secting vectors on the upper surface of the slab (in the x-y
plane of the ''floating'' cartesian coordinate system mentioned
above) was chosen. This conformal transformation, often used
by structural engineers and apparently theoretically justifiable
in structural mechanics (Lenschow and Sozen, 1966), is based
on an arbitrary point ot be used as origin (Fig. 19), and two
arbitrary vectors intersecting at this point.
Fig. 19 - ‘Floating’ control for coordinate transformation
In Fig. 19, the transformation system is defined by
two vectors ( (1) and (2 ) intersecting in a point (A) and
passing through two arbitrary points (B & C). Point P is a
general point whose coordinates X Y 2 in one coordinate
system is to be transformed in another coordinate system (X',
Y', Z'). The X and X'-axes may be chosen along the vectors AB
and A'B' respectively.
Let the direction cosines of lines 1, 2, and 3 with respect
to the first coordinate system be as given in Table ll.