to the displacement profile curves (Fig. 4-22). The fitted lines were in good agreement
with the displacement data (average R2 = 0.997). The polynomial displacement profile
equation of the beam was used to determine the curvature at specific points along the
length of the pile. The second derivative of the polynomial displacement profile equation
is the curvature equation.
Displacement Location from North Support (in)
0 30 60 90 120 150 180
0 --I I I I I
y =2.6E-13x6 1.3E-10x + 2.1E-08x 1.3E-06x3 + 3.6E-05x2 -4.0E-03x- 5.8E-02
-0.1
-0.2
-0.3
0 P= 43.7 kips
Poly. (P = 43.7 kips)
-0.4
Figure 4-22. Displacement curve and fitted polynomial line for control beam at 43.7 kips
To model the behavior of the beams a program that generated the sectional
moment-curvature (M-PD) relationship was used (Consolazio, Fung and Ansley 2004).
The program describes cross sectional geometry using piecewise linear segments
for both the exterior and interior boundaries of the section. Interior boundaries represent
voids in the section. Curved boundaries such as the boundaries of circular sections are
approximated by using multiple linear segments. The reinforcing bars are modeled as
cross-sectional areas located at specific locations.
Some of the assumptions associated with the program are the following:
* Sign convention is positive for compression and negative for tension
* Plain sections remain plain which means that the strain distribution for the cross-
section is linear