Reliability-based design recommendations for composite corrugated-web beams

Developments and advances in fabrication technology have led to a new generation of structural shapes in the composite construction market, among them, the composite sinusoidal-web girder. A sinusoidal-web girder is a built-up I-girder with a thin-walled corrugated web (with a sinusoidal profile) and flat plate flanges. The corrugated web considerably increases the rigidity and the resistance to shear forces and local effects, thus reducing the occurrence of local and shear buckling. In spite of the advantages this type of composite construction may offer, there are no standards addressing the design of such girders. In this paper, the development of reliability-based design recommendations for both composite sinusoidal beams and their connections to adjacent elements is reported. To this end: (i) finite-element models for connections and composite girders are developed and validated, (ii) theoretical models are proposed, (iii) reliability analyses are performed, and (iv) implicit reliability levels are checked against current practice. It is shown that the proposed theoretical models, despite all the complexities involved, are in good agreement with both experimental and numerical analyses. It is found that the safety levels resulting from the proposed design recommendations are consistent with current trends in structural engineering practice.     

GFRP筋橡胶集料混凝土梁受弯性能

为提高纤维增强聚合物复合材料(FRP)筋混凝土梁抗裂性能,改善其脆性破坏特征,将玻璃纤维增强聚合物复合材料(GFRP)筋与橡胶集料混凝土共同应用于梁构件中。采用ABAQUS对GFRP筋橡胶集料混凝土梁的受弯性能进行有限元模拟及参数分析,探究了橡胶掺量、GFRP筋配筋率、混凝土强度等级及截面高度对梁受弯性能的影响。结果表明:增加混凝土中橡胶颗粒的掺量可提高梁的开裂荷载,当橡胶掺量为15%时,开裂荷载提高了29%;增加配筋率可提高梁的开裂荷载和承载力,当受拉筋直径由10 mm增加至18 mm时,橡胶掺量为10%的GFRP筋橡胶混凝土梁开裂荷载提高了约15%,承载力提高了约85%,但配筋率增加至一定数值后,其影响不再明显;提高橡胶混凝土强度等级,可提高梁的开裂荷载及承载力,当橡胶混凝土强度等级由C25提高至C40时,开裂荷载提了高约53.7%,承载力提高了约23%;为更好地满足正常使用极限状态,GFRP筋橡胶混凝土梁的截面高度宜适当增加。      

Reliability-based design of sheet pile structures

This paper concerns the use of the conventional Coulomb theory of lateral earth pressure against retaining structures with some empirical modifications in the design of cantilever sheet piles. The design procedure adopted basically involves the computation of the embedment depth and the maximum bending moment in the sheet pile. Design charts are developed for a wide range of soil types, water level heights and loading conditions.In order to portray the actual conditions on the sheet pile, the design factors, namely the soil properties, height of water level and surcharge loads, are treated as random variables. Using the developed design charts and through a first-order Taylor's series expansion, the variation in the embedment depth as well as the maximum moment are evaluated and presented in a graphical form. The final design process entails the combination of the mean and variance of the design requirements based on a given probability of failure (reliability). Examples to illustrate the use of the reliability-based design method are presented.     

Reliability-based design of automotive transmission systems

A reliability-based approach is presented for the design of three-speed automotive transmission systems. The design of an automotive transmission system involves the design of the gear train, shafts (input, connecting, and output), bearings, keys, and splines. The gear train is idealized as a weakest-link kinematic chain, and the design is conducted with respect to failure due to bending and surface wear. The shafts are designed with respect to fatigue failure due to bending and torsion. The design of bearings (cylindrical roller bearings), keys, and splines are based on the maximum allowable stress in the components. The failure of the system is assumed to correspond to zero output power from the transmission system based on a series-parallel model. The reliability-based design is conducted for a specified value of the reliability of the system. The structural and kinematic designs of the transmission system (i.e. the gear train) are assumed to be known. The design parameters such as power transmitted, gear face widths, dimensions of roller bearing, length of splines, length of keys, and material properties are considered as random variables. The reliability-based design results are compared with those obtained by a deterministic design procedure. The effects of variation of design parameters, such as the reliability of the system and coefficient of variation of the input speed are also studied. In addition, a comparison of the designs obtained with different distributions of the random variables is also made and conclusions drawn.     

