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# 21.2 Strength Reduction Factors for Structural Concrete Members and Connections

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Strength reduction factors

**ϕ**shall be in accordance with Table 21.2.1, except as modified by 21.2.2, 21.2.3, and 21.2.4.**Table 21.2.1—Strength reduction factors ϕ**

Action or structural element | ϕ | Exceptions | |
---|---|---|---|

(a) | Moment, axial force, or combined moment and axial force | 0.65 to 0.90 in accordance with 21.2.2 | Near ends of pretensioned members where strands are not fully developed, ϕ shall be in accordance with 21.2.3. |

(b) | Shear | 0.75 | Additional requirements are given in 21.2.4 for structures designed to resist earthquake effects. |

(c) | Torsion | 0.75 | — |

(d) | Bearing | 0.65 | — |

(e) | Post-tensioned anchorage zones | 0.85 | — |

(f) | Brackets and corbels | 0.75 | — |

(g) | Struts, ties, nodal zones, and bearing areas designed in accordance with strut-and-tie method in Chapter 23 | 0.75 | — |

(h) | Components of connections of precast members controlled by yielding of steel elements in tension | 0.90 | — |

(i) | Plain concrete elements | 0.60 | — |

(j) | Anchors in concrete elements | 0.45 to 0.75 in accordance with Chapter 17 | — |

Strength reduction factor for moment, axial force, or combined moment and axial force shall be in accordance with Table 21.2.2.

**Table 21.2.2—Strength reduction factor ϕ for moment, axial force, or combined moment and axial force**

Net tensile strain ε_{t} |
Classification | ϕ | |||
---|---|---|---|---|---|

Type of transverse reinforcement | |||||

Spirals conforming to 25.7.3 | Other | ||||

ε_{t} ≤ ε_{ty} |
Compression-controlled | 0.75 | (a) | 0.65 | (b) |

ε_{ty} < ε_{t} < 0.005 |
Transition^{[1]} |
(c) | (d) | ||

ε_{t} ≥ 0.005 |
Tension-controlled | 0.90 | (e) | 0.90 | (f) |

^{[1]}For sections classified as transition, it shall be permitted to use ϕ corresponding to compression-controlled sections. |

For deformed reinforcement,

**ε**shall be_{ty}**. For Grade 60 deformed reinforcement, it shall be permitted to take***f*/_{y}*E*_{s}**ε**equal to 0.002._{ty}For all prestressed reinforcement,

**ε**shall be taken as 0.002._{ty}For sections in pretensioned members where strand is not fully developed,

**ϕ**shall be calculated at each section in accordance with Table 21.2.3, where**is calculated using Eq. (21.2.3),***ℓ*_{tr}**is the debonded length at the end of the member,***ℓ*_{db}**is the effective stress in the prestressed reinforcement after allowance for all losses, and***f*_{se}**is given in 25.4.8.1.***ℓ*_{d}(21.2.3) |

**Table 21.2.3—Strength reduction factor ϕ for sections near the end of pretensioned members**

Condition near end of member | Stress in concrete under service load^{[1]} | Distance from end of member to section under consideration | ϕ | |
---|---|---|---|---|

All strands bonded | Not applicable | ≤ ℓ_{tr} | 0.75 | (a) |

ℓ to _{tr}ℓ_{d} | Linear interpolation from 0.75 to 0.90^{[2]} | (b) | ||

One or more strands debonded | No tension calculated | ≤ (ℓ+ _{db}ℓ)_{tr} | 0.75 | (c) |

(ℓ+ _{db}ℓ) to (_{tr}ℓ+ _{db}ℓ)_{d} | Linear interpolation from 0.75 to 0.90^{[2]} | (d) | ||

Tension calculated | ≤ (ℓ+ _{db}ℓ)_{tr} | 0.75 | (e) | |

(ℓ+ _{db}ℓ) to (_{tr}ℓ+ 2_{db}ℓ)_{d} | Linear interpolation from 0.75 to 0.90^{[2]} | (f) |

^{[1]}Stress calculated using gross cross-sectional properties in extreme concrete fiber of precompressed tension zone under service loads after allowance for all prestress losses at section under consideration.

^{[2]}It shall be permitted to use a strength reduction factor of 0.75.

For structures that rely on elements in (a), (b), or (c) to resist earthquake effects

**, the value of***E***ϕ**for shear shall be modified in accordance with 21.2.4.1 through 21.2.4.3:(c) Intermediate precast structural walls in structures assigned to Seismic Design Category D, E, or F

For any member designed to resist

**,***E***ϕ**for shear shall be 0.60 if the nominal shear strength of the member is less than the shear corresponding to the development of the nominal moment strength of the member. The nominal moment strength shall be calculated considering the most critical factored axial loads and including**.***E*For diaphragms,

**ϕ**for shear shall not exceed the least value of**ϕ**for shear used for the vertical components of the primary seismic-force-resisting system.### Related Code Sections

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is given in 25.4.8.1. (21.2.3) Table 21.2.3—

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