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: