Constant Safety Factor Research Articles

Assessing wind turbine blade durability longevity utilizing national renewable energy laboratory tools

With the escalating significance of renewable energy, there exists a pressing demand for precise software and tools capable of designing and forecasting wind turbine blade service life. OpenFAST, TurbSim, and MLife are pivotal open-source wind turbine simulation tools that integrate aerodynamics, structural dynamics, wind simulation, and control systems. They enable accurate prediction of wind turbine performance. This study aims to leverage these software resources to model turbulent wind conditions using predefined basic parameters and then calculate fatigue and longevity of the wind turbine blade to determine service life. Particularly, MLife was employed for rose loading, enhancing the fidelity of the loading cycle simulation. Collaboration between the National Renewable Energy Laboratory and the research team played a crucial role in establishing a foundational baseline and implementing realistic input parameters for evaluating the ultimate load, determining damage equivalent loads (DEL), and projecting service life. In all simulations, a constant factor of safety (FOS) of 1.5 was consistently applied. Additionally, Finite Element Analysis (FEA) was employed to validate our numerical experiments, ensuring the accuracy of the obtained results by correlating simulation outcomes with real-world scenarios, further strengthening the credibility of the study.

Probabilistic back analysis of rainfall-induced slope failure considering slope survival records from past rainfall events

Many rainfall-induced landslides occur on slopes that have limited, or even no, site investigation data before failure. Probabilistic back analysis of slope failure provides an effective tool to back analyze possible pre-failure soil parameters, thus gaining insights into the mechanism of slope failure. For a slope failure induced by rainfall, the actual factor of safety (FS) is time-variant when time-variant rainfall and infiltration are explicitly modeled. This study proposes a novel probabilistic back analysis method that models explicitly the rainfall triggering mechanism for a rainfall-induced slope failure. Unlike existing methods that are based on a constant FS = 1, the proposed method utilizes FS inequality information for probabilistic back analysis, including slope failure record with FS < 1 and slope survival records from past rainfall events with FS > 1. The proposed method is suitable for high-dimensional problems when soil hydraulic properties are also back analyzed. The proposed method converges to the conventional methods with FS = 1 when the time span of slope failure is narrowed down to a few hours and slope survival records are ignored. Incorporating both slope failure and survival records effectively reduces uncertainties in soil strength and hydraulic parameters.

Analytical Solutions for General Two-Wedge Stability

A force-based limit equilibrium analysis is presented for the stability of a general two-dimensional, two-wedge sliding mass of soil, including a vertical or nonvertical wedge interface. The analysis is conducted using three failure planes and can accommodate variable conditions for wedge geometry, pore pressure, shear strength parameters, reinforcement, applied loads, and pseudostatic seismic coefficients. A constant factor of safety is assumed for each failure plane and reinforcement element, although this assumption can be relaxed through selection of strength parameters. The factor of safety is obtained analytically and requires solution for the roots of a polynomial equation. Verification checks show exact agreement with existing solutions for simplified conditions, including Mononobe–Okabe dynamic active force. Numeric examples are provided to demonstrate the method and illustrate the importance of several parameters for stability of a landfill bottom liner system and reinforced soil retaining wall. The analytical solutions take compact form, provide insight for the two-wedge method, and offer good capability to tailor conditions for applications that can be suitably characterized by wedge failure.

Spacing Policies for Adaptive Cruise Control: A Survey

Adaptive cruise control (ACC) systems are designed to provide longitudinal assistance for drivers to enhance safety and reduce workload. As the core of all ACC control algorithms, the spacing policy plays a crucial role in various aspects. This paper presents a comprehensive survey on spacing policies for existing ACC solutions in the literature. The objectives of this paper are to clarify the operating mechanisms and characteristics of the common spacing policies, and to reveal their advantages and shortcomings by means of a comparative study. In this survey, the general evaluation criteria for spacing policies are first introduced. Then, the existing spacing policies are categorized into different types according to their operating mechanisms, and their characteristics are carefully reviewed and explained. A comparative study is followed to analyze the performances of five typical spacing policies in the literature, including the constant spacing policy, constant time headway, traffic flow stability, constant safety factor and human driving behavior spacing policies. The contents provided in this paper serve as a tool for understanding current ACC spacing policies, and pave the way for future ACC enhancement.

