Beams of Uniform Strength Subjected to Uniformly Distributed Loading

1957 ◽  
Vol 24 (1) ◽  
pp. 105-108
Author(s):  
W. A. Gross ◽  
J. P. Li
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Constant Width ◽  
Integral Form ◽  
Constant Ratio ◽  
Flexural Stress ◽  
Uniform Strength ◽  
Constant Height ◽  
Uniform Cross Section ◽  
Large Material

Abstract Beams with uniform strength subjected only to bending have the same maximum flexural stress at any cross section. The shapes, deflections, and weights are given for cantilever, simple, and fixed beams of uniform strength and appreciable weight subjected to uniformly distributed loadings. Explicit solutions are given for beams having rectangular cross sections and constant height. Solutions in integral form are provided for rectangular beams of constant width. This method is also applicable to beams with constant ratio of height to width, as well as beams with circular cross sections. Examples illustrate the large material savings over uniform cross-section beams which may be achieved.

Deflection of Beams of Varying Cross Section

1937 ◽  
Vol 4 (2) ◽  
pp. A49-A52
Author(s):  
Miklós Hetényi
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Original Problem ◽  
New Method ◽  
Constant Cross Section ◽  
Deflection Curve ◽  
Force System ◽  
Uniform Cross Section ◽  
The Cross

Abstract This paper calls attention to a new method of dealing with deflections of beams, the cross sections of which vary by steps. It is shown that the effect of this variation on the shape of the deflection curve can be represented by a properly chosen force system acting on a beam of uniform cross section. There is no approximation involved in this substitution, whereby the original problem is reduced to one of computing deflections of beams of constant cross section.

Centrifuge tests on axially loaded tapered piles with different cross-sections under compressive and tensile loading

2021 ◽  
Author(s):  
Alireza Shabanpour ◽  
Mahmoud Ghazavi
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Compressive Loading ◽  
Tensile Tests ◽  
Construction Costs ◽  
Geotechnical Centrifuge ◽  
Head Displacement ◽  
Centrifuge Tests ◽  
Uniform Cross Section ◽  
Pile Length

The compressive behavior of tapered piles, particularly those with circular cross-sections, has been investigated during the last few decades. However, the tensile behavior of such piles has been rarely studied in the literature. In this paper, 12 static axial tests, including six compressive and also six tensile tests, were performed on instrumented piles with uniform and tapered cross-sections by using a geotechnical centrifuge. Three of the piles had correspondingly circular, square and X-shaped uniform cross-sections along their length, while the other three ones were non-uniform (tapered), all of which had the same length and volume. The results are presented in three main forms: the variation of load versus pile head displacement, the distribution of axial force along the pile length, and the distribution of the unit shaft resistance along the pile length. The behavior of tapered piles is compared with that of uniform cross-section piles. The results confirm the superiority of tapered piles over uniform cross-section piles in terms of load-bearing capacity and construction costs under both tensile and compressive loading.

The Centre of Shear of Aerofoil Sections

1953 ◽  
Vol 57 (508) ◽  
pp. 235-237 ◽  
Author(s):  
John A. Jacobs
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Lateral Surface ◽  
The Other ◽  
Principal Axes ◽  
Unstrained State ◽  
Uniform Cross Section ◽  
Single Force ◽  
The Cross ◽  
Fixed End

Consider a cantilever beam of uniform cross section whose generators are parallel to the z-axis and whose lateral surface is free from surface tractions. The line of centroids of the cross sections in the unstrained state is taken as the z-axis, and the x- and y-axes are the principal axes of the cross section at the centroid of the fixed end z = 0.The other end of the beam (z = l) is subject to forces which reduce to a single force with components (Wx, Wv, 0), transverse to the z-axis, acting through the load point L of this end section (see Fig. 1). The co-ordinates of L are taken as (p, q, l).

scholarly journals Cross hole sonic test results for analysis of pile load test

2020 ◽  
Vol 1 (1) ◽  
Author(s):  
Swapan Kunar Bagui ◽  
S. K. Puri ◽  
K. Subbiah
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Wide Band ◽  
Load Test ◽  
Test Results ◽  
Pile Capacity ◽  
Uniform Cross Section ◽  
Cell Test ◽  
Pile Load Test ◽  
Sonic Logging

