CHAPTER 15 — WALLS - American Concrete Institute · PDF file1 CHAPTER 15 — WALLS 2 ... (tilt-up) 16 17 15.1.2 — ... 141 15.5.4.23 —For in-plane shear design, h is...

ACI 318-14 Chapter 15 Code, Approved Version, 2012-10-24

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CHAPTER 15 — WALLS 1 2 Add the following definition to Chapter 2: 3 4 Msa = maximum moment in wall due to service loads , excluding P∆ effects, in.-lb. 5 6

Text highlighted in yellow denotes changes made. . 7 8 15.1 — Scope 9 10 15.1.1 —Provisions of this chapter shall apply to the design of nonprestressed and prestressed 11 walls including: <14.1.1> < R16.1.1> <10.1> 12

• (a) Cast-in-place 13 • (b) Precast in-plant 14 • (c) Precast on-site including (tilt-up) 15

16 15.1.2 — Design of special structural walls shall be in accordance with Chapter 20. <~> 17 18 15.1.3 — Design of plain concrete walls shall be in accordance with Chapter 25. <~> 19 20 15.1.4 — Design of cantilever retaining walls shall be in accordance with 9.2 through 9.4, with 21 minimum horizontal reinforcement according to 15.7. <14.1.2> 22 23 15.2 — General 24 25 15.2.1 — Materials 26 27 15.2.1.1 — Design properties for concrete shall conform to Chapter 5. <~> 28 29 15.2.1.2 — Design properties for steel reinforcement shall conform to Chapter 6. <~> 30 31 15.2.2 — Connection to other members 32 33 15.2.2.1 — For precast walls, connections shall satisfy the force transfer requirements of 17.3. 34 <~> 35 36 15.2.2.2 — Connections of walls to foundations shall satisfy the force transfer requirements of 37 17.4. <14.2.8> 38 39 15.2.3 – Load distribution 40 41 15.2.3.1 — Unless otherwise demonstrated by an analysis, the horizontal length of wall 42 considered as effective for each concentrated load shall not exceed the smaller of the center-to-43 center distance between loads, and the bearing width plus four times the wall thickness. <14.2.4> 44 45


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15.2.4 — Intersecting elements 46 47 15.2.4.1 — Walls shall be anchored to intersecting elements, such as floors and roofs; or to 48 columns, pilasters, buttresses, of intersecting walls; and to footings. <14.2.6> 49 50 15.3 — Design limits 51 52 15.3.1 — Minimum wall thickness 53

54 15.3.1.1 –Minimum wall thicknesses shall be in accordance with the requirements of Table 55 15.3.1.1. These requirements need not applyThinner walls are permitted if structural analysis 56 shows adequate strength and stability can be demonstrated by structural analysis. 57 <14.2.7><14.5.3><14.6.1> 58 59 Table 15.3.1.1 —Minimum wall thickness, h 60 61

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63 64 15.4 — Required strength 65 66 15.4.1 - General 67 68 15.4.1.1 — Required strength shall be calculated in accordance with the factored load 69 combinations defined in Chapter 7 and analysis procedures defined in Chapter 8. (<~>) 70 71 15.4.1.2 — Slenderness effects shall be calculated in accordance with 8.6.4, 8.7, or 8.8. 72 Alternately, out-of-plane slenderness analysis shall be permitted using 15.8 for walls meeting the 73 requirements of that section. <14.8.1>. 74

Wall type Minimum thickness, h

Bearing* Greater of (a) and (b)

4 in. (a)

1/25 the lesser of unsupported length

and unsupported height

(b)

Nonbearing Greater of (c) and (d)

4 in. (c)

1/30 the lesser of unsupported length

and unsupported height

(d)

Exterior basement and foundation*

7.5 in.

* Only applies to walls designed in accordance with the simplified design method of 15.5.3.


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75 15.4.1.3— Walls shall be designed for eccentric axial loads and any lateral or other loads to 76 which they are subjected. <14.2.1> 77 78 15.4.2 — Factored axial loadforce and moment 79 80 15.4.2.1 — Walls shall be designed for the maximum factored moment that can accompany the 81 factored axial loadforce for each applicable load combination. The factored axial force Pu at 82 given eccentricity shall not exceed that φPn,max where Pn,max shall be as given in 9.4.3.1 and 83 strength reduction factor φ shall be that for compression-controlled sections in Table 9.4.2.1 . 84 The maximum factored moment Mu shall be magnified for slenderness effects in accordance 85 with 8.6.4, 8.7, or 8.8.<10.3.7> 86 87 15.4.3 — Factored shear 88 89 15.4.3.1 — Walls shall be designed for the maximum calculatedfactored in-plane and out-of-90 plane shear Vu. <~> 91 92 15.5 — Design strength 93 94 15.5.1 — General 95 96 15.5.1.1 — Design strength at all wall sections shall be in accordance with (a), (b), and (c) for 97 each applicable factored load combination. <9.1.1> <10.3.6> <14.2.1> <11.1.1> 98 99

(a) φPn ≥ Pu 100 (b) φMn ≥ Mu 101 (c) φVn ≥ Vu 102

103 Interaction between axial load and flexure shall be considered. 104 105 15.5.2 — Axial load and in-plane or out-of-plane flexure 106 107 15.5.2.1 —For bearing walls, φPn and φMn (in-plane or out-of-plane) shall be calculated in 108 accordance with 9.4. Alternatively, out-of-plane flexure mayshall be permitted to be considered 109 using 15.5.3. <14.2.2> <14.4> <10.3.6><10.3.7> <14.5.1> 110 111 15.5.2.2 — For nonbearing walls, φMn shall be calculated in accordance with 9.3. 112 113 15.5.3 — Axial load and out-of-plane flexure – simplified design method 114 115 15.5.3.1 —If the resultant of all factored loads is located within the middle third of the overall 116 thickness of a solid wall with a rectangular cross- section, φPn shall be permitted to be calculated 117 by: <14.4> <14.5.1> <14.5.2> 118 119


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⎡ ⎤⎛ ⎞φ = φ −⎢ ⎥⎜ ⎟

⎝ ⎠⎢ ⎥⎣ ⎦

2

0.55 ' 132

cn c g

kP f A

hl

(15.5.3.1) 120

121 15.5.3.2 — Effective length factor k for use with Eq. (15.5.3.1) shall be in accordance with Table 122 15.5.3.2. <14.5.2> 123 124 Table 15.5.3.2 — Effective length factor k for walls 125

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) (b) Unrestrained against rotation at both ends

0.8

1.0Walls not braced against lateral translation 2.0 126 15.5.3.3 — Strength reduction factor φ in Eq. (15.5.3.1) shall be that for compression-127 controlled sections in Table 9.4.2.1. <9.3.2.2> 128 129 15.5.3.4 —Wall reinforcement shall not be less than that required by 15.6. 130 131 132 15.5.4 — In-plane shear <14.2.3> 133 134 15.5.4.1 — φVn shall be calculated in accordance with 15.5.4.2 through 15.5.4.7. Alternatively, 135 for walls with hw ≤ 2ℓw, it shall be permitted to design for in-plane shear in accordance with the 136 strut-and-tie procedure of 18.5. In all cases, 15.6, 15.7.2, and 15.7.3 shall apply. <11.9.1> 137 138 15.5.4.2 — Strength reduction factor φ shall be as given in Section 9.5.2.1. <~> 139 140 15.5.4.23 —For in-plane shear design, h is thickness of wall and d shall be taken equal to 0.8ℓw. 141 A larger value of d, equal to the distance from extreme compression fiber to center of force of all 142 reinforcement in tension, shall be permitted to be used whenif determined by a strain 143 compatibility analysis. <11.9.4> 144

145 15.5.4.34 —φVn at any horizontal section shall not be taken greater thanexceed φ10 '

cf hd . 146 <11.9.3> <11.9.3> 147 148 15.5.4.45 —φVn shall be calculated by <11.1.1> 149 150

