Limit State Design Research Articles

Unified Flexural Resistance Design Method and Evaluation Frame for the B-Regions of RC Flexural Members—Theory and Application

The load and resistance factor design (LRFD) method is normally used to design B-regions of reinforced concrete (RC) flexural members. The design includes many checks corresponding to different limit states. The LRFD method requires many loop calculation steps in the design, demonstrating its relative inefficiency. It cannot be applied to compare limit states directly and quantitatively. Different design limit states are separated and isolated. How to improve the analytical calculation efficiency of the LRFD method and to realize direct and quantitative comparisons between limit states are very important problems in structural engineering. This paper presents an innovative unified flexural resistance design (UFRD) method and a unified flexural resistance evaluation (UFRE) frame to solve these problems to some extent. The main contents include the unified flexural resistance (UFR) principles, formulas for the unified flexural resistance design (UFRD) method, the operation procedure to facilitate its usage, the UFRE framework to compare limit states, and three examples. The results show that the UFRD method can provide the same design outcomes as the LRFD one. However, UFRD calculations are simpler, requiring at most 20% of the calculation steps of the LRFD method. The UFRE frame can make different limit states compare with each other directly and quantitatively, which cannot be realized by the LRFD method. It helps expose some potential and insufficient flexural resistance hazards for some limit states, such as the only 10% relative strength reservation of one example. Thus, the UFRD method and the UFRE frame supplement and develop the LRFD method to some degree. The simplicity and practicality of the approach and the frame make them appropriate for many applications.

Structural Behavior of Concrete Beams Reinforced with Biaxial Geogrid

In recent decades, corrosion in steel reinforcement has been one of the fundamental risks in steel-reinforced concrete (RC) structures. Geosynthetics can be an alternative approach to solve corrosion problems. The current experimental research work investigates the structural performance of geogrid-reinforced concrete (GRC) elements. Initially, five different geotextiles and biaxial geogrid materials were selected and embedded in the concrete specimens separately to study their mechanical properties. The results of the testing showed that the geogrid embedded specimen behaved more mechanically than the conventional concrete (CC) specimens due to increased bonding characteristics. The limiting moment and load-carrying capacities of the RC and GRC beams were determined with reference to limit state design principles. In order to compare the structural performance of the beams, two RC beams and two GRC beams with the size of 150 mm × 300 mm × 2100 mm were cast. The structural performances in terms of the load-carrying capacity, energy absorption, stiffness degradation, and ductility were examined. The results of the tests indicated that even though the load-carrying capacity of the GRC beams was slightly lower, they demonstrated enhanced performance by 42%, 40%, and 68% higher in the energy absorption, stiffness degradation, and ductility, respectively, than those of the RC beams on average. The augmented inelastic performance and better bonding properties of the GRC beams aid in noticeable structural performance.

Experimental study of a composite beam externally bonded with a carbon fiber-reinforced plastic plate

According to the characteristics of steel fiber reinforced concrete (SFRC) with high tensile strength and carbon fiber reinforced plastic (CFRP) with high strength and light weight, a composite beam composed of CFRP plate, SFRC and ordinary concrete (OC) is developed in the paper. Eight specimens, including four CSOCBs with different heights of the SFRC and four SFRC–OC composited beams with varying heights of the SFRC, were tested to analyze the flexural behavior. The results show that the composite beam composed of OC, SFRC and CFRP improves the ultimate load capacity of the beam under unidirectional load, enhances the cracking and deformation resistance of the beam, and solves the defects of the weak tensile capacity of ordinary concrete beams. Applying them to the building structure can improve the stability of the structure and prolong the service life of the building. A prediction model for the bending capacity of the CSOCB was proposed and validated. Based on the limit state design method, the design formula for the bending capacity of the composite beam is described in detail herein.

