# Strength Reduction Factors

Strength Reduction Factors are selected by user.

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

Strength reduction factors

**ϕ**are defined by default according to**ACI Table 21.2.1**and**Table 21.2.2**.

Strength Reduction Factor for combined moment and axial force is calculated automatically according to

**ACI Table 21.2.2**. The column capacity interaction volume is calculated by a series of discrete points that are generated on the three-dimensional interaction failure surface.

Shear strength reduction factor for Earthquake-Resistant Structures is determined automatically.

**Notation**

* E_{c }= *modulus of elasticity of concrete, psi

*modulus of elasticity of reinforcement, psi*

**E**_{s }=*specified compressive strength of concrete, psi*

**f**_{c}^{'}_{ }=*specified yield strength for nonprestressed reinforcement, psi*

**f**_{y }=*net tensile strain in extreme layer of longitudinal tension reinforcement at nominal strength, excluding strains due to effective prestress, creep, shrinkage, and temperature*

**ε**_{t }=*value of net tensile strain in the extreme layer of longitudinal tension reinforcement used to define a compression-controlled section*

**ε**_{ty }=**ϕ**

*strength reduction factor*

_{ }=Strength reduction factors **ϕ** used in design are shown in **ACI Table 21.2.1**.

**Strength Reduction Factor for Combined Moment and Axial Force**

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

For deformed reinforcement, * ε_{ty}* is calculated by

*/*

**f**_{y}*.*

**E**_{s}The nominal strength of a reinforced concrete member that is subjected to 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 * ε_{t}* is the tensile strain calculated in the extreme tension reinforcement at nominal strength and it is determined from a linear distribution at norminal strength.

An upper **ϕ**-factor is used for tension-controlled sections than for 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. For reinforced concrete sections within the transition region, the value of strength reduction factor ϕ is determined by linear interpolation, as shown in **ACI Figure R21.2.2b**.

**Strength Reduction Factor for Earthquake-Resistant Structures**

To resist earthquake effects, the value of **ϕ** for shear will be taken as described in **ACI 21.2.4**, for 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 **the value of **ϕ** for shear will be 0.85, for beam-column joints and diagonally reinforced coupling beams.

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