Determination of the Stress State of the Disk Using the Stress Function

2021 ◽  
pp. 36-42
Author(s):  
V. N. Strelnikov
Keyword(s):  
Stress State ◽  
Stress Function

Generalized plane stress in a semi-infinite strip under arbitrary end-load

1964 ◽  
Vol 281 (1385) ◽  
pp. 184-206 ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Conditions ◽  
Fourth Order ◽  
Plane Stress ◽  
Stress Function ◽  
Infinite Strip ◽  
Order Ordinary Differential Equation ◽  
Orthogonal Functions

The problem involves the determination of a biharmonic generalized plane-stress function satisfying certain boundary conditions. We expand the stress function in a series of non-orthogonal eigenfunctions. Each of these is expanded in a series of orthogonal functions which satisfy a certain fourth-order ordinary differential equation and the boundary conditions implied by the fact that the sides are stress-free. By this method the coefficients involved in the biharmonic stress function corresponding to any arbitrary combination of stress on the end can be obtained directly from two numerical matrices published here The method is illustrated by four examples which cast light on the application of St Venant’s principle to the strip. In a further paper by one of the authors, the method will be applied to the problem of the finite rectangle.

Graphical-Numerical Solution of Problems of Saint-Venant Torsion and Bending

1953 ◽  
Vol 20 (3) ◽  
pp. 321-326
Author(s):  
B. A. Boley
Keyword(s):  
Cross Section ◽  
Stress Function ◽  
Arbitrary Cross Section ◽  
Successive Approximations ◽  
Shear Stresses ◽  
Shearing Stress ◽  
First Approximation ◽  
Difference Form ◽  
Bending Of Beams

Abstract A simple successive-approximations procedure for the solution of the problems of Saint-Venant torsion and bending of beams of arbitrary cross section is presented. The shear stresses in a cross section of the beam are first calculated from the formulas valid for thin-walled sections, on the basis of an assumed set of lines of shearing stress. From these a first approximation to the stress function of either the torsion or the bending problem is found. The second approximation to the stress function is then obtained from the governing equation of the problem, expressed in finite-difference form; this in turn allows the determination of an improved set of lines of shearing stress, and hence of the shearing stress itself. The procedure can be repeated until the results of two successive steps are sufficiently close. Applications are presented for a beam cross section for which the exact solutions are known, and it is shown that no further difficulties arise in applications to more complicated shapes.

scholarly journals THE ANALYTICAL DETERMINATION OF THE PARAMETERS OF THE WELL WHILE ELIMINATING UNEQUAL SETTLEMENT OF FOUNDATIONS METHOD OF DRILLING-OUT OF THE SOIL

2020 ◽  
Vol 11 (2) ◽  
pp. 40-48
Author(s):  
Y. A Pronosin ◽  
M. D Kaygorodov ◽  
A. M Karaulov
Keyword(s):  
Stress State ◽  
Clay Soil ◽  
Reduction Process ◽  
Soil Characteristics ◽  
Shallow Foundations ◽  
Analytical Determination ◽  
Advantages And Disadvantages ◽  
Drilling Parameters ◽  
Soil Destruction

Existing approaches which allow to reduce the settlement unevenness of buildings and structures have their own advantages and disadvantages. One of the promising methods for reducing shallow foundations the settlement unevenness, which are based on soft dust and clay soil, is the building or its part lowering. The effect is achieved by drilling vertical wellbores in the immediate proximity to the existing foundation from the side of the least settlement. At different times, domestic and foreign scientists were engaged in to the methods of horizontal and inclined drilling of wellbores, an important issue, when applying this technology, is the determination of drilling parameters, the influence of soil characteristics and the stress state of the soil around the well, on the roll reduction process. The article considers the influence of the soil strength characteristics on the stress state of the soil which are surrounding the wellbore, and the effect of the drilled wellbore radius on the formation of the critical state regions. The analytical solution is based on the use of the well-known relationship for determining the stress state around the well during pressiometric tests. From this ratio, tangential and radial stresses are determined, which are then checked according to the condition of the law of strength, thereby forming a picture of the stress state around the well. According to the presented methodology, the stress state of the soil around the wells was calculated, which allows calculating the zones of soil destruction and thereby determining the parameters of the wells and the geometry of their location depending on the goals, when regulating the sediment of slab foundations.

Ring Specimen Geometry for Determining the Ductility of Tubulars

2016 ◽  
Author(s):  
M. A. Al Khaled ◽  
I. Barsoum
Keyword(s):  
Stress State ◽  
Plane Strain ◽  
Stress Triaxiality ◽  
Ductile Failure ◽  
Pressure Vessels ◽  
Ring Specimen ◽  
Lode Parameter ◽  
Wide Range ◽  
Failure Locus

Pressure vessels designed in accordance with the ASME BPVC code are protected against local ductile failure. Recent work has shown that local ductile failure highly depends on the stress state characterized by both stress triaxiality (T) and the Lode parameter (L). In this paper, the effect of stress state on the ductility of a tubular steel is studied. Two ring specimen configurations were optimized to allow the determination of the ductile failure locus of both tensile and plane strain loadings. The geometry of both ring specimen configurations was optimized to achieve a plane strain (L = 0) condition and a generalized tension (L = −1) condition. Notches with different radii were machined on both types to achieve a wide range of stress triaxiality. Specimens were manufactured from SA-106 carbon tubular steel and were tested to determine the ductile failure loci as a function of T and L. Failure locus of SA-106 steel was constructed based on the failure instants and was found to be independent of the variation in the Lode parameter. The ASME-BPVC local failure criterion showed close agreement with experimental results.

scholarly journals The Determination of Stress State of Structures Considering Sequence of Construction and Load Application

2016 ◽  
Vol 73 ◽  
pp. 04001
Author(s):  
Vladimir Kuroedov ◽  
Luka Akimov ◽  
Artem Frolov ◽  
Alexey Savchenko ◽  
Anton Kuznetsov ◽  
...  
Keyword(s):  
Stress State ◽  
Load Application
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