This chapter shall apply to the design of nonprestressed and prestressed walls including (a) through (c):

(a) Cast-in-place

(b) Precast in-plant

(c) Precast on-site including tilt-up

Design of special structural walls shall be in accordance with Chapter 18.

Design of cantilever retaining walls shall be in accordance with 22.2 through 22.4, with minimum horizontal reinforcement in accordance with 11.6.

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Design properties for concrete shall be selected to be in accordance with Chapter 19.

Design properties for steel reinforcement shall be selected to be in accordance with Chapter 20.

Materials, design, and detailing requirements for embedments in concrete shall be in accordance with 20.7.

Unless otherwise demonstrated by an analysis, the horizontal length of wall considered as effective for resisting each concentrated load shall not exceed the lesser of the center-to-center distance between loads, and the bearing width plus four times the wall thickness. Effective horizontal length for bearing shall not extend beyond vertical wall joints unless design provides for transfer of forces across the joints.

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Minimum wall thicknesses shall be in accordance with Table 11.3.1.1. Thinner walls are permitted if adequate strength and stability can be demonstrated by structural analysis.

**Table 11.3.1.1—Minimum wall thickness**

*h*Wall type | Minimum thickness h |
||
---|---|---|---|

Bearing^{[1]} |
Greater of: | 4 in. | (a) |

^{1}/_{25} the lesser of unsupported length and unsupported height |
(b) | ||

Nonbearing | Greater of: | 4 in. | (c) |

^{1}/_{30} the lesser of unsupported length and unsupported height |
(d) | ||

Exterior basement and foundation^{[1]} |
7.5 in. | (e) |

Required strength shall be calculated in accordance with the factored load combinations in Chapter 5.

Required strength shall be calculated in accordance with the analysis procedures in Chapter 6.

Walls shall be designed for the maximum factored moment

**that can accompany the factored axial force for each applicable load combination. The factored axial force***M*_{u}**at given eccentricity shall not exceed***P*_{u}**ϕ**, where*P*_{n,max}**shall be as given in 22.4.2.1 and strength reduction factor***P*_{n,max}**ϕ**shall be that for compression-controlled sections in 21.2.2. The maximum factored moment**shall be magnified for slenderness effects in accordance with 6.6.4, 6.7, or 6.8.***M*_{u}For each applicable factored load combination, design strength at all sections shall satisfy

**ϕ**, including (a) through (c). Interaction between axial load and moment shall be considered.*S*≥_{n}*U*(a)

**ϕ***P*≥_{n}*P*_{u}(b)

**ϕ***M*≥_{n}*M*_{u}(c)

**ϕ***V*≥_{n}*V*_{u}If the resultant of all factored loads is located within the middle third of the thickness of a solid wall with a rectangular cross section,

**shall be permitted to be calculated by:***P*_{n}(11.5.3.1) |

Effective length factor

**for use with Eq. (11.5.3.1) shall be in accordance with Table 11.5.3.2.***k***Table 11.5.3.2—Effective length factor**

*k*for wallsBoundary conditions | k |
---|---|

Walls braced top and bottom against lateral translation and: | |

(a) Restrained against rotation at one or both ends (top, bottom, or both) | 0.8 |

(b) Unrestrained against rotation at both ends | 1.0 |

Walls not braced against lateral translation | 2.0 |

Wall reinforcement shall be at least that required by 11.6.

*V*shall be calculated in accordance with 11.5.4.2 through 11.5.4.8. Alternatively, for walls with

_{n}**, it shall be permitted to design for in-plane shear in accordance with the strut-and-tie method of Chapter 23. In all cases, reinforcement shall satisfy the limits of 11.6, 11.7.2, and 11.7.3.**

*h*≤ 2_{w}*ℓ*_{w}For in-plane shear design,

**is thickness of wall and***h***shall be taken equal to***d***0.8**. A larger value of*ℓ*_{w}**, equal to the distance from extreme compression fiber to center of force of all reinforcement in tension, shall be permitted if the center of tension is calculated by a strain compatibility analysis.***d**V*at any horizontal section shall not exceed .

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

_{n}V = _{n}V+ _{c}V_{s} | (11.5.4.4) |

It shall be permitted to calculate

**in accordance with Table 11.5.4.6, where***V*_{c}**is positive for compression and negative for tension, and the quantity***N*_{u}**is expressed in psi.***N*/_{u}*A*_{g}**Table 11.5.4.6—**

*V*_{c}: nonprestressed and prestressed wallsCalculation option | Axial force | V_{c} |
||
---|---|---|---|---|

Simplified | Compression | (a) | ||

Tension | Greater of: | (b) | ||

0 | (c) | |||

Detailed | Tension or compression | Lesser of: | (d) | |

Equation shall not apply if ( M/_{u}V— _{u}ℓ/2) is negative._{w} |
(e) |

Sections located closer to wall base than a distance

**or one-half the wall height, whichever is less, shall be permitted to be designed for***ℓ*/2_{w}**calculated using the detailed calculation options in Table 11.5.4.6 at a distance above the base of***V*_{c}**or one-half the wall height, whichever is less.***ℓ*/2_{w}If in-plane

**, minimum***V*≤ 0.5ϕ_{u}*V*_{c}**ρ**and minimum_{ℓ}**ρ**shall be in accordance with Table 11.6.1. These limits need not be satisfied if adequate strength and stability can be demonstrated by structural analysis._{t}**Table 11.6.1—Minimum reinforcement for walls with in-plane**≤

