scholarly journals New Compound Open Channel Section with Polynomial Sides: Improving Cost and Aesthetics

Water ◽  
2019 ◽  
Vol 11 (8) ◽  
pp. 1545 ◽  
Author(s):  
Said M. Easa ◽  
Yan-Cheng Han
Keyword(s):  
Cross Sections ◽  
Construction Cost ◽  
Physical Constraints ◽  
Discharge Flow Rate ◽  
Section Shape ◽  
Special Cases ◽  
Side Section ◽  
Optimal Construction ◽  
Compound Section ◽  
Horizontal Bottom

Previous research on compound trapezoidal cross sections has mainly focused on improving the prediction of the discharge (flow rate) because of its inherent challenges. This paper focuses on two other important aspects: Section shape and optimal construction cost. First, the paper proposes a new compound section with third-degree polynomial sides of main channel with horizontal bottom (HB) that allows its top corners to be smooth, called herein compound polynomial section. The special cases of this versatile section include the simple polynomial section, polygonal section, trapezoidal-rectangular section, two-segment linear-side section, and parabolic bottom-trapezoidal section. The simple polynomial section, which is the bank-full part of the compound polynomial section, can further produce parabolic (with or without HB), trapezoidal, rectangular, and triangular sections. Second, an optimization model that minimizes construction cost (excavation and lining) of the compound (or simple) polynomial section is developed. The model includes discharge and physical constraints. Theoretical and empirical methods of discharge prediction were used in the model. The results show that the simple polynomial section was more economical than the popular parabolic section by up to 8.6% when the side slopes were restricted. The new polynomial-based sections not only reduced construction cost, but also improved maintenance and aesthetics. As such, the new sections should be of interest to researchers and practitioners in hydraulic engineering.

scholarly journals Dynamic modeling of tunnel survey spatiotemporal data

2014 ◽  
Vol 20 (2) ◽  
pp. 354-375
Author(s):  
Xiaolong Li ◽  
Jiansi Yang ◽  
Bingxuan Guo ◽  
Hua Liu ◽  
Jun Hua
Keyword(s):  
Survey Data ◽  
Cross Section ◽  
Cross Sections ◽  
3D Modeling ◽  
3D Model ◽  
Three Dimensional ◽  
Spatiotemporal Data ◽  
Excavation Process ◽  
Special Cases ◽  
Time Stamps

Currently, for tunnels, the design centerline and design cross-section with time stamps are used for dynamic three-dimensional (3D) modeling. However, this approach cannot correctly reflect some qualities of tunneling or some special cases, such as landslips. Therefore, a dynamic 3D model of a tunnel based on spatiotemporal data from survey cross-sections is proposed in this paper. This model can not only playback the excavation process but also reflect qualities of a project typically missed. In this paper, a new conceptual model for dynamic 3D modeling of tunneling survey data is introduced. Some specific solutions are proposed using key corresponding technologies for coordinate transformation of cross-sections from linear engineering coordinates to global projection coordinates, data structure of files and database, and dynamic 3D modeling. A 3D tunnel TIN model was proposed using the optimized minimum direction angle algorithm. The last section implements the construction of a survey data collection, acquisition, and dynamic simulation system, which verifies the feasibility and practicality of this modeling method.

scholarly journals Self-Inductance of the Circular Coils of the Rectangular Cross-Section with the Radial and Azimuthal Current Densities

Physics ◽  
2020 ◽  
Vol 2 (3) ◽  
pp. 352-367
Author(s):  
Slobodan Babic ◽  
Cevdet Akyel
Keyword(s):  
Cross Sections ◽  
Special Functions ◽  
Rectangular Cross Section ◽  
The Self ◽  
Thin Wall ◽  
Elementary Functions ◽  
Special Cases ◽  
Current Densities ◽  
New Formula ◽  
Azimuthal Current

In this paper, we give new formulas for calculating the self-inductance for circular coils of the rectangular cross-sections with the radial and the azimuthal current densities. These formulas are given by the single integration of the elementary functions which are integrable on the interval of the integration. From these new expressions, we can obtain the special cases for the self-inductance of the thin-disk pancake and the thin-wall solenoids that confirm the validity of this approach. For the asymptotic cases, the new formula for the self-inductance of the thin-wall solenoid is obtained for the first time in the literature. In this paper, we do not use special functions such as the elliptical integrals of the first, second and third kind, nor Struve and Bessel functions because that is very tedious work. The results of this work are compared with already different known methods and all results are in excellent agreement. We consider this approach novel because of its simplicity in the self-inductance calculation of the previously-mentioned configurations.

