where nc is the number of micro columns in each radial layer which was determined by
dividing the 360 degrees of the circle by the angle 0, E was the initial modulus of
elasticity of concrete, I was the moment of inertia of the micro column, Ao was the area
of the cylinder, and L was the length of the micro column. The modulus of elasticity of
concrete was assumed to be constant to simplify the model. Both the length and the
moment of inertia varied between the micro columns. The micro columns located on the
exterior layers of the concrete cylinder had longer lengths and higher moments of inertia
than the micro columns located towards the center of the cylinder.
n@t
Figure 8-5. Concrete cylinder micro columns
The cross section of the micro columns was idealized and assumed to have a
trapezoidal shape (dotted lines in Fig. 8-6) even though their shape was like a circular
segment (solid lines in Fig. 8-6). The height of the trapezoid was equal to the radial crack
spacing (t). The lengths of the sides of the trapezoid were calculated based on the
longitudinal crack spacing angle (0) and their distance from the center of the cylinder.