The Shearing of a Rectangular Block Between Rough Plates

1953 ◽  
Vol 20 (2) ◽  
pp. 270-272
Author(s):  
J. W. Craggs
Keyword(s):  
Approximate Solution ◽  
Analytical Solution ◽  
Shear Stresses ◽  
Rectangular Block ◽  
Uniform Shear ◽  
Published Paper ◽  
General Method

Abstract In a recently published paper, W. T. Read gives an approximate solution of a problem in elasticity which occurs in the testing of materials. This is the problem of determining the stresses in a rectangular block when a pair of opposite faces are mutually displaced in the direction of an edge. The conditions are not those of uniform shear, for that would imply shear stresses on the free faces of the block. In the present paper an analytical solution of the same problem is obtained and the results are compared for a particular case. The method used is a particular case of the general method described by G. Pickett.

Zur Lösung der BETHE-GOLDSTONE-Gleichung bei nicht-verschwindendem Gesamtimpuls I

1963 ◽  
Vol 18 (4) ◽  
pp. 531-538
Author(s):  
Dallas T. Hayes
Keyword(s):  
Approximate Solution ◽  
Analytical Solution ◽  
Nuclear Matter ◽  
Analytical Solutions ◽  
Projection Operator ◽  
Center Of Mass ◽  
Separable Potential ◽  
Localized Solutions ◽  
Non Local ◽  
Square Well

Localized solutions of the BETHE—GOLDSTONE equation for two nucleons in nuclear matter are examined as a function of the center-of-mass momentum (c. m. m.) of the two nucleons. The equation depends upon the c. m. m. as parameter due to the dependence upon the c. m. m. of the projection operator appearing in the equation. An analytical solution of the equation is obtained for a non-local but separable potential, whereby a numerical solution is also obtained. An approximate solution for small c. m. m. is calculated for a square-well potential. In the range of the approximation the two analytical solutions agree exactly.

A General Method for the Fatigue-Resistant Design of Mechanical Components—Part 2: Analytical

1975 ◽  
Vol 97 (3) ◽  
pp. 970-975
Author(s):  
D. T. Vaughan ◽  
L. D. Mitchell
Keyword(s):  
Analytical Solution ◽  
Fatigue Fracture ◽  
Fracture Criterion ◽  
Fatigue Loading ◽  
General Analytical Solution ◽  
Failure Theory ◽  
Straight Line ◽  
Mechanical Components ◽  
General Method

This paper develops the general analytical solution to the design of mechanical components under fatigue loading. Its only limitation is that the overloading lines must be a straight line on the σa−σm diagram. The designer is free to select his own failure theory for the material he intends to use as well as to select his own fatigue fracture criterion.

Stress Distribution in a Uniformly Rotating Equilateral Triangular Shaft

1955 ◽  
Vol 22 (2) ◽  
pp. 255-259
Author(s):  
H. T. Johnson
Keyword(s):  
Approximate Solution ◽  
Stress Distribution ◽  
Boundary Conditions ◽  
Plane Strain ◽  
Cross Section ◽  
Plane Stress ◽  
Biharmonic Equation ◽  
Approximate Solutions ◽  
Distribution Of Stresses ◽  
General Method

Abstract An approximate solution for the distribution of stresses in a rotating prismatic shaft, of triangular cross section, is presented in this paper. A general method is employed which may be applied in obtaining approximate solutions for the stress distribution for rotating prismatic shapes, for the cases of either generalized plane stress or plane strain. Polynomials are used which exactly satisfy the biharmonic equation and the symmetry conditions, and which approximately satisfy the boundary conditions.

scholarly journals A New Approach for Solving the Undamped Helmholtz Oscillator for the Given Arbitrary Initial Conditions and Its Physical Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Alvaro H. Salas S ◽  
Jairo E. Castillo H ◽  
Darin J. Mosquera P
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Analytical Solution ◽  
Initial Conditions ◽  
Negative Ions ◽  
Nonlinear Problems ◽  
New Approach ◽  
Weierstrass Elliptic Function ◽  
Electronegative Plasma ◽  
The Given

In this paper, a new analytical solution to the undamped Helmholtz oscillator equation in terms of the Weierstrass elliptic function is reported. The solution is given for any arbitrary initial conditions. A comparison between our new solution and the numerical approximate solution using the Range Kutta approach is performed. We think that the methodology employed here may be useful in the study of several nonlinear problems described by a differential equation of the form z ″ = F z in the sense that z = z t . In this context, our solutions are applied to some physical applications such as the signal that can propagate in the LC series circuits. Also, these solutions were used to describe and investigate some oscillations in plasma physics such as oscillations in electronegative plasma with Maxwellian electrons and negative ions.

