Design Safety Factors Research Articles

An efficient and accurate framework to determine the failure surface/envelop in composite lamina

Failure criteria in composite material involves some unknown parameters that need to be determined through multiple biaxial testing. Inaccuracy in the determination of these parameters may require a larger safety factor for a reliable structural design. However, an accurate prediction of these parameters through multiple biaxial testing is a challenging task. In this context, we focus on loading mode sensitivity analysis and provide a framework for accurate and quick prediction of failure envelop in composite material. Although we demonstrate the effectiveness of the proposed framework by using Tsai-Wu failure criteria, but it can be extended for other failure criteria as well. Here, we determine an optimal loading mode for unknown parameters in failure criteria. We then obtain the failure surface via a fast convergence process and find that only two biaxial tests in different loading quadrants are sufficient to obtain an accurate failure surface for the considered cases. Furthermore, we take into account the scattering in experimental data and establish a failure criteria with failure possibility. Overall, this work can be used as a guideline for a reliable failure prediction in composite materials.

Structure Design and Performance Test of CO2 Scroll Compressor for Heat Pump

Scroll profile design and shell strength design are important in the development of CO2 scroll compressors for heat pumps. In order to meet the multi-operating conditions of the heat pump, the non-clearance profile correction method and the clearance profile correction method are analysed, and the clearance profile correction method was adopted to complete the profile design. The safety factor design method was compared with the reliability design method, and the shell of the CO2 scroll compressor for heat pump was designed based on the reliability design method. The test results show that the scroll tooth with clearance correction method meets the design requirements of heating capacity of 4.8kW±10%, the energy efficiency ratio is not less than 4.6, and the shell structure with 99.38% reliability can meet the structural safety requirements.

Investigating the Factor of Safety for the Design of Columns Using Properties of Steel Rebar’s Manufactured in Pakistan

Investigating the Factor of Safety for the Design of Columns Using Properties of Steel Rebar’s Manufactured in Pakistan

Importance of Lower-Bound Shear Strengths in the Reliability of Spatially Random Clayey Slopes

The random finite element method is used to investigate the effect of including a lower-bound shear strength on the reliability of undrained slopes. The lower bound is represented by the remolded undrained shear strength, which is determined using information about the sensitivity of the clay. This lower-bound strength is used to truncate the left-hand tail of the undrained strength probability distribution. Results indicate that for clayey slopes, the probability of failure is reduced when the lower-bound strength is incorporated in the random field. This reduction allows for reducing the design factor of safety while maintaining the same risk level in the slope design.

Challenging choice of safety factor for design of strip footings on gypsum-rich soils

A fine-grained gypsum-rich clayey soil having a gypsum content of 33% is subjected, in CBR moulds, to modified American association of state highway and transportation officials compaction at optimum moisture content. Two sets of samples were prepared. The first set remained unsoaked, while the second was soaked in fresh water for 120 days. From each CBR sample, three specimens were extracted for unconsolidated undrained triaxial test and the Mohr–Coloumb failure envelopes were obtained for soaked and unsoaked conditions. Soaked samples suffered a significant drop in both cohesion and angle of internal friction. The ultimate bearing capacity of a strip footing was calculated for each of soaked and unsoaked conditions revealing the critical region. For important structures on gypsum-rich soil, the paper shows that the allowable bearing capacity should be based on soaked condition. Based on unsoaked conditions, a safety factor of 8 is required to assure a safety factor of 3 based on soaked condition. For less important structures in regions of hot dry climate with low probability of soaking, safety factors of 4 and 3, based on unsoaked conditions, are required to give safety factors of 1.5 and 1.1 based on soaked conditions, respectively.

Wind Loads of an Irregularly Shaped Tall Building in Warsaw – Eurocode 1 Standard Analysis and Wind Tunnel Testing

This paper analyses wind loads of an irregularly shaped skyscraper in Warsaw. The aim of this study was to compare the results of two methods: analysis conducted according to the Eurocode 1 Standard and wind tunnel testing. The wind pressure distribution on façades and net force values were analysed. In the Eurocode-based analysis, the role played by the form of the building is treated in general terms and the aerodynamic interference with surrounding buildings is not taken into account. The results are characterized by a high design factor of safety. The results of wind tunnel experiments are much more accurate, more reliable, and could be the basis for bassuming lower wind loads.

