# Strength Reduction Factors per ACI 318-19 with ideCAD

How does ideCAD define strength reduction factors according to ACI 318-19?

• Strength Reduction Factors are calculated automatically.

• The nominal strength of a reinforced concrete member is calculated automatically using the Strength Reduction Factor.

• Strength reduction factors ϕ are defined by default according to ACI Table 21.2.1 and Table 21.2.2.

• The strength Reduction Factor for a combined moment and axial force is calculated automatically according to ACI Table 21.2.2. A series of discrete points generated on the three-dimensional interaction failure surface calculates the column capacity interaction volume.

• The shear strength reduction factor for Earthquake-Resistant Structures is determined automatically.

Notation

Ec = modulus of elasticity of concrete, psi
Es = modulus of elasticity of reinforcement, psi
fc' = specified compressive strength of concrete, psi
fy = specified yield strength for non-prestressed reinforcement, psi
εt = net tensile strain in the extreme layer of longitudinal tension reinforcement at nominal strength, excluding strains due to effective prestress, creep, shrinkage, and temperature
εty = value of net tensile strain in the extreme layer of longitudinal tension reinforcement used to define a compression-controlled section
ϕ = strength reduction factor

Strength reduction factors ϕ used in the design are shown in ACI Table 21.2.1.

Section Design Force Classification

ϕ

Moment, axial force, or combined moment and axial force

0.65 to 0.90

Tension Controlled Moment and axial tension

0.90

Compression Controlled Moment and axial compression

0.65

Shear

0.75

Shear Seismic

0.60

Joint Shear

0.85

Torsion

0.75

Bearing

0.65

Strength Reduction Factor for Combined Moment and Axial Force

Strength reduction factor ϕ shown in section (a) of Table 21.2.1, for a moment, axial force, or combined moment and axial force, are given in ACI Table 21.2.2.

Strain, εt

Section Classification

ϕ

εtεty

Compression Controlled Moment

0.65

εty < εt < (εty + 0.003)

Transition region

0.65 + 0.25[(εt - εty)/0.003]

εt ≥ (εty + 0.003)

Compression Controlled Moment

0.90

For deformed reinforcement, εty is calculated by fy/Es.

The nominal strength of a reinforced concrete member subjected to the moment or combined moment and axial force is determined for the condition where the concrete strain in the extreme compression is equal to the assumed strain limit of 0.003. The net tensile strain εt is the tensile strain calculated in the extreme tension reinforcement at nominal strength, and it is determined from a linear distribution at nominal strength.

An upper ϕ-factor is used for tension-controlled sections than compression-controlled sections because tension-controlled sections have more ductility. Columns with spiral reinforcement are assigned a higher ϕ-factor than columns with other types of transverse reinforcement because spiral columns have greater ductility.

Strength Reduction Factor for Earthquake-Resistant Structures

The value of ϕ for shear is taken as described in ACI 21.2.4 for earthquake-resistant structures with elements in (a), (b), or (c):

(a) Special moment frames
(b) Special structural walls
(c) Intermediate precast structural walls in structures assigned to Seismic Design Category D, E, or F

It is stated in ACI 21.2.4.1 that the value of ϕ for shear will be 0.60 if the nominal shear strength of the reinforced concrete member is less than the shear corresponding to the development of the nominal moment strength of the member.

It is stated in ACI 21.2.4.4 that the value of ϕ for shear will be 0.85 for beam-column joints and diagonally reinforced coupling beams.