Ultimate Limit State Design Research Articles

Reliability design for bearing capacity of steel plate strengthened RC beams based on the improved design value method

AbstractThe partial factor method is widely employed as a design approach for structural reliability and serves as a crucial foundation for structural design codes. However, in practical applications, this method has gradually revealed shortcomings, such as issues with generality and insufficient precision in reliability control. In this article, an improved design value method for the bearing capacity design of steel plate strengthened RC beams was established. Additionally, considering the impact of the live‐to‐dead load effect ratio on the partial safety factor of resistance, a simplified expression for the ultimate limit state design of bearing capacity was proposed. The results show that the reliability index calculated using the partial factor method for the bearing capacity of steel plate strengthened RC beams has a significantly larger relative error. In contrast, the reliability indexes calculated based on the improved design value method are all greater than the target reliability index, ensuring the requirements of reliability design and providing a higher degree of precision in reliability control.

Prediction of ultimate tensions in mooring lines for a floating offshore wind turbine considering extreme gusts

The design of mooring line parameter for a floating offshore wind turbine (FOWT) should consider the ultimate limit state. Typhoons should be considered as a threatening condition for mooring design, and the characteristics of transient changing wind should be studied. Currently, few extreme value predictions consider gust features, and extreme mooring tensions may be underestimated in practical FOWT design. We conducted the simulations of the 5 MW wind turbine from the National Renewable Energy Laboratory (NREL) in the environmental conditions of extreme gusts, waves, and currents. Extreme gusts were found to cause dramatic increases in mooring tensions under 100-year typhoon conditions. The average conditional exceedance rate (ACER) method is used to predict extreme mooring tensions. The impacts of simulation duration and sample size on the prediction results are then discussed. The results show that in extreme gust conditions, the tail data of the average conditional exceedance rate of mooring tension presents a different extrapolation trend from stable wind conditions. Short-term predicted values in gust conditions are 14–20% larger than those in stable wind conditions. The research shows the necessity of considering threatening gust conditions in the ultimate limit state design of mooring system of FOWT.

Influence of wave spreading on offshore wind turbine design: IEA 15-MW scenario

Offshore ocean waves are directionally spread, whereby the propagation of energy travels in different directions. Despite this multi-directionality, the use of 3-dimensional wave models for loading on fixed offshore wind turbines has been limited. This is partially due to the common assumption that uni-directional sea-states are conservative within a design philosophy. This may not always be true given that in operating conditions the amount of aerodynamic damping in the side-side direction is much lower than the fore-aft direction. This paper aims to address this issue by providing the influence of wave spreading on various offshore wind turbine design scenarios: fatigue, ultimate and service limit state design. This study demonstrates that wave spreading indeed results in more fatigue damage for operating load cases. Despite this, the overall fatigue and ultimate limit state utilisation is still reduced when a wave spreading is adopted.

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.

Ultimate limit state design of wind turbine tower: A review

Ultimate limit state design of wind turbine tower: A review

Design of precast UHPFRC retaining walls – Experimental and numerical validations

This paper focuses on the design as well as on the experimental and numerical validations of the mechanical behavior of a precast ultra-high performance fibre reinforced concrete (UHPFRC) retaining walls. The design, made in accordance with the Canadian Highway Bridge Design Code ( CSA S6, 2019 ), led to the fabrication of a full-scale UHPFRC retaining wall with 3% fibre content which had dimensions of 3 m in height, 2 m in length, 2 m in width, with two vertical and horizontal stiffeners, and very thin vertical and horizontal panels of 40 and 65 mm, respectively. The experimental tests showed that the UHPFRC retaining wall exceeded by 42% the ultimate limit state (ULS) design factored bending moment and showed a very ductile behavior under flexural loading. At service limit state (SLS), the retaining wall had maximum crack opening between 0.15 and 0.28 mm, and a maximum lateral displacement of 4 mm. The finite-element model developed for the application captured accurately the flexural behavior of the UHPFRC retaining wall and was used later in parametric studies to optimize the design. The retaining wall optimal design includes UHPFRC with 3% fibre content and stiffeners with variable cross-section which allows volume reductions of 73% for concrete and 86% for rebars in comparison to the conventional reinforced concrete design.