Experimental study on ultimate strength of bolted L shaped sleeve joints between CFS lipped channel sections

This study aims to understand the behavior of bolted L shape sleeve joint connecting two Cold-Formed Steel (CFS) channel sections. A total of thirty-two specimens were experimentally tested under three-point bending. Three different series namely, (A) control specimen with two different span lengths, (B) sleeved specimen with the flange of sleeve connector capping the compression zone, and (C) sleeved specimen with the flange of sleeve connector capping the tension zone were tested. The parameters considered in this study include (i) the span length (Lt), (ii) sleeve length to section depth ratio (β), and (iii) thickness of sleeve connector (LS). The experimental results revealed that the ultimate moment resistance of specimens with a 2.5 mm thick sleeve connector was 19 to 73% higher than 2.0 mm thick sleeve specimens. The moment capacity of series C specimens was about 90–103% of that of the series B specimens. Based on the experimental results, design predictor equations were suggested to determine the moment resistance of sleeve specimens with respect to β. In addition, reliability studies were done for test series B to determine the safety and resistance factors for allowable strength design (ASD) method and load and resistance factor design (LRFD) method respectively. The equivalent and design uniformly distributed load (UDL) was determined based on the combined effect of shear and bending.

Improved limit analysis method of piled slopes considering the pile axial forces

For the analysis and design of piled slopes using the upper-bound limit analysis method, the axial force on the pile cross-section, where the pile is intersected by the slip surface, contributes to a resistant work rate of the pile; yet this has been omitted in past investigations. Based on analysis of the related work rate and energy dissipation rate of the piled slope, a closed-form solution to internal forces of the pile on the cross-section and some characteristic parameters of the critical slip surface under a specified factor of safety are provided with full consideration of the axial force. The calculation results for two examples show that the axial force has a possibly minor and non-conservative effect on the shear force and bending moment in some cases, but has a major effect on the location of the slip surface, which naturally causes additional design length of the pile. The existing methods without considering the axial force are less conservative or safer than the proposed method in terms of the requisite pile length, particularly under a smaller design factor of safety.

Effect of non-liquefiable layer on bearing capacity and settlement of shallow foundations

Liquefaction during earthquake excitations is one of the most important causes of damage imposed on structures. This phenomenon in saturated loose sand deposits increases water pressure and reduces stiffness. An increase in pore-water pressure during excitations can reduce soil shear strength, and consequently, lead to a decrease of the soil bearing capacity and an increase of settlement. In this study, using physical modelling, the effect of the presence of a non-liquefiable layer with different thicknesses on the improvement of the bearing capacity and settlement of shallow foundations has been investigated for both full and partial liquefaction cases. In these experiments, various constant excess pore-water pressure ratios are generated using the steady-state seepage. The tests are carried out in two different groups. The first group is designed for determining the effect of excess pore-water pressure generation on the bearing capacity; the second group is designed for assessing the effect of design safety factor on the settlement of shallow foundations located on non-liquefiable layers with different thicknesses. The presence of non-liquefiable layers causes considerable improvement in the bearing capacity and settlement of shallow foundations, and this issue may be considered in the engineering problems.

Influence of soil spatial variability on the response of strip footing on geocell-reinforced slope

Abstract The present study investigates the influences of spatial variability and randomness of the soil strength parameters on the load-settlement response of a strip footing placed on a geocell-reinforced soil slope by combining finite difference method with random field model. Both isotropic and anisotropic random fields of lognormally distributed soil friction angle are generated with the utilization of Cholesky-Decomposition technique. In some representative cases, cross-correlation between soil friction angle and soil cohesion, and spatial variability of soil dilation angle are considered. The mean and variation in the load carrying capacity of the footing corresponding to a particular settlement value are obtained after running several numbers of Monte-Carlo simulations. Mean load carrying capacity of the footing reduces with increasing randomness and spatial variation in soil properties, which are defined by the higher values of coefficient of variation and lower values of correlation lengths in both the horizontal and vertical directions. Influence of soil dilatancy is found significant for higher values of soil friction angle. Apart from the above-mentioned parameters, effects of footing setback distance, position of water table, and flexural rigidity of the geocell mattress on the load-settlement response of the footing are examined. Finally, the importance of performing probabilistic analysis is explained from the point of view of failure probability of the footing, calculated with respect to few design factors of safety.

