With the critical stress calculated based on the Euler buckling equation the load can
be determined by simply multiplying the stress by the area of the cylinder:
P, = ucr, Ao (8-6)
where P, was the total load on the cylinder, acr, was the Euler buckling stress of the
micro columns, and Ao was the area of the cylinder.
The total axial compressive strain (e,) in the cylinder was determined based on the
areas for each section of the cylinder and the micro column lengths relative to the length
of the cylinder. The lengths for the micro columns were expressed as fractions of the
length of the cylinder to simplify the strain equation (see Fig. 3-20).
Ao (1-a)Lo/2
(Ao + Ac)/2 (a-a) Lo
Ac a, Lo Lo
(Ao + Ac)/2 (a-a)Lo
Ao (1-a)Lo/2
Figure 8-8. Cylinder set up for total strain determination
The fraction for each micro column length was denoted as a, and was determined as
follows: