The Stress Distributions Induced by Concentrated Loads Acting in Isotropic and Orthotropic Half Planes

1953 ◽  
Vol 20 (1) ◽  
pp. 82-86
Author(s):  
H. D. Conway
Keyword(s):  
Half Plane ◽  
Complex Variable ◽  
Integral Method ◽  
Fourier Integral ◽  
Straight Edge ◽  
Variable Method ◽  
Stress Distributions ◽  
Concentrated Loads ◽  
Concentrated Load ◽  
Method Of Solution

Abstract Using a Fourier integral method, the solution is obtained to an isotropic half plane subjected to a concentrated load acting at some distance from the straight edge. This problem was discussed previously by Melan, using a complex variable method of solution. The Fourier integral method is then extended to solve the corresponding problems of the orthotropic half plane.

scholarly journals Stress systems in aeolotropic plates. IV

1942 ◽  
Vol 180 (981) ◽  
pp. 173-208 ◽  
Keyword(s):  
Circular Hole ◽  
Elastic Constants ◽  
Complex Variable ◽  
Isotropic Plate ◽  
Poisson's Ratio ◽  
Stress Distributions ◽  
Numerical Work ◽  
Zero Force ◽  
Isotropic Materials ◽  
Method Of Solution

Stress distributions in an aeolotropic plate containing a circular hole are discussed theoretically when the material of the plate has two directions of sym metry at right angles to one another. Some examples of stress distributions are included which have non-zero force resultants on the edge of the hole, corresponding to cases in isotropic materials for which the solution is dependent on Poisson’s ratio. The use of the complex variable makes the method of solution comparatively simple, and as an introduction to the work for an aeolotropic material the same method is applied to problems of stresses in an isotropic plate containing a circular hole in order to obtain results which Bickley previously found by another method. Numerical work is carried out using the elastic constants found in experiments with specimens cut from the highly aeolotropic materials spruce and oak.

A Fourier Integral Solution for the Plane-Stress Problem of a Circular Ring With Concentrated Radial Loads

1951 ◽  
Vol 18 (2) ◽  
pp. 173-182
Author(s):  
Carl W. Nelson
Keyword(s):  
Plane Stress ◽  
Integral Method ◽  
Fourier Integral ◽  
Circular Ring ◽  
Outer Radius ◽  
Integral Solution ◽  
Concentrated Loads ◽  
Stress Problem ◽  
Plane Stress Problem ◽  
Circular Rings

Abstract A Fourier integral solution for the stresses in a straight bar of uniform cross section loaded by various combinations of loads applied normally to the edges of the bar was published by L. N. G. Filon in 1903 (3). Solutions for the stresses in circular rings, loaded on one or both boundaries by radial loads, have been limited to Fourier-series solutions for closed circular rings (1, 12, 13, 14, 15), except that solutions in closed form have been obtained for the limiting cases which occur either when the inner radius becomes very small or when the outer radius becomes very large. This paper presents a Fourier integral solution for the plane-stress problem of a curved bar bounded by two concentric circles and loaded by radial loads on the circular boundaries. It treats only the particular case of a curved bar in equilibrium under the action of two equal and opposite radial forces, one on each boundary. However, the method can be extended so as to deal with other combinations of loads. Sufficient numerical results are given to show that the Fourier integral method permits the calculation of numerical values of the stresses in the particular case considered. It is the purpose of this paper to show that the Fourier integral method can be used successfully in what is probably the simplest problem of concentrated loads acting on a curved bar and to furnish a background of material for use in less simple problems such as bending of curved bars due to concentrated loads.

The Elastic Half Plane Subjected to Surface Tractions With Random Magnitude or Separation

1960 ◽  
Vol 27 (4) ◽  
pp. 701-709 ◽  
Author(s):  
A. C. Eringen ◽  
J. W. Dunkin
Keyword(s):  
White Noise ◽  
Stress Tensor ◽  
Half Plane ◽  
Second Order ◽  
Concentrated Loads ◽  
Random Boundary ◽  
Concentrated Load ◽  
Random Intervals ◽  
Random Location ◽  
Elastostatic Problem

First and second-order moments of the stress tensor are obtained for the elastostatic problem concerning the half-plane subjected to random boundary tractions. The cases treated include the following types of applied surface tractions: (a) A purely random Gaussian load (white noise); (b) concentrated loads of random magnitudes separated by equal intervals; (c) a concentrated load acting at a random location; and (d) concentrated loads of equal magnitudes separated by random intervals.

Exact determination of gravity stresses in finite elastic slopes: Part I. Theoretical considerations

1983 ◽  
Vol 20 (1) ◽  
pp. 47-54 ◽  
Author(s):  
V. Silvestri ◽  
C. Tabib
Keyword(s):  
Plane Strain ◽  
Half Plane ◽  
Inclination Angle ◽  
Complex Variable ◽  
Earth Pressure ◽  
Exact Distributions ◽  
Exact Determination ◽  
Upper Half Plane ◽  
Theoretical Considerations

The exact distributions of gravity stresses are obtained within slopes of finite height inclined at various angles, −β (β = π/2, π/3, π/4, π/6, and π/8), to the horizontal. The solutions are obtained by application of the theory of a complex variable. In homogeneous, isotropic, and linearly elastic slopes under plane strain conditions, the gravity stresses are independent of Young's modulus and are a function of (a) the coordinates, (b) the height, (c) the inclination angle, (d) Poisson's ratio or the coefficient of earth pressure at rest, and (e) the volumetric weight. Conformal applications that transform the planes of the various slopes studied onto the upper half-plane are analytically obtained. These solutions are also represented graphically.

scholarly journals ANALISIS PENGARUH BENTUK DAN LOKASI BUKAAN PADA BALOK TINGGI MENGGUNAKAN METODE ELEMEN HINGGA

2020 ◽  
Vol 3 (4) ◽  
pp. 1209
Author(s):  
Anthony Fariman ◽  
Leo S. Tedianto
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Wall Structure ◽  
Deep Beam ◽  
Stress Distributions ◽  
Stress Concentrations ◽  
Offshore Structure ◽  
Deep Beams ◽  
Concentrated Load ◽  
Cable Networks

ABSTRAKBalok tinggi beton bertulang merupakan salah satu struktur khusus yang dapat memikul beban cukup besar dan umumnya digunakan sebagai transfer girder, struktur lepas pantai, struktur dinding, dan pondasi. Kehadiran bukaan pada balok tinggi dapat memfasilitasi jalur saluran AC, saluran pipa, jaringan kabel dan lain-lain. Dengan adanya bukaan pada balok tinggi dapat memberikan beberapa efek samping yaitu terjadinya diskontinuitas geometri, tegangan terdistribusi non-linier pada balok tinggi, berkurangnya kekuatan dari balok, dan timbulnya konsentrasi tegangan di sekitar bukaan. Penelitian ini bertujuan untuk menganalisis efek dari kehadiran bukaan pada balok tinggi di atas dua perletakan (sendi-rol) dan dibebani beban terpusat di tengah bentang balok lalu memvariasikan bentuk bukaan (persegi, persegi panjang, dan lingkaran) dan lokasi bukaan. Tegangan lentur pada balok tinggi dan konsentrasi tegangan yang terjadi di sekitar bukaan merupakan hal yang akan dibahas dalam penelitian. Analisis akan dibantu dengan Midas FEA yang merupakan program berbasis elemen hingga dan  pemodelan dilakukan dengan elemen solid tiga dimensi. Hasil dari analisis ini menunjukkan bahwa kehadiran bukaan pada balok tinggi menyebabkan kenaikan tegangan secara signifikan. Lokasi dari bukaan yang mendekati daerah tengah bentang balok juga sangat mempengaruhi besarnya tegangan yang terjadi.ABSTRACTReinforced concrete deep beam is one of the special structures that can carry quite a big load and generally used as a transfer girder, offshore structure, wall structure, and foundation. The appearance of openings in deep beams can facilitate AC pipelines, plumbing pipes, cable networks, etc. The existence of openings in deep beams can provide a few side effects such as geometric discontinuity, non-linear stress distributions over the deep beams, reduced strength of the deep beams, and stresses concentration will emerged around the openings. The purpose of this research is to analyze the effects from the existence of openings in deep beams on two supports (hinge and roller) and loaded by concentrated load in mid-span then variate the shape of openings (square, rectangle, and circle) and location of the openings. Flexural stresses in deep beams and the stress concentrations that occur around the openings are discussed in this research. The analysis will be assisted by Midas FEA which is a finite element based program and modelling will be executed in three dimensional solid elements. The result of this analysis showed that the existence of the openings in deep beams can cause stresses to increase significantly high. The location of the openings close to the mid-span of the deep beams also affect the amount of the stresses that occurs.

scholarly journals Strengthening of Reinforced Concrete Beams Subjected to Concentrated Loads

2022 ◽  
Author(s):  
Paolo Foraboschi
Keyword(s):  
Reinforced Concrete ◽  
Carrying Capacity ◽  
Concrete Beams ◽  
Shear Capacity ◽  
Reinforced Concrete Beams ◽  
Load Carrying Capacity ◽  
Reinforced Concrete Structure ◽  
Concentrated Loads ◽  
Concentrated Load ◽  
Load Carrying

Renovation, restoration, remodeling, refurbishment, and retrofitting of build-ings often imply modifying the behavior of the structural system. Modification sometimes includes applying forces (i.e., concentrated loads) to beams that before were subjected to distributed loads only. For a reinforced concrete structure, the new condition causes a beam to bear a concentrated load with the crack pattern that was produced by the distributed loads that acted in the past. If the concentrated load is applied at or near the beam’s midspan, the new shear demand reaches the maximum around the midspan. But around the midspan, the cracks are vertical or quasi-vertical, and no inclined bar is present. So, the actual shear capacity around the midspan not only is low, but also can be substantially lower than the new demand. In order to bring the beam capacity up to the demand, fiber-reinforced-polymer composites can be used. This paper presents a design method to increase the concentrated load-carrying capacity of reinforced concrete beams whose load distribution has to be changed from distributed to concentrated, and an analytical model to pre-dict the concentrated load-carrying capacity of a beam in the strengthened state.

Complex Variable Method for Eigensolution Sensitivity Analysis

AIAA Journal ◽  
2006 ◽  
Vol 44 (12) ◽  
pp. 2958-2961 ◽  
Author(s):  
B. P. Wang ◽  
A. P. Apte
Keyword(s):  
Sensitivity Analysis ◽  
Complex Variable ◽  
Complex Variable Method ◽  
Variable Method
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