Reliability-based Limit State Design Research Articles

Practical method for determining load and resistance factorsusing third-moment transformation

Load and resistance factor design (LRFD) is a suitable format for the reliability-based limit state design of structures. It has been adopted in many countries, such as the United States, Europe, Canada, and Japan. Usually, the first-order reliability method (FORM) is used to estimate the load and resistance factors, but it requires the determination of design points and complicated double iterative computations. Therefore, FORM is not easy or practical for engineers to use. This paper presents a simple, accurate method to determine the load and resistance factors utilizing the third-moment transformation, which does not require derivative-based iterations and can estimate the load and resistance factors without using the distribution of random variables. In addition, the proposed method provides enough accurate results within a wide range of target reliability indices. Therefore, this method should be effective and convenient for calculating the load and resistance factors in actual practice. Five numerical examples illustrate the proposed method's efficiency and accuracy; FORM provides a benchmark for comparison.

System reliability-based limit state design of support scaffolding systems

The safety of scaffold systems during construction is vital to prevent failures with catastrophic consequences. Engineering practice in the scaffolding industry, however, does not have a rational structural reliability basis as that used for buildings and bridges. The implementation of design clauses for scaffold systems in the current standards partially relies on judgement suffering from the lack of data. With this regard, a reliability-based limit state design approach is developed in this study, making full use of the advanced finite element (FE) method and the recently accumulated statistical data of scaffolding resistance and construction loads. A stochastic finite element method is used to obtain the probabilistic characteristics of the ultimate load-carrying capacities of typical scaffolding frames, accounting for the uncertainties associated with structural geometry, material and stiffness properties. The latest construction load survey data is utilized. System reliability assessment is then performed to develop new design criteria which are consistent with generally accepted structural reliability targets.

Quantification of uncertainty in compressive strength of fly ash brick masonry

The compressive strength of brick masonry, an important property for the structural assessment and design, can show a significant variation because of several influencing factors like source and proportion of constituent materials, workmanship, curing condition, etc. Quantification of uncertainty in masonry compressive strength is essential for reliability based limit state design of masonry structures. The present study investigates this aspect of fly ash brick masonry and recommends the most suitable statistical distribution to describe the variability in compressive strength. Experimentally obtained compressive strength data are analysed using various probability distribution functions capable of modelling strength properties of brittle materials and three goodness of fit tests, i.e. Kolmogorov-Smirnov, Kolmogorov-Smirnov-Lilliefors and Anderson-Darling tests. The analysis concludes that lognormal distribution is best suited among other distributions to describe the variability associated with the compressive strength of fly ash brick masonry.

Statistical evaluation of model factors in reliability calibration of high-displacement helical piles under axial loading

An industry survey suggests an increasing application of high-displacement helical piles with greater shaft and helix diameters to support various structures. In this paper, a database of 84 static load tests is compiled and analyzed to evaluate the disturbance effect and characterize the model factors that can be used for reliability-based limit state design. The measured capacity is defined as the load at a pile head settlement equal to 5% of helix diameter. For similar helix configurations tested at the same site, the ratio of uplift to compression capacity indicates a low degree of disturbance for very stiff clay (0.8–1) and a medium degree of disturbance for dense sand (0.6–0.8). At the ultimate limit state, the model factor is defined as the ratio between measured and calculated capacity, where three design guidelines are considered. A hyperbolic model with two parameters is used to fit the load–displacement curves. At the serviceability limit state, the model factor can be defined with the hyperbolic parameters. Based on the database, probabilistic distributions of the capacity model factor and hyperbolic parameters are established. Finally, the capacity model statistics are applied to calculate the resistance factor in the load and resistance factor design.

사용중 PSC-I 거더 철도 교량의 휨모멘트에 대한 신뢰도 분석

철도교량의 신뢰도 기반 한계상태설계법 도입 시 목표신뢰도지수 산정을 위하여 기존 철도교량의 신뢰도지수 산정이 선행되어야 한다. 대표적인 복선 철도교량 중 하나인 6주형 PSC-I형 거더교량에 대해 신뢰도지수를 산정하였다. 최외측 거더의 휨모멘트에 대한 신뢰도 해석을 수행하였다. 휨저항강도 및 고정하중효과는 도로교 한계상태설계법 도입 시 적용된 선행연구자들의 평균과 변동계수를 활용하였고, 열차의 활하중 효과는 여객/화물 혼용선 중 중량화차 통행이 빈번한 중앙선에서 현장계측 데이터를 활용하였다. 한계상태방정식에 대하여 개선된 일계이차 모멘트법(AFOSM)으로 신뢰도 분석을 수행하였으며, 하중효과와 저항효과의 각 요소가 신뢰도지수에 미치는 민감도를 분석하여 중요도를 검토하였다. It is necessary to determine reliability indexes of existing railway bridges prior to setting up a proper target reliability index that can be used to introduce a reliability based limit state design method to design practice. Reliability is evaluated for a six PSC-I girder railway bridge, which is one of many representative types of double-track railway bridges. The reliability assessment is carried out for an edge girder subjected to bending moment. In the assessment, the flexural resistance and the fixed-load effect were obtained using existing statistical values from previous research on the introduction of limit state design to road bridge design. On the other hand, the live-load effect was determined using statistical values obtained from field measurement for the Joong-ang corridor, on which heavy freight trains are frequently passing. The reliability assessment is performed by AFOSM(Advanced First Order Second Moment method) for the limit state equation, and a sensitivity analysis for the reliability is performed for each factor of the load and resistance effects.

Reliability analysis of laterally loaded piles for an offshore wind turbine support structure using response surface methodology

With an increasing demand of a renewable energy, new offshore wind turbine farms are being planned in some parts of the world. Foundation installation asks a significant cost of the total budget of offshore wind turbine (OWT) projects. Hence, a cost reduction from foundation parts is a key element when a cost-efficient designing of OWT budget. Mono-piles have been largely used, accounting about 78% of existing OWT foundations, because they are considered as a most economical alternative with a relatively shallow-water, less than 30 m of seawater depth. OWT design standards such as IEC, GL, DNV, API, and Eurocode are being developed in a form of reliability based limit state design method. In this paper, reliability analysis using the response surface method (RSM) and numerical simulation technique for an OWT mono-pile foundation were performed to investigate the sensitivities of mono-pile design parameters, and to find practical implications of RSM reliability analysis.

Sensitivity Analysis by Parametric Study of Load Factor for a Concrete Box Girder Railway Bridge Using Limit State Design

Reliability based limit state design method is replacing traditional deterministic designs such as allowable stress design and/or ultimate strength design methods in world trends. European design code(Eurocode) has adopted limit state design, and Korea road bridge design standard has also recently been transferred to limit state design method. In this trend, Korea railroad design standard is also preparing for adopting the same design concept. While safety factors are determined empirically in traditional design, load combinations as well as load factors are determined by solving limit state equations. General partial safety factors are evaluated by using AFORM(Advanced First Order Reliability Method) in the reliability based limit state design method. In this study sensitivity analysis is carried out for a dead load factor and a live load factor. Relative precisions of the dead load and the live load factors are discussed prior to the AFORM analysis. Furthermore the sectional forces of design and the material quantities required by two different design methods are compared for a PSC box girder railway bridge.

Probabilistic models of combinations of stochastic loads for limit state design

When more than one load act on a structure, the maximum intensity of the combined load effect needs to be evaluated. Turkstra's rule is often used in reliability-based limit state design because of its simplicity; however, the approximation is unconservative. This paper presents the theoretical expressions of the cumulative distribution function (cdf) of the maximum intensity during a reference period taking the temporal variation of load intensity into account. Theoretical investigation and numerical examples show that the theoretical expression provides a fairly good estimate regardless of the statistical characteristics of the load processes. To avoid considering time-dependency in determining a design point, it is proposed to consider the intensities of the load processes at the time when the combination takes its maximum value. Based on the observation that the cross section of the joint probability density function (pdf) of these intensities cut by the limit state surface is similar to that of the joint pdf of the basic random variables, the design point is determined in the basic variable space using AFOSM.

Design criteria for the seismic rehabilitation of buildings

SUMMARY A methodology was presented by the author in a previous paper for the development of design criteria for buildings. This methodology was based on the principles of structural reliability and structural dynamics. This paper illustrates how many elements of this methodology have been implemented and extended to develop design criteria for reinforced concrete and steel buildings by special blue ribbon committees selected by the City of Los Angeles Building Department. This paper presents the design criteria developed by these committees and discusses some of the more contentious issues. Reinforced concrete buildings built prior to 1976 have performed very poorly in recent earthquakes. They can certainly be identified as having a special life safety concern in the event of the occurrence of a major earthquake. This concern is not recent. Perhaps the first clear documentation of this concern was the proposed new design approach presented in the book entitled Reinforced Concrete Design Book by Blume, Newmark and Corning published in the early 1960s. Since one generation of structural engineers has been educated since the publication of this book and since numerous failures and near collapses of reinforced concrete frame buildings occurred during the Northridge and Kobe earthquakes, now is the time to take action. The building department of the City of Los Angeles has on numerous occasions been a leader in design criteria development. Consistent with this past tradition of excellence the city formed a special committee of structural engineers to document damage to concrete buildings during the Northridge earthquake and also to advise them on courses of action. Design criteria for the seismic rehabilitation of existing reinforced concrete buildings located in the City of Los Angeles were developed by the members of this committee. The acknowledgement section of this paper identifies the committee. This draft was based on and extended the methodology presented in a 1992 The Masonry Society Journal paper entitled ‘A philosophy of a reliability based limit state design approach’. The author as a member of this committee was asked to write the first draft for these new seismic rehabilitation criteria. The new design criteria were entitled ‘Evaluation and rehabilitation criteria for concrete structures’ and were approved by the committee in June 1994. The 1994 Northridge earthquake also presented structural engineers with an unexpected new class of hazardous existing buildings. These buildings are defined as ‘special moment resisting