Experimental energy confinement time scaling with dimensionless parameters in C-Mod I-mode plasmas

The dependence of energy confinement time on gyroradius, , and normalized collisionality in I-mode plasmas is investigated through dedicated C-Mod experiments scanning dimensionless parameters with constant safety factor. The gyroradius scaling is calculated to be , which suggests core transport may scale with gyro–Bohm physics, indicating favorable extrapolation of the I-mode regime to future devices at low . The scaling exponent for is calculated to be small, but positive (), and the exponent for is deemed inconclusive () due to high correlation with the other two dimensionless variables in the dataset, and therefore requires further investigation. The individual dimensionless parameter scaling is compared to calculations from larger C-Mod I-mode datasets as well as multi-machine scaling laws for ELMy H-mode and L-mode plasmas. Multiple regression techniques and principal component analysis are used to clarify the single parameter scalings and analyze parameter significance within the dataset.

Energy Generation Efficiency and Strength Coupled Design and Optimization of Wind Turbine Rotor Blades

Wind turbine rotor failures have been reported that resulted in substantial damage and cost for maintenance and recovery. This work developed a wind turbine rotor blade design and optimization method to address a coupled energy generation efficiency and blade structural strength design issue, as a generic procedure applicable to both turbine rotors and propellers, in air and water. The optimization procedure was developed for optimum radial blade sectional thickness distribution with a prescribed constant safety factor across the span. While maintaining the required structural strength and integrity of the rotor blades, this procedure is to achieve the following objectives: (1) reduce material use to minimum and (2) obtain the optimum power generation efficiency with the optimum structural strength. A propeller-turbine rotor code coupling aerodynamic and structural properties was developed. For a given blade geometry and chosen material, performance prediction of the instantaneous loading acting on all blade sections and the strength of a local blade section was performed and optimized. A time-domain, three-dimensional unsteady panel method was implemented, developed, and used to perform the optimization. A wind turbine 10 m in diameter from the National Renewable Energy Laboratory (NREL) (Golden, Colorado) was used as a base design example and for optimization based on an extreme wind speed of 100 km/h. The final result achieved a total savings of 18.72% in blade material.

Size effect on seismic performance of high-strength reinforced concrete columns subjected to monotonic and cyclic loading

It has been shown that as concrete strength increases, the size effect becomes more pronounced in both samples and members. However, the effect of section size on the seismic performance of high-strength reinforced concrete columns requires further confirmation. For this purpose, six high-strength reinforced concrete columns were subjected to monotonic and cyclic loading in this study. The experimental results indicate that the relative nominal flexural strength, average energy dissipation coefficient, factor of safety, and local factor of safety all exhibited a strong size effect by decreasing as the column size increased. Moreover, the size effect on the factor of safety was stronger for high-strength columns than for conventional columns. The observed changes in the factor of safety were in good agreement with the Type 2 size effect model proposed by Bažant; so, using the local factor of safety and Bažant’s Type 2 model, the code equation for moment capacity was modified to provide a constant factor of safety regardless of column size.

English

In an autofrettage process a given thick cylinder is subjected to such a pressure which gives a specified depth of elasto-plastic boundary. The outside diameter expansion during autofrettage process is a function of depth of autofrettage. To obtain a specified depth of elastic-plastic interface, the applied autofrettage pressure increases in direct proportion to the proof stress of the pressure vessel material. Although this increases the load bearing capacity of the barrel, resulting in enhanced factor of safety, this increases the maintenance cost of a hydraulic autofrettage plant. To assure quality, product safety and manufacturing economy, an optimal autofrettage pressure is defined. The paper proposes that the minimum autoftrettage pressure is the pressure at which the pressure exterior expansion curve intersects line of constant factor of safety. At higher values of 0.2 per cent proof stress of tube material autofrettaging based on line of constant factor of safety will result in a reduction in fatigue life. The point of intersection of exterior expansion curve with line of constant fatigue life has been defined as the optimal pressure because the specifications of factor of safety and fatigue life are simultaneously achieved. The proposed process design based on above concept has been validated using finite element simulation and empirical post-autofrettage measurements. The verification of the shakedown condition for reverse yielding due to the Bauschinger effect (Huang’s model) and fatigue life has also been satisfied. Defence Science Journal, Vol. 64, No. 4, July 2014, pp. 385-392, DOI:http://dx.doi.org/10.14429/dsj.64.3886