The Distribution of Shear Stress along the Anchoring Section of Prestressed Bolt

2011 ◽  
Vol 90-93 ◽  
pp. 2243-2247
Author(s):  
Bo Zhang ◽  
Shu Cai Li ◽  
Xue Ying Yang ◽  
Dun Fu Zhang ◽  
Ming Tian Li
Keyword(s):  
Shear Stress ◽  
Analytical Solution ◽  
Uniform Distribution ◽  
Elastic Theory ◽  
Shear Stresses ◽  
Stress Peak ◽  
Peak Value

In this paper the distribution of shear stress along the anchoring section of prestressed bolt was presented. The distribution of shear stress along the anchoring section of prestressed bolt was analyzed with the plane elastic theory. The analytical solution of shear stress along the anchoring section was deduced. Several cases of shear stresses were analyzed with the analytical solution. The results show that shear stress of prestressed bolt are not uniform distribution along the anchoring section; it is has no relations with the prestress value where the shear stress peak value is; the shear stress is at a certain range along the anchoring section; the shear stress peak value increases with the increase of prestress value;the larger the diameter of the anchoring section is, the less of shear stress peak value is.

The Influence of Cyclic and Uniform Shear Stresses Concurrent with Cyclic Stretch on the Gene Expression of Human Umbilical Vein Endothelial Cells

2013 ◽  
Vol 3 (6) ◽  
pp. 673-678 ◽  
Author(s):  
Shahrokh Shojaei ◽  
Mohammad Tafazzoli-Shadpour ◽  
Mohammad Ali Shokrgozar ◽  
Nooshin Haghighipour ◽  
Najmeh Safaei ◽  
...  
Keyword(s):  
Gene Expression ◽  
Endothelial Cells ◽  
Umbilical Vein ◽  
Cyclic Stretch ◽  
Shear Stresses ◽  
Human Umbilical Vein ◽  
Uniform Shear ◽  
Umbilical Vein Endothelial Cells

scholarly journals The Use of Cubic Splines in the Numerical Solution of Fractional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
W. K. Zahra ◽  
S. M. Elkholy
Keyword(s):  
Approximate Solution ◽  
Analytical Solution ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Spline Function ◽  
Shooting Method ◽  
Polynomial Spline ◽  
Cubic Polynomial ◽  
Fractional Differential ◽  
Fractional Boundary Value Problems

Fractional calculus became a vital tool in describing many phenomena appeared in physics, chemistry as well as engineering fields. Analytical solution of many applications, where the fractional differential equations appear, cannot be established. Therefore, cubic polynomial spline-function-based method combined with shooting method is considered to find approximate solution for a class of fractional boundary value problems (FBVPs). Convergence analysis of the method is considered. Some illustrative examples are presented.

Does the shear strength of reinforced concrete beams and slabs depend upon the flexural reinforcement ratio or the reinforcement strain?

2013 ◽  
Vol 40 (11) ◽  
pp. 1068-1081 ◽  
Author(s):  
Mitra Noghreh Khaja ◽  
Edward G. Sherwood
Keyword(s):  
Shear Strength ◽  
Reinforced Concrete ◽  
Concrete Beams ◽  
Reinforcement Ratio ◽  
Reinforced Concrete Beams ◽  
Shear Stresses ◽  
Shear Design ◽  
Reinforced Polymer ◽  
Fibre Reinforced Polymer ◽  
General Method

Beam tests are conducted to investigate the effect of the reinforcement ratio, ρ, and the shear span to depth ratio, a/d, on the shear strength of reinforced concrete beams and slabs without stirrups. The a/d ratio is shown to have a very significant effect on shear strength at both low values of a/d (where failure is governed by strut-and-tie mechanisms) and large values of a/d (where failure is governed by breakdown in beam action). Increases in ρ associated with increases in a/d such that the strain, or M/ρVd ratio, is kept constant will result in constant failure shear stresses. Shear design methods that do not account for a/d (e.g., ACI Committee 440) cannot predict the observed experimental behaviour, whereas the general method of the CSA A23.3 code can. Using the ACI 440 equation for Vc may reduce the economic competitiveness of fibre-reinforced polymer reinforcement versus steel reinforcement.

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