Since the curve [alpha](t) is also in space, there exists Frenet frame {T, N, B} at each points of the curve where T is unit tangent vector, N is

principal normal vector and B is binormal vector, respectively.

1] consisting of the tangent,

principal normal, first binormal vector field, and second binormal vector field, respectively.

The

principal normal stresses and maximum shear stress together with the angle of the principal axis can be determined from the applied stresses (fx, fy and fs) using the following equations [Bruhn, 1973], [Niu, 2005]:

1) are called the vectors of the tangent,

principal normal and the binormal line of c, respectively.

In order to explain the results, the

principal normal stress difference, [[sigma].

Well-known partner curves are the Bertrand curves, which are defined by the property that at the corresponding points of two space curves the

principal normal vectors are common.

1] be a unit-speed spacelike curve with timelike

principal normal.

On the basis the resultants of three papers earlier mentioned, the

principal normal stresses in the plastic and elastic region is calculated.

The

principal normal stress difference increases nonlinearly with shear stress.

The vector field N and B are called the

principal normal and binormal vector field of [gamma] respectively.

3], it is well-known that to each unit speed curve with at least four continuous derivatives, one can associate three mutually orthogonal unit vector fields T, N and B are respectively, the tangent, the

principal normal and the binormal vector fields [3].

2] are, respectively, the tangent, the

principal normal, the first binormal and the second binormal vector fields.