A calculation method for the embedded depth of stabilizing piles in reinforced slopes

SummaryEmbedded stabilizing piles are a significant optimization measure for traditional piles used to reinforce slopes or landslides. The determination of the embedded depth of the pile top is essential for engineering design. On the basis of the potential overtop‐sliding failure mechanism for a piled slope, the corresponding overall slip surface is assumed to consist of the upper part from the original slip surface of the landslide, and the lower part occurs in the local slide mass upslope of the piles. The imbalanced thrust force method is used to determine the thrust force of the upper slide mass, and a variational calculus method within the framework of limit equilibrium for the lower slide mass is provided to calculate its limit resistance. According to the equilibrium relationship between the thrust force and the limit resistance under a design factor of safety of the piled slope, a closed‐form solution to the piled‐slope stability is specifically derived. It can quantitatively exhibit the influences of some important factors, including the embedded depth on the factor of safety and the corresponding slip surface of the slope. The analysis results of some practical examples show that the factor of safety decreases nonlinearly as the embedded depth increases. The proposed method can be applied in practical engineering.

Empirical Formulation for Compressive Capacity of Gusset Plates

Gusset plates play a critical role in the behavior and stability of bracing systems and truss bridges. While the behavioral characteristics of gusset plates have been widely investigated and analysis procedures have been developed, considerable uncertainty exists in the design equations, due primarily to the complexity of stress distribution in the connection area. Current design procedures rely heavily on highly simplified approaches, which typically result in an inconsistent design factor of safety for various gusset configurations and boundary conditions. In this research, a powerful genetic programming (GP) tool is employed to develop an empirical formulation for compressive capacity of corner gusset plates using a comprehensive database collected from previously published test results and test-validated finite element models. The predictive model correlates the ultimate compressive strength of gusset plates with their mechanical and geometrical properties. A comparative study is performed to evaluate the performance of the derived expression compared to the results of the well-known effective length factor method. The results indicate that the GP-based equation accurately estimates the compressive capacity of gusset plates and its prediction performance is significantly better than that of the current procedures.

Comparing the factors of safety from finite element and limit equilibrium analyses in lateral support design

Soil-nails and anchors as means of lateral support in surface excavations require stability analyses as part of design. Generally, the acceptance criterion is some arbitrary 'factor of safety' which can be routinely computed using well-established principles of limit equilibrium analyses. These methods have been tested over many years and have been shown to be adequate for design. There is an increasing trend towards the use of the finite element strength reduction methods to determine factors of safety in lateral support design. Differences are often reported between factors of safety calculated using these methods. There is also a danger that engineers might use finite element modelling without full appreciation of the impact of choices and assumptions made in using the software. This paper compares the results of limit equilibrium and finite element calculations to assess factors of safety. Under certain conditions the factor of safety from the finite element strength reduction technique is comparable with limit equilibrium methods, provided that the same failure mechanism is evaluated. In addition, in the case of anchors, the same capacity must be specified in both analyses. In defining in-situ stress states, the friction angle and Poisson's ratio should be specified so as to not violate the yield criterion. Modelling parameters (mesh grading and boundary distances) were found to have relatively minor influences on the factor of safety for the strength reduction technique.

Graphic illustration for mechanical reliability design (2): theory and method

In this paper, the connotation and an extension of the mechanical reliability design theory and method are presented via charts and texts. The abstruse mechanical reliability theories and methods are illustrated intuitively and scientifically via easy-to-understand language and simple and clear illustrations. Topics such as mechanical strength design, mechanical reliability design, dynamic and gradual reliability design, reliability optimization design, reliability sensitivity design and reliability robust design are covered to help the readers understand the wonder and practicality of mechanical reliability engineering. Diagrams of reliability design, dynamic and gradual reliability theory and technology, reliability optimization design, reliability sensitivity design and reliability robust design are illustrated for the first time. Additionally, the relationship between mechanical product reliability design and conventional safety factor design is elaborated in a table. This paper provides a solid mechanical reliability engineering foundation for design, manufacturing, usage and evaluation of mechanical products.