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A novel design of a hybrid glulam-steel substructure for the IEA 15-MW floating wind turbine

Wind energy has become increasingly recognised as a very promising type of renewable energy. In addition, floating offshore wind turbines have facilitated the development of electricity production in intermediate (45-150 m) and deep sea (>150 m) depths. Despite this, wind turbine manufacturing, installation, and operation may generate substantial greenhouse gas emissions. A novel hybrid glulam-steel floating substructure design is presented in this research, intended for the IEA 15 MW floating wind turbine. The objective is to contribute to advancing floating wind energy while minimising costs and carbon dioxide emissions. The objective of the novel design is to substitute steel with glued laminated lumber (glulam). It showcases an altered iteration of the UMaine VolturnUS-S semi-submersible platform originally created for the IEA 15 MW turbine. Before selecting one of three preliminary hybrid wood-steel models, the Ansys Workbench 2020 R1 is used to evaluate and appraise them per a set of criteria extracted from pertinent timber and steel standards. The chosen hybrid design conserves about 590 metric tonnes of steel mass compared to the UMaine VolturnUS-S semi-submersible platform. The selected model is then validated by executing a fully coupled aero-hydro-servo-elastic dynamic analysis with OpenFAST. Consideration is limited to the ultimate limit state design (ULS) for normal and severe operating situations. The utilisation factor of the glulam supporting structure for the IEA 15 MW turbine ranges from 74% to 94%, indicating that it is an effective load-bearing solution.

Probabilistic calibration of the p-y method considering model uncertainty for ultimate limit state design of monopiles

ABSTRACT The API p-y method is widely used in the design of offshore wind turbines (OWTs) monopiles at present. This study systematically evaluates the model uncertainty of the p-y method for OWT monopiles and proposes a two-stage calibration approach for evaluating the model bias factor. To overcome the difficulty of limited field tests, a high-fidelity base model is employed as a bridge between the field test data to the p-y method. The field test data is used to calibrate the base model and determine the model error of the base model. Synthetic numerical cases are subsequently generated using the base model to evaluate the correction factor of the p-y method. By combining the model error of the base model and the correction factor of the p-y method, the model bias factor of the p-y method can be evaluated. The reliability analysis of the monopile in an offshore wind project in China is taken as an example. The results serve as a valuable tool for correcting the lateral bearing capacity of OWT monopiles based on the specific soil conditions and risk preferences for the offshore wind turbine project.

Rolling Shear Strength of Cross Laminated Timber (CLT)—Testing, Evaluation, and Design

Cross laminated timber (CLT), with its typical orthogonal layering and exposure to out-of-plane bending, develops inherent rolling shear stresses. These stresses need to be checked during the ultimate limit state design process. With the ongoing revision of Eurocode 5, a discussion regarding the characteristic value of the rolling shear strength of CLT has arisen. One obstacle in the discussion is seen in the lack of harmonized regulations concerning how to determine rolling shear properties. This circumstance manifests in the greatly diverging test results of different institutions testing the rolling shear strength. The paper at hand aims to propose a candidate for such harmonized regulations. To achieve this, the most common test setups, such as the inclined shear test, three- and four-point bending tests, etc., were numerically and experimentally investigated. Within the numerical investigations, a comparison of the most common calculation methods (Timoshenko beam theory, modified γ-method, Shear Analogy Method, and Finite Element Analysis) for evaluating rolling shear stresses was included. In the experimental program, parameters such as the specimen width, number, and thickness of the cross layer(s), shear length, optional reinforcement against the stresses perpendicular to the grain, and the overall test setup were varied. It was found that the used test setups themselves and the area of the cross layer(s) (shear length, number, and thickness of the cross layer(s)) have a major impact on the rolling shear strength. In contrast, no effect was found from the calculation methods. Based on these findings and on a database of approx. 300 four-point bending rolling shear tests on CLT specimens from five well-established CLT manufacturers, a model for the regulation of the rolling shear strength of CLT is proposed, in combination with a corresponding four-point bending test setup. Afterwards, with two additionally conducted four-point bending test series, the proposed model is successfully validated. The conclusions and recommendations in respect to the test setup (four-point bending), evaluation procedure (Timoshenko beam theory), reference characteristic rolling shear strength, and the model, which allows adapting the reference rolling shear strength to individual conditions, are seen as a worthy basis for a more objective discussion on this topic.

