a, = (8-7)
Lo
The total strain was equal to the total displacement of the cylinder over the length
of the cylinder (Lo). The total strain of the cylinder was expressed in terms of the cross
sectional areas and the length fractions as follows:
S- + a + -a (8-8)
E Ao ) Ac, (Ao + Ac )/2
where ao was the length fraction for the exterior micro column, a, was the length fraction
for the micro column under the buckling stress and Ac, was the area of the cylinder that
remained unbuckled. The unbuckled area of the cylinder was the circular area enclosed
by the micro columns under stress. The radius of the area was the distance of the micro
columns from the center of the cylinder (r,). Therefore, the unbuckled area was:
Ac, = r, 2 (8-9)
Eq. 8-8 was applicable for micro columns in the region 1. When buckling preceded
into the second region the strain equation became:
P, a, + r- ar, ) -a, (8-10)
=E Ao iAc, (Ao +Ac~)/2 (Ac, + Ac,)/2 (
To evaluate the sensitivity of the model to the variation of the number of micro
columns in each buckling layer the angle 0 was varied while the other parameters were
kept constant. The effect of the number of micro columns on the peak strength is shown
in Fig. 8-9. It was found that the model was sensitive to the number of micro columns
only if the number was less than 18. For 18 or more micro columns the calculated peak
stress did not change and was the same as the experimental peak stress. Based on this the