scholarly journals Constant Stress Arches

2021 ◽  
Author(s):  
Wanda Lewis
Keyword(s):  
Cross Section ◽  
Line Profile ◽  
Design Space ◽  
Axial Stress ◽  
Analytical Form ◽  
Constant Stress ◽  
Form Finding ◽  
Cross Section Area ◽  
Section Area ◽  
Design Options

It is generally accepted that an optimal arch has a funicular (moment-less) form and least weight. However, the feature of least weight restricts the design options and raises the question of durability of such structures. The work presented here shows that arches of least weight are just a sub-set of constant stress arches discussed here. Building on the analytical form-finding approach presented in [1], this study gives a complete description of two-pin arches that are moment-less and of constant axial stress along their entire length, when subjected to permanent (statistically prevalent) load. The theory considers a general case of an asymmetric arch, deriving the equation of its centre-line profile, horizontal reactions, and varying cross-section area. The analysis of symmetric arches follows, with the equation for the span/rise ratio minimising the arch volume being derived. It is shown that a previously claimed limit on arch span is always satisfied. Newly found limits, determining the existence of constant stress arches, lead to a concept of the design space. In the case of stand-alone arches, the design space takes the form of a constraint relationship between constant stress and span/rise ratio.

scholarly journals Constant stress arches and their design space

2022 ◽  
Vol 478 (2257) ◽  
Author(s):  
Wanda J. Lewis
Keyword(s):  
Moving Objects ◽  
Design Space ◽  
Axial Stress ◽  
Analytical Form ◽  
Design Criterion ◽  
Constant Stress ◽  
Variable Load ◽  
Cross Section Area ◽  
Section Area ◽  
Design Options

It is generally accepted that an optimal arch has a funicular (moment-less) form and least weight. However, the feature of least weight restricts the design options and raises the question of durability of such structures. This study, building on the analytical form-finding approach presented in Lewis (2016. Proc. R. Soc. A 472 , 20160019. ( doi:10.1098/rspa.2016.0019 )), proposes constant axial stress as a design criterion for smooth, two-pin arches that are moment-less under permanent (statistically prevalent) load. This approach ensures that no part of the structure becomes over-stressed under variable load (wind, snow and/or moving objects), relative to its other parts—a phenomenon observed in natural structures, such as trees, bones, shells. The theory considers a general case of an asymmetric arch, deriving the equation of its centre-line profile, horizontal reactions and varying cross-section area. The analysis of symmetric arches follows, and includes a solution for structures of least weight by supplying an equation for a volume-minimizing, span/rise ratio. The paper proposes a new concept, that of a design space controlled by two non-dimensional input parameters; their theoretical and practical limits define the existence of constant axial stress arches. It is shown that, for stand-alone arches, the design space reduces to a constraint relationship between constant stress and span/rise ratio.

Thermoacoustic Shape Optimization of a Subsonic Nozzle

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
Alexis Giauque ◽  
Maxime Huet ◽  
Franck Clero ◽  
Sébastien Ducruix ◽  
Franck Richecoeur
Keyword(s):  
Acoustic Emission ◽  
Cross Section ◽  
Source Term ◽  
Combustion Noise ◽  
Noise Emission ◽  
Cross Section Area ◽  
Section Area ◽  
The Cross ◽  
Nozzle Flows ◽  
Subsonic Nozzle

Indirect combustion noise originates from the acceleration of nonuniform temperature or high vorticity regions when convected through a nozzle or a turbine. In a recent contribution (Giauque et al., 2012, “Analytical Analysis of Indirect Combustion Noise in Subcritical Nozzles,” ASME J. Eng. Gas Turbies Power, 134(11), p. 111202) the authors have presented an analytical thermoacoustic model providing the indirect combustion noise generated by a subcritical nozzle when forced with entropy waves. This model explicitly takes into account the effect of the local changes in the cross-section area along the configuration of interest. In this article, the authors introduce this model into an optimization procedure in order to minimize or maximize the thermoacoustic noise emitted by arbitrarily shaped nozzles operating under subsonic conditions. Each component of the complete algorithm is described in detail. The evolution of the cross-section changes are introduced using Bezier's splines, which provide the necessary freedom to actually achieve arbitrary shapes. Bezier's polar coordinates constitute the parameters defining the geometry of a given individual nozzle. Starting from a population of nozzles of random shapes, it is shown that a specifically designed genetic optimization algorithm coupled with the analytical model converges at will toward a quieter or noisier population. As already described by Bloy (Bloy, 1979, “The Pressure Waves Produced by the Convection of Temperature Disturbances in High Subsonic Nozzle Flows,” J. Fluid Mech., 94(3), pp. 465–475), the results therefore confirm the significant dependence of the indirect combustion noise with respect to the shape of the nozzle, even when the operating regime is kept constant. It appears that the quietest nozzle profile evolves almost linearly along its converging and diverging sections, leading to a square evolution of the cross-section area. Providing insight into the underlying physical reason leading to the difference in the noise emission between two extreme individuals, the integral value of the source term of the equation describing the behavior of the acoustic pressure of the nozzle is considered. It is shown that its evolution with the frequency can be related to the global acoustic emission. Strong evidence suggest that the noise emission increases as the source term in the converging and diverging parts less compensate each other. The main result of this article is the definition and proposition of an acoustic emission factor, which can be used as a surrogate to the complex determination of the exact acoustic levels in the nozzle for the thermoacoustic shape optimization of nozzle flows. This acoustic emission factor, which is much faster to compute, only involves the knowledge of the evolution of the cross-section area and the inlet thermodynamic and velocity characteristics to be computed.

