Analysis of Buckling Column Spring With Pivoted Ends and Uniform Rectangular Cross Section

1961 ◽  
Vol 83 (1) ◽  
pp. 61-66
Author(s):  
Alexander Blake
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Experimental Results ◽  
Strength Of Materials ◽  
Bending Stresses ◽  
Deflection Analysis ◽  
Uniform Cross Section

Design formulas and working charts are derived for predicting load-deflection characteristics and maximum bending stresses in initially straight buckling column springs, of uniform cross section, considered to be pin jointed at the supports. Load-deflection analysis is based on the study of a slender bar, compressed beyond critical buckling, made by Lagrange. Stresses are calculated using the elementary strength of materials theory. The predicted load-deflection curves for typical spring proportions are compared with the experimental results.

The Investigation of the Kinetic Energy of Slug in a Horizontal Channel Using VOF Method

2018 ◽  
Author(s):  
Nariman Ashrafi ◽  
Mohammad Reza Ansari ◽  
Armin Chegini ◽  
Ali Sadeghi
Keyword(s):  
Kinetic Energy ◽  
Pressure Gradient ◽  
Cross Section ◽  
Volume Fraction ◽  
Rectangular Cross Section ◽  
Vof Method ◽  
Experimental Results ◽  
Two Phase ◽  
Trapped Air ◽  
Helmholtz Condition

In this article, two-phase slug regime in a duct with rectangular cross-section is investigated numerically, using the volume of fluid (VOF) method. Equations of mass, momentum and advection of volume fraction are solved accompanying k-∈ realizable turbulence equations. To ensure the creditability, numerical results have been compared with experimental results using same geometry. With occurrence of instability in the entrance of duct, Kelvin-Helmholtz condition satisfies and with increasing instability, slug phenomenon occurs. With closing the cross-section of duct, slug causes pressure gradient in it. Trapped air behind a slug transfers the momentum and increases the kinetic energy of slug. In this research the kinetic energy of a slug is investigated.

Condensation Phenomena in High Speed Flow of Steam—Experimental Apparatus

1973 ◽  
Vol 187 (1) ◽  
pp. 199-205 ◽  
Author(s):  
B. A. Campbell ◽  
F. Bakhtar
Keyword(s):  
Cross Section ◽  
Test Section ◽  
High Speed ◽  
Rectangular Cross Section ◽  
Experimental Results ◽  
Theoretical Treatment ◽  
Wet Steam ◽  
High Speed Flow ◽  
Speed Flow ◽  
Experimental Apparatus

The paper describes a steam circuit for studies of nucleation and behaviour of wet steam. The test section is a duct of rectangular cross-section in which particular geometries are produced by fitting shaped profiles to its sides. To deliver steam to the test section, at required conditions, a turbine, cooler and superheater are included in the circuit. The experimental results presented are concerned with the variations of Wilson point as a function of pressure. Comparisons are made with the results of a theoretical treatment already published (1)‡ and agreement is shown to be good.

Collapse loads for thin cantilevers with rectangular holes along the centre-line

1976 ◽  
Vol 11 (2) ◽  
pp. 84-96 ◽  
Author(s):  
A S Ranshi ◽  
W Johnson ◽  
N R Chitkara
Keyword(s):  
Lower Bound ◽  
Plane Strain ◽  
Cross Section ◽  
Plane Stress ◽  
Slip Line ◽  
Rectangular Cross Section ◽  
Local Buckling ◽  
Experimental Results ◽  
Line Field ◽  
Theoretical Results

Plane stress slip-line field solutions, which provide the modes of yielding and the corresponding yield loads, are presented for the plastic bending of end-loaded thin cantilevers of rectangular cross-section containing rectangular holes. The theoretical results obtained from these solutions are compared with some experimental results and those obtained from plane strain slip-line fields and lower bound estimates, all presented previously by the authors (1)‡. It is observed that the correlation of the experimental results was much better with the plane stress solutions than with either the plane strain or lower bound results. The effect of adjacent holes and possible lateral or local buckling on the ultimate strength of the cantilevers is also examined.

Deflection of a Thick Ring in Diametral Compression by Test and by Strength-of-Materials Theory

1959 ◽  
Vol 26 (2) ◽  
pp. 294-295
Author(s):  
Alexander Blake
Keyword(s):  
Cross Section ◽  
Strain Energy ◽  
Rectangular Cross Section ◽  
Theoretical Estimate ◽  
Shear Stresses ◽  
Strength Of Materials ◽  
Diametral Compression ◽  
Normal And Shear Stresses

Abstract Experimental and theoretical deflection studies are briefly described for several steel rings, of uniform rectangular cross section, compressed by two forces along a diameter and having D/d ratios ranging from 1.3 to 1.9. The calculations are based on the principle of Castigliano and expressions for strain energy due to bending, normal, and shear stresses. Discrepancies between the theoretical estimate and the tests are shown.

