Position of a point on the cross-section

To transform vector-valued functions from the Cartesian coordinate system of the beam to the curvilinear coordinate system of the wall, the unit vec- 

Then with the aid of Eq. (7.20), respectively in addition with Eq. (7.17), the following relationships are found  

With the introduction of the parameter s, the total displacement of a point on the beam wall, according to Eq. (7.12), is given in the Cartesian coordinate system of the beam as 

To determine the strains in the beam wall, the total displacement must be expressed in the associated curvilinear coordinate system. With the aid of the transformation of Eq. (7.21), this may be expressed in the following form  

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Fig. 7.1. Position of a point on the cross-section and associated unit vectors.

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