Evaluation of Neutron-induced Cross Sections and their Related Covariances with Physical Constraints

2018 ◽  
Vol 148 ◽  
pp. 383-419 ◽  
Author(s):  
C. De Saint Jean ◽  
P. Archier ◽  
E. Privas ◽  
G. Noguère ◽  
B. Habert ◽  
...  
Keyword(s):  
Cross Sections ◽  
Physical Constraints

The Influence of Torsional-Rigidity Bounds for Composite Shafts with Specific Cross-Sections

2011 ◽  
Vol 462-463 ◽  
pp. 674-679
Author(s):  
I Tung Chan ◽  
Tung Yang Chen ◽  
Min Sen Chiu
Keyword(s):  
Shear Modulus ◽  
Cross Sections ◽  
Variational Principles ◽  
Torsional Rigidity ◽  
Lower And Upper Bounds ◽  
Imperfect Interfaces ◽  
Section Shape ◽  
The Matrix ◽  
Rigorous Bounds ◽  
Low Shear

We consider the Saint-Venant torsion problem of composite shafts. Two different kinds of imperfect interfaces are considered. One models a thin interphase of low shear modulus and the other models a thin interphase of high shear modulus. The imperfect interfaces are characterized by parameters given in terms of the thickness and shear modulus of the interphases. Using variational principles, we derive rigorous bounds for the torsional rigidity of composite shafts with cross-sections of arbitrary shapes. The analysis is based on the construction of admissible fields in the inclusions and in the matrix. We obtain the general expression for the bounds and demonstrate the results with some particular examples. Specifically, circular, elliptical and trianglar shafts are considered to exemplify the derived bounds. We incorporate the cross-section shape factor into the bounds and show how the position and size of the inclusion influence the bounds. Under specific conditions, the lower and upper bounds will coincide and agree with the exact torsional rigidity.

Electron energy distributions in uniform electric fields and the Townsend ionization coefficient

1958 ◽  
Vol 244 (1237) ◽  
pp. 166-185 ◽  
Keyword(s):  
Differential Equation ◽  
Cross Section ◽  
Electric Fields ◽  
Cross Sections ◽  
Collision Cross Section ◽  
Present Theory ◽  
Uniform Electric Field ◽  
Ionization Coefficient ◽  
Special Cases ◽  
Wide Range

The second-order differential equation which expresses the equilibrium condition of an electron swarm in a uniform electric field in a gas, the electrons suffering both elastic and inelastic collisions with the gas molecules, is solved by the Jeffreys or W.K.B. method of approximation. The distribution function F(ε) of electrons of energy ε is obtained immediately in a general form involving the elastic and inelastic collision cross-sections and without any restriction on the range of E/p (electric strength/gas pressure) save that introduced in the original differential equation. In almost all applications the approximation is likely to be of high accuracy, and easy to use. Several of the earlier derivations of F(ε) are obtained as special cases. Using the function F(ε) an attempt is made to relate the Townsend ionization coefficient a to the properties of the gas in a more general manner than hitherto, using realistic functions for the collision cross-section. It is finally expressed by the equation α/ p = A exp ( — Bp/E ) in which A and B are functions involving the properties of the gas and the ratio E/p . The important coefficient B is directly related to the form and magnitude of the total inelastic cross-section below the ionization potential and can be evaluated for a particular gas once the cross-section is known experimentally. The present theory shows clearly the influence of E/p on both A and B, a matter which has not been satisfactorily discussed previously. The theory is illustrated by calculations of F (ε) and a/p for hydrogen over a range of E/p from 10 to 1000. The agreement between the calculated results and recent reliable observations of α/ p is surprisingly good considering the nature of the calculations and the wide range of E/p .

Cross Section Optimization of Plane Truss among Different Spans

2014 ◽  
Vol 679 ◽  
pp. 1-5 ◽  
Author(s):  
Sumayah Abdulsalam Mustafa ◽  
Mohd Zulham Affandi bin Mohd Zahid ◽  
Md.Hadli bin Abu Hassan
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Element Analysis ◽  
Cross Sectional ◽  
Analysis And Design ◽  
Cross Section Shape ◽  
Design Variables ◽  
Section Shape ◽  
Steel Sections ◽  
Research Show

Cross sectional areas optimization is to be implemented to study the influence of the cross section shape on the optimum truss weight. By the aid of analysis and design engines with advanced finite element analysis that is the steel design software STAAD. Four rolled steel sections (angle, tube, channel, and pipe) which are used in industrial roof trusses are applied for comparison. Many previous studies, use the areas of cross sections as design variables without highlight to the shape of cross section at the start of the process, consequently the result area will be adequate if the designer choose the effective shape than others. Results of this research show that the chosen cross section shape has a significant impact on the optimum truss weight for same geometry of truss type under the same circumstances of loading and supports.