Design and optimization for strength and integrity of tidal turbine rotor blades

Tidal turbine rotor blade fractures and failures have resulted in substantial damage and hence cost of repair and recovery. The present work presents a rotor blade design and optimization method to address the blade structural strength design problem. The generic procedure is applicable to both turbine rotors and propellers. The optimization method seeks an optimum blade thickness distribution across the span with a prescribed constant safety factor for all the blade sections. This optimization procedure serves two purposes: while maintaining the required structural strength and integrity for an ultimate inflow speed, it aims to reduce the material to a minimum and to maintain power generation efficiency or improve the hydrodynamic efficiency. The value of the chosen minimum safety factor depends on the actual working conditions of the turbine in which the sectional peak loading and frequency are used: the harsher the environment, the larger the required safety factor. An engineering software tool with both hydrodynamic and structural capabilities was required to predict the instantaneous loading acting on all the blade sections, as well as the strength of a local blade section with a given blade geometry and chosen material. A time-domain, 3D unsteady panel method was then implemented based on a marine propeller software tool and used to perform the optimization. A 3-blade 20-m tidal turbine that was prototyped in parallel with the current work for the Bay of Fundy was used as an example for optimization. The optimum thickness distribution for a required safety factor at the ultimate possible inflow speed resulted in 37.6% saving in blade material. The blade thickness and distribution as a function of a maximum inflow speed of 6 m/s is also presented. The blade material used in the example was taken as nickel–aluminium–bronze (NAB) but the procedure was developed to be applicable to propeller or turbine blades of basically any material.

Reliability analysis and design of cantilever RC retaining walls against sliding failure

Among the various modes of failure of reinforced concrete (RC) cantilever retaining walls, the sliding mode of failure is invariably seen to be the critical mode governing the proportions of the wall. Traditionally, a constant factor of safety (usually 1.5) is adopted in the design of cantilever retaining walls against sliding and overturning instability, regardless of the actual uncertainties in the various design variables. This paper presents the stability analysis of cantilever retaining walls, accounting for uncertainties in the design variables in the framework of probability theory. The first order reliability method (FORM), second order reliability method (SORM) and Monte Carlo simulation (MCS) method are used as alternative ways to evaluate the probability of failure associated with the sliding failure of retaining walls of various heights (ranging from 4 to 8 m). Sensitivity analysis has shown that the angle of internal friction (Φ) and the coefficient of friction below the concrete base slab (μ) are the most sensitive random variables. It is shown that cantilever retaining walls, optimally proportioned to achieve a factor of safety of 1.5 against sliding failure, can have significant variations in the reliability index (or probability of failure). In order to achieve consistently a ‘target’ reliability index (β = 2.5 or 3.0), the factor of safety must be appropriately chosen, accounting for uncertainties, especially with regard to Φ and μ. In this paper, easy-to-use design tables have been developed for this purpose.

Reliability Analysis of Counterfort Retaining Walls

Traditionally, a constant factor of safety (usually 1.5) is adopted in the design of counterfort retaining walls against instability failure, regardless of the actual uncertainties in the various design variables. This constant factor of safety may not be able to quantify the uncertainties associated with the random variables. This paper presents the stability analysis of a typical counterfort retaining wall, accounting for uncertainties in the ‘design variables’ in the framework of probability theory. The first order reliability method (FORM), second order reliability method (SORM) and Monte Carlo Simulation (MCS) method are used in this study to evaluate the probability of failure associated with the various modes (both geotechnical and structural) of a typical counterfort retaining wall. Sensitivity analysis reveals that the angle of internal friction of the soil, is the most sensitive random variable, which affects all the modes of failure. Plots of reliability index and factor of safety are generated for critical modes of failure, where the constant factor of safety (as recommended in various design codes) is not able to get a desired reliability index/probability of failure.