φVn = φVc + φVs (15.5.54.45) 151 152


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15.5.4.56 — Unless a more detailed calculation is made in accordance with 15.5.4.7, Vc shall not 153 be taken greater than 2λ√fc’ hd for walls subject to axial compression or greater than the value 154 given in 9.5.8 for walls subject to axial tension. <11.9.2><11.9.5> 155 156 Technical Change: 11.9.6 in 318-11 is being proposed for removal in an accompanying technical ballot. If the ballot fails, the contents of that section will be restored. 157 15.5.4.7 — It shall be permitted to calculate φVc in accordance with Table 15.5.4.7, where Nu is 158 positive for compression and negative for tension and the quantity Nu/Ag is expressed in psi. 159 <11.9.5> <11.2.1.2> <11.9.6>> <11.1.1> <11.2.2.3> <11.9.1> <11.9.2> <11.9.5> 160 161 Table 15.5.4.7 — Vc : nonprestressed and prestressed walls 162 163 Calculation

Option Axial Force Vc

Simplified

Compression 2 cf hdλ ′ hdf 'cλ2 (a)

Tension Greater of:

2 1500

uc

g

N f hdA

λ⎛ ⎞

′+⎜ ⎟⎜ ⎟⎝ ⎠

hdfA

N 'c

g

u λ⎟⎟⎠

⎞⎜⎜⎝

⎛+

50012

(b)

0 (c)

Detailed Tension or Compression

Lesser of:

3.34

uc

w

N df hdλ ′ +l w

u'c

dNhdf.

l433 +λ (d)

'

'

1.25 0.20.6

2

uw c

wc

u w

u

Nfh

f hdMV

λλ

⎡ ⎤⎛ ⎞+⎢ ⎥⎜ ⎟

⎝ ⎠⎢ ⎥+⎢ ⎥

−⎢ ⎥⎢ ⎥⎣ ⎦

ll

l

hd

VM

hN

.f.f.

w

u

u

w

u'cw

'c

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

−

⎟⎟⎠

⎞⎜⎜⎝

⎛+

+

2

2025160

l

ll λ

λ

(e)*

Notes: * Equation (e) shall not apply if (Mu /Vu - ℓw/2) is negative. 164 15.5.4.8 — Sections located closer to wall base than a distance ℓw/2 or one-half the wall height, 165 whichever is less, shall be permitted to be designed for the same value of Vc calculated using the 166 detailed calculation options in Table 15.5.4.7 at a distance ℓw/2 or one-half the wall height, 167 whichever is less. <11.9.7> 168 169


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170 15.5.4.69 — Vs shall be provided by transverse shear reinforcement, where Vs shall be calculated 171 by <11.9.9.1> 172 173

v yts

A f dV

s=

sdfA

V ytvs =

(15.5.54.79) 174

175 15.5.5 — Out-of-plane shear <14.2.3> 176 177 15.5.5.1 — φVn shall be calculated in accordance with 9.5. 178 179 15.5.5.2 — Strength reduction factor φ shall be as given in Section 9.5.2.1 or 9.6.2.1. <~> 180 181 182 15.6 — Reinforcement limits 183 184 15.6.1 — If in-plane Vu ≤ 0.5φVc, minimum ρℓ and minimum ρt shall be in accordance with 185 Table 15.6.1. These limits need not apply if structural analysis shows adequate strength and 186 stability.<11.9.8> <14.3.1> <14.3.2> <14.3.3><16.4.1> <16.4.2><14.2.7><18.11.2.1> 187 <18.11.2.3> 188

189 Table 15.6.1 — Minimum reinforcement for walls with in-plane Vu < ≤ 0.5φVc 190

Wall type Type of

nonprestressed reinforcement

Limits Minimum Longitudinal†, ρℓ

Minimum Transverse,

ρt dbBar/wire

size fy, psi

Cast-in-place

Deformed bars

≤ No. 5

<≥ 60,000 0.00120.0015 0.00250020

≥ < 60,000 0.00150.0012 0.00200025

> No. 5 AnyNot applicabl

e 0.0015 0.0025

Welded wire reinforcement ≤ W31 or D31

AnyNot applicabl

e 0.0012 0.0020

Precast* Deformed bars or welded wire reinforcement

AnyNot applicable

AnyNot applicabl

e 0.0010 0.0010

*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. †Prestressed walls with an average effective compressive stress of at least 225 psi need not meet the