Comparison of CCFL Experiments Performed in Two Different Models of the Hot Leg of a PWR With Rectangular Cross-Section

2010 ◽  
Author(s):  
Christophe Valle´e ◽  
Tobias Seidel ◽  
Dirk Lucas ◽  
Akio Tomiyama ◽  
Michio Murase
Keyword(s):  
Cross Section ◽  
Flow Rate ◽  
Current Flow ◽  
Characteristic Length ◽  
Rectangular Cross Section ◽  
Experimental Results ◽  
Channel Height ◽  
Flow Limitation ◽  
Counter Current Flow ◽  
Counter Current

In order to investigate the two-phase flow behaviour during counter-current flow limitation in the hot leg of a pressurised water reactor, two test models were built: one at the Kobe University and the other at the TOPFLOW test facility of Forschungszentrum Dresden-Rossendorf (FZD). Both test facilities are devoted to optical measurement techniques, therefore, a flat hot leg test section design was chosen. Counter-current flow limitation (CCFL) experiments were performed, simulating the reflux condenser cooling mode appearing in some accident scenarios. The fluids used were air and water, both at room temperature. The pressure conditions were varied from atmospheric at Kobe to 3.0 bar absolute at TOPFLOW. According to the presented review of the literature, very few data is available on flooding in channels with rectangular cross-section, and no experiments were performed in the past in such rectangular models of a hot leg. Usually, the macroscopic effects of CCFL are represented in a flooding diagram, where the gas flow rate is plotted versus the discharge water flow rate. Commonly, the non-dimensional superficial velocity (also known as the Wallis parameter) is used to plot the flooding diagram. However, the classical definition of the Wallis parameter contains the pipe diameter as characteristic length, which was originally defined by Wallis (1969) for counter-current flow limitation in vertical pipes and not in near horizontal channels with rectangular cross-section. In order to be able to perform comparisons with pipe experiments and to extrapolate to the power plant scale, the appropriate characteristic length should be determined. Because the experimental projects on this subject at the Kobe University and at FZD were launched independently, a detailed comparison of both test facilities is presented. With respect to the CCFL behaviour, it is shown that the essential parts of the two hot leg test sections are very similar. This geometrical analogy allows to perform meaningful comparisons. However, clear differences in the dimensions of the cross-section (H × W = 150 × 10 mm2 in Kobe, 250 × 50 mm2 at FZD) make it possible to point out the right characteristic length for hot leg models with rectangular cross-sections. The hydraulic diameter, the channel height and the Laplace critical wavelength (leading to the Kutateladze number) were tested. The experimental results obtained in the two test facilities clearly show that the channel height is the suited characteristic length. Finally, the experimental results are compared with similar experiments and empirical correlations for pipes available in the literature. In spite of the scatter of the data and of the different correlations, it was noticed that flooding is reached at slightly lower gas fluxes in the hot leg models with rectangular cross-section compared to pipes.

Large deflection analysis of cantilever beams of symmetrical cross-section subjected to a rotational distributed loading including the effect of material nonlinearity

1988 ◽  
Vol 92 (916) ◽  
pp. 230-234
Author(s):  
B. Nageswara Rao ◽  
G. Venkateswara Rao
Keyword(s):  
Cross Section ◽  
Large Deflection ◽  
Rectangular Cross Section ◽  
Neutral Axis ◽  
Central Axis ◽  
Nonlinear Ordinary Differential Equations ◽  
Combined Effects ◽  
Cantilever Beams ◽  
Stress Strain Relation ◽  
Deflection Analysis

AbstractCombined effects of geometrical and material non-linearities on a cantilever beam having symmetrical cross-section about its central axis with a rotational distributed loading are studied. It is assumed that the stress-strain relation in compression is identical to that in tension. Due to this, the neutral axis coincides with the central axis of the beam. The problem is formulated by means of an integral equation which is suitably converted to a system of nonlinear ordinary differential equations which are solved using a simple and accurate numerical method. Details of the load deflection characteristics for an I-beam and for a beam of rectangular cross-section are presented.

Condensation Phenomena in High Speed Flow of Steam—Experimental Apparatus

1973 ◽  
Vol 187 (1) ◽  
pp. 199-205 ◽  
Author(s):  
B. A. Campbell ◽  
F. Bakhtar
Keyword(s):  
Cross Section ◽  
Test Section ◽  
High Speed ◽  
Rectangular Cross Section ◽  
Experimental Results ◽  
Theoretical Treatment ◽  
Wet Steam ◽  
High Speed Flow ◽  
Speed Flow ◽  
Experimental Apparatus

The paper describes a steam circuit for studies of nucleation and behaviour of wet steam. The test section is a duct of rectangular cross-section in which particular geometries are produced by fitting shaped profiles to its sides. To deliver steam to the test section, at required conditions, a turbine, cooler and superheater are included in the circuit. The experimental results presented are concerned with the variations of Wilson point as a function of pressure. Comparisons are made with the results of a theoretical treatment already published (1)‡ and agreement is shown to be good.

Axial capacity of tapered piles established from model tests

1999 ◽  
Vol 36 (6) ◽  
pp. 1185-1194 ◽  
Author(s):  
M Hesham El Naggar ◽  
Jin Qi Wei
Keyword(s):  
Cross Section ◽  
Large Scale ◽  
Load Transfer ◽  
Design Procedure ◽  
Experimental Results ◽  
Unit Load ◽  
Axial Capacity ◽  
Laboratory Setup ◽  
Standard Design ◽  
Uniform Cross Section

Tapered piles represent a more efficient distribution of pile material than uniform cross section piles in several respects. An extensive experimental research program was conducted to study the efficiency of tapered piles compared with piles of uniform cross section with the same material input. Three instrumented model steel piles with different degrees of taper were used in this program. The piles were tested in a large-scale laboratory setup under compressive and tensile loads. The pile head load and displacement and the strain along the piles were measured simultaneously. The objectives of the present paper were twofold: to examine the validity of the experimental results, and to use the unit load transfer curves established from the experimental results to predict the bearing capacity of prototype tapered piles. The shaft resistance for straight-sided wall piles established from the experimental results compared well with the theoretical predictions using the standard design procedure. The beneficial effect of pile taper was significant up to a depth of 20 pile diameters. The negative effect of the pile taper on the uplift capacity diminished quickly with depth and hence the performance of actual tapered piles (with greater length) would be comparable to that of straight-sided wall piles.

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