Partial Safety Factors Research Articles

Reliability Study on FRP Composites Exposed to Wet-Dry Cycles

Due to lack of research data on the rates of deterioration of FRP properties under a harsh environment exposure, it was pointed out in the design guidelines that the durability of FRP needs to be further developed. Therefore, in this study, 48 FRP samples were tested under wet-dry cycles exposure. The effect of wet-dry cycling times on the failure modes, tensile strength, and the probability distribution of different FRP (GFRP and CFRP) composite specimens were investigated. The experimental results showed that the wet-dry cycles have a significant adverse influence on the tensile strength, have a certain adverse effect on the elongation, and a very limited influence on the elastic modulus of FRP. According to the experimental results, a probability analysis was conducted on the degradation of tensile strength. Five widely used test methods were adopted to verify the possible distribution types of tensile strength, and a reliability index β was then calculated. Subsequently, the effects of the design tensile strengths of ACI-440, TR-55, GB 50608-2010, GB 50367-2013, European Fib Bulletin 14 and Italian CNR guidelines on the β were investigated. The investigation illustrates that only the design value of the TR-55 code can guarantee sufficient long-term safety of a CFRP composite, whereas all the six codes cannot guarantee the long-term safety of a GFRP composite and the partial safety factors in these codes are still not conservative. Therefore, a more conservative safety factor was suggested. Moreover, the design value of tensile strength needs to be further conservative when the standard deviation of the load is large.

Comparison of Safety Factor Evaluation Methods for Flexural Buckling of HSS Welded Box Section Columns

The statistical evaluation of the experimental and numerical results is an essential task in case of resistance model development for civil engineering structures. If a design model is developed which has analytical or empirical background, its safety level has to be confirmed and it should be proved that the developed design method fits the safety requirements of the EN 1990 [1]. However, in the EN 1990 and also in the international literature there are several different safety factor evaluation methods that can be used to check the necessary safety level of the analyzed design method (e.g.: 5% quantile level, 2.3% quantile level, 1‰ quantile level, γM partial safety factor, γM⁎ partial safety factor, β reliability index). In the international literature different calculation methods can be found even for the calculation of the same partial safety factor as well. In the present study the flexural buckling resistance of high strength steel (HSS) welded box sections is analyzed and the application of different safety approaches are demonstrated and compared. The authors investigated the buckling resistance of the analyzed columns by laboratory tests and by numerical simulations and the necessary partial safety factors are determined by different approaches. Based on the comparison tendencies are identified and the differences between the statistical evaluation methods are demonstrated.

Determination of partial factor for model uncertainty for unreinforced masonry shear walls

AbstractExperiments in structural engineering can play an important role in the prediction and characterization of the material properties and behaviour of structural components. In order to cover all aspects in tests and use the results for design purposes, several methods have been included in EN 1990 Annex D for design based on test data. The calculation of characteristic values and design values for material resistance are the main aspects. In this study, the recommended methods in Annex D of EN 1990 for resistance of the material will be used to extract the partial safety factors for masonry structures based on the formulation of design and characteristic values. A database including more than 100 tests on unreinforced masonry shear walls will be used to evaluate the results. The resistance model for shear walls based on the recommendation in the Eurocode will be compared with the test results. The main aim will be to compare the model prediction and the test results. Deviation of the prediction from the test is caused by model error or model uncertainty. The test database includes results for three types of masonry units – fired clay, calcium silicate and autoclaved aerated concrete. The evaluation of partial factors for masonry shear models will be undertaken based on the scatter and the model bias for the whole database. Further analysis will also be performed for each type of masonry unit for classification of the outcome.

Application of European design principles to cross laminated timber

The design of cross laminated timber (CLT) structures is not included in the current version of European structural timber design standards of EN 1995 (Eurocode 5, EC 5). Due to the increasing importance of CLT, in different applications such as complete wall or floor elements as well as girders, it is one of the main goals of the currently ongoing revision of EC 5 to provide design principles for CLT structures. In the present paper some general aspects, relevant for the implementation of CLT in European standards in order to be consistent with the general philosophy of the Eurocodes are summarized and discussed. The differences between standard test specimens and structural components as well as the uncertainties related to the production procedure of CLT and the non-standardized test procedure are discussed. An investigation of 12 different test series from five different producers clearly indicates a large variation between different production series. Based on the investigation from the test series a reliability analysis is performed. The results indicate that the same partial safety factor as recommended for glued laminated timber (GLT) is appropriate in order to achieve an acceptable reliability. However, the analysis also indicates the potential for a smaller partial safety factor in the future, in case that the production of CLT is standardized and appropriate standardized test methods for the individual material properties exist.

