Engineering Plasticity: Theory and Application to Metal by R. A. C Slater

By R. A. C Slater

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3. Direct strains and shear strains in the yz plane side CD elongates to C'D' and has an angular movement KC'D' and the side DB elongates to D'B' and has an angular movement LD'B'. 4 it will be appreciated that the angle JA'C' has a component parallel to the plane XOZ and also to the plane XOY and similarly for all other angles. The displacement of B relative to A is thus compounded of all these motions. For the sake of clarity, the displacements shown in the various figures have been grossly exaggerated.

192, Wilhelm Ernst, Berlin (1914) 3 Strain Analysis If the relative position of any two points in a continuous body is changed then the body is said to be deformed or strained. When the distance between every pair of points in a body remains constant during its movement then the body is referred to as a rigid body. The displacements of a rigid body may be either translations or rotations which are known as rigid body displacements. The analysis of strain is the study of displacements of points in a body relative to one another when the body is deformed and is, therefore, not directly concerned with rigid body displacements.

8 Principal shear stresses and maximum shear stress Assume that the coordinate axes are chosen to coincide with the principal directions then the shear stresses referred to these axes are zero. 8. 18~ respectively. 36) It is already known that on the principal planes the shear stresses are a minimum, that is, zero. The planes on which the shear stresses attain extremum values are determined by obtaining the particular values of the direction cosines l, m and n such that s. 36) is a maximum. However, there is a restriction on the values of the direction cosines, since [2 + m2 + n2 = 1, and therefore only two of them can be independent.

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