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requirement for minimum longitudinal reinforcement, ρℓ. 191 192 15.6.2 — If in-plane Vu � 0.5φVc, (a) and (b) shall apply: 193 194 a) minimum ρℓ shall be the greater of the value calculated by Eq. (15.6.2) and 0.0025, but need 195 not exceed ρt required by 15.5.5.74.9. 196 197 b) ρt shall be at least 0.0025. <11.9.9.4> <11.9.8><11.9.9.2> 198 199

ρℓ ≥ 0.0025 + 0.5 (2.5 - hw/ℓw) (ρt - 0.0025) (15.6.2) 200 201 b) minimum ρt shall be at least 0.0025. <11.9.9.4> <11.9.8><11.9.9.2> 202 203 204 15.7 — Reinforcement detailing 205 206 15.7.1 — General 207 208 15.7.1.1 — Concrete cover for reinforcement shall be in accordance with 6.11.1. <~> 209 210 15.7.1.2 — Development lengths of deformed and prestressed reinforcement shall be calculated in 211 accordance with 21.4. <~> 212 213 15.7.1.3 — Splice lengths of deformed reinforcement shall be calculated in accordance with 214 21.5. <~> 215 216 15.7.2 — Spacing of longitudinal reinforcement 217 218 15.7.2.1— Maximum spacing, s, of longitudinal bars in cast-in-place walls shall be the lesser of 219 3h and 18 in. If shear reinforcement is required for in-plane strength, spacing of longitudinal 220 reinforcement shall not exceed ℓw / 3. <7.6.5> <11.9.9.5> <14.3.5> 221 222 15.7.2.2 — Maximum spacing, s, of longitudinal bars in precast walls shall be the lesser of: 223 224

(a) 5h and 225 (b) 18 in. for exterior walls or 30 in. for interior walls. 226 227

If shear reinforcement is required for in-plane strength, spacing of longitudinal reinforcement 228 shall not exceed the smallest of 3h, 18 in., and ℓw / 3.<7.6.5> <10.6.4> <11.9.9.5> <14.3.5> 229 <16.4.2> 230 231 232 233


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234 235 15.7.2.3 — For walls with h greater than 10 in., except basement walls and cantilever retaining 236 walls, distributed reinforcement for each direction shall be placed in two layers parallel with wall 237 faces in accordance with (a) and (b): <14.3.4> 238 239

(a) one layer consisting of a minimum of 1/2 and a maximum of 2/3 of total 240 reinforcement required for each direction shall be placed within a minimum of 2 in. and a 241 maximum of h/3 from the exterior surface; 242 243 (b) the other layer, consisting of the balance of required reinforcement in that direction, 244 shall be placed within a minimum of 3/4 in. and a maximum of h/3 from the interior 245 surface. 246 (a) One layer consisting of not less than ½ and not more than 2/3 of total reinforcement 247 required for each direction shall be placed not less than 2 in. nor more than h/3 from the 248 exterior surface; 249 250 (b) The other layer, consisting of the balance of required reinforcement in that direction, 251 shall be placed not less than 3/4 in. nor more than h/3 from the interior surface. 252

253 15.7.2.4 — Flexural tension reinforcement shall be well distributed and placed as close as 254 practicable to the tension face. <18.8.3> <18.9.2.1> <10.6.3> 255 256 15.7.3 — Spacing of transverse reinforcement 257 258 15.7.3.1 — Maximum spacing, s, of transverse reinforcement in cast-in-place walls shall be the 259 lesser of 3h and 18 in. 260 261 If shear reinforcement is required for in-plane strength, spacing of transverse reinforcement shall 262 not exceed ℓw / 5. <7.6.5> <11.9.9.3> <14.3.5> 263 264 15.7.3.2— Maximum spacing, s, of transverse bars in precast walls shall be the lesser of: 265 266

(a) 5h and 267 (b) 18 in. for exterior walls or 30 in. for interior walls. 268

269 If shear reinforcement is required for in-plane strength, spacing of transverse reinforcement shall 270 not exceed the smallest of 3h,18 in., and ℓw / 5 <7.6.5> <11.9.9.3> <14.3.5> <16.4.2> 271 272 15.7.4 — Lateral support of longitudinal reinforcement 273 274 15.7.4.1 — Longitudinal reinforcement, if required as compression reinforcement or if Ast 275 exceeds 0.01Ag, shall be laterally supported by transverse reinforcementties. <14.3.6> 276 277 278 15.7.5 — Reinforcement around openings 279


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280 15.7.5.1 — In addition to the minimum reinforcement required by 15.6, a minimum of two No. 5 281 bars in walls having two layers of reinforcement in both directions and one No. 5 bar in walls 282 having a single layer of reinforcement in both directions shall be provided around window, door, 283 and similarly sized openings. Such bars shall be anchored to develop fy in tension at the corners 284 of the openings. <14.3.7> 285 286 15.8 — Alternate method for out-of-plane slender wall analysis 287 288 15.8.1 — General 289 290 15.8.1.1 — It shall be permitted to analyze Oout-of-plane slenderness effects shall be permitted 291 to be analyzed using the requirements of this section for walls satisfying (a) through (e). 292 <14.8.2> 293 294 (a) The cCross section is constant over the height of the wall.<14.8.2.2> 295 296 (b) The wWall is tension-controlled for out-of-plane flexural effects. <14.8.2.3> <14.8.1> 297 298 (c) Reinforcement shall provides a design strength φMn not less than Mcr, where Mcr is calculated 299 using fr as provided in 5.2.3. <14.8.2.4> 300 301 (d) Pu at the midheight section does not exceed 0.06f′cAg. <14.8.2.6> 302 303 (e) The cCalculated out-of-plane deflection due to service loads, Δs, including PΔ effects, shall 304 does not exceed lc/150 <14.8.4> 305 306 15.8.2 — Modeling 307 308 15.8.2.1 —The wall shall be analyzed as a simply-supported, axially-loaded member subject to 309 an out-of-plane uniformly distributed lateral load, with maximum moments and deflections 310 occurring at midheight. <14.8.2.1> 311 312 15.8.2.2 — Concentrated gravity loads applied to the wall above any section shall be assumed to 313 be distributed over a width equal to the bearing width, plus a width on each side that increases at 314 a slope of 2 vertical to 1 horizontal, but not extending beyond (a) or (b): <14.8.2.5> 315

316 (a) the spacing of the concentrated loads, 317 318 (b) the edges of the wall panel. 319

320 15.8.3 — Factored moment 321 322 15.8.3.1 — Mu at midheight of wall due to combined flexure and axial loads shall include the 323 effects of wall deflection in accordance with (a) or (b): <14.8.3> 324

325


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(a) By iterative calculation using: 326 327 Mu = Mua + PuΔu (15.8.3.1a) 328 329 where Mua is the maximum factored moment at midheight of wall due to lateral and 330 eccentric vertical loads, not including PΔ effects. 331 332 Δu shall be calculated by: 333 334

25

0 75 48

Mu cu ( . ) E Ic cr

Δ =l

(15.8.3.1b) 335

336 where Icr shall be calculated by: 337 338

( )E P chs u wI A d ccr sE f dc y

⎛ ⎞⎜ ⎟= + − +⎜ ⎟⎜ ⎟⎝ ⎠

32

2 3

l (15.8.3.1c) 339

340 and the value of s cE / E shall not be taken less than 6. 341 342 (b) By direct calculation using: 343

( )