Bone rigidity to neuromuscular performance ratio in young and elderly men

Given the adaptation of bone to prevalent loading, bone loss should follow, but lag behind, the decline in physical performance during aging. Furthermore, bone responsiveness to load-induced strains is believed to decrease with aging. However, the relationship between bone and lean body (∼ muscle) mass appears to remain rather constant throughout adulthood. The purpose of this study was to examine the association between age and bone to neuromuscular performance ratio. Young ( N = 20, age 24 SD ± 2 years, body mass 77 ± 11 kg, height 178 ± 6 cm) and elderly ( N = 25, 72 ± 4 years, 75 ± 9 kg, 172 ± 5 cm) men served as subjects. Bone structural traits were measured at the right distal tibia and tibial mid-shaft with peripheral quantitative computed tomography (pQCT). Maximal section modulus ( Z max50), total area (ToA d), cortical area (CoA 50), total density (ToD d) and cortical density (CoD 50) were determined from the pQCT images. Neuromuscular performance was measured by recording vertical ground reaction force (GRF) in maximal bilateral hopping. Load-induced strains were estimated by calculating appropriate indices for compressive and tensile loading that took into account both the bone structure and apparent biomechanics of the given bone site. Young subjects had significantly higher maximal GRF compared to older men (4260 ± 800 N vs. 3080 ± 600 N, P < 0.001). They also had smaller ToA d (1100 ± 170 mm 2 vs. 1200 ± 100 mm 2, P = 0.028) while their ToD d was higher (370 ± 46 g/cm 3 vs. 330 ± 22 g/cm 3, P = 0.002). The Z max50 did not differ significantly between young (1660 ± 320 mm 3) and elderly men (1750 ± 320 mm 3) ( P = 0.224). Compressive (0.484 ± 0.102 vs. 0.399 ± 0.078, P = 0.016) and tensile (0.107 ± 0.016 vs. 0.071 ± 0.018, P < 0.001) strain indices were significantly higher in the younger group. In conclusion, the difference in bone to loading ratio at the tibial mid-shaft is bigger than expected from the delay in bone adaptation alone. Potential candidates to explain this phenomenon include a decrease in mechanosensitivity with aging, inability of maximal physical performance to adequately represent the bone loading environment, or the need to maintain constant safety factors to functional strains.

Avaliação da confiabilidade de tubos de concreto armado no estado limite de fissuração

Com a teoria da confiabilidade avaliam-se as duas formulações apresentadas pela norma de projeto de estruturas de concreto NBR 6118:2003 para a estimativa da abertura de fissuras em tubos de concreto armado. Os métodos de confiabilidade FOSM (método de primeira ordem e segundo momento) e o método de simulação de Monte Carlo com amostragem por importância são utilizados. Uma primeira análise de confiabilidade revela as variáveis de projeto com maior contribuição nas probabilidades de falha. Uma análise paramétrica é realizada nestas variáveis, de maneira a identificar a influência destas na confiabilidade dos tubos. O estudo mostra que as formulações da NBR 6118:2003 levam a valores não uniformes para o índice de confiabilidade, para um mesmo fator de segurança. Isto significa que o coeficiente de segurança unitário especificado em norma para o estado limite de fissuração não reflete a incerteza nos parâmetros de resistência do tubo.

Basic biomechanics of self-supporting plants: wind loads and gravitational loads on a Norway spruce tree

