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Historical Notes
Published in Vladimir Raizer, Isaac Elishakoff, Philosophies of Structural Safety and Reliability, 2022
Vladimir Raizer, Isaac Elishakoff
As Doorn and Hansson (2011) state,The use of safety factors is a well-established method in the various branches of structural engineering. A safety factor is typically intended to protect against a particular integrity-threatening mechanism, and different safety factors can be used against different such mechanisms. Most commonly, a safety factor is defined as the ratio between a measure of the maximum load not leading to failure and a corresponding measure of the applied load. In some cases, it may instead be defined as the ratio between the estimated design life and the actual service life. In addition to safety factors, the related concept of safety margin is used in several contexts. Safety margins are additive rather than multiplicative; typically, a safety margin in structural engineering is then defined as capacity minus load. It is generally agreed in the literature on structural engineering that safety factors are intended to compensate for five major types of sources of failure: (1) Higher loads than those foreseen, (2) Worse properties of the material than foreseen, (3) Imperfect theory of the failure mechanism in question, (4) Possibly unknown failure mechanisms, and (5) Human error (e.g., in design).(Knoll 1976; Moses 1997)
Strain and Stress in One Dimension
Published in Jenn Stroud Rossmann, Clive L. Dym, Lori Bassman, Introduction to Engineering Mechanics, 2015
Jenn Stroud Rossmann, Clive L. Dym, Lori Bassman
Engineers include safety factors in designs. A safety factor is a margin of insurance against unforeseen conditions, material imperfections, fabrication errors, and other uncertainties. The allowable (actually induced) stress in a design must be less than the failure strength or (more conservatively) the yield strength. The safety factor is simply the ratio of failure (or yield) strength to the allowable stress in the current loading conditions (a limit determined from several factors, including material properties, confidence in load prediction, type of loading, possible deterioration, and design life of the structure). Although different applications have different established values, safety factors should have values over 2.0 in robust designs. That is, our analysis should assure us that the allowed stress will never exceed half of the reference (failure or yield) value. For higher-risk applications, we may prefer to use higher safety factors, which can reduce the risk but also increase costs, requiring engineers to use their judgment to make ethical and judicious tradeoffs.
Application of N-value to design of foundations in Japan
Published in A. Verruijt, F.L. Beringen, E.H. De Leeuw, Penetration Testing, 2021
In the case of the road bridge foundations in Japan, design is done with a safety factor of 3 used for the bearing capacity. The safety factor should normally be determined in consideration of the variation of load, variation of the resistance of the structure, analytical error, error in work and uncalculable factors. Here, the relation between the safety of ultimate bearing capacity of the pile according to the calculation formula and the variation of the N-value was formulated upon the reliability theorem using the above data on the accuracy of N-value measurements and load tests, and the safety factor of the calculation formulas of the bearing capacity specified in the Road Bridge Specification were examined.
Estimation of P-multipliers for laterally loaded pile groups in clay and sand
Published in Ships and Offshore Structures, 2019
The safety factor is extremely important in engineering practice due to existing uncertainties regarding the quality of materials and construction, errors of calculations, etc. Box plots were used to describe the variations of the safety factors with different risk levels. The box plots of Figures 9 and 10 indicate that the recommendations of AASHTO and FEMA are more conservative than the new models since the scattering is greater in their box plots. This is while the models proposed using the GP method have made more reliable predictions since their safety factors are closer to one with generally less scattering in the box plots. For instance, by accepting a 10% risk for the piles located in clay, the safety factor of GP model is about 1.1, while it is around 1.3 based on FEMA. Also for the piles in sandy soil, the GP model safety factor is less than 1.2 for 10% risk, but it is 1.3 with respect to AASHTO recommendations.
Damage management and safety evaluation for operating highway tunnels: a case study of Liupanshan tunnel
Published in Structure and Infrastructure Engineering, 2020
Fei Ye, Xin Han, Nan Qin, Aohui Ouyang, Xing Liang, Changxin Xu
The calculation method for the safety factor of the other units is the same as for unit No. 14 given above. The safety factors for the tunnel are shown in Figure 13. The minimum safety factor is 5.69, which satisfies the requirement that the safety factor for concrete structures in the design specification must be greater than 2.4 (Ministry of Transport of People’s Republic of China 2004). Thus, the Liupanshan Tunnel after reinforcement is in a safe state.
Topology Optimization of Thermal Insulators considering Thermal–Structural Multi-Objective Function
Published in Engineering Optimization, 2022
Younghwan Joo, Jaeho Jung, Minho Yoon
For the quantitative analysis of the optimized results, the average temperature of the heat flux boundary and the maximum von Mises stress of each design can be examined. Furthermore, from these values, the safety factor (SF) and the relative thermal conductance (TCrel) are defined as non-dimensional performance indices, as follows: where is the maximum stress; is the total amount of input heat per unit depth; T0 is the constant temperature, given as zero in this study; and ks is the thermal conductivity of solid material. The safety factor provides practical information for structural design by checking whether the structure is able to withstand the given mechanical load. The relative thermal conductance provides information on how much the suggested design is thermally insulative compared to the design filled entirely with solid material. Since heat transfer is maximized when the domain is fully filled with solid material, the relative thermal conductance physically means how much heat transfer is suppressed from the maximum heat transfer capability. These values, obtained for different domain sizes and boundary condition types, are presented in Tables 2 and 3. As indicated by the topology-optimized designs, both the maximum values of the von Mises stress and the temperature increase as the weighting factor increases. However, the design in Figure 6 (, boundary condition type A, W = 0.1 m) is still a possible solution, because its maximum stress is lower than the yield stress of 215 MPa for STS 304. It can be seen that the average heat source temperature varied with different domain sizes. This means that the optimal topologies were affected by the domain size, since thermoelastic load is determined by the temperature field.