GFRP Bars Anchorage Resistance in a GFRP-Reinforced Concrete Bridge Barrier.

In the present paper, experimental and numerical investigations were conducted on concrete bridge barriers utilizing glass fiber reinforced polymer (GFRP) bars with a hook at their ends. Implementation of these hooked bars instead of the bent bars or headed-end bars in the bridge barriers presented in the Canadian Highway Bridge Design Code (CHBDC) was investigated on American Association for State Highway and Transportation Officials (AASHTO) test level 5 (TL-5) concrete bridge barriers. This research aimed to reach a cost effective and safe anchorage method for GFRP bars at the barrier–deck junction, compared to the conventional bend bars or headed-end bars. Therefore, an experimental program was developed and performed to qualify the use of the recently-developed, small radius hooked bars at the barrier–deck junction. The experimental findings were compared with the design factored applied transverse load specified in CHBDC for the design of the barrier–deck junction as well as factored applied bending moment obtained at the barrier–deck junction using a recently-conducted finite-element modeling. Satisfactory behavior for the developed hooked GFRP bars as well as their anchorage resistance was established and a reasonable factor of safety in design of barrier–deck joint was achieved.

A Case Study: Determination of the Optimal Tailings Beach Distance as a Guideline for Safe Water Management in an Upstream TSF

Most tailings storage facility (TSF) failures occur in active, upstream-type TSFs, often due to extreme and unexpected weather conditions—specifically, heavy rainfall and strong winds. This case study of a TSF in southern Arizona examines the use of the optimum safe beach distance (Doptimal, the optimum distance between the crest and decant pond) as a tool for monitoring geotechnical stability and reducing catastrophic failures. A digital model of the TSF was used to determine the critical beach distance (Dcritical) under normal weather conditions, and Doptimal was then determined by adding incremental distances to account for the effects of heavy rainfall (Drainfall) and strong winds (Dwind). To overcome accessibility issues, a drone was used to map the TSF geometry and create a digital model. This model served as the basis for conducting a coupled stress-seepage, finite-element (FEM) analysis with a safety factor of 2.0 to assess geotechnical stability (Dcritical). The safe beach distance increments were determined using the PMP (probable maximum precipitation) and possible maximum wind speed. Based on this analysis, the optimal safe beach distance at the study site was identified as 202.2 m. Since the current beach distance (371 m) exceeds this value, the TSF was considered to be stable and satisfied the design safety factor of 2.0. However, this distance should be reassessed periodically to account for changes in the TSF geometry and other conditions. Furthermore, it applies only TSFs that are well-managed and feature a smooth, non-undulating beach surface with a consistent slope.

Structural performance on bolted sleeved connections between two CFS channel sections subjected to combined bending and shear

An experimental investigation was carried out to study the behavior of the sleeve connection between two cold-formed steel (CFS) channel sections subjected to combined bending and shear. A total of thirty-nine specimens including three control specimens were tested under three-point bending for different parameters such as three types of the span to section depth ratio, three different sleeve lengths, two sleeve thicknesses and two bolt configurations. Each tested specimen consisted of a pair of channel sections braced together using hot rolled angle sections along the length to ensure lateral stability. The test results indicate two different failure modes; local buckling due to combined bending and shear in the purlin section adjacent to sleeve end, and the other is shearing of the self-drilling screw at the tension zone. The moment resistance of the sleeve connection varied directly with the sleeve length to section depth ratio. The interaction study carried out between the proposed critical sleeve moment and shear capacity of the sleeve specimens is found to be conservative with respect to the AISI interaction equation. The resistance factor for load and resistance factor design (LRFD) method and safety factor for allowable strength design (ASD) method is proposed for the design of sleeve connection by considering it as a flexural member. The design uniformly distributed load (wD) of sleeve specimens having an average sleeve length to section depth ratio of 2.17, 3.51, and 4.85 are found to be 80, 103, and 125% the capacity corresponding to control specimen respectively. The proposed design method is also applicable to the design of continuous channel purlin/girt sections with 150 mm depth for any number of spans subjected to UDL.

