A theoretical study of in-plane bending of a single unreinforced mitred-bend

N Jones; R Kitching

doi:10.1243/03093247v013264

A theoretical study of in-plane bending of a single unreinforced mitred-bend

Journal of Strain Analysis ◽

10.1243/03093247v013264 ◽

1966 ◽

Vol 1 (3) ◽

pp. 264-276 ◽

Cited By ~ 6

Author(s):

N Jones ◽

R Kitching

Keyword(s):

Strain Energy ◽

Close Agreement ◽

Theoretical Study ◽

Compatibility Conditions ◽

Curved Pipe ◽

Exact Analysis ◽

Von Karman ◽

Plane Bending ◽

Experimental Values ◽

Von Kármán

It can be shown that an exact analysis of the deformations or stresses in a single mitred-bend would involve some terms which rapidly decay along the pipe axes and others which would have a relatively long damping length. The overall flexibility and radial deformations of a single unreinforced mitred-bend have been estimated by minimizing the strain energy contributed by the long damping length terms in a manner similar to that used by von Kármán for curved pipe-bends. Finally, the short damping length terms are introduced in order to satisfy the equilibrium and compatibility conditions across the oblique intersection of the two pipes forming the mitred-bend. The theoretical values of overall flexibility, diameter changes, and stresses were found to be in close agreement with experimental values for a single right-angled unreinforced mitred-bend.

Download Full-text

In-Plane Bending of a Short-Radius Curved Pipe Bend

Journal of Engineering for Industry ◽

10.1115/1.3610039 ◽

1967 ◽

Vol 89 (2) ◽

pp. 271-277 ◽

Cited By ~ 7

Author(s):

N. Jones

Keyword(s):

Power Series ◽

Radial Displacement ◽

Neutral Axis ◽

Pipe Bend ◽

Curved Pipe ◽

Original Theory ◽

Von Karman ◽

Plane Bending ◽

Von Kármán ◽

Logical Extension

The analysis developed in this article is a logical extension, or generalization, of Von Karman’s original theory [1] on curved pipe bends. It can be shown, for long-radius pipe bends which have a negligible shift of the neutral axis, that the solution presented here reduces to that of Von Karman. It is evident from the results of this analysis that the stresses in and flexibility of curved pipe bends are virtually independent of γ(a/ρ) (even for γ approaching unity) and depend almost entirely on the simple Von Karman pipe factor λ(tρ/a2). Errors arising from premature truncation of the selected power series for the radial displacement are discussed, and a guide given to the number of terms necessary for a particular problem.

Download Full-text

A New Value of the von Kármán Constant: Implications and Implementation

Journal of Applied Meteorology and Climatology ◽

10.1175/2008jamc1951.1 ◽

2009 ◽

Vol 48 (5) ◽

pp. 923-944 ◽

Cited By ~ 7

Author(s):

Edgar L. Andreas

Keyword(s):

Boundary Layer ◽

Similarity Theory ◽

Stable Stratification ◽

Transfer Coefficients ◽

Obukhov Length ◽

Von Karman ◽

Roughness Lengths ◽

Experimental Values ◽

Definition Of ◽

Von Kármán

Abstract The von Kármán constant k occurs throughout the mathematics that describe the atmospheric boundary layer. In particular, because k was originally included in the definition of the Obukhov length, its value has both explicit and implicit effects on the functions of Monin–Obukhov similarity theory. Although credible experimental evidence has appeared sporadically that the von Kármán constant is different than the canonical value of 0.40, the mathematics of boundary layer meteorology still retain k = 0.40—probably because the task of revising all of this math to implement a new value of k is so daunting. This study therefore outlines how to make these revisions in the nondimensional flux–gradient relations; in variance, covariance, and dissipation functions; and in structure parameters of Monin–Obukhov similarity theory. It also demonstrates how measured values of the drag coefficient (CD), the transfer coefficients for sensible (CH) and latent (CE) heat, and the roughness lengths for wind speed (z0), temperature (zT), and humidity (zQ) must be modified for a new value of the von Kármán constant. For the range of credible experimental values for k, 0.35–0.436, revised values of CD, CH, CE, z0, zT, and zQ could be quite different from values obtained assuming k = 0.40, especially if the original measurements were made in stable stratification. However, for the value of k recommended here, 0.39, no revisions to the transfer coefficients and roughness lengths should be necessary. Henceforth, use the original measured values of transfer coefficients and roughness lengths but do use similarity functions modified to reflect k = 0.39.

Download Full-text

Nonlinear Transverse Vibrations of a Spinning Disk

Journal of Applied Mechanics ◽

10.1115/1.3629573 ◽

1964 ◽

Vol 31 (1) ◽

pp. 72-78 ◽

Cited By ~ 77

Author(s):

Jerzy L. Nowinski

Keyword(s):

Large Amplitude ◽

Close Agreement ◽

Vibration Mode ◽

Linear Case ◽

Field Equations ◽

Spinning Disk ◽

Transverse Vibrations ◽

Von Karman ◽

Large Amplitude Vibrations ◽

Von Kármán

Using the von Karman field equations, large amplitude vibrations of a spinning disk are analysed. For definiteness, the disk is assumed to be free, and its deflection is represented by a two-term polynomial. A vibration mode associated with two nodal diameters is studied in more detail. A familiar phenomenon of a decreasing period of vibration with an increasing amplitude is corroborated. The results specialized to the linear case show a close agreement with the classical results of Lamb and Southwell. The dependence of the membrane stresses on the amplitude of vibration and the velocity of spin is discussed.

Download Full-text