=⎛ ⎞⎜ ⎟−⎜ ⎟⎜ ⎟⎝ ⎠

251

0.75 48

MuaMu Pu cE Ic cr

l (15.8.3.1d) 344

345 15.8.4 — Out-of-plane deflection – service loads 346 347 15.8.4.1 — Out-of-plane deflection due to service loads, Δs, shall be calculated in accordance 348 with Table 15.8.4.1, where Ma is calculated by 15.8.4.2. <14.8.4> 349 350 Table 15.8.4.1 — Calculation of sΔ 351

Ma sΔ

( )2 3 crM≤ Δ Δas cr

cr

MM

⎛ ⎞= ⎜ ⎟⎝ ⎠

( )2 3 crM> ( ) ( )( )( )( ) ( )( )2 3

2 3 2 32 3

a crs cr n cr

n cr

M M

M M

−Δ = Δ + Δ − Δ

− 352


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15.8.4.2 — The maximum moment Ma at midheight of wall due to service lateral and eccentric 353 vertical loads, including PsΔs effects, shall be calculated by Eq. (15.8.4.2) with iteration of 354 deflections <14.8.4> 355

356 M M Pa sa s s= + Δ (15.8.4.2) 357

358 15.8.4.3 — Δcr and Δn shall be calculated using Eq. (15.8.4.3a) and Eq. (15.8.4.3b). <14.8.4> 359

360 25

48Mcr c

cr E Ic gΔ =

l (15.8.4.3a) 361

25

48

Mn cn E Ic cr

Δ =l

(15.8.4.3b) 362

363 15.8.4.4 — Icr shall be calculated by Eq. 15.8.3.1c. <14.8.3> 364 365

ACI 318-14 Chapter 15 Commentary Approved Version, 2013-10-08

1

Notes: 1

2

Code shown in Ariel. Code has been previously approved. However, the comments cast on the 3

first ballot of the commentary necessitated changes to the code. Please comment if you 4

disagree with the code changes. 5

Commentary shown in Times New Roman in boxes. It is subject to the present ballot. 6

7

8

CHAPTER 15 — WALLS 9

10

Add the following definition to Chapter 2: 11

12

Msa = maximum moment in wall due to service loads , excluding P∆ effects, in.-lb. 13

14

15.1 — Scope 15

16

15.1.1 —Provisions of this chapter shall apply to the design of nonprestressed and prestressed 17

walls including: <14.1.1> < R16.1.1> <10.1> 18

(a) Cast-in-place 19

(b) Precast in-plant 20

(c) Precast on-site, such asincluding tilt-up 21

22

R15.1.1 — Chapter 15 applies generally to walls as vertical and lateral force-resisting members. 23

Cantilever retaining walls are designed according to the flexural design provisions of Chapter 10. Walls 24

designed to resist shear forces, such as shear walls, should be designed in accordance with Chapter 14 and 25

11.9 as applicable. Provisions for in-plane shear in ordinary structural walls (as opposed to special 26

structural walls conforming to 20.9) are included in this chapter. 27

In the 1977 Code, walls could be designed according to Chapter 14 or 10.15. In the 1983 Code, these two 28

were combined in Chapter 14. <R14.1> 29

30

31

32

33


2

15.1.2 — Design of special structural walls shall be in accordance with Chapter 20. <~> 34

35

R15.1.2 — Special meansstructural walls are specially detailed according to the provisions of 36 Section 20.10. ACI 318 uses the term structural wall as being synonymous with shear wall. The 37 definition of a structural wall in 2.2 states: “A shear wall is a structural wall.” The term shear 38 wall is not defined in this CodeACI 318. ASCE 7 defines a structural wall as a wall that meets 39 the definition for a bearing wall or a shear wall. A bearing wall is defined as a wall that supports 40 vertical load beyond a certain threshold value. A shear wall is defined as a wall, 41 bearing or nonbearing, designed to resist lateral forces acting in the plane of the wall. The ASCE 42 7 definitions are widely accepted. 43

44 45 15.1.3 — Design of plain concrete walls shall be in accordance with Chapter 25. <~> 46

47

15.1.4 — Design of cantilever retaining walls shall be in accordance with 9.2 through 9.4, with 48

minimum horizontal reinforcement according to 15.7. <14.1.2> 49

50

R15.1.1 — Chapter 15 applies generally to walls as vertical and lateral load-carrying members. 51

