ACI 318-19 Table 21.2.1 | Strength Reduction Factors (φ)
To protect structures against variations in material strength, dimensions, and workmanship, nominal strengths are scaled down by a strength reduction factor (φ). Beams with ductile, yielding steel receive a favorable φ = 0.90, while brittle compression columns are penalized with φ = 0.65.
Governing Formula
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Notation & Variables
Worked Example
Calculate net tensile strain
From strain compatibility, calculate extreme tension steel strain: et = 0.003 * (d - c) / c. For a beam with d = 21.5" and neutral axis depth c = 4.2", et = 0.0123.
Determine limit for Grade 60
For Grade 60 steel (fy = 60 ksi), yield strain ety = 60 / 29000 = 0.00207. The tension-controlled limit is ety + 0.003 = 0.00507.
Select phi factor
Since et (0.0123) is much greater than 0.00507, the section is fully tension-controlled.
When does this govern?
The transition zone governs heavily reinforced beams, shallow foundations, and columns subjected to combined axial load and significant bending moment.
Common Mistake
Using the old ACI 318-14 constant 0.005 tensile strain limit for high-strength rebar (Grade 80 or Grade 100). Under ACI 318-19, the tension-controlled limit is now tied to yield strain (ety + 0.003), meaning Grade 80 requires et ≥ 0.00576 to reach φ = 0.90.