基于多目标优化策略的扭杆可靠性稳健优化设计

为提高机械零部件的安全性和稳健性,应用可靠性稳健优化设计理论和多目标决策方法,建立了适合结构可靠性稳健优化设计的多目标优化模型.为能迅速准确地对具有约束条件的多目标优化模型进行求解,提出一种利用模糊理论对约束条件进行处理的方法,然后应用灰色粒子群算法对多目标优化模型进行求解.通过对正态分布参数和任意分布参数的扭杆可靠性稳健优化设计,表明该方法行之有效.     

Reliability-based design optimization with progressive surrogate models

Reliability-based design optimization (RBDO) has traditionally been solved as a nested (bilevel) optimization problem, which is a computationally expensive approach. Unilevel and decoupled approaches for solving the RBDO problem have also been suggested in the past to improve the computational efficiency. However, these approaches also require a large number of response evaluations during optimization. To alleviate the computational burden, surrogate models have been used for reliability evaluation. These approaches involve construction of surrogate models for the reliability computation at each point visited by the optimizer in the design variable space. In this article, a novel approach to solving the RBDO problem is proposed based on a progressive sensitivity surrogate model. The sensitivity surrogate models are built in the design variable space outside the optimization loop using the kriging method or the moving least squares (MLS) method based on sample points generated from low-discrepancy sampling (LDS) to estimate the most probable point of failure (MPP). During the iterative deterministic optimization, the MPP is estimated from the surrogate model for each design point visited by the optimizer. The surrogate sensitivity model is also progressively updated for each new iteration of deterministic optimization by adding new points and their responses. Four example problems are presented showing the relative merits of the kriging and MLS approaches and the overall accuracy and improved efficiency of the proposed approach.     

Reliability-based optimal design using sample average approximations

An algorithm for reliability-based optimal design is developed using sampling techniques for estimating the failure probability. The algorithm applies a new method for sensitivity calculations of the failure probability. Initially, the estimates of the failure probability are coarse. As the algorithm progresses towards an optimal design, the number of sample points is increased in an adaptive way leading to better estimates of the failure probability. The algorithm is proven to converge to an optimal design. The applicability of the algorithm is shown in an example from the area of highway bridge design.     

基于鞍点逼近的机械结构可靠性稳健优化设计

将可靠性优化设计理论与可靠性灵敏度分析方法相结合,讨论了机械零部件稳健优化设计的问题.系统地推导了基于鞍点逼近的可靠性灵敏度公式,并把可靠性灵敏度计算结果融入可靠性稳健优化设计模型之中,将可靠性稳健优化设计归结为满足可靠性要求的多目标优化问题.在基本随机参数概率分布已知的前提下,应用鞍点逼近技术,得到极限状态函数的分布函数与概率密度函数,并且将此结果应用到机械零部件的可靠性灵敏度分析中,进而实现了机械零部件的可靠性稳健优化设计.通过与Monte-Carlo方法计算所得的结果相比可知,应用鞍点逼近技术可以迅速、准确地得到机械零部件可靠性稳健设计信息．     

Reliability-based design and optimization of adaptive marine structures

The objectives of this work are to quantify the influence of material and operational uncertainties on the performance of self-adaptive marine rotors, and to develop a reliability-based design and optimization methodology for adaptive marine structures. Using a previously validated 3D fluid–structure interaction model, performance functions are obtained and used to generate characteristic response surfaces. A first-order reliability method is used to evaluate the influence of uncertainties in material and load parameters and thus optimize the design parameters. The results demonstrate the viability of the proposed reliability-based design and optimization methodology, and demonstrate that a probabilistic approach is more appropriate than a deterministic approach for the design and optimization of adaptive marine structures that rely on fluid–structure interaction for performance improvement.     

Reliability-based design optimization under stationary stochastic process loads

Time-dependent reliability-based design ensures the satisfaction of reliability requirements for a given period of time, but with a high computational cost. This work improves the computational efficiency by extending the sequential optimization and reliability analysis (SORA) method to time-dependent problems with both stationary stochastic process loads and random variables. The challenge of the extension is the identification of the most probable point (MPP) associated with time-dependent reliability targets. Since a direct relationship between the MPP and reliability target does not exist, this work defines the concept of equivalent MPP, which is identified by the extreme value analysis and the inverse saddlepoint approximation. With the equivalent MPP, the time-dependent reliability-based design optimization is decomposed into two decoupled loops: deterministic design optimization and reliability analysis, and both are performed sequentially. Two numerical examples are used to show the efficiency of the proposed method.     

Reliability-based optimal structural design by the decoupling approach

A decoupling approach for solving optimal structural design problems involving reliability terms in the objective function, the constraint set or both is discussed and extended. The approach employs a reformulation of each problem, in which reliability terms are replaced by deterministic functions. The reformulated problems can be solved by existing semi-infinite optimization algorithms and computational reliability methods. It is shown that the reformulated problems produce solutions that are identical to those of the original problems when the limit-state functions defining the reliability problem are affine. For nonaffine limit-state functions, approximate solutions are obtained by solving series of reformulated problems. An important advantage of the approach is that the required reliability and optimization calculations are completely decoupled, thus allowing flexibility in the choice of the optimization algorithm and the reliability computation method.     

Reliability-based robust multi-objective optimization applied to engineering system design

ABSTRACT

Probabilistic and non-probabilistic methods have been proposed to deal with design problems under uncertainties. Reliability-based design and robust design are probabilistic strategies traditionally used for this purpose. In the present contribution, reliability-based robust design optimization (RBRDO) is formulated as a multi-objective problem considering the interaction of both approaches. The proposed methodology is based on the differential evolution algorithm associated with two strategies to deal with reliability and robustness, respectively, namely inverse reliability analysis and the effective mean concept. This multi-objective optimization problem considers the maximization of reliability and robustness coefficients as additional objective functions. The effectiveness of the methodology is illustrated by two classical test cases and a rotor-dynamics application. The results demonstrate that the proposed methodology is an alternative method to solve RBRDO problems.     

Reliability-based design of blast-resistant composite laminates incorporating carbon nanotubes

Research efforts have reported on the ability of carbon nanotubes (CNTs) to enhance the stiffness and strength of carbon fiber composites. Systematic design of blast-resistant composites requires considering CNTs–carbon composites characteristics and the uncertainty of blast events. This article suggests a systematic reliability-based design approach where system reliability is used to compute the probability of failure of a composite laminate. A case study for the design of a five-layer composite laminate incorporating CNTs and subjected to uncertain blast event is demonstrated. 0.5–1% CNTs contents by weight seem capable of significantly reducing the composite probability of failure during blast.     

Probabilistic bond strength model for reinforcement bar in concrete

In order to overcome the disadvantages of traditional deterministic models, a probabilistic bond strength model of reinforcement bar in concrete was presented. According to the partly cracked thick-walled cylinder model, a deterministic bond strength model of reinforcement bar in concrete was developed first by taking into account the influences of various important factors. Then the analytical expression of probabilistic bond strength model of reinforcement bar in concrete was derived by taking into consideration both aleatory and epistemic uncertainties. Subsequently, a probabilistic bond strength model of reinforcement bar in concrete was proposed by determining the statistical characteristics of probabilistic model parameters based on the Markov Chain Monte Carlo method and the Bayesian theory. Finally, applicability of the proposed probabilistic model were validated by comparing with 400 sets of experimental data and four typical deterministic bond strength models. Analysis shows that the probabilistic model provides efficient approaches to describe the probabilistic characteristics of bond strength and to calibrate traditional deterministic bond strength models.     

Design criteria for early-age bond strength in reinforced concrete

The main objective of the extensive research programme involving 238 test specimens was to provide bond strength criteria between type 2 deformed bars and concrete in models for predicting early-age rracking. The major variables included bar diameter, concrete cover, age of concrete, transverse reinforcement and anchorage length. Both the pull-out load and slip displacement were determined using specially developed tensile bond tests where both steel and concrete were in tension. The bond strength of deformed bars showed a significant age effect and design equations suitable for toth ultimate and serviceability limit states at early age have been developed. BS 8110 and BS 8007 Code values underestimated the ultimate bond strength for the concrete strengths considered, while the same values from BS 8110 and BS 8007 overestimated or compared approximately with, respectively, the average bond stress test results at 0.1 mm slip. AC1-318 Building Code, on the other hand, overestimated the bond strength for concrete cube strengths up to 15 MPa and then became conservative.

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Resume On a réalisé un vaste programme de recherche sur 238 éprouvettes, dont l'objectif principal était d'obtenir des critères d'adhérence entre des barres déformées de type 2 et le béton dans des modèles permettant de prévoir la fissuration aux jeunes ages. Les principales variables étaient: le diamètre de la barre, l'enrobage du béton, son age, le renforcement transversal et la longueur de l'ancrage. On a déterminé à la fois la charge d'arrachement et la longueur de glissement par des essais d'adhérence où l'acier comme le béton étaient soumis à la traction. On a constaté l'importance de l'age des barres, et on a établi des équations variables à la fois pour les états limites ultimes et en service aux jeunes ages. Les valeurs de calcul données par BS 8110 et BS 8007 sous-estiment l'adhérence maximale pour les résistances du béton considérées, tandis que les mêmes valeurs extraites des mêmes documents surestimaient ou rejoignaient à peu près la moyenne des résultats d'essai de la contrainte d'adhérence pour un glissement de 0,1 mm. D'autre part, ACI-318 surestime l'adhérence pour des résistances sur cubes du béton allant jusqu'à 15 MPa, et, au-delà, devient normal.

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Tensile bond testing of concrete repairs

The development and maintenance of a sound band is an essential requirement of a concrete patch repair. Tensile bond tests are increasing in popularity as a means of measuring this adhesive property, both on site for quality control and in the laboratory for materials evaluation. This paper discusses the main issues relevant to tensile bond testing, namely material properties, surface conditions, geometry, loading and the effects of material mismatch. Analytical and experimental work is presented, along with the results of other researchers, with an emphasis on the core pull-off technique. The latter is shown to be a good method for evaluating bond strength provided that appropriate precautions are taken to minimize the influence of flaws and stress concentrations, and that the effects of mismatch in repair and substrate properties (particularly modulus, shrinkage and thermal expansion) are fully understood.     

A limit state anchorage bond test for reinforcement in concrete

A new standard anchorage bond test for steel reinforcement in concrete has been developed in accordance with limit state principles. The basis of the test is non-failure of the anchorage. The application of the test to all types of deformed bars leads to two main categories, namely plain surface square twisted bars and all types of ribbed bars. The relationship between the test lengths and the lengths of anchorages used in design is discussed.     

Reliability-based design optimization using a moment method and a kriging metamodel

Reliability-based design optimization (RBDO) has been used for optimizing engineering systems with uncertainties in design variables and system parameters. RBDO involves reliability analysis, which requires a large amount of computational effort, so it is important to select an efficient method for reliability analysis. Of the many methods for reliability analysis, a moment method, which is called the fourth moment method, is known to be less expensive for moderate size problems and requires neither iteration nor the computation of derivatives. Despite these advantages, previous research on RBDO has been mainly based on the first-order reliability method and relatively little attention has been paid to moment-based RBDO. This article considers difficulties in implementing the moment method into RBDO; they are solved using a kriging metamodel with an active constraint strategy. Three numerical examples are tested and the results show that the proposed method is efficient and accurate.     

Shear bond strength in repaired concrete structures

A good bond between old and new concrete is necessary for a successful repair of concrete structures. The bond is usually determined through pure tension tests,e.g., the common pull off test. However, in most applications, the shear bond strength is more interested. A test apparatus for torsion tests has been developed. Laboratory and field tests have been carried out on cast in place concrete and shotcrete repairs. For waterjetted surfaces, the obtained shear bond strength exceeds 3 MPa,i.e., considerably more than the tensile bond strength which usually varies between 1 and 2 MPa. The shear bond strength is also markedly higher than design strength values found in international codes.

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Résumé Une bonne adhérence entre l'ancien béton et le nouveau est nécessaire à la réussite de la réparation des structures en béton. L'adhérence est habituellement déterminée à partir d'essais en traction pure, comme par exemple un essai classique d'adhérence. Cependant, pour la plupart des applications, la résistance au cisaillement de l'adhérence est un problème plus pertinent. Un équipement pour des essais de torsion a été développé. Des tests en laboratoire et sur site, concernant du béton coulé sur place et du béton projeté, ont été menés. Pour les surfaces traitées par hydrodémolition, la résistance au cisaillement de l'adhérence dépasse 3 MPa, ce qui est largement supérieur à la résistance à la traction, qui varie habituellement entre 1 et 2 MPa. Ainsi, la résistance au cisaillement de l'adhérence est sensiblement plus élevée que les valeurs préconsisées par les codes internationaux.

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Editorial note Prof. J. Silfwerbrand is a RILEM Senior Member. He is the Director of the Swedish Cement and Concrete Research Institute, a RILEM Titular Member.