**designed using strut-and-tie models shall satisfy 16.5.2, 16.5.6, and Eq. (23.2.9).**

*a*/_{v}*d*< 2.0A ≥ 0.04(_{sc}f'/_{c}f)(_{y}b)_{w}d | (23.2.9) |

**ϕ**, including (a) through (c):

*S*≥_{n}*U*(a) Struts: **ϕ F_{ns} ≥ F_{us}**

(b) Ties: **ϕ F_{nt} ≥ F_{ut}**

(c) Nodal zones: **ϕ F_{nn} ≥ F_{us}**

**, shall be calculated by (a) or (b):**

*F*_{ns}(a) Strut without longitudinal reinforcement

F = _{ns}f_{ce}A_{cs} |
(23.4.1a) |

(b) Strut with longitudinal reinforcement

F = _{ns}f+ _{ce}A_{cs}A'_{s}f'_{s} |
(23.4.1b) |

where ** F_{ns}** shall be evaluated at each end of the strut and taken as the lesser value;

**is the cross-sectional area at the end of the strut under consideration;**

*A*_{cs}**is given in 23.4.3;**

*f*_{ce}**is the area of compression reinforcement along the length of the strut; and**

*A'*_{s}**is the stress in the compression reinforcement at the nominal axial strength of the strut. It shall be permitted to take**

*f'*_{s}**equal to**

*f'*_{s}**for Grade 40 or 60 reinforcement.**

*f*_{y}**, shall be calculated by:**

*f*_{ce}f = 0.85β_{ce}'_{s} f_{c} | (23.4.3) |

where **β _{s}**, in accordance with Table 23.4.3, accounts for the effect of cracking and crack-control reinforcement on the effective compressive strength of the concrete.

**Table 23.4.3—Strut coefficient β _{s}**

Strut geometry and location | Reinforcement crossing a strut | β_{s} | |
---|---|---|---|

Struts with uniform crosssectional area along length | NA | 1.0 | (a) |

Struts located in a region of a member where the width of the compressed concrete at midlength of the strut can spread laterally (bottle-shaped struts) | Satisfying 23.5 | 0.75 | (b) |

Not Satisfying 23.5 | 0.60λ | (c) | |

Struts located in tension members or the tension zones of members | NA | 0.40 | (d) |

All other cases | NA | 0.60λ | (e) |

**when calculating**

*f*_{ce}**.**

*F*_{ns}**β**, reinforcement to resist transverse tension resulting from spreading of the compressive force in the strut shall cross the strut axis. It shall be permitted to determine the transverse tension by assuming that the compressive force in a bottle-shaped strut spreads at a slope of 2 parallel to 1 perpendicular to the axis of the strut.

_{s}= 0.75**.**

*f*' ≤ 6000 psi_{c}(23.5.3) |

where ** A_{si}** is the total area of distributed reinforcement at spacing

**in the**

*s*_{i}*i*-th direction of reinforcement crossing a strut at an angle

**α**to the axis of a strut, and

_{i}**is the width of the strut.**

*b*_{s}**α**and

_{1}**α**to the axis of the strut, or in one direction at an angle

_{2}**α**to the axis of the strut. Where the reinforcement is placed in only one direction,

_{1}**α**shall be at least 40 degrees.

_{1}**at the face of the nodal zone, where**

*f'*_{s}**is calculated in accordance with 23.4.1.**

*f'*_{s}**, along the length of the strut shall not exceed the smallest of (a) through (c):**

*s*(a) Smallest dimension of cross section of strut

(b) **48 d_{b}** of bar or wire used for closed tie reinforcement

(c) **16 d_{b}** of compression reinforcement

**0.5**from the face of the nodal zone at each end of a strut.

*s***, shall be calculated by:**

*F*_{nt}F = _{nt}A+ _{ts} f_{y}A(_{tp}f+ Δ_{se}f)_{p} | (23.7.2) |

where **( f_{se} + Δf_{p})** shall not exceed

**, and**

*f*_{py}**is zero for nonprestressed members.**

*A*_{tp}**Δ**equal to 60,000 psi for bonded prestressed reinforcement and 10,000 psi for unbonded prestressed reinforcement. Higher values of

*f*_{p}**Δ**shall be permitted if justified by analysis.

*f*_{p}(a) The difference between the tie force on one side of a node and the tie force on the other side shall be developed within the nodal zone.

(b) At nodal zones anchoring one or more ties, the tie force in each direction shall be developed at the point where the centroid of the reinforcement in the tie leaves the extended nodal zone.

**, shall be calculated by:**

*F*_{nn}F = _{nn}f_{ce}A_{nz} | (23.9.1) |

where ** f_{ce}** is defined in 23.9.2 or 23.9.3 and

**is given in 23.9.4 or 23.9.5.**

*A*_{nz}**, shall be calculated by:**

*f*_{ce}f = 0.85β_{ce}'_{n} f_{c} | (23.9.2) |

where **β _{n}** shall be in accordance with Table 23.9.2.

**Table 23.9.2—Nodal zone coefficient β _{n}**

Configuration of nodal zone | β_{n} | |
---|---|---|

Nodal zone bounded by struts, bearing areas, or both | 1.0 | (a) |

Nodal zone anchoring one tie | 0.80 | (b) |

Nodal zone anchoring two or more ties | 0.60 | (c) |

**when calculating**

*f*_{ce}**.**

*F*_{nn}**, shall be taken as the smaller of (a) and (b):**

*A*_{nz}(a) Area of the face of the nodal zone perpendicular to the line of action of *F _{us}*

(b) Area of a section through the nodal zone perpendicular to the line of action of the resultant force on the section