Proposed Enhancements to the Risk-Informed and Performance-Based Regulatory Framework for Seismic Hazard Design at NRC-Regulated Nuclear Power Plants

The commercial nuclear power plant industry initiated the licensing modernization project (LMP) to enhance the risk-informed and performance-based (RIPB) regulatory basis for advanced nuclear power reactors. The LMP framework relies heavily on RIPB concepts and approaches that together integrate the defense-in-depth philosophy. One example approach for seismic design is to align the LMP concepts with the performance targets described in the American Society of Civil Engineers (ASCE) standard, ASCE 43-19. The underlying strategy of this approach is to consider the performance of individual structures, systems, and components (SSCs) in seismic design, as well as the role they play in an accident event sequence. This approach contrasts with current regulations, in which every individual safety-related SSC is designed to the same seismic criteria irrespective of the role the SSC plays in the overall system performance. This new philosophy envisions more flexible seismic design options for each SSC, such that the overall seismic design can meet system-level acceptability criteria as well as plant-level acceptability criteria. The objective of this paper is to illustrate the flexibility and benefits of this proposed approach to the seismic design of SSCs in terms of reduced SSC demands (by reducing the design ground motions for SSCs) and improved SSC capacities (by allowing for alternative damage state limits). A simple shear wall was designed using ASCE 43-19 for a hard rock site in the Central Eastern United States considering alternate seismic design category and limit state combinations to examine the physical designs and functional fragilities of these combinations and their impact on seismic performance. The flexibility of this proposed approach is illustrated by an example that shows reduced SSC demands, while the SSC capacities and margins remain consistent with the required safety performance without any loss in overall plant safety.

Dynamic Response of 15 MW Floating Wind Turbine With Non-Redundant and Redundant Mooring Systems Under Extreme and Accidental Conditions

AbstractThis work focuses on examining the dynamic behavior of large floating offshore wind turbine (FOWT) exposed to extreme (wind and wave with 50-year return period) and accidental (mooring line breakage) loadings. The FOWT considered is 15 MW reference turbine supported on semi-submersible platform stationed using catenary moorings. As the mooring configuration greatly affects the response of FOWT, two different mooring configurations namely non-redundant (three-line) and redundant (six-line) systems were studied and compared. The coupled multi-body dynamic system was solved using Openfast. When simulating the mooring line failure, both the operating and extreme loading conditions were considered. Failure of one mooring was considered at a time. The response of the coupled system due to breakage of the mooring indicates high displacements in surge and sway directions in comparison to the intact system especially for the non-redundant mooring system. Furthermore, change in platform yaw angle and increased tension in the other intact mooring lines were observed. The findings from this study will be helpful in accidental limit state design and preventing failure of similar large FOWT systems. In addition, insights into using non-redundant and redundant mooring configurations for such large structures with respect to extreme and accidental loadings were also discussed.

Capacity of piles subject to downdrag: a comparison of North American bridge design codes and observations from a full-scale test pile program

Negative skin friction caused by ground settlement is an important consideration for deep foundations in limit states design. However, there are inconsistencies in the methodology whereby negative skin friction and associated drag force are considered in assessing the geotechnical capacity or geotechnical ultimate limit state (ULS) in various design codes. This includes two current North American bridge design codes, the Canadian Highway Bridge Design Code, and AASHTO LRFD Bridge Design Specifications. A test pile program was developed to observe effects of ground settlement on pile settlement, capacity, and drag force. Two instrumented steel H-piles were driven through a compressible clay layer to a hard end-bearing stratum, subjected to ground settlement by constructing a 1.5 m high embankment, followed by static load testing. A load-transfer model was calibrated from the test pile program observations. Test results and the calibrated model were used to compare geotechnical ULS requirements of the two bridge design codes. It is demonstrated that drag force did not detrimentally impact pile capacity. The results showed that for conditions of the test pile program, assessing the geotechnical ULS can be more conservative when adhering to the current AASHTO LRFD Bridge Design Specifications than the Canadian Highway Bridge Design Code.

A performance‐based seismic loading protocol: The generated sequential ground motion

AbstractA realistic performance‐based seismic loading protocol called generated sequential ground motion (GSGM) has been developed in this paper. GSGM is a ground motion fabricated from segments of real recorded ground motions that could enable the introduction of performance‐based seismic assessment and design to experimental testing in setups such as shaking table testing. It can also significantly reduce the number of nonlinear time history analyses required in performance‐based seismic design. The protocol optimizes the behavioral information output of an experimental test or numerical analysis by incorporating dynamic demands corresponding to design limit states with different probabilities of exceedance (i.e. 10%, 5%, and 2% in 50 years) in a single record. In addition, since the segments are matched to relevant target spectra, the number of ground motions required to estimate the mean response is reduced. This paper presents the algorithm developed to produce the GSGM. The capability of the GSGM to replicate the structural responses produced by code‐compliant suites, and a suite of 100 ground motions as a more robust estimation of the actual response is investigated. The results of the case study bridge pier show that the drift variation of the GSGMs compared to code‐compliant suites is within 10%. Compared to the estimate of the actual response, the drift variation of GSGMs and the code‐compliant suites is 20% and 15%, respectively, and the damage variation is 30% and 15%, respectively. Furthermore, considering other relevant intensity measures when producing GSGMs can reduce these variations. This study suggests that the GSGM can replicate structural responses of the current code procedures.

