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Concept# Factor of safety

Summary

In engineering, a factor of safety (FoS), also known as (and used interchangeably with) safety factor (SF), expresses how much stronger a system is than it needs to be for an intended load. Safety factors are often calculated using detailed analysis because comprehensive testing is impractical on many projects, such as bridges and buildings, but the structure's ability to carry a load must be determined to a reasonable accuracy.
Many systems are intentionally built much stronger than needed for normal usage to allow for emergency situations, unexpected loads, misuse, or degradation (reliability).
Definition
There are two definitions for the factor of safety (FoS):

- The ratio of a structure's absolute strength (structural capability) to actual applied load; this is a measure of the reliability of a particular design. This is a calculated value, and is sometimes referred to, for the sake of clarity, as a realized factor of safety.
- A constant required value, imposed by l

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The construction principles of "Timber-Glass-Composite-Girders" demand practical and theoretical research to ensure reliable designs. Toward this objective the mathematical description of load-bearing and the non-rigid bond is the subject of this work, i.e. to define the contributing parameters for the design of these girders. The non-rigid-bond of the adhesive joint is of great importance because of its influence on the load-bearing of the system as a whole. The loading of girders is dominated by permanent forces thus leading to the obligation of knowing the long-term behaviour of the system and its components. The definition of the characteristic values, taking into account the long-term load-bearing, is an intrinsic part of this investigation. It can be shown that the load-bearing of the girders depends on the fracture of the glass panes. The properties of glass-fractures are a function of the residual internal prestresses due to the heat-strengthening of the panes. The load-bearing, particularly the post-cracked behaviour, changes with respect to the intensity of these internal prestresses. The timber is able to reinforce the cracked glass, leading to a ductile load-bearing behaviour as in the girders, with a dependency upon the size of the remaining fractures. A model based on the differential equations of the non-rigid bond is defined in order to calculate the loading-peaks of the adhesive joint and the material loading itself. The characteristic values of the non-rigid bond, such as the number and distances between cracks and the load introducing length, were evaluated in tests on composite slabs and small scale girders. The existing calculation models which take into account non-rigid bonding were modified to adapt the influence of the width and thickness of the adhesive joint. In order to calculate the stressing of the material the existing calculation models were adapted to calculate the post-cracked situation. The load-bearing behaviour of glass-panes bent with respect to its strong neutral axis needs other safety-considerations than panes, bent off their plane. It is shown that the existing safety considerations subject to the use of glass can not easily be adapted onto the composite girders. The bending with respect to the strong neutral axis and the reinforcement of the glass of the timber demands a different hypothesis to adapt the fractural mechanical analysis and to establish a safe limit conception. This is part of the performed research of this document. The following descriptions present briefly the obtained results: Depending on the quality of the glass (residual stresses due to heat-strengthening, e.g. annealed glass, heat-strengthened glass, fully tempered glass), the ductility and the mode of failure of the girders does change. As a result of its failure mode, annealed glass without internal prestresses offers the highest remaining load-carrying potential after the first crack has appeared. This ductility and thus the structural safety, diminishes with an increasing degree of internal prestressing due to thermal treatment. Heat-strengthened glass (with various degrees of prestressing, various residual stresses) shows a decrease in remaining load-carrying capacity with an increasing degree of prestressing until it fails in a brittle mode as fully toughened glass does. This has to be well considered in respect to safety considerations. Girders with panes made of glass having internal residual stresses due to heat strengthening below 50N/mm2 are considered to collapse ductily, residual stresses bigger than 50N/mm2 cause brittle failure. The effective stiffness of the girders decreases under permanent loads in function of the bondage. Both, timber and adhesive take part in this decrease; the influence of both of the involved materials has been defined. Since the design of conventional glass constructions which uses the concept of principle stresses cannot be adapted, unidirectional shear stresses had to be determined for the shear strength of glass, which is defined as 25N/mm2 for annealed glass. The characteristic values of the adhesive to define the non-rigid bonds have been determined, likewise the influence of the width and thickness of the adhesive joint. The load introducing length, the distances between cracks and the number of cracks are defined with tests on composite slabs. A model to describe the theoretical bond with the defined parameters based on the differential equations was developed. This model allows the calculation of the material stressing at the load introduction and on both sides of a crack. To calculate the stressing of glass and timber existing calculation models which take into account non-rigid bonding were modified to adapt the influence of the width and thickness of the adhesive joint. In order to calculate the stressing of the material the existing calculation models were adapted to calculate the post-cracked situation. The safety factors for the influences of the glass surface, environmental conditions, load duration and the parameters of fracture mechanical analysis as developed as they are known for semi-probabilistic safety concepts for glass constructions cannot easily be adopted. The bending with respect to the strong neutral axis demands a different hypothesis in order to adapt the fractural mechanical analysis and to develop the safety parameters. For the reliable design of timber-glass-composite-girders a contribution to the appropriate use of probabilistic, semi-probabilistic and deterministic safety concepts are given. A realised construction (Hotel "Palafitte" in Monruz (NE)) shows an example and the experience made in designing girders.

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It has been known for more than 150 years that action effects in bridges due to traffic action are higher than it has to be expected for purely static loads. In the design of road bridges, this difference is considered by multiplying static traffic loads with a "dynamic amplification factor". The amplification factors defined in codes are based on dynamic load tests on existing bridges. Despite of hundreds of tests in several countries, experimental investigation has not given satisfactory explanation of the observed phenomena, which has resulted in marked differences between amplification factors defined in different codes. This is due to the fact that the core of the matter – the dynamic interaction between vehicles and bridges– is a complex mechanical problem. Based on a detailed analysis it is shown in the introduction, that it can also be attributed to the fact, that the experimental investigation is more part of the problem than its solution. This thesis aims at getting a solid and systematic grounding in the problem using theoretical analysis. The centre of attention is the question, which importance dynamic phenomena have in those scenarios which are effectively relevant for the structural safety of a bridge. All scenarios are considered that justify an amplification factor, and not only dynamic vehicle – bridge interaction. The structural safety evaluation of a bridge includes the verification of the ultimate and the fatigue limit state. Accordingly, this thesis distinguishes between the interaction at ultimate limit state, for which inelastic bridge behaviour is assumed, and the interaction at service limit state with linear elastic bridge behaviour. 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In the contrary, this thesis aims at capturing the fundamental connections by simple models, which facilitates the identification of the key parameters and the interpretation of their influence. The most important result of the analysis of vehicle – bridge interaction at service limit state is that the amplification factor is most influenced by the weight and the number of vehicles on a bridge. Whereas the amplification is negligible for high vehicle loads, tests with relatively lightweight vehicles on long bridges lead to a significant over-estimation of amplification factors. Furthermore it is shown that neither the span nor the natural frequency of a bridge is appropriate for fixing the amplification factor for a particular bridge and safety verification, respectively. It has been observed in dynamic load tests that deflection measurements consistently result in higher amplification factors than strain measurements. This phenomenon has been known for more than fifty years, but no explanation has been given so far. In this thesis an explanation is proposed and it is shown that deflection measurements result in an over-estimation of amplification factors. Similar considerations lead to a proposal for a more suitable application of amplification factors in the verification of shear force. A completely new approach is chosen for the analysis of vehicle – bridge interaction at ultimate limit state. The effective behaviour at rupture is taken into account, which necessitates first to deal with the influence of loading velocity on material strength. It is shown that only for impact loading of deck slabs due to dynamic tyre forces a minor increase in concrete strength can be expected. An important prerequisite for the understanding of dynamic behaviour at ultimate limit state is the "gravity effect", which is shown to cause massive reduction in the dissipation capacity of a structure. 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