Reinforced concrete bridges - Computational Analysis and Design of Bridge Structures - page 106

For the longitudinal steel, a bilinear stress-strain relationship was esti-
mated and employed (Figure 4.3b).

4.2.3 FRc and FRp
As mentioned in Section 4.1, the cracking behavior of FRC can be studied
using the smeared crack approach. To determine the material properties of
steel-FRC (SFRC), the inverse analysis techniques can be used to establish
the stress-strain response of SFRC. This technique obtains the flexural
response from bending tests to back calculate the stress-strain relationship.
Both M -ϕ (moment-curvature) and P -δ (force-displacement) responses
can be obtained from the test. The measured M -ϕ or P -δ responses reflect
the influence of the steel fiber parameters and the concrete matrix.

4.2.3.1 Inverse analysis method
For this method, a three-step procedure is used to calculate the P -δ response
of SFRC beams (Elsaigh et al. 2011a):

1. Assume a σ-ε relationship for the SFRC.

2. Calculate the M -ϕ response for a section.

3. Calculate the P -δ response for an element.

At the end of either step (2) or (3), the results from the analysis are
compared to experimental results and adjustments are made to the σ-ε
response until the analytical and experimental results agree within accept-
able limits.
Based on the study by Elsaigh et al. (2011a and b), the tensile σ-ε response
and results obtained from the nonlinear FEA of the beam were used in the
analysis involving an SFRC slab manufactured using a similar material of the

σ

σ t 0
σ tu

Tension

+

ε cu ε c 0

ε

ε t 0 ε t 1 ε tu

E c

Compression

−

σ cu

Figure 4.4 Stress-strain response of SFRC.