An Analytical Method of Analyzing the Heat Conduction for the Unequal Cross-Section Straight Fin

2013 ◽  
Vol 365-366 ◽  
pp. 1211-1216
Author(s):  
Fan Zhang ◽  
Peng Yun Song
Keyword(s):  
Heat Conduction ◽  
Cross Section ◽  
Analytical Method ◽  
Thermal Analyses ◽  
Cross Sectional ◽  
Cross Section Area ◽  
Section Area ◽  
Calculation Results ◽  
The Cross ◽  
Analytical Expressions

The cross-section area of straight fin is often considered to be equal in the thermal analyses of straight fin, but sometimes it is unequalin actual situation. Taking a straight fin with two unequal cross-sectional areas as an example,an analytical method of heat conduction for unequal section straight fin is presented. The analytical expressions of temperature field and heat dissipating capacity about the fin,which has a smaller cross-section area near the fin base and a larger one, is obtained respectively. The calculation results of the unequal cross-section are fully consistent with the equal area one, so the method is proved right. The results show that the larger the cross section areanear the base,the better is the heat transfer, and the temperature at the base with larger cross-section area is lower than that with smaller cross-section area when the amount of heat is fixed.

Rotational Temperature Measurement in Multicomponent Gases Using Raman Scattering Spectroscopy

1976 ◽  
Vol 30 (2) ◽  
pp. 179-183 ◽  
Author(s):  
R. S. Hickman ◽  
A. E. Kassem ◽  
L. H. Liang
Keyword(s):  
Temperature Field ◽  
Raman Scattering ◽  
Temperature Measurement ◽  
Cross Section ◽  
Room Temperature ◽  
Rotational Temperature ◽  
Raman Scattering Spectroscopy ◽  
Scattering Experiment ◽  
Cross Section Area ◽  
Section Area

The rotational temperature at pressures near 1 atm and at room temperature has been successfully measured using spectra obtained in an intracavity Raman scattering experiment. The accuracy of the method is sufficient to allow local temperature measurement of multicomponent gases with no disturbance in the temperature field. The advantage of the method lies in the fact that it does not require knowledge of the relative scattering cross-section area of the component gases.

scholarly journals Load bearing capacity of thin-walled rectangular and I-shaped steel sections of short both empty and concrete-filled columns

2021 ◽  
Vol 15 (58) ◽  
pp. 77-85
Author(s):  
Amor Bouaricha ◽  
Naoual Handel ◽  
Aziza Boutouta ◽  
Sarah Djouimaa
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Load Capacity ◽  
Cross Sectional ◽  
Short Columns ◽  
Cross Section Area ◽  
Section Area ◽  
Specimen Height ◽  
Steel Sections ◽  
Thin Walled

In this experimental work, strength results obtained on short columns subjected to concentric loads are presented. The specimens used in the tests have made of cold-rolled, thin-walled steel. Twenty short columns of the same cross-section area and wall thickness have been tested as follows: 8 empty and 12 filled with ordinary concrete. In the aim to determine the column section geometry with the highest resistance, three different types of cross-sections have been compared: rectangular, I-shaped unreinforced and, reinforced with 100 mm spaced transversal links. The parameters studied are the specimen height and the cross-sectional steel geometry. The registered experimental results have been compared to the ultimate loads intended by Eurocode 3 for empty columns and by Eurocode 4 for compound columns. These results showed that a concrete-filled composite column had improved strength compared to the empty case. Among the three cross-section types, it has been found that I-section reinforced is the most resistant than the other two sections. Moreover, the load capacity and mode of failure have been influenced by the height of the column. Also, it had noted that the experimental strengths of the tested columns don’t agree well with the EC3 and EC4 results.

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