*V*_{u}**0.5**

_{ϕ}*V*_{c}Wall type | Type of nonprestressed reinforcement | Bar/wire size | f, psi_{y} |
Minimum longitudinal^{[1]}, ρ_{ℓ} |
Minimum transverse, ρ_{t} |
---|---|---|---|---|---|

Cast-in-place | Deformed bars | ≤ No. 5 | ≥ 60,000 | 0.0012 | 0.0020 |

< 60,000 | 0.0015 | 0.0025 | |||

> No. 5 |
Any | 0.0015 | 0.0025 | ||

Welded-wire reinforcement | ≤ W31 or D31 | Any | 0.0012 | 0.0020 | |

Precast^{[2]} |
Deformed bars or welded-wire reinforcement | Any | Any | 0.0010 | 0.0010 |

^{[1]}Prestressed walls with an average effective compressive stress of at least 225 psi need not meet the requirement for minimum longitudinal reinforcement ρ

_{ℓ}.

^{[2]}In one-way precast, prestressed walls not wider than 12 ft and not mechanically connected to cause restraint in the transverse direction, the minimum reinforcement requirement in the direction normal to the flexural reinforcement need not be satisfied.

If in-plane

**, (a) and (b) shall be satisfied:***V*≥ 0.5ϕ_{u}*V*_{c}(a)

**ρ**shall be at least the greater of the value calculated by Eq. (11.6.2) and 0.0025, but need not exceed_{ℓ}**ρ**required by 11.5.4.8._{t}ρ _{ℓ} ≥ 0.0025 + 0.5(2.5 — h_{w}/ℓ)(ρ_{w}_{t} — 0.0025) |
(11.6.2) |

(b)

**ρ**shall be at least 0.0025_{t}Upcodes Diagrams

Spacing

**of longitudinal bars in cast-in-place walls shall not exceed the lesser of***s***3**and 18 in. If shear reinforcement is required for in-plane strength, spacing of longitudinal reinforcement shall not exceed*h***.***ℓ*/3_{w}Spacing

**of longitudinal bars in precast walls shall not exceed the lesser of (a) and (b):***s*(a)

**5***h*If shear reinforcement is required for in-plane strength,

**shall not exceed the smallest of***s***3**, 18 in., and*h***.***ℓ*/3_{w}For walls with

**greater than 10 in., except basement walls and cantilever retaining walls, distributed reinforcement for each direction shall be placed in two layers parallel with wall faces in accordance with (a) and (b):***h*(a) One layer consisting of at least one-half and not exceeding two-thirds of total reinforcement required for each direction shall be placed at least 2 in., but not exceeding

**, from the exterior surface.***h*/3(b) The other layer consisting of the balance of required reinforcement in that direction, shall be placed at least

^{3}/_{4}in., but not greater than**from the interior surface.***h*/3,Flexural tension reinforcement shall be well distributed and placed as close as practicable to the tension face.

Spacing

**of transverse reinforcement in cast-in-place walls shall not exceed the lesser of***s***3**and 18 in. If shear reinforcement is required for in-plane strength,*h***shall not exceed***s***.***ℓ*/5_{w}If longitudinal reinforcement is required for compression and if

**exceeds***A*_{st}**0.01**, longitudinal reinforcement shall be laterally supported by transverse ties.*A*_{g}Upcodes Diagrams

In addition to the minimum reinforcement required by 11.6, at least two No. 5 bars in walls having two layers of reinforcement in both directions and one No. 5 bar in walls having a single layer of reinforcement in both directions shall be provided around window, door, and similarly sized openings. Such bars shall be anchored to develop

**in tension at the corners of the openings.***f*_{y}It shall be permitted to analyze out-of-plane slenderness effects in accordance with this section for walls satisfying (a) through (e):

(a) Cross section is constant over the height of the wall

(b) Wall is tension-controlled for out-of-plane moment effect

(d)

**at the midheight section does not exceed***P*_{u}**0.06***f'*_{c}*A*_{g}(e) Calculated out-of-plane deflection due to service loads,

**Δ**, including_{s}**effects, does not exceed***P*Δ*ℓ*/150_{c}*M*at midheight of wall due to combined flexure and axial loads shall include the effects of wall deflection in accordance with (a) or (b):

_{u}(a) By iterative calculation using

M = _{u}M+ _{ua}PΔ_{u}_{u} | (11.8.3.1a) |

where

**is the maximum factored moment at midheight of wall due to lateral and eccentric vertical loads, not including***M*_{ua}**effects.***P*Δ**Δ**shall be calculated by:

_{u}(11.8.3.1b) |

where

**shall be calculated by:***I*_{cr}(11.8.3.1c) |

and the value of

**shall be at least 6.***E*/_{s}*E*_{c}(b) By direct calculation using:

(11.8.3.1d) |

Out-of-plane deflection due to service loads,

**Δ**, shall be calculated in accordance with Table 11.8.4.1, where_{s}**is calculated by 11.8.4.2.***M*_{a}**Table 11.8.4.1—Calculation of**Δ

_{s}

M_{a} | Δ_{s} | |
---|---|---|

≤ (2/3)M_{cr} | (a) | |

> (2/3)M_{cr} | (b) |

Δ

_{cr}and**Δ**shall be calculated by (a) and (b):_{n}(a) | (11.8.4.3a) |

(b) | (11.8.4.3b) |