Mechanical constraints are major determinants of size and shape of self-supporting plants, for instance upright stems will become mechanically unstable due to their own weight if too slender (Euler buckling). Both gravitational forces and wind loads induce bending moments which the structure has to be able to withstand. Straightforward is the computation of gravitational loads on side branches and stems leaning to various degrees, provided that the geometrical parameters like their tapering mode and the number and size of primary and secondary branches is known. The limit of the structure is reached if at any point the bending moment induced is larger than the critical bending moment. This in turn depends on structural parameters (the geometry of the cross-section) and properties of the material (the modulus of elasticity and the critical stresses at which failure occurs). In many cases, depending on the root–soil interaction, the bending moment on the trunk may lead to root lodging. Most important also from an economical point of view is the assessment of wind loads. It requires an estimate of the effective sail-area (which due to the flexibility of the branches will depend on the wind speed) and the drag coefficient and particularly the knowledge of the wind profile, which may be very different for a solitary tree than for a tree within a dense stand. Flexibility combined with viscoelastic behaviour is the plant’s answer to dynamic wind loads. Although our comprehension may still seem fragmentary, one general conclusion emerges from a comparison of biomechanical calculations with empirical data: plants are often structured in such a way that they approach their biomechanical limits within controlled safety margins. This safety factor applies to ‘normal’ environmental loads, either gravitational loads or wind loads and may be overruled by excessive snow loads or by extreme winds like hurricanes. For a biologist it is a challenge to trace the ‘principle of constant safety factors’ to adaptive growth as response to mechanical stimuli. The phenomenon has been demonstrated qualitatively, but neither the mechanoreceptor nor the signal transduction chain has as yet been identified.

Yield strain behavior of trabecular bone

If bone adapts to maintain constant strains and if on-axis yield strains in trabecular bone are independent of apparent density, adaptive remodeling in trabecular bone should maintain a constant safety factor (yield strain/functional strain) during habitual loading. To test the hypothesis that yield strains are indeed independent of density, compressive ( n=22) and tensile ( n=22) yield strains were measured without end-artifacts for low density (0.18±0.04 g cm -3) human vertebral trabecular bone specimens. Loads were applied in the superior–inferior direction along the principal trabecular orientation. These ‘on-axis’ yield strains were compared to those measured previously for high-density (0.51±0.06 g cm -3) bovine tibial trabecular bone ( n=44). Mean (±S.D.) yield strains for the human bone were 0.78±0.04% in tension and 0.84±0.06% in compression; corresponding values for the bovine bone were 0.78±0.04 and 1.09±0.12%, respectively. Tensile yield strains were independent of the apparent density across the entire density range (human p=0.40, bovine p=0.64, pooled p=0.97). By contrast, compressive yield strains were linearly correlated with apparent density for the human bone ( p<0.001) and the pooled data ( p<0.001), and a suggestive trend existed for the bovine data ( p=0.06). These results refute the hypothesis that on-axis yield strains for trabecular bone are independent of density for compressive loading, although values may appear constant over a narrow density range. On-axis tensile yield strains appear to be independent of both apparent density and anatomic site.

Mechanical Properties of Black Locust (Robinia pseudoacaciaL.) Wood. Size- and Age-dependent Variations in Sap- and Heartwood

Abstract Variations in the density and stiffness (Young's elastic modulus) of fresh wood samples drawn from different parts of the three main trunks of a 32-year-old black locust tree, Robinia pseudoacacia (measuring 19.8 m at its highest point), were studied to determine whether tree ontogeny can achieve a constant safety factor against mechanical failure. Based on the properties of isolated wood samples, the fresh density of sapwood decreased along radial transects from bark to pith, while that of progressively older heartwood samples increased, on average, towards the centre of each of the three trunks. Along the same radial transects, the Young's elastic modulus of sap- and heartwood increased. In terms of longitudinal changes in wood properties, mean wood moduli (averages of sap- and heartwood samples) increased, on average, towards the base of each of the three trunks of the tree. However, the mean fresh densities of wood samples increased towards the top and the bottom of each trunk and were lowest roughly near trunk mid-length. The mean density-specific stiffness (the quotient of Young's modulus and fresh density) of wood was thus lower toward the top and the bottom of the trunks and highest near trunk mid-length. Mean values of fresh wood density-specific stiffness were used to estimate the critical buckling heights for sections of the trunks differing in diameter and age. These estimates indicated that ontogenetic variation in the physical properties and relative amounts of sap- and heartwood in trunks could maintain a constant factor of safety (approximately equal to 2) as a sapling grows in height and girth into a mature tree. This expectation was supported by data from 16 black locust trees differing in height and diameter at breast height (DBH).

