11). This generated extra load which was manifested into higher stresses and higher
strains (higher ductility) for the cylinder.
----------------------------------- -----------
5 -------------- -J-R
----------------------------------- -----------
i ... 3 2 1 0
Figure 8-11. Restraint of micro columns by CFRP grid strand
Because it was assumed that the micro columns buckle prior to being braced by the
CFRP grid the model in Fig. 8-11 treated the micro columns as axially rigid columns with
real hinges and rigid body motions. It was assumed that only the micro columns adjacent
to the CFRP grid strand were restrained and the entire extra load from confinement was
carried by those micro columns.
The lateral displacement (5) was determined using geometry (Fig. 8-12) in terms of
the length of the micro column (L) and the axial compressive strain (e). The strain used to
determine the lateral displacement was the strain calculated using Equations 8-8 and 8-
10. Using the Pythagorean Theorem and rearranging the equation the lateral displacement
at a given strain was equal to:
L 2
= 2 E, E, (8-11)
The load (PR) contributed by the restrained micro column was calculated by
summing moments about point B (Fig. 8-12). After rearranging the equation the load PR
was: