# 22.5 One-Way Shear Strength

**, shall be calculated by:**

*V*_{n}V = _{n}V+ _{c}V_{s} | (22.5.1.1) |

(22.5.1.2) |

*V*shall be calculated in accordance with 22.5.10.

_{s}**.**

*V*_{n}**.**

*V*_{c}**.**

*V*_{c}**and**

*V*_{c}**in prestressed members,**

*V*_{s}**shall be taken as the distance from the extreme compression fiber to the centroid of prestressed and any nonprestressed longitudinal reinforcement but need not be taken less than**

*d***0.8**.

*h***and**

*V*_{c}**in solid, circular sections,**

*V*_{s}**shall be permitted to be taken as 0.8 times the diameter, and**

*d***shall be permitted to be taken as the diameter.**

*b*_{w}**,**

*V*_{c}**, and**

*V*_{ci}**for one-way shear shall not exceed 100 psi, unless allowed in 22.5.3.2.**

*V*_{cw}**,**

*V*_{c}**, and**

*V*_{ci}**for reinforced or prestressed concrete beams and concrete joist construction having minimum web reinforcement in accordance with 9.6.3.3 or 9.6.4.2.**

*V*_{cw}**for composite members, no distinction shall be made between shored and unshored members.**

*V*_{n}**for composite members where the specified concrete compressive strength, unit weight, or other properties of different elements vary, properties of the individual elements shall be used in design. Alternatively, it shall be permitted to use the properties of the element that results in the most critical value of**

*V*_{n}**.**

*V*_{n}**assuming a monolithically cast member of the same crosssectional shape.**

*V*_{c}**assuming a monolithically cast member of the same crosssectional shape if shear reinforcement is fully anchored into the interconnected elements in accordance with 25.7.**

*V*_{s}**shall be calculated by:**

*V*_{c}(22.5.5.1) |

unless a more detailed calculation is made in accordance with Table 22.5.5.1.

**Table 22.5.5.1—Detailed method for calculating V_{c}**

V_{c} | ||
---|---|---|

Least of (a), (b), and (c): | ^{[1]} | (a) |

(b) | ||

(c) |

^{[1]}*M _{u}* occurs simultaneously with

*V*at the section considered.

_{u}**shall be calculated by:**

*V*_{c}(22.5.6.1) |

unless a more detailed calculation is made in accordance with Table 22.5.6.1, where ** N_{u}** is positive for compression.

**Table 22.5.6.1—Detailed method for calculating V_{c} for nonprestressed members with axial compression**

V_{c} | ||
---|---|---|

Lesser of (a) and (b): | ^{[1]}Equation not applicable if | (a) |

(b) |

^{[1]}*M _{u}* occurs simultaneously with

*V*at the section considered.

_{u}**shall be calculated by:**

*V*_{c}(22.5.7.1) |

where ** N_{u}** is negative for tension, and

**shall not be less than zero.**

*V*_{c}**for post-tensioned and pretensioned members in regions where the effective force in the prestressed reinforcement is fully transferred to the concrete. For regions of pretensioned members where the effective force in the prestressed reinforcement is not fully transferred to the concrete, 22.5.9 shall govern the calculation of**

*V*_{c}**.**

*V*_{c}**,**

*A*≥ 0.4(_{ps}f_{se}*A*+_{ps}f_{pu}*A*)_{s}f_{y}**shall be calculated in accordance with Table 22.5.8.2, but need not be less than the value calculated by Eq. (22.5.5.1). Alternatively, it shall be permitted to calculate**

*V*_{c}**in accordance with 22.5.8.3.**

*V*_{c}**Table 22.5.8.2—Approximate method for calculating V_{c}**

V_{c} |
||
---|---|---|

Least of (a), (b), and (c): | ^{[1]} |
(a) |

(b) | ||

(c) |

^{[1]}*M _{u}* occurs simultaneously with

*V*at the section considered.

_{u}**shall be permitted to be the lesser of**

*V*_{c}**calculated in accordance with 22.5.8.3.1 and**

*V*_{ci}**calculated in accordance with 22.5.8.3.2 or 22.5.8.3.3.**

*V*_{cw}**shall be the greater of (a) and (b):**

*V*_{ci}(a) | (22.5.8.3.1a) |

(b) | (22.5.8.3.1b) |

where ** d_{p}** need not be taken less than

**0.80**, the values of

*h***and**

*M*_{max}**shall be calculated from the load combinations causing maximum factored moment to occur at section considered, and**

*V*_{i}**shall be calculated by:**

*M*_{cre}(22.5.8.3.1c) |

**shall be calculated by:**

*V*_{cw}(22.5.8.3.2) |

where ** d_{p}** need not be taken less than

**0.80**, and

*h***is the vertical component of the effective prestress.**

*V*_{p}**as the shear force corresponding to dead load plus live load that results in a principal tensile stress of at location (a) or (b):**

*V*_{cw}(a) Where the centroidal axis of the prestressed cross section is in the web, the principal tensile stress shall be calculated at the centroidal axis.

