S=,1 +- ,
X +X1 X+ X,+2 (5-3)
2 2
Dn Dn-1 D5 D4 D3 D2 D1
On-1 On-2 04 03 02 01
)n-2 03 02 01
X2
X3
X4
X5
Xn
Figure 5-19. Illustration of the numerical differential method
The average curvature calculated is the curvature of a point located at equal
distances from the two rotation points. This is repeated for increasing loads up to failure.
The moment-curvature diagram is the curvature values of a point at increasing loads. The
curves calculated using this method were called differential.
The theoretical moment-curvature curves were calculated by the theoretical M-(
program described in chapter 4.
The experimentally calculated M-( curves were compared with the theoretical M-
( curves for specimen 1 (Fig. 5-20) and for specimen 2 (Fig. 5-21).
The theoretical moment curvature curve of specimen 1 was significantly different
than the displacement moment curvature curve. The most obvious difference was the
slope of the curve. The theoretical curve had a slope approximately 32% lower than the
displacement moment curvature curve. It is unknown why the theoretical program
underestimated the slope of the curve. On the other hand the differential curve was in
good agreement with the displacement curve but had a higher slope approximately 18%.