On the Determination of Stresses and Deflections for Anisotropic Homogeneous Cantilever Beams

1976 ◽  
Vol 43 (1) ◽  
pp. 75-80 ◽  
Author(s):  
S. Nair ◽  
E. Reissner
Keyword(s):  
Cross Section ◽  
Lower Bounds ◽  
Basic Assumption ◽  
Rectangular Cross Section ◽  
Upper And Lower Bounds ◽  
Cantilever Beams ◽  
Normal Stresses ◽  
Complementary Energy ◽  
Minimum Potential

We analyze the effect of anisotropy on beam flexibility by the derivation of upper and lower bounds, through use of the principles of minimum potential and complementary energy, for the load-deflection ratios of narrow rectangular cross-section cantilever beams. The basic assumption is a class of stress-strain relations of such nature that normal strains are caused not only by normal stresses but also by shearing stresses, and shearing strains are caused not only by shearing stresses but also by normal stresses.

The Effect of Shear and Normal Forces on the Fully Plastic Moment of a Beam of Rectangular Cross Section

1961 ◽  
Vol 28 (2) ◽  
pp. 269-274 ◽  
Author(s):  
B. G. Neal
Keyword(s):  
Cantilever Beam ◽  
Cross Section ◽  
Lower Bounds ◽  
Rectangular Cross Section ◽  
Bending Moment ◽  
Upper And Lower Bounds ◽  
Collapse Load ◽  
Shear Forces ◽  
Normal Forces ◽  
Interaction Relations

The value of the fully plastic moment of a beam is known to be reduced by both normal and shear forces, and their separate effects have been studied in some detail, but little attention has been paid to the reduction caused by normal and shear forces acting simultaneously. This problem is discussed with reference to a cantilever beam of rectangular cross section subjected to both shear and normal forces at the free end. Upper and lower bounds to the collapse load are determined, and the results are presented in the form of interaction relations between the shear and normal forces and the bending moment at the clamped end of the cantilever at collapse.

The Uniform Flexure of an Incomplete Tore

1949 ◽  
Vol 2 (4) ◽  
pp. 469
Author(s):  
W Freiberger ◽  
RCT Smith
Keyword(s):  
General Solution ◽  
Cross Section ◽  
Harmonic Functions ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Elasticity Problems ◽  
Three Dimensional Elasticity ◽  
Derivatives Of ◽  
Special Case

In this paper we discuss the flexure of an incomplete tore in the plane of its circular centre-line. We reduce the problem to the determination of two harmonic functions, subject to boundary conditions on the surface of the tore which involve the first two derivatives of the functions. We point out the relation of this solution to the general solution of three-dimensional elasticity problems. The special case of a narrow rectangular cross-section is solved exactly in Appendix II.

Bending Vibrations of Variable Section Beams

1956 ◽  
Vol 23 (1) ◽  
pp. 103-108
Author(s):  
E. T. Cranch ◽  
Alfred A. Adler
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Circular Cross Section ◽  
Beam Theory ◽  
Cantilever Beams ◽  
Constant Depth ◽  
Bending Vibrations ◽  
Variable Section

Abstract Using simple beam theory, solutions are given for the vibration of beams having rectangular cross section with (a) linear depth and any power width variation, (b) quadratic depth and any power width variation, (c) cubic depth and any power width variation, and (d) constant depth and exponential width variation. Beams of elliptical and circular cross section are also investigated. Several cases of cantilever beams are given in detail. The vibration of compound beams is investigated. Several cases of free double wedges with various width variations are discussed.

Effect of Slenderness Ratio on the Natural Frequencies of Pre-Twisted Cantilever Beams of Uniform Rectangular Cross-Section

1971 ◽  
Vol 13 (1) ◽  
pp. 51-59 ◽  
Author(s):  
B. Dawson ◽  
N. G. Ghosh ◽  
W. Carnegie
Keyword(s):  
Differential Equations ◽  
Shear Deformation ◽  
Cross Section ◽  
Natural Frequencies ◽  
Rectangular Cross Section ◽  
Slenderness Ratio ◽  
Twist Angle ◽  
Equations Of Motion ◽  
Rotary Inertia ◽  
Cantilever Beams

This paper is concerned with the vibrational characteristics of pre-twisted cantilever beams of uniform rectangular cross-section allowing for shear deformation and rotary inertia. A method of solution of the differential equations of motion allowing for shear deformation and rotary inertia is presented which is an extension of the method introduced by Dawson (1)§ for the solution of the differential equations of motion of pre-twisted beams neglecting shear and rotary inertia effects. The natural frequencies for the first five modes of vibration are obtained for beams of various breadth to depth ratios and lengths ranging from 3 to 20 in and pre-twist angle in the range 0–90°. The results are compared with those obtained by an alternative method (2), where available, and also to experimental results.

FLOW MODIFICATION INDUCED BY QUINCKE ROTATION IN A CAPILLARY

2002 ◽  
Vol 16 (17n18) ◽  
pp. 2603-2609 ◽  
Author(s):  
A. CEBERS ◽  
E. LEMAIRE ◽  
L. LOBRY
Keyword(s):  
Cross Section ◽  
Flow Rate ◽  
Effective Viscosity ◽  
Rectangular Cross Section ◽  
Colloidal Suspension ◽  
Direct Determination ◽  
Flow Modification ◽  
Insulating Liquid ◽  
Quincke Rotation

When particles immersed in a semi-insulating liquid are submitted to a sufficiently high DC field, they can rotate spontaneously around any axis perpendicular to the field (Quincke rotation). Recently we have shown that due to Quincke effect the effective viscosity of a colloidal suspension could be reduced. When the suspension is submitted to a shear, the particles rotation is amplified by the electric torque and drives the suspending liquid. For a flow in a capillary, this effect manifests itself by an increase of the flow rate. We present the results of our experiments carried out with a rectangular cross section capillary. These results are compared with the direct determination of the apparent viscosity in a Couette flow rheometer.

scholarly journals The determination of normal stresses in cross-sections of the three-flue reinforced concrete chimney

2008 ◽  
Vol 3 (2) ◽  
pp. 081-095
Author(s):  
Małgorzata Dobrowolska ◽  
Marta Słowik
Keyword(s):  
Reinforced Concrete ◽  
Cross Section ◽  
Cross Sections ◽  
Analytical Form ◽  
Normal Stresses ◽  
Full Cross Section ◽  
Steel Bars ◽  
Reinforced Concrete Chimney ◽  
Physical Laws

In the paper there is presented the algorithm of calculation of normal stresses in reinforced concrete three-flue chimney. The calculation has been made for full cross-section and for cross-section weakened by openings. The governing equations has been derived in an analytical form assuming linear physical laws for concrete and steel and, as for as considered cross-section weakened by openings, taking into account the additional reinforcing steel bars at the openings. In addition coefficients B and C have been determined, which are useful at dimensioning.

scholarly journals Ramsey numbers for certain k-graphs

1981 ◽  
Vol 30 (3) ◽  
pp. 284-296 ◽  
Author(s):  
Stefan A. Burr ◽  
Richard A. Duke
Keyword(s):  
Lower Bounds ◽  
Complete Solution ◽  
Ramsey Number ◽  
Upper And Lower Bounds ◽  
Uniform Hypergraph ◽  
Steiner Systems ◽  
Ramsey Numbers ◽  
Existence Question

AbstractWe are interested here in the Ramsey number r(T, C), where C is a complete k-uniform hypergraph and T is a “tree-like” k-graph. Upper and lower bounds are found for these numbers which lead, in some cases, to the exact value for r(T, C) and to a generalization of a theorem of Chváta1 on Ramsey numbers for graphs. In other cases we show that a determination of the exact values of r(T, C) would be equivalent to obtaining a complete solution to existence question for a certain class of Steiner systems.

scholarly journals Spectral Analysis of Pressure, Noise and Vibration Velocity Measurement in Cavitation

2017 ◽  
Vol 17 (6) ◽  
pp. 250-256 ◽  
Author(s):  
Jana Jablonská ◽  
Miroslav Mahdal ◽  
Milada Kozubková
Keyword(s):  
Experimental Investigation ◽  
Cross Section ◽  
Noise Intensity ◽  
Structural Changes ◽  
Rectangular Cross Section ◽  
Vibration Velocity ◽  
Nozzle Wall ◽  
Air Flow Rate ◽  
Laboratory Equipment

Abstract The article deals with experimental investigation of water cavitation in the convergent-divergent nozzle of rectangular cross-section. In practice, a quick and simple determination of cavitation is essential, especially if it is basic cavitation or cavitation generated additionally by the air being sucked. Air influences the formation, development and size of the cavity area in hydraulic elements. Removal or reduction of the cavity area is possible by structural changes of the element. In case of the cavitation with the suction air, it is necessary to find the source of the air and seal it. The pressure gradient, the flow, the oxygen content in the tank, and hence the air dissolved in the water, the air flow rate, the noise intensity and the vibration velocity on the nozzle wall were measured on laboratory equipment. From the selected measurements the frequency spectrum of the variation of the water flow of the cavity with cavitation without air saturation and with air saturation was compared and evaluated.

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