Model factor for ultimate limit state design of bored pile foundations

This paper will be primarily concerned with the determination model factor for designing bearing capacity of bored pile foundations ultimate limit state (ULS). For geotechnical designs, the source of uncertainty consists of factors: (i) calculation methods uncertainnties, and (ii) uncertainnties associated with design soil properties. Eurocode 7 Part 1 allows a ‘model factor’ γRd>1 to be applied in design by calculation to ‘correct’ the resistance factors γR. The model factor value is determined from comparing the ratio of the static load test results Rc,m with the calculated prediction results Rc,p. By analyzing the bored pile data set from the axial compression static load test, the paper uses reliability theory to determine the value of γRd when designing the bored pile foundation according to ultimate limit state.

Methodology of load effect analysis and ultimate limit state design of semi-submersible hulls of floating wind turbines: With a focus on floater column design

A main challenge in the design of hull structures of floating wind turbines (FWTs) is to properly estimate the load effects and resistance to perform the safety design check. While great efforts have been devoted to the load effects in terms of global motions, there is a lack of effective methods to calculate internal loads and lateral pressures of hulls in a fully coupled aero-hydro-servo-elastic environment, which should serve as the basis for the assessment of load effects in hulls. Moreover, very limited knowledge and experience exist in the current guidelines and research publications to deal with the detailed design of hull structures of FWTs. This study outlines an effective methodology and procedure to determine load effects for structural design of semi-submersible hulls, and demonstrates their application in a case study of column design based on the ultimate limit state (ULS) criteria. First, a novel multi-body floater model is established in a fully coupled FWT numerical system, which is capable of calculating floater internal loads. Second, the environmental contour approach is employed to initially choose load cases for ULS design, based on important wind speed conditions and criterial wave periods. Next, a screening of the critical load cases is made based on Von Mises stress analysis of columns considering global loads. Then, lateral pressure on columns is calculated, and a detailed design check is made based on combined global loads and lateral pressure as well as relevant safety factors for loads and resistance. Furthermore, the relative influence of global loads and lateral pressure on ULS performance of columns is investigated, which serves as the basis to reset the critical load cases for ULS design check. Subsequently, sensitivity analysis of ULS performance with respect to column design parameters, extreme value estimation, and shell buckling design checks, are performed to determine the plate thickness and ring stiffener distances of central and outer columns. Finally, optimized ring stiffener dimensions are estimated for different design cases based on panel buckling design criteria, and detailed design parameters for the central and outer columns are obtained. The methodology and procedure established and applied in a case study in this work, contribute to improving engineering practice and establishing improved design standards.

A comparison of extreme mooring loads and response of a spar-buoy wind turbine using conditional waves

Three-hour random sea-state evaluations for ultimate limit state design of floating offshore wind installations are time-consuming and prevent the use of high-fidelity numerical methods from being implemented. In this work, three conditional waves, Most-Likely Wave (MLW), Most-Likely Response Wave (MLRW) and Conditional Random Response Wave (CRRW), are experimentally investigated as alternative means to generate statistical extreme responses in surge and mooring line loads of a spar-buoy substructure, with shorter time-series duration compared to a 3-hour JONSWAP sea-state. MLW and MLRW are found to generate the greatest mooring line loads, far greater than the statistical expected maximum from a 3-hour random sea-state. However, MLW is uncorrelated with the substructure’s linear transfer function of response, and the MLRW includes no memory effects from a random background sea, indicating possible conservatism in the associated load magnitudes. CRRW is a MLRW embedded within a random background and is found to excite a similar mooring load as the 3-hour sea-state, with memory effects included. CRRW could thus be an appropriate method of generating statistically appropriate load responses within a reduced time-series. However, nonlinear effects on the mooring are not accounted for in any of the methods and will be included in future work.

Wrapped Composite Joints for Circular Hollow Section Structures

AbstractAn innovative bonding joining technology for truss/lattice circular hollow section (CHS) supporting structures is being developed as replacement for welded joints. Wrapped Composite Joint uses bonding instead of welding to transfer the joint forces and bending moments between the chord and brace CHS members through a dedicated fibre reinforced polymer composite wrap. It is aimed to replace all welds in different types of joints such as X, K, KK and splice joints in fatigue and/or corrosion dominated designs of truss/lattice structures such as offshore wind jackets and floaters, fish farms, truss bridges, etc. Composite material is known for good fatigue performance from aerospace industry and wind turbine blades. Number of joint experiments showed superior fatigue performance of the wrapped composite joints compared to welded CHS joints. This new concept allows for huge reduction of thickness of CHS members resulting in significant truss/lattice structure weight reduction and increase of fatigue lifetime. This paper presents state of development and outlook of the wrapped composite joint technology in terms of design, production and joint performance for ultimate limit state, fatigue and influence of the environment. Framework of prediction methods and design principles based on ongoing experimental and numerical research will be presented. The scope includes material, interface, and joint level experiments from small to full scale (100‐600 mm member diameter) and finite element modeling of complex steel‐composite bonded joints. Advantage of using state‐of‐the‐art monitoring techniques such as Digital Image Correlation, Fibre Optics Strain Measurement and 3D scanning is highlighted

Rigorous lower and upper bounds for the generalised failure loads of pile groups

A renewed philosophy for the ultimate limit-state design of pile groups is based on the adoption of multiaxial strength envelopes. In this view, this study proposes a limit analysis-based framework providing high-fidelity predictions for the generalised failure loads of piled foundations. This is accomplished through: (a) the development of an upper-bound solution that better approximates the exact solution compared to existing ones and (b) the integration of a recently developed lower-bound solution with a formulation accounting for pile–soil–pile interaction at failure. The comparison between these complementary methods proved to be satisfactory on many load combinations. The proposed framework is readily applicable in design, at a minimal computational effort, and in a more refined assessment of structures, as it provides the ultimate limit-state surface for a plasticity-based macroelement representation of deep foundations. The framework is used herein to investigate the horizontal efficiency of a well-documented piled foundation, and theoretical predictions are compared with results of fully coupled numerical analyses. The resulting strength envelopes point out the effect of the vertical load on the mutual interaction between piles, which is an indicator of the contribution of the pile's axial capacity in the activation of multiaxial failure modes.

Design of reinforced concrete structures based on three‐dimensional stress fields

AbstractThe ultimate limit state design of reinforced concrete members usually derives from the analyses of structural models composed of unidimensional or bidimensional elements (bar and shell elements, respectively). Less recurrent in these structural models is the use of solid elements, which may be ascribed to the difficulties arising when dimensioning the structure for the complete stress field with six stress components (σx, σy, σz, τxy, τxz, τyz) derived from the analyses. In the present work, the design method for three‐dimensional stress fields combining linear analysis and limit design is revisited, with the description of the resisting mechanism in which the applied stresses are balanced with stresses in the concrete and in the reinforcement. Expressions for the verification of concrete crushing and the evaluation of the required reinforcement are deduced analytically and interpreted physically. The design process is organized into four design cases, according to the internal stresses mobilized in concrete. The proposed equations are presented in a framework for direct application to engineering practice, as demonstrated in noted design examples for selected stress states.

Behavior and design of earthquake resistant concrete structure

Earthquake and seismic-resistant concrete structures are essential components and requirements of structural design. The performance and response of concrete structures during/after the earthquake event are significant to determine the condition of the structures as well as to identify the possibility of structural failure. The main objective is to investigate the appropriate method to evaluate the impact on the structure due to earthquakes based on closed-form solutions, and to determine its differences with the results of numerical modelling. The seismic behavior of structures is required to be designed in accordance with the minimum design requirements specified in the Standard. Seismic design, where ground behavior is considered, is presented as a significant part of design analyses, and ground movement and shaking, are associated with the ground deformation which is the primary seismic load consideration for the design of plain or reinforced concrete structures. The outcome of the longitudinal analysis provided the maximum axial and bending strain which is adopted to calculate the combined strain. These results of strain are considered with the design of concrete structures against Ultimate Limit State and Service Limit State design phases. Therefore, the results evaluate the effect of seismic design on the performance of the concrete structure.

