The angle 0 was constant which meant that the length of the trapezoid sides was
dependent only on the distance from the center of the cylinder. The distance from the
center of the cylinder was smaller closer to the center which meant that the trapezoids
were also smaller in size close to the center of the cylinder.
For the exterior micro column the lengths of the trapezoid sides were equal to Xo
and X1 (see Fig. 8-6). The lengths for the micro column adjacent to that were equal to X1
and X2 (see Fig. 8-6). Therefore, the moment of inertia of the idealized micro column
cross section was generally expressed as follows:
St'[(Xi)2 +(4Xi -Xi, )+(Xi+)2] (8-3)
36.(Xi + X, )
The angle 01 by which the length varies for the exterior layers was assumed to be
equal to approximately 60 degrees. For a given t value the angle 02 was varied until the
resulting curve matched the experimental results but was kept close to 10 degrees.
The length of the exterior micro columns (region 1 in Fig. 8-3) was calculated
based on the first exterior micro column length (e), the distance of the micro column from
the exterior surface of the cylinder and the angle 01:
d
L,e 2- ( r,) tan ( (8-4)
2
The length of the interior micro columns (region 2 in Fig. 8-3) was calculated based
on the last micro column length (LB) of the first region discussed in the previous
paragraph, the number of micro columns in the first region (B), the distance of the micro
column from the center of the cylinder (r,) and the angle 02:
d
L, = LB -2.(- B -t -r1). tan 02 (8-5)
2