From experiments to design: A probabilistic definition of design formulations from empirical and semi-empirical resistance models

The definition of design equations from empirical or semi-empirical resistance models is a matter of relevance for structural engineering. In common practice, the limit states design approach predicts the direct application of partial safety factors to the resistance of the materials in order to obtain design formulations coherent with a prescribed level of reliability. As empirical or semi-empirical models are calibrated, adjusting empirical coefficients to fit a set of experimental data, the application of partial safety factors to material properties alone is not able to provide a correct estimation of structural reliability.In the present paper, a methodology based on the Monte Carlo method for probabilistic calibration of empirical and semi-empirical resistance models is proposed. Its application related to the probabilistic calibration of the semi-empirical model proposed by fib Model Code 2010 for the estimation of laps and anchorages tensile strength in reinforced concrete structures is reported and discussed.

Load-computational methods of anti-slide piles

Anti-slide piles composed of reinforced concrete are commonly used in landslide mitigation engineering. How to calculate the load acting on the piles plays a crucial role in their design process. To estimate the load exerted on anti-slide piles based on the partial safety factor numerical method and limit equilibrium method, the landslide body is subdivided into two independent parts according to the positions of piles: the lower part of the landslide body and the upper one of the landslide body. The corresponding loads acting on the anti-slide piles are respectively computed, and the shear strength of the upper section of the landslide body can be determined according to the given designed safety factors. The locations of the piles are set as the fixed boundary, and the horizontal stress exerted on the anti-slide piles from the upper one of the landslide body is taken as the landslide thrust. The thrust forces are then applied to the lower portion of the landslide body, and the maximum force that the lower of the landslide body can effectively resist, and that satisfies well the given designed safety factors is taken as the maximum resistance of the lower portion of the landslide body. Comparing the results of the numerical computational method, the strict slice method and transfer coefficient method, it is found that the computational results agree well with each other. However, the numerical computational method is employed here in this research because the load distribution can be directly derived, which favors the subsequent calculation process and shortens the computational time.

Application of the partial safety concept for complex non‐linear calculations through the example of Friedrichswerder Church in Berlin

AbstractNon‐linear analysis of special structures is routine practice in every engineering design office. Current code provisions provide no sufficient regulations or clear procedures on how to use partial safety factors in non‐linear analyses. The present paper introduces some specific problems of masonry structures from practice.Limit state functions of vertically loaded masonry walls were investigated. A reliability study shows that the decisive case of verification can be obtained by considering a special combination of material parameters. The study also indicates the importance of considering a partial factor for the elastic modulus to account for stability failure.This proposed procedure has been applied to a practical example, the Friedrichswerder Church. The stability of the church has been checked with many FEM models at the macro level.

Experimental and numerical investigation of the static performance of innovative prefabricated high-strength composite columns

An innovative high-performance precast beam-to-column joint for multi-storey framed structures is introduced. The proposed solution consists of coupling between Composite Steel Truss Concrete (CSTC) beams with a concrete base and High-Strength Concrete (HSC) columns. This paper focuses mainly on the static performance of prefabricated HSC columns, including experimental and numerical investigations. The finite element model of the structural system is calibrated on experimental static testing evidence. On the basis of the data collected, the finite element model is used to evaluate the strength domain of members and optimize the related coupling system between columns. Aiming to limit time-consuming analyses and provide practical rules for design, an analytical simplified procedure is introduced to compute the assembly’s strength domain. An analytical approach is adopted to estimate the reference design strength for the considered composite columns, accounting for the partial safety factor imposed by codes and allowing for estimation of the limit on the number of storeys for frames adopting the proposed precast technology.

Resistance uncertainty and structural reliability of hypar tensioned membrane structures with PVC coated polyesters

This paper presents the resistance uncertainty and structural reliability of hypar tensioned membrane structures with PVC coated polyesters. First, series of tensile tests are carried out to study the resistance uncertainty of membrane materials. Then, the uncertainties of computational model and load effects are discussed and the resistance partial coefficients for membrane structures are proposed, regarding to different load combinations. Finally, the reliability indexes are studied according to the serviceability limit state and ultimate limit states. Results show that the proposed partial safety factors could satisfy the target reliability index in current design codes. This paper can provide important references for the design and analysis of tensioned membrane structures.

Harmonized European Standards for Proof of Competence of Cranes

With EN 13001-1 ff. a harmonized set of standards for safety of cranes was and is established. Due to harmonization the use of the standards leads to the assumption of conformity with the safety requirements of the machinery directive. A major argument for the application of the standards. The standards comprise new concepts of proof of competence in comparison to previous standards. Keywords of these new concepts are “Classification”, “Limit state method”, “Mass Distribution Class” and “Partial safety factors”. The article gives an overview to EN 13001-1, EN 13001-2 and EN 13001-3-1. This is the set of standards for proof of the structural parts of a crane. The main aspects of the standards are shown and discussed with regard to their impact on calculation.

