Optimisation under uncertainty applied to a bridge collision problem

We consider the problem of modelling the load on a bridge pillar when hit by a vehicle. This load depends on a number of uncertain variables, such as the mass of the vehicle and its speed on impact. The objective of our study is to analyse their effect on the load. More specifically, we are interested in finding the minimum distance of the pillar to the side of the road passing under the bridge such that a given constraint on the load is satisfied in 99% of impact cases, i.e., such that the probability of satisfying the constraint is 0.99. In addition, we look for solutions to the following optimisation problem: find the distance that minimises a given cost function while still satisfying a given constraint on the load. This optimisation problem under uncertain constraints is not a well-posed problem, so we turn it into a decision problem under uncertainty. For both problems, we consider two typical cases. In the first, so-called precise-probability case, all uncertain variables involved are modelled using probability distributions, and in the second, so-called imprecise-probability case, the uncertainty for at least some of the variables (in casu the mass) is modelled by an interval of possible values, which is a special imprecise-probabilistic model. In the first case, we compute the joint distribution using simple Monte Carlo simulation, and in the second case, we combine Monte Carlo simulation with newly developed techniques in the field of imprecise probabilities. For the optimisation problem with uncertain constraints, this leads to two distinct approaches with different optimality criteria, namely maximality and maximinity, which we discuss and compare

Reliability analysis in vehicle collision with bridge pier

Much work has been done in bridge design specification via a set of structural design standards called Eurocodes to cover the design of all types of structures. We analyse the accidental force on a bridge pier when it is hit by vehicles in order to assess the reliability of a bridge. The force that comes from a vehicle—called vehicle impact force—is not deterministic and it depends on some uncertain parameters, such as the mass of the vehicle and its speed on impact. All the data and uncertainty models for the parameters are given by Eurocode 1. In this paper we analyse the force that is affected by these parameters. For doing that we consider two kinds of problems where in the both problems this force is a function on a distance—the distance between the bridge pier and the side of a road passing under the bridge. One of the problems proposes a design force as a function of the distance—called reliable distance—using a strength condition, the condition on the design forces and the other one suggests a tool for obtaining an economical optimum distance—called cost-optimal distance—by taking into account the optimum economical costs—the cost of bulding and repairing the bridge and human life. In both problems, we consider the safety of the distance where affects dynamic and static design forces and the impact force of vehicle which is not a constant. We show how reliable are Eurocodes by comparing these two distances calculated in two different problems. In other words, through these two problems/criteria we show the danger of using the data represented via Eurocodes for the parameters. In addition, we found linear functions on the distance and the (dynamic and static) design forces of the bridge

Shear capacity of slabs with voiding elements

In the current version of EN 1992-1-1, the shear and punching capacity of beams and slabs without shear reinforcement is governed by the smallest width of the cross section in the tensile area. The semi-empirical formula in this code is appropriate for rather deep beam elements without contribution of the flanges and transfer stiffeners to the shear capacity. However, it can be presumed that for rather stocky beams or slabs with small void formers these components contribute and improve the shear capacity of the global element. To evidence the increased capacity of such slabs in comparison with the single beam theory, a limited test program was set up by Airdeck Building Concepts and Hasselt University (Belgium). Four-point bending tests were carried out on elements with a width of 600 mm, span of 2400 mm and thicknesses of 220 and 340 mm with or without void formers. Because these systems are mostly composed by a precast plank with a thickness from about 60 to 70 mm (with fixed void formers) and a topping cast on site, special attention was taken to the interface to avoid an early failure at the shear interface. Different approximations are investigated for deducing the resistance of the slab with voiding elements by application of a reduction factor on the resistance of a solid slab. It appears from this preliminary set of tests that a volumetric reduction ratio provides the best though safe estimate for this slabs.status: publishe

Reliability analysis in vehicle collision with bridge pier

Much work has been done in bridge design specification via a set of structural design standards called Eurocodes to cover the design of all types of structures. We analyse the accidental force on a bridge pier when it is hit by vehicles in order to assess the reliability of a bridge. The force that comes from a vehicle—called vehicle impact force—is not deterministic and it depends on some uncertain parameters, such as the mass of the vehicle and its speed on impact. All the data and uncertainty models for the parameters are given by Eurocode 1. In this paper we analyse the force that is affected by these parameters. For doing that we consider two kinds of problems where in the both problems this force is a function on a distance—the distance between the bridge pier and the side of a road passing under the bridge. One of the problems proposes a design force as a function of the distance—called reliable distance—using a strength condition, the condition on the design forces and the other one suggests a tool for obtaining an economical optimum distance—called cost-optimal distance—by taking into account the optimum economical costs—the cost of bulding and repairing the bridge and human life. In both problems, we consider the safety of the distance where affects dynamic and static design forces and the impact force of vehicle which is not a constant. We show how reliable are Eurocodes by comparing these two distances calculated in two different problems. In other words, through these two problems/criteria we show the danger of using the data represented via Eurocodes for the parameters. In addition, we found linear functions on the distance and the (dynamic and static) design forces of the bridge.Much work has been done in bridge design specification via a set of structural design standards called Eurocodes to cover the design of all types of structures. We analyse the accidental force on a bridge pier when it is hit by vehicles in order to assess the reliability of a bridge. The force that comes from a vehicle—called vehicle impact force—is not deterministic and it depends on some uncertain parameters, such as the mass of the vehicle and its speed on impact. All the data and uncertainty models for the parameters are given by Eurocode 1. In this paper we analyse the force that is affected by these parameters. For doing that we consider two kinds of problems where in the both problems this force is a function on a distance—the distance between the bridge pier and the side of a road passing under the bridge. One of the problems proposes a design force as a function of the distance—called reliable distance—using a strength condition, the condition on the design forces and the other one suggests a tool for obtaining an economical optimum distance—called cost-optimal distance—by taking into account the optimum economical costs—the cost of bulding and repairing the bridge and human life. In both problems, we consider the safety of the distance where affects dynamic and static design forces and the impact force of vehicle which is not a constant. We show how reliable are Eurocodes by comparing these two distances calculated in two different problems. In other words, through these two problems/criteria we show the danger of using the data represented via Eurocodes for the parameters. In addition, we found linear functions on the distance and the (dynamic and static) design forces of the bridge.status: Published onlin