# 18.7 Columns of Special Moment Frames

(a) The shortest cross-sectional dimension, measured on a straight line passing through the geometric centroid, shall be at least 12 in.

(b) The ratio of the shortest cross-sectional dimension to the perpendicular dimension shall be at least 0.4.

∑ M≥ (6/5)∑_{nc}M_{nb} | (18.7.3.2) |

where

**∑ M_{nc}** is sum of nominal flexural strengths of columns framing into the joint, evaluated at the faces of the joint. Column flexural strength shall be calculated for the factored axial force, consistent with the direction of the lateral forces considered, resulting in the lowest flexural strength.

**∑ M_{nb}** is sum of nominal flexural strengths of the beams framing into the joint, evaluated at the faces of the joint. In T-beam construction, where the slab is in tension under moments at the face of the joint, slab reinforcement within an effective slab width defined in accordance with 6.3.2 shall be assumed to contribute to

**if the slab reinforcement is developed at the critical section for flexure.**

*M*_{nb}Flexural strengths shall be summed such that the column moments oppose the beam moments. Equation (18.7.3.2) shall be satisfied for beam moments acting in both directions in the vertical plane of the frame considered.

**, shall be at least**

*A*_{st}**0.01**and shall not exceed

*A*_{g}**0.06**.

*A*_{g}**from each joint face and on both sides of any section where flexural yielding is likely to occur as a result of lateral displacements beyond the elastic range of behavior. Length**

*ℓ*_{o}**shall be at least the greatest of (a) through (c):**

*ℓ*_{o}(a) The depth of the column at the joint face or at the section where flexural yielding is likely to occur

(b) One-sixth of the clear span of the column

(c) 18 in.

(a) Transverse reinforcement shall comprise either single or overlapping spirals, circular hoops, or rectilinear hoops with or without crossties.

(b) Bends of rectilinear hoops and crossties shall engage peripheral longitudinal reinforcing bars.

(c) Crossties of the same or smaller bar size as the hoops shall be permitted, subject to the limitation of 25.7.2.2. Consecutive crossties shall be alternated end for end along the longitudinal reinforcement and around the perimeter of the cross section.

(d) Where rectilinear hoops or crossties are used, they shall provide lateral support to longitudinal reinforcement in accordance with 25.7.2.2 and 25.7.2.3.

(e) Reinforcement shall be arranged such that the spacing ** h_{x}** of longitudinal bars laterally supported by the corner of a crosstie or hoop leg shall not exceed 14 in. around the perimeter of the column.

(f) Where ** P_{u} > 0.3A_{g}f'_{c}** or

**in columns with rectilinear hoops, every longitudinal bar or bundle of bars around the perimeter of the column core shall have lateral support provided by the corner of a hoop or by a seismic hook, and the value of**

*f'*> 10,000 psi_{c}**shall not exceed 8 in.**

*h*_{x}**shall be the largest value in compression consistent with factored load combinations including**

*P*_{u}**.**

*E*(a) One-fourth of the minimum column dimension

(b) Six times the diameter of the smallest longitudinal bar

(c) ** s_{o}**, as calculated by:

(18.7.5.3) |

The value of ** s_{o}** from Eq. (18.7.5.3) shall not exceed 6 in. and need not be taken less than 4 in.

The concrete strength factor ** k_{f}** and confinement effectiveness factor

**are calculated according to Eq. (18.7.5.4a) and (18.7.5.4b).**

*k*_{n}(a) | (18.7.5.4a) |

(b) | (18.7.5.4b) |

where ** n_{l}** is the number of longitudinal bars or bar bundles around the perimeter of a column core with rectilinear hoops that are laterally supported by the corner of hoops or by seismic hooks.

**Table 18.7.5.4—Transverse reinforcement for columns of special moment frames**

Transverse reinforcement | Conditions | Applicable expressions | |
---|---|---|---|

A/_{sh}sb for rectilinear hoop_{c} | P ≤ 0.3_{u}A' and _{g}f_{c}f' ≤ 10,000 psi_{c} | Greater of (a) and (b) | |

P > 0.3_{u}A' or _{g}f_{c}f' > 10,000 psi_{c} | Greatest of (a), (b), and (c) | ||

ρ_{s} for spiral or circular hoop | P ≤ 0.3_{u}A' and _{g}f_{c}f' ≤ 10,000 psi_{c} | Greater of (d) and (e) | |

P > 0.3_{u}A' or _{g}f_{c}f' > 10,000 psi_{c} | Greatest of (d), (e), and (f) |

**given in 18.7.5.1, the column shall contain spiral or hoop reinforcement satisfying 25.7.2 through 25.7.4 with spacing**

*ℓ*_{o}**not exceeding the lesser of six times the diameter of the smallest longitudinal column bars and 6 in., unless a greater amount of transverse reinforcement is required by 18.7.4.3 or 18.7.6.**

*s*(a) Transverse reinforcement required by 18.7.5.2 through 18.7.5.4 shall be provided over the full height at all levels beneath the discontinuity if the factored axial compressive force in these columns, related to earthquake effect, exceeds ** A_{g}f_{c}'/10**. Where design forces have been magnified to account for the overstrength of the vertical elements of the seismic-force-resisting system, the limit of

**shall be increased to**

*A*'/10_{g}f_{c}**.**

*A*'/4_{g}f_{c}(b) Transverse reinforcement shall extend into the discontinued member at least ** ℓ_{d}** of the largest longitudinal column bar, where

**is in accordance with 18.8.5. Where the lower end of the column terminates on a wall, the required transverse reinforcement shall extend into the wall at least**

*ℓ*_{d}**of the largest longitudinal column bar at the point of termination. Where the column terminates on a footing or mat, the required transverse reinforcement shall extend at least 12 in. into the footing or mat.**

*ℓ*_{d}**shall be calculated from considering the maximum forces that can be generated at the faces of the joints at each end of the column. These joint forces shall be calculated using the maximum probable flexural strengths,**

*V*_{e}**, at each end of the column associated with the range of factored axial forces,**

*M*_{pr}**, acting on the column. The column shears need not exceed those calculated from joint strengths based on**

*P*_{u}**of the beams framing into the joint. In no case shall**

*M*_{pr}**be less than the factored shear calculated by analysis of the structure.**

*V*_{e}**, given in 18.7.5.1, shall be designed to resist shear assuming**

*ℓ*_{o}**when both (a) and (b) occur:**

*V*= 0_{c}(a) The earthquake-induced shear force, calculated in accordance with 18.7.6.1, is at least one-half of the maximum required shear strength within ** ℓ_{o}**.

(b) The factored axial compressive force ** P_{u}** including earthquake effects is less than

**.**

*A*'/20_{g}f_{c}### Related Code Sections

*columns*of

*special*

*moment*

*frames*that form part of the seismic-force-resisting system and are proportioned primarily ...

*Longitudinal Reinforcement*

*columns*with circular hoops, there shall be at least six longitudinal bars ...

*Longitudinal Reinforcement*

*columns*of

*special*

*moment*

*frames*that form part of the seismic-force-resisting system and are proportioned primarily ...

*Scope*> 18.7.1.1

*Columns*supporting reactions from discontinued stiff members, such as walls, shall satisfy (a) and (b): (a) Transverse reinforcement required ...

*Transverse Reinforcement*> 18.7.5.6

*Design Forces*

*column*. These joint forces shall be calculated using the maximum probable flexural strengths, M pr , at each end of the

*column*associated ...

*Shear Strength*> 18.7.6.1

*Design Forces*