of fibre-reinforced polymer matrix (FRP) laminates. The ULS design criterion is based on the design guidelines for above-ground, pressure, FRP composite tanks and the Tsai-Wu failure criterion, which is used to predict the onset of FRP laminates damage. The SLS criterion is based on vertical deflections and natural frequencies limitations of the analysed FRP footbridge. As a part of the research, a special design procedure is established for FRP footbridges design process, covering both the preliminary and detailed engineering calculations. As an illustrative example, the procedure is applied to glass-fibre reinforced vinylester laminate with 90°C heat deflection temperature and 50-year service life. A deflection-based serviceability limit state criterion is established using the same approach as that currently used in the design of steel footbridges. Moreover, the second serviceability limit state criterion is proposed. It limits the range of possible fundamental natural frequency of footbridge without any load and loaded with an additional mass 70 kg/m2 applied to simulate load created by moderate pedestrian traffic.

Cracking and deflections in GFRP RC beams: An experimental study

Fibre Reinforced Polymers (FRPs) have emerged as an alternative to steel for Reinforced Concrete (RC) elements in aggressive environments. The low modulus of elasticity of FRP bars can yield to large crack widths and deflections and, as a result, the design of FRP RC elements is often governed by serviceability limit state criterion. This paper presents the results of an experimental programme on the cracking and deflections of 14 Glass-FRP RC beams. The adequacy of the most representative prediction models for the serviceability limit states of cracking and deflections of FRP RC beams is investigated. The influence of the most relevant parameters is analysed, and the suitability of different prediction models, as well as the adjustment of empirical coefficients, is analysed and discussed.

Reliability assessment on ultimate and serviceability limit states and determination of critical factor of safety for underground rock caverns

The observational design method which uses extensometers to measure the displacements during cavern construction and then adopt these data for back analysis does not always guarantee satisfactory performance because the displacements provide little information about the strength to stress ratio that ultimately determines the stability of the rock caverns. In this study, both the ultimate and serviceability limit states are investigated by means of the Finite Difference program FLAC3D. The global factor of safety obtained using the shear strength reduction technique is used as the criterion for the ultimate limit state and the calculated percent strain around the opening is adopted as the serviceability limit state criterion. High deformability, low shear strength and the high in situ stress state are the major factors that govern the underground rock cavern stability and serviceability. Through the identification of the key influencing parameters for calculating the factor of safety and the percent strain, numerical experimentations are performed in accordance with the methodology of 2k factorial design, from which polynomial regression models are developed for each rock mass condition. The First-Order Reliability Method (FORM) was used to determine the probability of failure for the limit states. Through the use of the automated spreadsheet search algorithm to determine the design point, to meet the different target performance levels, the required minimum FS is obtained and termed as the critical value. This proposed approach enables a cost-effective analysis to be conducted for a rational design of underground rock caverns.

Experimental study on bond performance of GFRP bars in self-compacting steel fiber reinforced concrete

Reinforcing bars made of Glass-Fiber-Reinforced Polymers (GFRPs) are more and more common as internal reinforcement of concrete structures and infrastructures. Since the design of GFRP reinforced concrete members is often controlled by serviceability limit state criteria (i.e. deflection or crack width control), an accurate knowledge of the GFRP-concrete bond behavior is needed to formulate sound design equations. Furthermore, bond laws currently available and widely accepted for conventional steel rebars cannot be straightforwardly applied for GFRP ones. Hence, an experimental program consisting of 36 pullout bending tests was carried out to evaluate the bond performance between GFRP bars and steel fiber reinforced self-compacting concrete (SFRSCC) by analyzing the influence of the following parameters: GFRP bar diameter, surface characteristics of the GFRP bars, bond length, and SFRSCC cover thickness. Based on the results obtained in this study, pullout failure was occurred for almost all the specimens. SFRSCC cover thickness and bond length plaid important role on the ultimate value of bond stress of GFRP bars. Moreover, the GFRP bars with ribbed and sand-coated surface treatment showed different interfacial bond behaviors.

Reliability of structures with tuned mass dampers under wind-induced motion: a serviceability consideration

Excessive wind-induced motion in tall buildings can cause discomfort, affect health, and disrupt the daily activities of the occupants of a building. Dynamic vibration absorbers such as the tuned mass dampers (TMDs) can be used to reduce the wind-induced motion below a specified tolerable serviceability limit state (SLS) criterion. This study investigates whether the same probability of not exceeding specified wind-induced motion levels can be achieved by torsionally sensitive structures without/with linear/nonlinear TMDs subjected to partially correlated wind forces, if they are designed to just meet the same SLS criterion. For the analyses, different structures and the uncertainty in the response, wind load and perception of motion is considered. Numerical results indicate that for structures that are designed or retrofitted without or with optimum linear TMDs and satisfying the same SLS criterion, their probability of exceeding the considered criterion is very consistent, if the inherent correlation between the wind forces is considered in design. However, this consistency deteriorates if nonlinear TMDs are employed. Furthermore, if the correlation is ignored in the design, in many cases a slightly unconservative design, as compared to the designed by considering correlation, is achieved.

Crack Width Analysis of Reinforced Self-Compacting Concrete Beams

Self compacting concrete is a concrete mixture specifically designed not to require external energy for compaction. This property results in many advantages for precast as well as ready-mix concrete applications. Especially, dense reinforcements or slender elements can be achieved. However, in current design codes this concrete is treated as traditional concrete although the mix composition is substantially different. Due to a decrease in coarse aggregates, combined with a higher amount of chemical and mineral admixtures, the overall mechanical behavior may differ from that of traditional concrete even when the compressive strength of both mixtures are equal. This is especially visible in the crack formation in the tensile zone of concrete beams. This paper presents results of an analysis of crack formation, distribution and width on reinforced concrete beams with varying reinforcement ratios. Differences in crack properties, favoring self-compacted over traditional concrete are found for all considered reinforcement ratios, although the results are less pronounced for the higher ratios. The results may allow a favorable serviceability limit state criteria for this material.

Serviceability Limit State criteria based on steel–concrete bond loss for corroded reinforced concrete in chloride environment

This paper will focus on the study of reinforced concrete beams stored in a chloride environment for a period of 14–23 years under service loading. According to the experimental results, a Serviceability Limit State (SLS) criteria is proposed based on an excessive steel–concrete bond reduction. Corrosion of reinforcement in chloride environment leads to a specific local steel cross-section loss as well as a steel–concrete bond loss. Experimental results have shown that, in the first stage of corrosion propagation period, the deflection is more sensitive to chloride-induced corrosion than the ultimate capacity due to the effect of the tension steel–concrete bond loss even if both are correlated. Given this high sensibility of the bending stiffness to corrosion pitting attacks, it appears that a Serviceability Limit State (SLS) criteria based on excessive deflection of structural members is an adequate factor for SLS assessment. Later in corrosion propagation period, when the bond is already significantly reduced, only the ultimate capacity is affected by the steel cross-section loss. This does not affect the serviceability, because pitting attacks are very localised with an insignificant influence on the global deflection. Then, once the steel–concrete bond is lost in critical parts of the beams (high bending moment areas), pitting corrosion propagation does not affect anymore serviceability (stiffness reduction, bending or corrosion cracks patterns) but still leads to an ultimate capacity reduction, which is not acceptable. As a result, excessive steel–concrete debonding can be considered as the SLS criteria.