信頼性手法に基づく設計基準決定システムの構築

A fatigue curve for design in which the reliability is taken into consideration is generally obtained by ASME code. A constant safety factor is used for design in this code though the fatigue life shows some dispersion. Therefore, a design margin decision system based on reliability, which is capable of evaluating fatigue statistically, has been developed in this paper. In the developed system, the following assumptions are used: (i) the distribution of fatigue strength follows one of the normal, log-normal and Weibull, (ii) the distribution of fatigue life follows either log-normal or Weibull, and (iii) ηD, the coefficient of variance for cumulative cycle ratio, coincides with ηN, the coefficient of variance for fatigue life. By using the developed system, a design fatigue curve for a given failure probability and confidence level was obtained and compared with that of ASME code. As a result, it has been clarified that design margin can be calculated statistically for various materials with different dispersion of fatigue life by the developed system.

The Scaling of Root Anchorage

The scaling of three anchorage systems, the fibrous systems of climbing plants and the tap and plate systems found in self-supporting plants, has been investigated. Optimal shapes for both fibrous and tap-root systems are identified; shapes which provide maximum anchorage for a minimum construction cost. To ensure a constant factor of safety against anchorage failure the linear dimensions of each of these anchorage systems must scale with stem radius.Optimal shapes for plate systems cannot readily be determined; however, their efficiency will rise with plant size because the anchorage provided by the weight of the root—soil plate increases faster than stem strength. As plants get larger, therefore, plate systems become relatively cheaper to construct. This may be one reason why tree saplings have tap-root systems but develop plate systems as they grow.The investment plants must make to anchorage systems will depend on the manner in which the shoot system scales. With isometric scaling of the stem the relative investment in anchorage will remain constant. With the additive scaling possible in climbing plants, large plants having relatively thinner stems than small ones, anchorage investment will fall. If elastic similarity is maintained, larger plants having relatively thicker stems, the relative investment in anchorage must rise.

Biomechanics of Mammalian Terrestrial Locomotion

Mammalian skeletons experience peak locomotor stresses (force per area) that are 25 to 50% of their failure strength, indicating a safety factor of between two and four. The mechanism by which animals achieve a constant safety factor varies depending on the size of the animal. Over much of their size (0.1 to 300 kilograms), larger mammals maintain uniform skeletal stress primarily by having a more upright posture, which decreases mass-specific muscle force by increasing muscle mechanical advantage. At greater sizes, increased skeletal allometry and decreased locomotor performance likely maintain stresses constant. At smaller sizes, skeletal stiffness may be more critical than strength. The decrease in mass-specific muscle force in mammals weighing 0.1 to 300 kilogram indicates that peak muscle stresses are also constant and correlates with a decrease in mass-specific energy cost of locomotion. The consistent pattern of locomotor stresses developed in long bones at different speeds and gaits within a species may have important implications for how bones adaptively remodel to changes in stress.

The functional morphology of weight bearing: limb joint surface area allometry in anthropoid primates

Biomechanical scaling of long bone joint surface areas was investigated in 13 species of anthropoid primates. It was proposed that joint surface areas should scale with positive allometry with respect to body size in order to maintain relatively constant safety factors for joints in small and large animals and that modifications from the overall pattern of scaling may be expected in the limb joints of species exhibiting specialized locomotor behaviours that radically alter limb loading. Within anthropoids, the brachiating primates, white‐handed gibbons (Hylobates lar) and black‐handed spider monkeys (Ateles geoffroyi), were used to test this hypothesis. Total joint surface areas were found to scale with significant positive allometry in 11 of 12 limb joints. The observed pattern of interspecific allometry supports the hypothesis that weight bearing is a major constraint on the design of joints. This positive interspecific allometry is reflected at the intraspecific level as well, with larger joints of larger species showing significant intraspecific scaling. Suspensory species showed no significant deviations from the overall anthropoid pattern, despite their reduced compressive loading of the limb joints, even after controlling for joint mobility. These results suggest that, while evolutionary changes in locomotor behaviour that produce significant increases in loading of a joint may be accompanied by selection for increased joint surface areas, adoption of locomotor repertoires that reduce limb loading may have no selective effect on joint morphology, and joint design in these cases will reflect the biomechanics of the ancestral locomotor condition.