Parametric Study of Reinforced Concrete Column Cross-Section for Strength and Ductility

2008 ◽  
Vol 400-402 ◽  
pp. 269-274 ◽  
Author(s):  
Naveed Anwar ◽  
Mohammad Qaasim
Keyword(s):  
Reinforced Concrete ◽  
Cross Section ◽  
Cross Sections ◽  
Strain Curve ◽  
Concrete Column ◽  
Loading Conditions ◽  
Reinforced Concrete Column ◽  
Section Shape ◽  
And Performance ◽  
Strength And Ductility

Several parameters and corresponding performance of reinforced concrete column cross-sections of different shapes (square, rectangular, circular, T-shape, I-shape, cross-shape, L-shape and C-shape) under various loading conditions have been studied in order to determine the suitable and optimum cross-sections for strength and ductility. In each cross-section shape, parameters include compressive strength of concrete (f’c), tensile strength of steel (fy), steel ratio (As/Ag), and angle of bending. In order to demonstrate the behavior and performance of the sections in terms of strength and ductility, CSISectionBuilder software was used to define the stress-strain curve for concrete and steel and then compute the moment-curvature relationship for each section. Considering different sections, the number of parameters in every section and various loading conditions, a total of around 1,800 sections were analyzed. The comparison procedures started within each section shape, and then across different sections in order to determine the most suitable cross-section for strength and ductility. Results of the study are deemed very useful in the system selection and preliminary design of important structures such as buildings with complicated geometry and high architectural demand including bridge piers and hydraulic structures.

scholarly journals Modeling and Simulation of stochastically deformed Waveguides using Schelkunoff's Method

2018 ◽  
Vol 16 ◽  
pp. 35-41
Author(s):  
Hoang Duc Pham ◽  
Soeren Ploennigs ◽  
Wolfgang Mathis
Keyword(s):  
Cross Sections ◽  
Electromagnetic Waves ◽  
Analytic Solution ◽  
Propagation Constant ◽  
Circular Waveguide ◽  
Transverse Field ◽  
Field Pattern ◽  
Coupled Mode ◽  
Special Cases ◽  
Cylindrical Waveguides

Abstract. This paper deals with the propagation of electromagnetic waves in cylindrical waveguides with irregularly deformed cross-sections. The general theory of electromagnetic waves is of high interest because of its practical use as a transmission medium. But only in a few special cases, an analytic solution of Maxwell's equations and the appropriate boundary conditions can be found (Spencer, 1951). The coupled-mode theory, also known as Schelkunoff's method, is a semi-numerical method for computing electromagnetic waves in hollow and cylindrical waveguides bounded by perfect electric walls (Saad, 1985). It allows to calculate the transverse field pattern and the propagation constant. The aim of this paper is to derive the so-called generalized telegraphist's equations for irregular deformed waveguides. Subsequently, the method's application will be used on a circular waveguide as an illustrating example.

scholarly journals Monte Carlo simulation of γ and fission transfer reactions using extended ℛ-matrix theory

2020 ◽  
Vol 239 ◽  
pp. 03013
Author(s):  
Olivier Bouland
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Matrix Theory ◽  
Transfer Reactions ◽  
Test Case ◽  
Compound System ◽  
Reaction Method ◽  
Average Cross Section ◽  
Special Cases ◽  
Induced Fission

This paper comes back on the accuracy of the surrogate-reaction method (SRM) historically used for neutron-induced average partial cross sections inference from measured surrogate-reaction probabilities. The SRM level of performance is examined in relation to a reasonably accurate reference calculation performed with the 𝒜𝒱𝒳𝒮ℱ-ℒ𝒩𝒢 code [1] through a challenging test case : the 240Pu* compound system. This paper argues on some ingredients of the reference calculation [2] and returns some hints about the failure now well-known of the neutron-induced γ average cross section inference. It shows also that in some special cases, the SRM can be poorly accurate also in terms of neutron-induced fission average cross section inference.

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