# 6.6.4 *Slenderness Effects, Moment Magnification Method*

**, shall be calculated by:**

*Q*(6.6.4.4.1) |

where **∑ P_{u}** and

**are the total factored vertical load and horizontal story shear, respectively, in the story being evaluated, and**

*V*_{us}**Δ**is the first-order relative lateral deflection between the top and the bottom of that story due to

_{o}**.**

*V*_{us}**(**shall be calculated in accordance with (a), (b), or (c):

*EI*)_{eff}(a) | (6.6.4.4.4a) |

(b) | (6.6.4.4.4b) |

(c) | (6.6.4.4.4c) |

where **β _{dns}** shall be the ratio of maximum factored sustained axial load to maximum factored axial load associated with the same load combination and

**in Eq. (6.6.4.4.4c) is calculated according to Table 6.6.3.1.1(b) for columns and walls.**

*I***δ**shall be calculated by:

(6.6.4.5.2) |

*C*shall be in accordance with (a) or (b):

_{m}(a) For columns without transverse loads applied between supports

(6.6.4.5.3a) |

where ** M_{1}**/

**is negative if the column is bent in single curvature, and positive if bent in double curvature.**

*M*_{2}**corresponds to the end moment with the lesser absolute value.**

*M*_{1}(b) For columns with transverse loads applied between supports.

C = 1.0_{m} |
(6.6.4.5.3b) |

*M*

_{2}in Eq. (6.6.4.5.1) shall be at least

**calculated according to Eq. (6.6.4.5.4) about each axis separately.**

*M*_{2,min}M_{2,min} = P(0.6 + 0.03_{u}h) |
(6.6.4.5.4) |

If ** M_{2,min}** exceeds

**,**

*M*_{2}**shall be taken equal to 1.0 or calculated based on the ratio of the calculated end moments**

*C*_{m}**/**

*M*_{1}**, using Eq. (6.6.4.5.3a).**

*M*_{2}*Moment magnification method: Sway frames*

**and**

*M*_{1}**at the ends of an individual column shall be calculated by (a) and (b).**

*M*_{2}(a) M_{1} = M_{1ns}+ δ_{s}M_{1s} | (6.6.4.6.1a) |

(b) M_{2} = M_{2ns}+ δ_{s}M_{2s} | (6.6.4.6.1b) |

**δ**shall be calculated by (a), (b), or (c). If

_{s}**δ**exceeds 1.5, only (b) or (c) shall be permitted:

_{s}(a) | (6.6.4.6.2a) |

(b) | (6.6.4.6.2b) |

(c) Second-order elastic analysis |

where **∑ P_{u}** is the summation of all the factored vertical loads in a story and

**∑**is the summation for all sway-resisting columns in a story.

*P*_{c}**is calculated using Eq. (6.6.4.4.2) with**

*P*_{c}*k*determined for sway members from 6.6.4.4.3 and

**(**from 6.6.4.4.4 or 6.6.4.4.5 as appropriate with

*EI*)_{eff}**β**substituted for

_{ds}**β**.

_{dns}### Related Code Sections

*Slenderness Effects, Moment Magnification Method*

*Moment*

*magnification*

*method*...

*Slenderness Effects, Moment Magnification Method*

*Moments*M 1 and M 2 at the ends of an individual column shall be calculated by (a) and (b). (a) M 1 = M 1 ns + δ s M 1 s ...

*Slenderness Effects, Moment Magnification Method*> 6.6.4.6 > 6.6.4.6.1

*Slenderness Effects, Moment Magnification Method*> 6.6.4.1

*Slenderness Effects, Moment Magnification Method*> 6.6.4.2

*Stability Properties*

*effective*length factor k shall be calculated using E c in accordance with 19.2.2 and I ...

*Slenderness Effects, Moment Magnification Method*> 6.6.4.4

*Stability Properties*