500
400
|300
S200
-e-Exp. Mid-Span
S-- Theoretical
100 -IE- Exp. South Load
-*- Fiber Model
0 0.0002 0.0004 0.0006 0.0008 0.001
Curvature (rads/in)
Figure 4-23. Experimental and theoretical M-D curves for control beam
The experimental M-D behavior of the tube beam was comparable to the behavior
calculated by fiber model (see Fig. 4-24). The theoretical 1 behavior is different than the
experimental in that it does not capture the loss in capacity due to cover concrete
crushing but this was expected because the program used only one stress-strain curve to
characterize the properties of the concrete section. The non-linear second part of the
curve was the behavior of the beam with the whole section confined with the top cover
layer removed. Curve theoretical 1 was a close match with the mid-span experimental
curve up to the peak load. Although the capacity loss was not captured by the theoretical
analysis the plateau noted on the experimental curve was also noted on the theoretical 1
curve. Curve theoretical 1 was a lower bound solution of the tube beam. Curve theoretical
2 had the same shape as curve theoretical 1. Curve theoretical 2 was obtained by
assuming confined concrete properties for the whole section and including the top cover
layer. Curve theoretical 2 was an upper bound solution of the tube beam.
The improvement in the ductility of the tube beam compared to the control beam
was evident when the experimental M-D curves for both beams were compared (See Fig.
4-25). The area under the load-displacement curves represents the amount of energy a