At the present time, there is no accepted procedure to determine the ultimate load that a masonry arch bridge can support. Unlike in the analysis of other structural typologies, it is not common to apply the finite element method to the structural analysis of this construction type. This is because it is rather complicated and expensive to know exactly many of the variables that characterize the structural behaviour of a model, such as material properties, load history, constructive sequence or its own geometric definition. On the other hand, the special configuration of masonry arches, with evident discontinuities in the joints between voussoirs, requires a unique and specific approach to the problem. It is not realistic to consider a totally homogenous structure, as occurs in other typologies and materials. In order to overcome these disadvantages, the purpose of this job is to develop a finite element model, which allows us to know with reasonable reliability, the maximum load that the bridge can support considering all the characteristics of the masonry structures, while keeping the computational cost under acceptable limits. The structure to be modelled is a stone arch bridge located next to the Caaveiro monastery in the northwest of Spain. The finite element model is a two-dimensional plane-stress model considering both geometric, material and contact nonlinearity. The results from this model are compared with those obtained from the limit analysis, considering the hypothesis of the plastic collapse of the structure.

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In this paper, the determination of the collapse load of an historical stone arch bridge situated in the Northwest of Spain is accomplished. The arch presents damage and its load bearing capacity is reduced, so repair works and restoration are needed. In such circumstances, the assessment of the ultimate load that the bridge can support is very important and so the limit analysis method is applied, which delivers the collapse load and the failure mechanism considering the hypothesis of plastic collapse of the structure. On the other hand, and taking into account that one of the major drawbacks in the analysis of this type of bridge is the lack of accurate data about material properties, a parametric study is performed selecting from all the mechanical parameters governing the bridge response, those with a wider range of variation or those having a more difficult characterization: masonry and backfill unit weight, compressive strength of the masonry, coefficient of radial friction between voussoirs, height of backing, earth pressure coefficient and load dispersion model. For each one of the properties considered, five values are selected, based upon recommendations found in technical literature or in previous experiences with similar bridges, and a series of analyses are performed, obtaining the influence line of kinematic safety factor, with respect to live load, and the critical failure load variation, with respect to each one of the material properties. Results show that the most significant properties having influence in the collapse load are the compressive strength of the masonry, the earth pressure coefficient and the unit weights of materials.

Aircraft engineering is subjected to many classes of uncertainties due to the lack of proper definition of loads, behaviour of new materials or even due to the inaccuracies produced during manufacturing. Because of that, the most advanced methods of analysis and optimization need to be used during the dimensioning of aircraft structures. One way to increase the safety level of a design could be to increase the safety coefficients for load values or material strength, but this approach would lead to an unacceptable amount of material for the aircraft. More proper approaches can be applied using probabilistic analysis during the design phase. In that case, some of the parameters, such as loads, material properties of manufacturing tolerances are defined as random variables and a probabilistic analysis is carried out to identify the safety of the design. This approach can be also enhanced by introducing the concept of design optimization. In that case the optimum solution for an aircraft structure is obtained even considering the random nature of some of the design variables. In this paper these methodologies will be described and some examples of aircraft structures will be presented to show the potential in real problems.

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