Flexural members - Reinforced Concrete with FRP Bars: Mechanics and Design - page 122

deflection multiplier for the additional deflection due to sustained loading.
Research has demonstrated that the approach used for estimating long-
term deflections of steel reinforced members can also be applied to FRP
reinforced members [4].
As noted in ACI 440.1R-06, the time-dependent deflection increase for
FRP RC can be expected to be proportionally less than steel reinforced
concrete. The creep-induced reduction of the concrete modulus of elastic-
ity causes an overall reduction of the members' flexural rigidity, E c I. The
reduced modulus also causes an increase of the neutral axis depth of the
cracked cross section, which, in turn, induces an increase of the moment of
inertia. This second effect is typically more significant in FRP reinforced
members because of the lower tensile modulus of the FRP reinforcement
compared to steel.
The following equation is proposed by ACI 440.1R-06 to compute long-
term deflections due to creep and shrinkage, Δ (cp+sh) :

Δ ( cp+sh ) = 0.6 ξ (Δ i ) sus (4.84)

where (Δ i ) sus is the immediate deflection due to sustained loads and ξ
is a factor varying between 0 and 2 depending on the time period over
which deflections are computed. Values of ξ are given by ACI 318-11. For
100 years, ξ = 2 is assumed.

4.9.3 FRP creep rupture and fatigue
Sustained loads can cause FRP bars to fail suddenly after a period of time
defined as the endurance time. This phenomenon is known in literature as
creep rupture (or static fatigue). ACI 440.1R-06 recommends limiting the
stress level in the FRP reinforcement induced by sustained loads (dead loads
and the sustained portion of the live load) to prevent creep rupture. The
stress level in the FRP can be computed using the Navier equation:

M
I

s

f = nd (1 − kk ) ≤ f (4.85)

fs , ff creep R − fu

cr

where M s is the bending moment acting on the cross section where the
FRP stress is computed, and k creep-R is the knock-down factor applied to
the design tensile strength of the FRP bars to account for creep rupture.
According to ACI 440.1R-06, k creep-R is equal to 0.20 for glass, 0.30 for
aramid, and 0.55 for carbon FRP.
The provision given in Eq. (4.85) indirectly implies that the concrete in
compression is still within its linear-elastic range. For this, it has to be
checked and verified that the maximum concrete compressive stress ( f c ) is
smaller than 0.45 f ′ c when the applied moment is M s .