Moment-Curvature Analysis
The experimental curvature for all four specimens was determined using the
displacement profile equations. As described in detail in chapter 4, 6th order polynomial
line was fitted through the displacement points. The second derivative of the
displacement profile equation is the curvature equation and was used to calculate the
curvature at increasing loads. The curves calculated using this method were called
displacement in this chapter.
The experimental curvature was also determined based on a numerical differential
method. With the numerical differential method the curvature is calculated based on
displacement values for adjacent points in contrast to the curvature based on the
displacement profile which the curvature is calculated based on a fitted line through all
displacement points that can neutralized localized effects.
The average rotation between two points is calculated based on the change in
displacement (D) between the two points and the length that the change is taking place
(Fig. 5-19). For an n number of displacement points the average rotations can be
calculated as follows:
D +1 D
0,= (5-2)
XI+1 + X
The average rotation that is calculated is the rotation at the point located halfway
between the two points used to calculate the rotation.
The average curvature is then calculated based on the change in the average
rotation between two adjacent rotation points (calculated in the previous step) and the
distance between the two average rotation points: