The compressive force in each fiber layer was calculated as the product of the area
of the fiber layer and the average stress. The average stress was determined based on the
strain in the fiber layer and the stress-strain curves of concrete. The Hognestad parabola
was used to calculate the stress-strain curve of unconfined concrete. The modified
Hognestad was used to calculate the stress-strain curve of confined concrete. The
parameters of the modified Hognestad were determined based on the available data from
confined concrete cylinder tests.
The tensile force was calculated as the product of the area of steel reinforcement
and the steel stress which was determined based on the average strain of the two steel
layers. The steel stress was calculated based on an assumed elastic perfectly plastic
stress-strain curve with yield strength of 60 ksi and modulus of elasticity of 29000 ksi.
The moment in the cross-section for the applied curvature distribution was
determined by summing moments about the neutral axis.
The moment curvature diagram was calculated by applying increasingly larger top
concrete compressive strains (ec) to the cross-section and varying the location of the
neutral axis (c) until equilibrium of the axial forces (zero) in the cross-section for the
applied strain was achieved. The curvature of the section (0 = c /c) was then calculated
based on the concrete compressive strain and the location of the neutral axis.
The fiber model peak loads were 151 kips for the control beam and 156 kips for the
tube beam. The experimental peak loads were 148 kips and 153 kips for the control and
tube beams respectively. Therefore the fiber model calculated the peak loads for both
beams and could be used to calculate peak loads for beams utilizing the CFRP grid tubes.
The fiber model peak loads were approximately 2% higher that the actual loads.