New Italian guidelines for design of externally bonded Fabric-Reinforced Cementitious Matrix (FRCM) systems for repair and strengthening of masonry and concrete structures

The paper summarizes the main features of a standardization activity carried out in Italy by the Ministry of Public Works, to which two of the authors have taken part, for the homologation and the acceptance of Fabric-Reinforced Cementitious Matrix (FRCM) composites. During the last years, such composite materials have becoming increseangly popular in the civil engineering field for strengthening existing constructions, even if difficulties can occur in their mechanical characterization that is strongly affected by different and complex failure mechanisms. The American ACI 549.4R-13 is currently the only available guideline for design and construction of these systems. In this framework, the paper describes the Italian proposals for the homologation process of FRCM materials as well as for the design of strengthening interventions with these composites. Comparisons with the American guideline are also reported together with some considerations regarding the different partial safety factors.

Reliability-based assessment of damaged concrete buildings

Damages in concrete structures due to aging and other factors could be a serious and immense matter. Making the best selection of the most viable and practical repairing and strengthening techniques are relatively difficult tasks using traditional methods of structural analyses. This is due to the fact that the traditional methods used for assessing aging structure are not fully capable when considering the randomness in strength, loads and cost. This paper presents a reliability-based methodology for assessing reinforced concrete members. The methodology of this study is based on probabilistic analysis, using statistics of the random variables in the performance function equations. Principles of reliability updating are used in the assessment process, as new information is taken into account and combined with prior probabilistic models. The methodology can result in a reliability index B that can be used to assess the structural component by comparing its value with a standard value. In addition, these methods result in partial safety factor values that can be used for the purpose of strengthening the R/C elements of the existing structure. Calculations and computations of the reliability indices and the partial safety factors values are conducted using the First-order Reliability Method and Monte Carlo simulation.

Designing NSM FRP systems in concrete using partial safety factors

This paper presents design procedures for fibre reinforced polymer (FRP) systems inserted in the cover of concrete elements according to the near-surface mounted (NSM) technique. Such strengthening system depends greatly on their bond strength. Two existing design formulations to estimate the bond strength of NSM FRP systems in concrete are studied. A reliability analysis is conducted with the purpose of making the design formulations consistent with the partial safety factors philosophy, including the Eurocodes. Hence, the necessary probabilistic distributions are calibrated based on a large database of bond tests. The results presented herein show that the existing guidelines can be extended and adopted under the framework of the Eurocodes. However, mainly due to their limitations in addressing individually all the possible failure modes, the variability of the probabilistic distributions found are quite high, leading to high partial coefficients of safety. Thus, in the future, new and improved formulations should be developed.

Using re‐calibrated design S‐N curves for fatigue assessment of road bridges

AbstractFatigue design of road bridges according to Eurocode standards can be based on damage accumulation, provided that information about loading spectrum is available. Characteristic values of fatigue resistance and load effects as well as partial safety factors are introduced in the design equation in order to achieve a target reliability level. Partial safety factors are used to obtain the fatigue design S‐N curves from the characteristic S‐N curves. New probabilistic framework proposed by authors for calibration of fatigue partial safety factors allows for re‐definition of Eurocode‐based design S‐N curves. The new framework improves the confidence in the reliability level represented by the design S‐N curves. In this paper a real case study showing the impact of re‐calibration of design S‐N curves on fatigue design of a road bridge is presented. Importance of choice of design S‐N curves is assessed both in terms of allowable traffic volume and of bridge fatigue design life.

Partial safety factors for berthing velocity and loads on marine structures

Design methods for marine structures have evolved into load and resistance factor design, however existing partial safety factors related to berthing velocity and loads have not been verified and validated by measurement campaigns. In this study, field observations of modern seagoing vessels berthing in Bremerhaven, Rotterdam and Wilhelmshaven were used to evaluate partial safety factors for berthing energy and berthing impact loads. Various types of vessels and navigation conditions were statistically examined. The results show that characteristic values of berthing velocity with a return period of 50 years are in line with design recommendations in literature. Design values of berthing velocity are sensitive to the number of berthing operations during the lifetime of a marine structure. Typical partial safety factors for sheltered and exposed navigation conditions were derived by extrapolating distribution fits and applying extreme value theory. Differences in structural response due to soil stiffness and the type of berthing system installed influence partial safety factors for berthing impact loads. The probability of an uncontrolled berthing event was higher for exposed navigation conditions (strong tidal currents). In these circumstances, higher partial safety factors for berthing velocity should be considered in the design of marine structures. When berthing aid systems are used, the probability of extreme berthing velocities is lower, resulting in lower partial safety factors. The key findings of this study could be beneficial for the structural design of new and lifetime extension of existing marine structures.

Reliability-based safety factor for metallic strip flexible pipe subjected to external pressure

Reliability-based safety factors for metallic strip flexible pipes(MSFP) subjected to external pressure are calibrated in this paper. The partial safety factors of such pipes are obtained by introducing a target reliability index and using a combination of Monte-Carlo simulation and FORM. The relationship between the safety factors and the coefficient of variation for key basic variables as well as the impact of different distribution types for both the resistance and load effect parameters on the calibrated results are investigated. Recommended design safety factor for MSFP is given similar to the widely used design safety factor for conventional metallic pipes. The calibration process presented in this paper is relatively easy to understand and to carry out. This also applies to cases with multiple components and even requiring complex iterations in relation to the mechanical model. The results obtained here can provide some guidance in connection with manufacturing procedures at the initial design stage of the MSFP.

On the probabilistic representation of the wind climate for calibration of structural design standards

The article presents a contribution to the current debate on the probabilistic representation of the wind speed extremes for calibration of the partial safety factor covering wind action. The requirements for the probabilistic model are formulated. The Gumbel distribution is shown to represents best the 10-min mean wind velocity yearly maxima based on theoretical considerations and analyses of real data with different statistical techniques. Data from locations across a large geographical region indicate that the coefficient of variation of the distribution varies over the territory. A method is proposed for accounting this variation in order to calibrate a single partial safety factor for the whole territory. The distribution location is indirectly given in design standards through the georeferenced characteristic wind speed values. A solution for including the uncertainty affecting these values is suggested. The findings are implemented in an illustrative calibration exercise. The proposed methods and concepts might be applied to other environmental actions such as the snow loads.

Reliability‐based evaluation of bond strength for tensed lapped joints and anchorages in new and existing reinforced concrete structures

The definition of design equations from semi‐empirical or empirical models is a matter of fundamental importance in structural engineering. The direct application of partial safety factors for materials strength in such models is not appropriate in order to obtain design formulations coherent with some level of reliability, as empirical or semi‐empirical formulations are calibrated adjusting empirical coefficients to fit a set of experimental data. Therefore, applying partial safety factors on material properties alone does not allow a correct estimation of structural reliability. In this paper, a reliability‐based design bond strength relationship for tensed lapped joints and anchorages in reinforced concrete structures is derived applying a consistent reliability format. The semi‐empirical model for mean laps and anchorages strength calculation proposed in fib Bulletin No 72 is studied. The probabilistic calibration of this model is performed defining the related model uncertainties, grounding on an extensive experimental database and distinguishing between new and existing structures. As a conclusion, the design expression for bond strength proposed by the authors is compared to current standards and its implications in laps and anchorage design in reinforced concrete structures are analyzed.

Buckling resistance of HSS box section columns part I: Stochastic numerical study

The accurate consideration of the flexural buckling resistance of high strength steel (HSS) structures is highly important in the design. Higher yield strength indicates the applicability of smaller cross-sections, which might be more sensitive for stability problems. The purpose of the current study is (1) to investigate the flexural buckling behaviour of HSS welded box section columns and (2) to determine a reliable column buckling curve. The characteristic and design values of the buckling resistances for HSS welded box section column are determined by using Monte Carlo simulation technique for a wide range of relative slenderness and steel grades. Based on the simulation results buckling curves are proposed for all the analysed steel grades. Required value for the partial safety factor is also determined considering the design resistance level of the Eurocode. The proposed buckling curves are applicable for HSS welded box section columns made from steel grades between S420–S960.

New framework for calibration of partial safety factors for fatigue design

In Eurocode standards, three verification schemes are proposed for fatigue design under variable amplitude loadings: 1) Based on constant amplitude fatigue limit; 2) Based on constant amplitude equivalent stress range at 2 ⋅ 106 cycles; 3) Based on accumulated damage. Characteristic values of fatigue resistance and load effects as well as partial safety factors are introduced in design equations in order to achieve a target reliability level. In this paper a new framework for calibration of fatigue partial safety factors is presented. Three different fatigue limit state functions are formulated for direct comparison with the three verification schemes proposed in Eurocodes. The variable amplitude S-N curves used in this framework are defined using an original probabilistic approach. The presented framework is then applied to two typical bridge fatigue sensitive welded joints. The comparison of results with partial safety factors values recommended in Eurocodes shows that the Eurocode-based partial safety factors should be revised by considering different fatigue sensitive details and by further differentiating between the three verification schemes.