ЗАХИСТ ЖИТЛОВИХ БУДИНКІВ ВІД СЕЙСМІЧНИХ НАВАНТАЖЕНЬ ТА ДИНАМІЧНИХ ВПЛИВІВ ЗАЛІЗНИЧНОГО ТРАНСПОРТУ

В статті представлені результати експериментально-теоретичних досліджень щодо вирішення проблеми віброізоляції багатоповерхових житлових будинків у рівні пальового ростверку від потягів залізниці. Результати виконаних робіт дозволили отримати акселерограми поверхні ґрунту на будівельному майданчику; здійснити розроблення розрахункових динамічних моделей віброізольованих 6, 10 та 13-поверхових секцій житлового будинку для проведення розрахунків та розроблення рекомендацій з конструювання вузлів влаштування віброізоляторів та системи сейсмо- та віброзахисту секцій будинку з метою зниження до допустимих за Санітарними нормами динамічних впливів від потягів залізниці. Для захисту від динамічних впливів потягів залізниці за результатами чисельних досліджень та випробувань гумових віброізоляторів, проведених в ДП НДІБК та ІГТМ НАНУ, згідно патенту на оголовок кожної палі перед бетонуванням плити ростверку встановлюється гумовий ізолятор та влаштовується система віброзахисту будинку у рівні підошви плити ростверку та стін підвалу. За результатами розрахунків просторових моделей будинків обґрунтовані параметри гумових ізоляторів для віброзахисту 6, 10 та 13-поверхових секцій. Виконані випробування двох типів гумових віброізоляторів вітчизняного виробництва з зовнішнім діаметром 340 мм і товщиною 40 і 50 мм з доведенням максимального вертикального навантаження до 3200 кН. Середня жорсткість гумового ізолятора діаметром 340 мм та товщиною 50 мм на стиск (при розрахункових навантаженнях на палі до 800 кН) дорівнює Кz = 67000 кН/м; ізолятора товщиною 40 мм Кz = 105000 кН/м (при розрахункових навантаженнях на палі до 1200 кН).Розрахункові коефіцієнти запасу проти перекидання секцій висотою 13, 10 та 6 поверхів дорівнюють від 5,4 до 16,5 при інтенсивності сейсмічних впливів 6 балів. При вітрових впливах коефіцієнти запасу дорівнюють від 101,6 до 196,6.

Discontinued Rock Slope Analysis through a New TFS-KGM Analytical Method

Slope stability analysis of jointed rocks has been the focus of many studies. The presence of joints and discontinuities in rock environments intensifies instability along with the development of block movements. Many analytical and numerical methods have been proposed and applied to analyze the stability of jointed rock slopes. Computation complexity, incapability of presenting a reliable safety factor to be used for developing a proper design operation and improper analysis speed are the known challenges of these methods. This paper has developed the well-known analytical Key Group Method (KGM) to Toppling-Free fall-Sliding Key Group (TFS_KGM) version. To this end, toppling and free fall failure are added to the existing method in order to have a better analysis of jointed rock slopes. In this method, unstable key blocks participate in creating groups which may rotate or free fall besides sliding. The new TFS_KGM computes stability conditions and final safety factors based on the most unstable sliding, rotating and free fall movements with consideration of in situ stresses. Results of using this method in jointed rock slopes and the comparison with DEM numerical, KBM and KGM analytical methods show that the method is very effective particularly when the geometrical conditions of the jointed rocks make the toppling and free fall failures potentially possible. The method demonstrates a simple computation method along with a proper analysis speed. It also provides accurate design safety factors and much more optimized critical failure areas than previous methods.

Comparison of the reliability-based and safety factor methods for structural design

Abstract Reliability-based design optimization theory has been widely acknowledged as an advanced and advantageous methodology for complex structural system design. Comparatively, the traditional safety factor design method has fallen out of favor with designers since it is simply just a comprehensive expression of all the uncertainties existing in a practical engineering structure, which has been verified to be unreasonable. Moreover, there is no description of the method for searching for the optimal design. In this paper, a comparison of the two approaches is performed for the optimization results and process. It is demonstrated that the weight of the designed structure by the reliability-based optimization is not heavier than that by the safety factor design method under the same reliability requirements. The time efficiency, error estimates and sensitivity analysis are also compared to discuss the advantages and disadvantages of the two approaches. Eventually, the advancement of the reliability-based design optimization is illustrated with optimization designs of a two-bar truss and one practical supersonic wing.