(b) Where the centroidal axis of the prestressed cross section is in the flange, the principal tensile stress shall be calculated at the intersection of the flange and the web.

**, the transfer length of prestressed reinforcement,**

*V*_{c}**, shall be assumed to be**

*ℓ*_{tr}**50**for strand and

*d*_{b}**100**for wire.

*d*_{b}**from the end of the prestressed reinforcement.**

*ℓ*_{tr}**shall be calculated in accordance with (a) through (c):**

*V*_{c}(a) The reduced effective prestress force shall be used to determine the applicability of 22.5.8.2.

(b) The reduced effective prestress force shall be used to calculate ** V_{cw}** in 22.5.8.3.

(c) The value of ** V_{c}** calculated using 22.5.8.2 shall not exceed the value of

**calculated using the reduced effective prestress force.**

*V*_{cw}**from that point.**

*ℓ*_{tr}**shall be calculated in accordance with (a) through (c):**

*V*_{c}(a) The reduced effective prestress force shall be used to determine the applicability of 22.5.8.2.

(b) The reduced effective prestress force shall be used to calculate ** V_{c}** in accordance with 22.5.8.3.

(c) The value of ** V_{c}** calculated using 22.5.8.2 shall not exceed the value of

**calculated using the reduced effective prestress force.**

*V*_{cw}**, transverse reinforcement shall be provided such that Eq. (22.5.10.1) is satisfied.**

*V*> ϕ_{u}*V*_{c}(22.5.10.1) |

**shall be calculated in accordance with 22.5.10.5.**

*V*_{s}**shall be calculated in accordance with 22.5.10.6.**

*V*_{s}**shall be the sum of the**

*V*_{s}**values for the various types of shear reinforcement.**

*V*_{s}(a) Stirrups, ties, or hoops perpendicular to longitudinal axis of member

(b) Welded wire reinforcement with wires located perpendicular to longitudinal axis of member

*V*for shear reinforcement in 22.5.10.5.1 shall be calculated by:

_{s}(22.5.10.5.3) |

where ** s** is the spiral pitch or the longitudinal spacing of the shear reinforcement, and

**is given in 22.5.10.5.5 or 22.5.10.5.6.**

*A*_{v}*V*for shear reinforcement in 22.5.10.5.2 shall be calculated by:

_{s}(22.5.10.5.4) |

where **α** is the angle between the inclined stirrups and the longitudinal axis of the member, ** s** is measured parallel to the longitudinal reinforcement, and

**is given in 22.5.10.5.5.**

*A*_{v}**shall be two times the area of the bar or wire within spacing**

*A*_{v}**.**

*s***, all bent the same distance from the support,**

*A*_{v}**shall be the lesser of (a) and (b):**

*V*_{s}(a) V = _{s}Asinα_{v}f_{y} | (22.5.10.6.2a) |

(b) | (22.5.10.6.2b) |

where **α** is the angle between bent-up reinforcement and longitudinal axis of the member.

**shall be calculated by Eq. (22.5.10.5.4).**

*V*_{s}### Related Code Sections

*one*-

*way*

*shear*

*strength*at a section, V n , shall be calculated by: V n = V c + V s (22.5.1.1 ...

*One-Way Shear Reinforcement*> 22.5.10.5

*One-Way Shear Strength Provided by Transverse Reinforcement*> 22.5.10.5.6

*shear*reinforcement in nonprestressed ...

*One-Way Shear Reinforcement*> 22.5.10.6

*One-Way Shear Strength Provided by Bent-Up Longitudinal Bars*> 22.5.10.6.1

*shear*reinforcement consists of a single bar or a single group of parallel bars having an area A v , all bent the same distance from ...

*One-Way Shear Reinforcement*> 22.5.10.6

*One-Way Shear Strength Provided by Bent-Up Longitudinal Bars*> 22.5.10.6.2

*shear*reinforcement consists of a series of parallel bent-up bars or groups of parallel bent-up bars at different distances from the support, V ...

*One-Way Shear Reinforcement*> 22.5.10.6

*One-Way Shear Strength Provided by Bent-Up Longitudinal Bars*> 22.5.10.6.3