scholarly journals Discussion: “The Wedge Under a Concentrated Couple: A Paradox in the Two-Dimensional Theory of Elasticity” (Sternberg, Eli, and Koiter, W. T., 1958, ASME J. Appl. Mech., 25, pp. 575–581)

1959 ◽  
Vol 26 (3) ◽  
pp. 473
Author(s):  
P. M. Naghdi
Keyword(s):  
Theory Of Elasticity ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Concentrated Couple

The Wedge Under a Concentrated Couple: A Paradox in the Two-Dimensional Theory of Elasticity

1958 ◽  
Vol 25 (4) ◽  
pp. 575-581
Author(s):  
Eli Sternberg ◽  
W. T. Koiter
Keyword(s):  
Wedge Angle ◽  
Theory Of Elasticity ◽  
Opening Angle ◽  
Two Dimensional ◽  
Elastic Wedge ◽  
Singular Behavior ◽  
Dimensional Theory ◽  
Dimensional Solution ◽  
Critical Opening ◽  
Concentrated Couple

Abstract The classical two-dimensional solution for the stress distribution in an elastic wedge which is subjected to a concentrated couple at the vertex, breaks down when the opening angle 2α of the wedge satisfies the equation tan 2α = 2α, i.e., when 2α is approximately 257 deg. As the foregoing critical opening angle 2α* is approached, all of the nonvanishing components of stress become infinite throughout the field, while the solution displays no obvious pathological characteristics for other values of the wedge angle. It is the purpose of the present paper to account for this peculiar singular behavior and to show that the solution under examination has physical significance only for wedge angles below the critical angle; for opening angles in the range 2α* ≤ 2α < 2π, the notion of a “concentrated couple” at the vertex of an elastic wedge, is found to be inherently deficient in meaning. The present investigation, as a by-product, augments the supply of counterexamples to the traditional version of Saint Venant’s principle.

Stress Analysis and the Characteristics of T-Shape Bolted Joints Under Tensile Loadings

2005 ◽  
Author(s):  
Toshiyuki Sawa ◽  
Seiichi Hamamoto
Keyword(s):  
Bending Moment ◽  
Theory Of Elasticity ◽  
Bolted Joints ◽  
Load Factor ◽  
Two Dimensional ◽  
Bolted Joint ◽  
Dimensional Theory ◽  
Matching Method ◽  
Point Matching ◽  
Bolt Stress

In designing a bolted joint, it is important to examine the interface stress distribution (clamping effect) and to estimate the load factor, that is the ratio of an additional axial bolt force to a load. In order to improve the clamping effect raised faces of the interface have been used. But these interfaces in bolted joints have been designed empirically and the theoretical grounds are not made clear. In the present paper, in the case of T-shaped flanges with raised faces the clamping effect is analyzed by a two-dimensional theory of elasticity and the point matching method. Then, the load factor is analyzed. Moreover, with the application of the load a bending moment is occurred in bolts and the stress is added due to this bending moment. The bending moment in the bolt is also analyzed. In order to verify these analyses experiments to measure the load factor and the maximum bolt stress were carried out. The values of the load factor and the load when interface start to separate are compared with those of the joints with flat-faces. The analytical results are in fairly good agreements with the experimental ones.

Exact Stress Distribution in Standard Gear Teeth and Geometry Factors

1973 ◽  
Vol 95 (4) ◽  
pp. 1159-1163 ◽  
Author(s):  
C. N. Baronet ◽  
G. V. Tordion
Keyword(s):  
Stress Distribution ◽  
Gear Tooth ◽  
Theory Of Elasticity ◽  
Tooth Profile ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Concentrated Load ◽  
Gear Teeth ◽  
Pressure Angle ◽  
Surface Stresses

Using the two-dimensional theory of elasticity and an appropriate transform function, the stress distribution in a gear tooth acted on by a concentrated load has been obtained. Computations were carried out for the 20 and 25-deg pressure angle, standard full-depth system, for numbers of teeth ranging from 20 to 150. The intensities of the maximum static surface stresses along the root fillets are given for different loading positions on the tooth profile. Some of the results are compared with others found in the literature.

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