ABSTRACT
M Mn uφ ≥ (5.1)
The nominal strengthened moment capacity Mn( ) with steel reinforcement and FRP is to be determined using
• Strain compatibility • Internal force equilibrium • Internal moment equilibrium • Expected failure mode
The strength reduction factor of a strengthened section is given by Equation (10.5) of ACI 440.2R-08 based on the requirements of ACI 318-05 (2005). This factor ϕ is a function of the net tensile strain in the most extreme tension steel layer at nominal strength:
0.9 for 0.005
0.65 0.25
0.005 for 0.005
0.65 for
( )φ = ε ≥
+ ε − ε
− ε ε < ε <
ε ≤ ε
(5.2)
The above values are set to ϕ = 0.9 for a tension-controlled failure (ductile) and to ϕ = 0.65 for a compression-controlled failure (brittle without yielding), while ϕ is determined from the linear interpolation between the two extremes in the transition zone, as seen in Figure 5.1.