Eurocode-compliant system safety factor for advanced design of hollow section Warren trusses

Eurocode allows for the design of structural systems by advanced analysis, i.e. by Geometrically and Materially Nonlinear Imperfection Analysis (GMNIA). In GMNIA, the entire structural system is designed by carrying out a nonlinear finite element analysis and by comparing the load proportionality factor obtained from the analysis to the predetermined system safety factor. This study determines the required Eurocode-compliant GMNIA system safety factor for the ultimate limit state design of Warren-type roof trusses. The system safety factor is determined based on system-level reliability studies conducted for 15 trusses. The investigated trusses are made of cold-formed rectangular hollow sections having a nominal yield strength of 700 MPa. The determined system safety factor is then applied for comparison calculations, in which three trusses are designed both by GMNIA and the conventional EN 1993-1-1 method. This comparison reveals a need for an accurate modelling method of hollow section connections in GMNIA. Furthermore, the comparison shows that GMNIA can offer reduced material consumption compared to the conventional method even in roof trusses, in which load redistribution capabilities are very limited. This reduction is achieved due to capability of GMNIA to accurately capture the buckling capacities of continuous top chords, whereas the conventional method must rely on conservative approximations of buckling lengths.

Site-Specific Response Spectra and Accelerograms on Bedrock and Soil Surface

This paper is aimed at serving the needs of structural engineering researchers who are seeking accelerograms that realistically represent the time histories of earthquake ground in support of their own investigations. Every record is identified with a specific earthquake scenario defined by the magnitude–distance combination and site conditions; the intensity of the presented records is consistent with ultimate limit state design requirements for important structures in an intraplate region. Presented in this article are accelerograms that were generated on the soil surface of two example class Ce sites and two example class De sites based on site response analyses of the respective soil column models utilizing bedrock excitations as derived from the conditional mean spectrum (CMS) methodology. The CMS that were developed on rock sites were based on matching with the code spectrum model stipulated by the Australian standard for seismic actions for class Be sites at reference periods of 0.2, 0.5, 1 and 2 s for return periods ranging from 500 to 2500 years. The reference to Australian regulatory documents does not preclude the adoption of the presented materials for engineering applications outside Australia. To reduce modeling uncertainties, the simulation of the soil surface ground motion is specific to the site of interest and is based on information provided by the borelogs. The site-specific simulation of the strong motion is separate to the CMS-based accelerogram selection–scaling for obtaining the bedrock accelerograms (utilizing strong motion data provided by the PEER). The decoupling of the two processes is a departure from the use of the code site response spectrum models and has the merit of reducing modeling uncertainties and achieving more realistic representation of the seismic actions.

Extreme response analysis of a floating vertical axis wind turbine based on modified environmental contour method

Floating vertical axis wind turbine (FVAWT) is a potential concept that could compete with the floating horizontal axis wind turbine (FHAWT) in the offshore wind industry. For a reliable FVAWT design, accurate prediction of extreme structural responses is crucial for ultimate limit state (ULS) design evaluation. Extreme structural responses of offshore wind turbines depend on operational modes and could present non-monotonic behavior with respect to environmental parameters. In this study, the extreme responses of a 3-bladed H-rotor semi-submersible FVAWT are evaluated using a simplified engineering approach, i.e., the modified environmental contour method (MECM). Judging from the response characteristics of the FVAWT with respect to increasing wind speed, the environmental contour with a return period of the cut-out wind speed is used. Along the selected environmental contour, the cut-out wind speed and the corresponding most probable sea state is chosen as the environmental design point. To generate statistical samples of structural responses, the Monte Carlo (MC) method is applied by carrying out fully-coupled time domain simulations under the selected environmental loadings. The Gumbel method, the Weibull tail method and the mean upcrossing rate (MUR) method are used to extrapolate the 50-yr long-term extreme responses. With a sufficiently large sample size, e.g. 100 MC simulations, the estimated extremes using different extrapolation methods are in close agreement with each other. However, the Weibull tail and MUR methods reduce the statistical uncertainty of the estimates due to higher data utilization. For practical engineering applications, massive amount of MC simulations is often not desirable. Therefore, the accuracy and statistical uncertainty of the estimated extreme responses associated with a reduced sample size is also investigated. For a sample of 10 simulations, the Weibull tail and MUR methods are able to predict extreme responses that are closer to the estimates using 100 simulations. The MUR method results in the lowest statistical uncertainty of the estimates.