(a) Direct design method in 8.10

(b) Equivalent frame method in 8.11

(a) For columns not braced against sidesway

(6.2.5a) |

(b) For columns braced against sidesway

(6.2.5b) |

and

(6.2.5c) |

where ** M_{1}**/

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

*M*_{2}If bracing elements resisting lateral movement of a story have a total stiffness of at least 12 times the gross lateral stiffness of the columns in the direction considered, it shall be permitted to consider columns within the story to be braced against sidesway.

**, shall not be taken greater than:**

*r*(6.2.5.2) |

Longitudinal bars located within a concrete core encased by structural steel or within transverse reinforcement surrounding a structural steel core shall be permitted to be used in calculating ** A_{sx}** and

**.**

*I*_{sx}**including second-order effects shall not exceed**

*M*_{u}**1.4**due to first-order effects.

*M*_{u}**shall include the beam web width**

*b*_{f}**plus an effective overhanging flange width in accordance with Table 6.3.2.1, where**

*b*_{w}**is the slab thickness and**

*h***is the clear distance to the adjacent web.**

*s*_{w}**Table 6.3.2.1—Dimensional limits for effective overhanging flange width for T-beams**

Flange location | Effective overhanging flange width, beyond face of web | |
---|---|---|

Each side of web | Least of: | 8h |

s/2_{w} | ||

ℓ/8_{n} | ||

One side of web | Least of: | 6h |

s/2_{w} | ||

ℓ/12_{n} |

**0.5**and an effective flange width less than or equal to

*b*_{w}**4**.

*b*_{w}(a) Maximum positive ** M_{u}** near midspan occurs with factored

**on the span and on alternate spans**

*L*(b) Maximum negative ** M_{u}** at a support occurs with factored

**on adjacent spans only**

*L***is known, the slab system shall be analyzed for that arrangement.**

*L***is variable and does not exceed**

*L***0.75**, or the nature of

*D***is such that all panels will be loaded simultaneously, it shall be permitted to assume that maximum**

*L***at all sections occurs with factored**

*M*_{u}**applied simultaneously to all panels.**

*L*(a) Maximum positive ** M_{u}** near midspan of panel occurs with 75 percent of factored

**on the panel and alternate panels**

*L*(b) Maximum negative ** M_{u}** at a support occurs with 75 percent of factored

**on adjacent panels only**

*L***and**

*M*_{u}**due to gravity loads in accordance with this section for continuous beams and one-way slabs satisfying (a) through (e):**

*V*_{u}(a) Members are prismatic

(b) Loads are uniformly distributed

(c) *L* ≤ 3*D*

(d) There are at least two spans

(e) The longer of two adjacent spans does not exceed the shorter by more than 20 percent

*M*due to gravity loads shall be calculated in accordance with Table 6.5.2.

_{u}**Table 6.5.2—Approximate moments for nonprestressed continuous beams and one-way slabs**

Moment | Location | Condition | M_{u} |
---|---|---|---|

Positive | End span | Discontinuous end integral with support | w_{u}ℓ_{n}^{2}/14 |

Discontinuous end unrestrained | w_{u}ℓ_{n}^{2}/11 | ||

Interior spans | All | w_{u}ℓ_{n}^{2}/16 | |

Negative^{[1]} | Interior face of exterior support | Member built integrally with supporting spandrel beam | w_{u}ℓ_{n}^{2}/24 |

Member built integrally with supporting column | w_{u}ℓ_{n}^{2}/16 | ||

Exterior face of first interior support | Two spans | w_{u}ℓ_{n}^{2}/9 | |

More than two spans | w_{u}ℓ_{n}^{2}/10 | ||

Face of other supports | All | w_{u}ℓ_{n}^{2}/11 | |

Face of all supports satisfying(a) or (b) | (a) slabs with spans not exceeding 10 ft (b) beams where ratio of sum of column stiffnesses to beam stiffness exceeds 8 at each end of span | w_{u}ℓ_{n}^{2}/12 |

^{[1]}To calculate negative moments, *ℓ _{n}* shall be the average of the adjacent clear span lengths.

*V*due to gravity loads shall be calculated in accordance with Table 6.5.4.

_{u}**Table 6.5.4—Approximate shears for nonprestressed continuous beams and one-way slabs**

Location | V_{u} |
---|---|

Exterior face of first interior support | 1.15w/2_{u}ℓ_{n} |

Face of all other supports | w/2_{u}ℓ_{n} |

(a) Solid slabs or one-way joist systems built integrally with supports, with clear spans not more than 10 ft, shall be permitted to be analyzed as continuous members on knife-edge supports with spans equal to the clear spans of the member and width of support beams otherwise neglected.

(b) For frames or continuous construction, it shall be permitted to assume the intersecting member regions are rigid.

**for columns and walls shall be divided by (**

*I***1 + β**), where

_{ds}**β**is the ratio of maximum factored sustained shear within a story to the maximum factored shear in that story associated with the same load combination.

_{ds}**Table 6.6.3.1.1(a)—Moment of inertia and crosssectional area permitted for elastic analysis at factored load level**

Member and condition | Moment of Inertia | Cross-sectional area | |
---|---|---|---|

Columns | 0.70I_{g} | 1.0A_{g} | |

Walls | Uncracked | 0.70I_{g} | |

Cracked | 0.35I_{g} | ||

Beams | 0.35I_{g} | ||

Flat plates and flat slabs | 0.25I_{g} |

**Table 6.6.3.1.1(b)—Alternative moments of inertia for elastic analysis at factored load**

Member | Alternative value of I for elastic analysis | ||
---|---|---|---|

Minimum | I | Maximum | |

Columns and walls | 0.35I_{g} | 0.875I_{g} | |

Beams, flat plates, and flat slabs | 0.25I_{g} | 0.5I_{g} |

Notes: For continuous flexural members, *I* shall be permitted to be taken as the average of values obtained for the critical positive and negative moment sections. *P _{u}* and

*M*shall be calculated from the load combination under consideration, or the combination of

_{u}*P*and

_{u}*M*that produces the least value of

_{u}*I*.

**for all members or to calculate**

*I*= 0.5*I*_{g}**by a more detailed analysis, considering the reduced stiffness of all members under the loading conditions.**

*I***for slab members shall be defined by a model that is in substantial agreement with results of comprehensive tests and analysis and**

*I***of other frame members shall be in accordance with 6.6.3.1.1 and 6.6.3.1.2.**

*I***defined in 6.6.3.1, or using a more detailed analysis, but the value shall not exceed**

*I***.**

*I*_{g}**, 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}(a) Flexural members are continuous

(b) **ε _{t} ≥ 0.0075** at the section at which moment is reduced

**1000ε**percent and 20 percent.

_{t}**given in 6.6.3.1, or calculated using a more detailed analysis, but the value shall not exceed**

*I***.**

*I*_{g}