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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11.2.4 Intersecting Elements

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11.2.4.1

Walls shall be anchored to intersecting elements, such as floors and roofs; columns, pilasters, buttresses, or intersecting walls; and to footings.

11.3 Design Limits

11.3.1 Minimum Wall Thickness

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11.3.1.1

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)
Bearing^[1]	Greater of:	¹/₂₅ the lesser of unsupported length and unsupported height	(b)
Nonbearing	Greater of:	4 in.	(c)
Nonbearing	Greater of:	¹/₃₀ the lesser of unsupported length and unsupported height	(d)
Exterior basement and foundation^[1]	7.5 in.		(e)

^[1]Only applies to walls designed in accordance with the simplified design method of 11.5.3.

11.4 Required Strength

11.4.1 General

11.4.1.1

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

11.4.1.2

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

11.4.1.3

Slenderness effects shall be calculated in accordance with 6.6.4, 6.7, or 6.8. Alternatively, out-of-plane slenderness analysis shall be permitted using 11.8 for walls meeting the requirements of that section.

11.4.1.4

Walls shall be designed for eccentric axial loads and any lateral or other loads to which they are subjected.

11.4.2 Factored Axial Force and Moment

11.4.2.1

Walls shall be designed for the maximum factored moment M_u that can accompany the factored axial force for each applicable load combination. The factored axial force P_u at given eccentricity shall not exceed ϕP_n,max, where P_n,max shall be as given in 22.4.2.1 and strength reduction factor ϕ shall be that for compression-controlled sections in 21.2.2. The maximum factored moment M_u shall be magnified for slenderness effects in accordance with 6.6.4, 6.7, or 6.8.

11.4.3 Factored Shear

11.4.3.1

Walls shall be designed for the maximum in-plane V_u and out-of-plane V_u.

11.5 Design Strength

11.5.1 General

11.5.1.1

For each applicable factored load combination, design strength at all sections shall satisfy ϕS_n ≥ U, including (a) through (c). Interaction between axial load and moment shall be considered.

(a) ϕP_n ≥ P_u

(b) ϕM_n ≥ M_u

11.5.1.2

ϕ shall be determined in accordance with 21.2.

11.5.2 Axial Load and In-Plane or Out-of-Plane Flexure

11.5.2.1

For bearing walls, P_n and M_n (in-plane or out-of-plane) shall be calculated in accordance with 22.4. Alternatively, axial load and out-of-plane flexure shall be permitted to be considered in accordance with 11.5.3.

11.5.2.2

For nonbearing walls, M_n shall be calculated in accordance with 22.3.

11.5.3 Axial Load and Out-of-Plane Flexure — Simplified Design Method

11.5.3.1

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, P_n shall be permitted to be calculated by:

(11.5.3.1)

11.5.3.2

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

Table 11.5.3.2—Effective length factor k for walls

Boundary 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

11.5.3.3

P_n from Eq. (11.5.3.1) shall be reduced by ϕ for compression-controlled sections in 21.2.2.

11.5.3.4

Wall reinforcement shall be at least that required by 11.6.

11.5.4 In-Plane Shear

11.5.4.1

V_n shall be calculated in accordance with 11.5.4.2 through 11.5.4.8. Alternatively, for walls with h_w ≤ 2ℓ_w, 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.

11.5.4.2

For in-plane shear design, h is thickness of wall and d shall be taken equal to 0.8ℓ_w. A larger value of d, 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.

11.5.4.3

V_n at any horizontal section shall not exceed

11.5.4.4

V_n shall be calculated by:

V_n = V_c+ V_s

(11.5.4.4)

11.5.4.5

Unless a more detailed calculation is made in accordance with 11.5.4.6, V_c shall not exceed

for walls subject to axial compression or exceed the value given in 22.5.7 for walls subject to axial tension.

11.5.4.6

It shall be permitted to calculate V_c in accordance with Table 11.5.4.6, where N_u is positive for compression and negative for tension, and the quantity N_u/A_g is expressed in psi.

Table 11.5.4.6—V_c: nonprestressed and prestressed walls

Calculation option	Axial force	V_c
Simplified	Compression			(a)
	Tension	Greater of:		(b)
	Tension	Greater of:	0	(c)
Detailed	Tension or compression	Lesser of:		(d)
Detailed	Tension or compression	Lesser of:	Equation shall not apply if (M_u/V_u— ℓ_w/2) is negative.	(e)

11.5.4.7

Sections located closer to wall base than a distance ℓ_w/2 or one-half the wall height, whichever is less, shall be permitted to be designed for V_c calculated using the detailed calculation options in Table 11.5.4.6 at a distance above the base of ℓ_w/2 or one-half the wall height, whichever is less.

11.5.4.8

V_s shall be provided by transverse shear reinforcement and shall be calculated by:

(11.5.4.8)

11.5.5 Out-of-Plane Shear

11.5.5.1

V_n shall be calculated in accordance with 22.5.

11.6 Reinforcement Limits

11.6.1

If in-plane V_u ≤ 0.5ϕV_c, minimum ρ_ℓ and minimum ρ_t 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.

Table 11.6.1—Minimum reinforcement for walls with in-plane V_u ≤ 0.5_ϕV_c

Wall type	Type of nonprestressed reinforcement	Bar/wire size	f_y, psi	Minimum longitudinal^[1], ρ_ℓ	Minimum transverse, ρ_t
Cast-in-place	Deformed bars	≤ No. 5	≥ 60,000	0.0012	0.0020
		≤ No. 5	< 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.

11.6.2

If in-plane V_u ≥ 0.5ϕV_c, (a) and (b) shall be satisfied:

(a) ρ_ℓ shall be at least the greater of the value calculated by Eq. (11.6.2) and 0.0025, but need not exceed ρ_t required by 11.5.4.8.

ρ _ℓ ≥ 0.0025 + 0.5(2.5 — h_w/ℓ_w)(ρ_t — 0.0025)

(11.6.2)

(b) ρ_t shall be at least 0.0025

11.7 Reinforcement Detailing

11.7.1 General

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11.7.1.1

Concrete cover for reinforcement shall be in accordance with 20.6.1.

11.7.1.2

Development lengths of deformed and prestressed reinforcement shall be in accordance with 25.4.

11.7.1.3

Splice lengths of deformed reinforcement shall be in accordance with 25.5.

11.7.2 Spacing of Longitudinal Reinforcement

11.7.2.1

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

11.7.2.2

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

(a) 5h

(b) 18 in. for exterior walls or 30 in. for interior walls

If shear reinforcement is required for in-plane strength, s shall not exceed the smallest of 3h, 18 in., and ℓ_w/3.

11.7.2.3

For walls with h 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):

(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 h/3, from the exterior surface.

(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 h/3, from the interior surface.

11.7.2.4

Flexural tension reinforcement shall be well distributed and placed as close as practicable to the tension face.

11.7.3 Spacing of Transverse Reinforcement

11.7.3.1

Spacing s of transverse reinforcement in cast-in-place walls shall not exceed the lesser of 3h and 18 in. If shear reinforcement is required for in-plane strength, s shall not exceed ℓ_w/5.

11.7.3.2

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

(a) 5h

(b) 18 in. for exterior walls or 30 in. for interior walls

If shear reinforcement is required for in-plane strength, s shall not exceed the least of 3h, 18 in., and ℓ_w/5

11.7.4 Lateral Support of Longitudinal Reinforcement

11.7.4.1

If longitudinal reinforcement is required for compression and if A_st exceeds 0.01A_g, longitudinal reinforcement shall be laterally supported by transverse ties.

11.7.5 Reinforcement Around Openings

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11.7.5.1

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 f_y in tension at the corners of the openings.

11.8 Alternative Method for Out-of-Plane Slender Wall Analysis

11.8.1 General

11.8.1.1

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) P_u at the midheight section does not exceed 0.06f'_cA_g

(e) Calculated out-of-plane deflection due to service loads, Δ_s, including PΔ effects, does not exceed ℓ_c/150

11.8.2 Modeling

11.8.2.1

The wall shall be analyzed as a simply supported, axially loaded member subject to an out-of-plane uniformly distributed lateral load, with maximum moments and deflections occurring at midheight.

11.8.2.2

Concentrated gravity loads applied to the wall above any section shall be assumed to be distributed over a width equal to the bearing width, plus a width on each side that increases at a slope of 2 vertical to 1 horizontal, but not extending beyond (a) or (b):

(a) The spacing of the concentrated loads

(b) The edges of the wall panel

11.8.3 Factored Moment

11.8.3.1

M_u at midheight of wall due to combined flexure and axial loads shall include the effects of wall deflection in accordance with (a) or (b):

(a) By iterative calculation using

M_u = M_ua+ P_uΔ_u

(11.8.3.1a)

where M_ua is the maximum factored moment at midheight of wall due to lateral and eccentric vertical loads, not including PΔ effects.

Δ_u shall be calculated by:

(11.8.3.1b)

where I_cr shall be calculated by:

(11.8.3.1c)

and the value of E_s/E_c shall be at least 6.

(b) By direct calculation using:

(11.8.3.1d)

11.8.4 Out-of-Plane Deflection — Service Loads

11.8.4.1

Out-of-plane deflection due to service loads, Δ_s, shall be calculated in accordance with Table 11.8.4.1, where M_a is calculated by 11.8.4.2.

Table 11.8.4.1—Calculation of Δ_s

M_a	Δ_s
≤ (2/3)M_cr		(a)
> (2/3)M_cr		(b)

11.8.4.2

The maximum moment M_a at midheight of wall due to service lateral and eccentric vertical loads, including P_sΔ_s effects, shall be calculated by Eq. (11.8.4.2) with iteration of deflections.

M_a = M_sa+ P_sΔ_s

(11.8.4.2)

11.8.4.3

Δ_cr and Δ_n shall be calculated by (a) and (b):

(a)	(11.8.4.3a)
(b)	(11.8.4.3b)

11.8.4.4

I_cr shall be calculated by Eq. (11.8.3.1c).