Advances and Challenges in Design of Connections in Steel-Braced Frame Systems with In-Plane Buckling Braces

A new type of connection has been developed for steel-braced frame systems that allows the brace members to undergo compression buckling in the in-plane direction. In addition to the inherent benefits of in-plane buckling (IPB) braces that help in reducing the extent of damage to the non-structural components, the IPB brace system is also considered to be an efficient way of retrofitting existing seismically deficient structures. The use of the compact and thicker gusset plate prevents the distortion of the free edges and the additional torsional force demand on beams and columns. However, IPB braced frame systems are not frequently used in practice, primarily due to the absence of limit state design criteria. As a result, some prominent failure modes observed in IPB frame systems are out-of-plane brace buckling, yielding of gusset plates, interface weld failure, and fracturing of knife plates. Recent studies on the IPB braced system have resolved some of these problems, such as design criteria being developed to prevent OOPB (out-of-plane buckling) of the IPB braced system. Other challenges need to be studied to achieve reliable performance of the braced frame system. This study focuses on recent advances and potential areas of improvement to achieve an efficient IPB braced system in highly seismic areas.

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.

Investigating the impact of design criteria on the expected seismic losses of multi-storey office buildings

The Ministry of Building, Innovation and Employment is developing advice on how to deliver Low Damage Seismic Design (LDSD) protection for buildings through their Tū Kahika: Building Resilience platform. The draft LDSD advice is considering a design drift limit for multi-storey buildings of 0.5% as part of new damage control limit state design checks. The potential impact of this design criterion on the expected annual loss due to repair costs is investigated for generic reinforced concrete wall case-study office buildings of 4- and 12-storeys in both Wellington and Christchurch. The equivalent static method, in line with NZS 1170.5 and NZS 3101, was used to design the buildings to conventional and draft LDSD specifications, representing current and future state-of-practice designs. The draft LDSD advice aims to limit the expected annual loss of complying buildings to below 0.1% of building replacement cost. This research tested this expectation. Losses were estimated in accordance with FEMA P-58, using building responses from non-linear time history analyses. Although it is found that the new drift limit alone may not limit seismic losses to the target values owing to damage to acceleration-sensitive elements, the results do support the intentions of the draft design advice to significantly reduce the expected seismic losses of complying buildings. The study also highlighted the importance of using an accurate approximation of RC wall stiffness for LDSD, and provides insight into different design strategies that could be followed to effectively limit losses in RC wall buildings as part of LDSD.

Design Method of Primary Structures of a Cost-Effective Cable-Supported Photovoltaic System

Cable-supported photovoltaic systems (CSPSs) are a new technology for supporting structures that have broad application prospects owing to their cost-effectiveness, light weight, large span, high headroom, few pile foundations, short construction period, and symbiosis with fisheries and farms. Recently, a new CSPS with a much smaller settlement and stronger wind resistance was proposed. The new CSPS, with a 10% lower cost compared with traditional fix-tilted PV support, is a better alternative to traditional photovoltaic (PV) support systems. In this study, the failure models and bearing capacity of the primary structures of the new CSPS were investigated in detail using the FEM method, and a design method for the new structure was proposed based on the limit state design method. The results showed that the structure had a strong load-bearing capacity. Failure of the cables and triangular brackets are the two main types of failure of the primary structure. The cross-sectional area of the cables is the most important factor affecting the load-bearing capacity of the structure and directly affecting the failure modes of the CSPS. The numerical case verified that the proposed design method works well and that the designed structure has sufficient loading capacity and is cost-effective.

On the existing test dataset of isotropic cylindrical metal shells under axial compression and the design of modern metal civil engineering shells

In the structural engineering limit state design philosophy of the Eurocodes, a target reliability is achieved by using partial safety factors on both the loading and the resistance that are, in principle, to be calibrated based on test data. The partial factor that is currently used for the buckling limit state of metal shells has been adopted from the knowledge base on other structural elements and has been retained for reasons of historical continuity and to maintain a close relationship between all Eurocode steel design standards. However, the mechanics of the behaviour of thin-walled metal shells gives strong reasons to believe that the partial factors for buckling should be dependent on the shell geometrical form, slenderness, load case and quality of fabrication for the target reliability to be consistently achieved. None of these are currently considered in defining the partial factor for resistance.The most ubiquitous thin-walled metal shell structures are imperfection-sensitive cylinders under uniform axial compression. A dataset of many hundreds of these test results has thus been accumulated over many decades, though it is of variable quality and sparsely documented. This paper shows that this dataset is an entirely inappropriate basis on which to calibrate the safety level of full-scale metal civil engineering shells. Indeed, the professional community should face the uncomfortable reckoning that an experimental test dataset suitable for the reliable calibration of the safety level of design relationships for full-scale metal civil engineering shells may likely never come into existance, and that the bolder approach of extensive computational simulation must instead be embraced.

Wind-Induced Responses and Wind Loads on a Super High-Rise Building with Various Cross-Sections and High Side Ratio—A Case Study

With the development of construction technology and material, more and more super high-rise buildings will be constructed in the future. In a specific metropolitan area, super high-rise building with various cross-section and high side ratio have to been designed and constructed due to the size limitation of construction site. This kind of building is also very prone to wind excitations. In this research, wind tunnel tests for a practical case of this kind of building with surrounding buildings were carried out in atmospheric boundary wind tunnel. Equivalent static wind loads (ESWLs), wind-induced responses and wind load distribution on the building were analyzed. In particular, the base overturning moment along the axis with weak lateral stiffness were investigated for bearing capacity limit state design of the building. The results demonstrate that the maximum value of wind-induced base overturning moments and acceleration responses appears at 60° or 330° wind directions instead of the orthogonal wind direction, and the aerodynamic interference of surrounding buildings affects the wind pressure distribution on facades of the building. These results and conclusion may be helpful to wind-resistant design of super high-rise buildings with high side ratio.

Reliability-assisted determination of partial factors for the design of main cables considering secondary stress effect

The main cables of suspension bridges typically serve as the primary load-carrying components. Determination of reasonable main cable sizes is crucial for the bridge safety and functionality. The limit state design method with the combination of partial factors has been widely used in multiple countries as a substitute for the factor of safety design method. Determination of reasonable partial factors that can properly satisfy a target reliability index has received much attention. However, most of the existing research neglects the secondary stress effect, which can be of a significant magnitude, for the main cable. To address the gap, this paper proposes a reliability-assisted framework for the determination of the partial factors considering both first and secondary stresses for the main cable design. Three suspension bridges with main span lengths ranging from 850 m to 2300 m are used as the engineering background. Results show that the recommended design factors can be used in the preliminary design stage to facilitate a reasonable cable design that yields the target reliability index, therefore validating the feasibility of the proposed framework.

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.

Exploring the potential of the critical shear crack theory for reinforced and post-tensioned glass beams: Initial analysis and experiments

In the evolution of structural glass beam elements, the requirements for post-fracture load bearing capacity and safe failure behaviour have led to the development of reinforced and post-tensioned beams. Maximum bending capacity in the post-fracture state is normally associated with extensive yielding of the reinforcement, providing a safe failure mechanism through apparent ductility of the composite beam section. This can be achieved as long as the propagation of primary flexural cracks does not compromise the transfer of shear from the load points to the supports. Although shear failure is typically not critical for the ultimate limit state design of ’normal’ unreinforced glass beams, it may govern the load-bearing and deformation capacity in the post-fracture state for reinforced and post-tensioned glass beams. This paper presents exploratory experiments and initial analysis of the shear failure phenomenon in the post-fracture state of reinforced and post-tensioned glass beams. Potential shear transfer mechanisms are identified based on the critical shear crack theory developed for reinforced concrete members and applied in the analysis of shear failures observed in four-point bending tests of post-tensioned glass beams. The behaviour of fractured laminated glass under mixed-mode (tension+shear) loading is explored on a limited set of small-scale double-notched glass specimens, demonstrating the feasibility of the applied test methodology. Preliminary findings of the present study may serve as a basis for further investigations of shear resistance of glass beams. Typical shear failure kinematics and suitable constitutive laws of the applied materials need further investigation in order to provide design recommendations for the prediction of shear resistance of reinforced and post-tensioned glass beams.

