Flexural members - Reinforced Concrete with FRP Bars: Mechanics and Design - page 76

Although the effect of temperature is included in the values of C E , ACI
440.1R-06 does not recommend using FRP bars in environments with a
service temperature higher than the glass transition temperature (T g ) of the
resin used for their manufacturing.

4.5 BENDING MOMENT CAPACITY

As it has been demonstrated experimentally, irrespectively of the reinforc-
ing material used (steel or FRP), the basic assumptions for the flexural
theory of RC members analyzed using the strength design method can be
summarized as follows:

1. Plane sections remain plane; this means that shear deformations can
be disregarded.

2. Perfect bond exists between reinforcing bars and the surrounding
concrete; in other words, the strain in the reinforcement is equal to
the strain in the concrete at the same level.

3. Stresses in both concrete and reinforcement are computed based on
the strain level reached in each material using the appropriate con-
stitutive laws for concrete and reinforcing bars. In particular, for the
case of concrete, up to the serviceability limit state, a linear-elastic
relationship will be used; past the linear elastic point up to crushing,
either the Todeschini model or the equivalent stress block can be used.
Regardless of the limit state considered, steel and FRP reinforcing
bars are considered elastic-plastic and linear-elastic, respectively.

Although not formally needed, the following two assumptions are usually
introduced to simplify the calculation process with little loss in the accu-
racy of the final results:

4. The tensile strength of the concrete is neglected.

5. The concrete is assumed to fail when it reaches a maximum preset
compressive strain.

The basic safety relationship at the ultimate limit state can be written as

ϕ M n ≥ M u (4.20)

In Equation (4.20), ϕ M n is the factored bending moment capacity of the
member and is a function of the member geometry, the location of the
reinforcement, and the mechanical properties of the materials; the term
“factored” means that the nominal calculated bending moment capacity
has been reduced by the safety factors associated with the materials or the
failure mode depending upon the calculation procedures followed.
The second term of Equation (4.20), M u , is the factored bending moment
resulting from the analysis of the member and is a function of the member