scholarly journals Approximate Calculation Method for Noncentral t-Distribution Quantile

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Jun Gao ◽  
Jitao Yao
Keyword(s):  
Normal Distribution ◽  
Calculation Method ◽  
Approximate Calculation ◽  
Material Strength ◽  
Theoretical Derivation ◽  
Application Range ◽  
Numerical Fitting ◽  
Numerical Table ◽  
T Distribution

In the process of structural design and structural performance evaluation, the inference of the reliable life of the structure and the representative value of the material strength is a necessary work. The determination of material strength is the presumption of the quantile of the normal distribution, and the determination of the confidence level of the quantile of the normal distribution involves the noncentral t-distribution function. However, the calculation of the quantile is very complicated and is often provided in the form of a numerical table, which often involves multiparameter interpolation calculation, so it is not convenient to apply. The existing approximate calculation methods for noncentral t-distribution quantiles have strict application conditions, and the calculation process is relatively cumbersome. It is still difficult to meet actual needs in terms of fitting accuracy, application range, and convenience. In this paper, a new calculation method for noncentral t-distribution quantiles is proposed by introducing new probability expressions and related approximate distributions, based on theoretical derivation and numerical fitting. The comparative analysis results show that the method not only is convenient for calculation but also has the advantages of higher accuracy and wider application range, and it is more in line with the actual needs of engineering.

EXPERIMENTAL STUDIES OF REINFORCED CONCRETE STRUCTURES WITH CROSS-SHAPED SPATIAL CRACK UNDER TORSION WITH BENDING

2020 ◽  
Vol 92 (6) ◽  
pp. 13-25
Author(s):  
Vl.I. KOLCHUNOV ◽  
◽  
A.I. DEMYANOV ◽  
M.M. MIHAILOV ◽  
◽  
...  
Keyword(s):  
Reinforced Concrete ◽  
Experimental Determination ◽  
Calculation Method ◽  
Experimental Studies ◽  
Concrete Structures ◽  
Design Parameters ◽  
Reinforced Concrete Structures ◽  
Experimental Scheme

The article offers a method and program for experimental studies of reinforced concrete structures with cross-shaped spatial crack under torsion with bending, the main purpose of which is to check the design assumptions and experimental determination of the design parameters of the proposed calculation method. The conducted experimental studies provide an opportunity to test the proposed calculation apparatus and clarify the regularities for determining deflections, angles of rotation of extreme sections, and stresses in the compressed zone of concrete. For analysis, the article presents a typical experimental scheme for the formation and development of cracks in the form of a sweep, as well as characteristic graphs of the dependence of the angles of rotation of end sections.

Optimization of a Specimen Size for the Determination of the Diffusible Hydrogen Content in Metals

2014 ◽  
Vol 698 ◽  
pp. 466-471
Author(s):  
Oleg V. Panchenko ◽  
Alexey M. Levchenko ◽  
Victor A. Karkhin
Keyword(s):  
Hydrogen Content ◽  
Calculation Method ◽  
Specimen Size ◽  
Experimental Results ◽  
Diffusible Hydrogen ◽  
Measuring Methods ◽  
Deposited Metal ◽  
Calculation Results

Specimens of various sizes are used to determine hydrogen content in deposited metals in such standards as ISO 3690, AWS A 4.3, and GOST 23338 while measuring methods are the same. It causes problems in comparison of experimental results and brings up the following question: what kind of specimen size is optimal to determine hydrogen content? An optimal specimen size was estimated using a calculation method. Experimental and calculation results obtained by using specimens with estimated dimensions were compared to the results obtained by using the specimen with dimensions of 100*25*8 mm to determine hydrogen content in a deposited metal.

Influence of Human Error on Structural Reliability

2017 ◽  
Author(s):  
Eric Brehm ◽  
Robert Hertle ◽  
Markus Wetzel
Keyword(s):  
Human Error ◽  
Structural Reliability ◽  
Failure Modes ◽  
Structural Model ◽  
Limit State ◽  
Design Procedure ◽  
Material Strength ◽  
Limit States ◽  
The Impact

In common structural design, random variables, such as material strength or loads, are represented by fixed numbers defined in design codes. This is also referred to as deterministic design. Addressing the random character of these variables directly, the probabilistic design procedure allows the determination of the probability of exceeding a defined limit state. This probability is referred to as failure probability. From there, the structural reliability, representing the survival probability, can be determined. Structural reliability thus is a property of a structure or structural member, depending on the relevant limit states, failure modes and basic variables. This is the basis for the determination of partial safety factors which are, for sake of a simpler design, applied within deterministic design procedures. In addition to the basic variables in terms of material and loads, further basic variables representing the structural model have to be considered. These depend strongly on the experience of the design engineer and the level of detailing of the model. However, in the clear majority of cases [1] failure does not occur due to unexpectedly high or low values of loads or material strength. The most common reasons for failure are human errors in design and execution. This paper will provide practical examples of original designs affected by human error and will assess the impact on structural reliability.

scholarly journals Constitutive Model of Rock Uniaxial Damage Based on Rock Strength Statistics

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Ming Ji ◽  
Kai Chen ◽  
Hong Jun Guo
Keyword(s):  
Constitutive Model ◽  
Rock Strength ◽  
Strength Criterion ◽  
Uniaxial Stress ◽  
Evolution Process ◽  
Growth Stages ◽  
Numerical Fitting ◽  
Damage Constitutive Model ◽  
Log Normal

Based on the assumption that rock strength follows the log normal distribution statistically, this paper establishes a damage constitutive model of rock under uniaxial stress conditions in combination with the Mohr–Coulomb strength criterion and damage mechanical theory. Experiments were carried out to investigate the damage evolution process of rock material, which can be categorized into nondamaging, accelerated growth, constant-speed, similar growth, and speed-reducing growth stages. The evolution process had a good corresponding relationship with the rock stress-strain curves. Based on the statistical damage constitutive model proposed in this paper, a numerical fitting analysis was conducted on the uniaxial compression testing data of laboratory sand rock and on experimental data from other literature, in order to validate the rationality of the constitutive equation and the determination of its parameters and to analyze the effect of internal friction variables on damage variables and compression strength. The research outcomes presented in this paper can provide useful reference for the theory of rock mechanics and for rock engineering.

Study on Calculation of Rock Pressure and Determination of Depth for Shallow Asymmetric Tunnel

2011 ◽  
Vol 261-263 ◽  
pp. 1034-1038 ◽  
Author(s):  
Xiao Jun Zhou
Keyword(s):  
Rock Pressure ◽  
Calculation Method ◽  
Tunnel Structure ◽  
The Way

The method to calculate rock pressure for shallow asymmetric tunnel is analyzed by means of taking a mountainous tunnel with semicircular crown and straight sidewall as the object in this paper. The calculation method of tunnel rock pressure has been presented with consideration of both tunnel structure size and its overburden depth. Finally the way to determine the shallow or profound depth of asymmetric tunnel is also obtained.

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