Reliability-based serviceability limit state design of spread foundations under uplift loading in cohesionless soils

ABSTRACT The design of foundations is often governed by the serviceability limit state (SLS) requirements of the supported structure, particularly for large spread foundations. This paper aims to develop a reliability-based SLS design method for spread foundations under uplift loading in cohesionless soils. A probabilistic framework was adopted for the empirical characterisation of the compiled load-displacement curves and the quantification of the associated uncertainties. By using the obtained statistics of the curves, reliability analysis was carried out with Monte-Carlo simulations to calibrate the resistance factors within the load and resistance factor design (LRFD) framework. The calibration results showed that the embedment ratio of the foundation and the fitting errors of the empirical model, which were previously unaddressed in the literature, had notable effects on the calibrated SLS resistance factors. The relationship of the SLS with the ultimate limit state was assessed, including the governing limit state at each allowable displacement level, and the probability of ultimate failure of the foundation at the SLS condition. By considering the relationship between the limit states, the procedures for determining the design resistance factor and foundation capacity were proposed.

Formation of post-buckling shear mechanisms in stiffened web panels of slender steel plate girders

A series of validated finite element models are used to investigate the formation of mechanisms in stiffened slender web panels of steel plate girders under pure shear. The prototype girder is based on the seminal tests by Basler and has a web slenderness of 267. Six model cases are analyzed with variations in web panel aspect ratio (1, 1.5, and 3), steel yield strength (Grades 36 and 50), initial imperfection magnitude, and flange thickness. When loaded in shear, the web panels exhibit a 3-stage response: (1) elastic behavior, (2) web mechanism formation, and (3) panel mechanism. In Stage 1, the web initially exhibits an elastic in-plane shear response with no distinct buckling bifurcation. During this stage, the web’s initial out-of-plane imperfections become engaged in second-order bending along its compression diagonal. Concurrently, tension develops in the opposite diagonal as a non-uniform membrane stress field, with highest intensities at locations where second-order bending is low. In Stage 2, a web mechanism is formed when connected bands of thru-thickness von Mises yielding develop across the tension diagonal. These bands emerge at locations where tension membrane stresses interact with locations of maximum second-order bending stress in the buckled shape. The shear load at the end of web mechanism formation is recommended as a target for plastic limit state design because it marks a significant decrease in shear stiffness. In Stage 3, von Mises yielding continues to saturate the web panel, and the bounding flanges and transverse stiffeners become increasingly engaged in load redistribution from the plastified web. Any hardening increase in shear resistance during the panel mechanism stage is modest in magnitude (up to ∼10% for some cases in this study) and is heavily dependent on the sizing of the flanges and stiffeners to carry redistributed forces.

Analysis of reinforced concrete beams with indirect reinforcement according to limit state design

When analyzing structures within the framework of the theory of limit state design, it is necessary to ensure sufficient reliability and safety at an acceptable level of risk. For these purposes, in engineering calculations, the mean experimental values of material strength are recalculated into design values. This article is devoted to the calculation of reinforced concrete beams with indirect reinforcement of the compressed area with transverse welded meshes for different accepted values of concrete strength (mean value of strength; design value of strength) and comparison of bearing capacity and deformations. For three series of tested beams, deformations were calculated at various stages of loading, and the bearing capacity was determined at the stage before peeling off the protective layer of concrete in the compressed area (operational stage). Calculations according to the method of the deformation model were carried out both on the basis of the mean experimental values of strength of concrete and reinforcement, and on the basis of the design values. It was found that in calculations based on the design values of the material strength, the ultimate deflections in some cases exceed the values obtained on the basis of the experimental mean strength values, which should not be. In this regard, it was indicated the need to calculate the parametric points of the design stress-strain diagram of concrete with indirect reinforcement according to the experimental mean strength values and only after that take into account the necessary reliability coefficients and obtain the final design values.

Dimensionamento de estruturas de concreto armado a partir de campos de tensão tridimensionais

abstract: The design of reinforced concrete structures starting from a linear analysis is allowed by design codes and leads to safe solutions. The structural model built for the analysis may be composed not only of bar and shell elements, but also solid elements. In the present work, the formulation of the Reinforced Solid Method (RSM) was reviewed and applied to the Ultimate Limit State design of a reinforced concrete member, with the computation of the required reinforcement and concrete check of each individual solid element within the structural model. The results were visualized in a post-processor and validated by numerical simulations. The RSM effectively allows for the design of concrete structures with general geometry and loading conditions, whilst identifying local effects throughout the volume of the structure.