AbstractQuality of concrete for pile can be checked using Cross-hole Sonic Logging (CSL) Test. A processing method wide-band CSL data is presented herein. First Time Arrival (FTA) is an important consideration. In pile capacity analysis or CSL analysis, it is assumed that pile cross section is uniform with uniform value of elastic modulus of concrete but in real practice both are non-uniform. The procedure identifies the location accuracy and further characterizes the features of the defect. FTA is used to find out the location of the distress in the pile. This method identifies the exact location of any void or defect inside the rebar cage of a drilled shaft. This method provides a significant improvement to current techniques used in quality control during construction of bridges. In this present paper, the analysis has been carried out based on uniform and non-uniform values of pile cross section and E value of concrete. Cross hole sonic and pile load test using O-Cell were carried out on same pile at 7 and 28 days of concreting. Same pipes were used for base grout after cross hole sonic test. These results were used to analyze O-cell test results based on a case study and presented in this paper. The distribution of skin frication and skin friction force has also been presented herein with both uniform and non-uniform cross section and E values of concrete. Based on the field test results and analysis a simplified methodology, has been proposed in this paper, for development of Equivalent Top Down Loading with consideration of elastic shortening of pile and surrounding soil for both cases i.e., uniform and non-uniform E values and pile cross sections.

scholarly journals On the ‘high spots’ of fundamental sloshing modes in a trough

2010 ◽  
Vol 467 (2129) ◽  
pp. 1491-1502 ◽  
Author(s):  
T. Kulczycki ◽  
N. Kuznetsov
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Eigenvalue Problem ◽  
Cross Section ◽  
Cross Sections ◽  
Orthogonal Projection ◽  
Free Oscillations ◽  
Uniform Cross Section ◽  
The Mean ◽  
The One

We study an eigenvalue problem with a spectral parameter in a boundary condition. The problem describes sloshing of a heavy liquid in a container, which means that the unknowns are the frequencies and modes of the liquid’s free oscillations. The question of ‘high spots’ (the points on the mean free surface, where its elevation attains the maximum and minimum values) is considered for fundamental sloshing modes in troughs of uniform cross section. For troughs, whose cross sections are such that the horizontal, top interval is the one-to-one orthogonal projection of the bottom, the following result is obtained: any fundamental eigenfunction attains its maximum and minimum values only on the boundary of the rectangular free surface of the trough.

Hydrostatic Stress and Triaxiality Factors in a Lotus Root Cross Section

2013 ◽  
Vol 461 ◽  
pp. 230-234
Author(s):  
Chang Jiang Wang ◽  
Diane Mynors
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Hydrostatic Stress ◽  
Water Pressure ◽  
External Pressure ◽  
Nelumbo Nucifera ◽  
Constant Ratio ◽  
Lotus Root ◽  
External Water Pressure ◽  
External Water

Engineers often use nature as an inspiration for generating designs. Plants have optimised their structures over millions of years of evolution. A lotus root, rhizome of Nelumbo Nucifera Gaertn having gas canals was studied in the paper. The lotus root cross section subjected to an external water pressure was analysed and compared with other cross sections including a circular hollow cross section. It was found that the lotus root cross section has more areas containing higher triaxiality factors due to the holes. The hydrostatic stress in the lotus root cross section varies from zero to several times that of the external water pressure. However, the hydrostatic stress in a circular hollow cross section has a constant ratio to the external pressure. The research results show that engineering components with designed multi-holes can affect its failure behaviour. The structure of lotus root may be adopted in the design of engineering materials and structures.

The Stress Analysis of the Circular Conical Fuselage with Flexible Frames

1955 ◽  
Vol 59 (536) ◽  
pp. 527-550
Author(s):  
W. J Goodey
Keyword(s):  
Stress Analysis ◽  
Cross Section ◽  
Cross Sections ◽  
Strain Energy ◽  
Circular Cross Section ◽  
Arbitrary Distribution ◽  
Skin Thickness ◽  
Complex Type ◽  
Uniform Cross Section ◽  
Minimum Strain Energy

Summary:This paper is concerned with the problem of the skin–and–stringer–covered conical fuselage of circular cross section, having flexible frames and being subjected to an arbitrary distribution of loads applied in the planes of these frames or on the end cross sections. The skin thickness and stringer cross section may vary from bay to bay but are assumed to be constant in a bay, i.e. between any two consecutive frames. The stringers are assumed to be uniformly spaced round the circumference. The frames are assumed to be of uniform cross section (circumferentially) but their stiffnesses are arbitrary, as is also their spacing along the fuselage.This paper is a sequel to one previously published in the Journal, but the method of analysis is now by minimum strain energy instead of by deflections. Owing to the generality of the investigation it is impossible to present the solution—in terms of the known loads and stiffnesses—in any explicit form, and attention has therefore been concentrated on the technique of numerical computation. A scheme of tabulation has been evolved, and its use is illustrated by a fully–worked numerical example of a moderately complex type.

scholarly journals Torsional Instability of Cantilevered Bars Subjected to Nonconservative Loading

1966 ◽  
Vol 33 (1) ◽  
pp. 102-104 ◽  
Author(s):  
S. Nemat-Nasser ◽  
G. Herrmann
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Load Distribution ◽  
Torsional Buckling ◽  
Compressive Loads ◽  
Uniform Cross Section ◽  
Nonconservative Loading ◽  
Torsional Instability

A cantilevered bar of uniform cross section and subjected at the free end to distributed, non-conservative, compressive loads is considered. It is shown that, for certain cross sections, stability may be lost by either torsional divergence (torsional buckling) or torsional flutter, depending upon the load distribution at the end section. In addition, transverse flutter also can occur, however, not transverse buckling.

Electron Irradiation Effects in Polyoxymethylene Crystals Grown Inside Trioxane Crystals

1971 ◽  
Vol 29 ◽  
pp. 78-79
Author(s):  
J. P. Colson ◽  
D. H. Reneker
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Detailed Examination ◽  
The Other ◽  
Electron Micrograph ◽  
Irradiation Effects ◽  
Threefold Axis ◽  
Typical Sample ◽  
Polymer Crystals ◽  
Chain Axis

Polyoxymethylene (POM) crystals grow inside trioxane crystals which have been irradiated and heated to a temperature slightly below their melting point. Figure 1 shows a low magnification electron micrograph of a group of such POM crystals. Detailed examination at higher magnification showed that three distinct types of POM crystals grew in a typical sample. The three types of POM crystals were distinguished by the direction that the polymer chain axis in each crystal made with respect to the threefold axis of the trioxane crystal. These polyoxymethylene crystals were described previously.At low magnifications the three types of polymer crystals appeared as slender rods. One type had a hexagonal cross section and the other two types had rectangular cross sections, that is, they were ribbonlike.

A quantitative approach to inner shell losses

1978 ◽  
Vol 36 (1) ◽  
pp. 526-527 ◽  
Author(s):  
R.D. Leapman ◽  
P. Rez ◽  
D.F. Mayers
Keyword(s):  
Energy Transfer ◽  
Cross Section ◽  
Cross Sections ◽  
Accurate Determination ◽  
Background Intensity ◽  
Core Excitation ◽  
Quantitative Basis ◽  
Cross Section Differential ◽  
Bound Electrons

Microanalysis by EELS has been developing rapidly and though the general form of the spectrum is now understood there is a need to put the technique on a more quantitative basis (1,2). Certain aspects important for microanalysis include: (i) accurate determination of the partial cross sections, σx(α,ΔE) for core excitation when scattering lies inside collection angle a and energy range ΔE above the edge, (ii) behavior of the background intensity due to excitation of less strongly bound electrons, necessary for extrapolation beneath the signal of interest, (iii) departures from the simple hydrogenic K-edge seen in L and M losses, effecting σx and complicating microanalysis. Such problems might be approached empirically but here we describe how computation can elucidate the spectrum shape.The inelastic cross section differential with respect to energy transfer E and momentum transfer q for electrons of energy E0 and velocity v can be written as

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