Cantilever retaining walls are designed according to the flexural design provisions of Chapter 10. Walls 52

designed to resist shear forces, such as shear walls, should be designed in accordance with Chapter 14 and 53

11.9 as applicable. Shear provisions for in-plane shear in ordinary structural walls are included in 54

this chapter. 55

In the 1977 Code, walls could be designed according to Chapter 14 or 10.15. In the 1983 Code, these two 56

were combined in Chapter 14. <R14.1> 57

58

59

15.2 — General 60

61

15.2.1 — Materials 62

63

15.2.1.1 — Design properties for concrete shall conform to Chapter 5. <~> 64

65

15.2.1.2 — Design properties for steel reinforcement shall conform to Chapter 6. <~> 66

67

15.2.2 — Connection to other members 68

69


3

15.2.2.1 — For precast walls, connections shall satisfy the requirements of 17.3. <~> 70

71

15.2.2.2 — Connections of walls to foundations shall satisfy the requirements of 17.4. <14.2.8> 72

73

15.2.3 – Load distribution 74

75

15.2.3.1 — Unless otherwise demonstrated by an analysis, the horizontal length of wall 76

considered as effective for each concentrated load shall be not exceed the smallerlesser of the 77

center-to-center distance between loads, and the bearing width plus four times the wall 78

thickness. <14.2.4> 79

80

15.2.4 — Intersecting elements 81

82

15.2.4.1 — Where intersecting elements are required for support, Wwalls shall be anchored to 83

intersectingthose elements, such as floors and roofs; or to columns, pilasters, buttresses, of 84

intersecting walls; and to footings., where such elements are required for support.. <14.2.6> 85

86

R15.2.4.1 — Walls that do not depend upon intersecting elements for support do not have to be 87

connected to those elements. It is fairly not uncommon to separate massive retaining walls from 88

intersecting walls to accommodate differences in deformations. 89

90

91

92

15.3 — Design limits 93

94

15.3.1 — Minimum wall thickness 95

96

15.3.1.1 –Minimum wall thicknesses shall be in accordance with Table 15.3.1.1. Thinner walls 97

are permitted if adequate strength and stability can be demonstrated by structural analysis. 98

<14.2.7><14.5.3><14.6.1> 99

100

Table 15.3.1.1 —Minimum wall thickness, h 101

102


4

103

104

R15.3.1.1 — The minimum thickness requirements need not be applied to bearing walls and exterior 105

basement and foundation walls designed by 9.415.5.2 or analyzed by 15.8. <R14.5.3> 106

107

108

15.4 — Required strength 109

110

15.4.1 - General 111

112

15.4.1.1 — Required strength shall be calculated in accordance with the factored load 113

combinations defined in Chapter 7 and analysis procedures defined in Chapter 8. <~> 114

115

15.4.1.2 — Slenderness effects shall be calculated in accordance with 8.6.4, 8.7, or 8.8. 116

Alternatively, out-of-plane slenderness analysis shall be permitted using 15.8 for walls meeting 117

Wall type Minimum thickness, h

Bearing*

Greater

of (a)

and (b)

4 in. (a)

1/25 the lesser of

unsupported

length and

unsupported

height

(b)

Nonbearing

Greater

of (c)

and (d)

4 in. (c)

1/30 the lesser of

unsupported

length and

unsupported

height

(d)

Exterior

basement and

foundation*

7.5 in. (e)

* Only applies to walls designed in accordance with

the simplified design method of 15.5.3.


5

the requirements of that section. <14.8.1>. 118

119

15.4.1.3— Walls shall be designed for eccentric axial loads and any lateral or other loads to 120

which they are subjected. <14.2.1> 121

122

R14.2 -- General 123

Walls should be designed to resist all loads to which they are subjected, including eccentric axial loads 124

and lateral forces. Design is to be carried out in accordance with 14.4 unless the wall meets the 125

requirements of 14.5.1. <<Just repeats the Code.>> 126

R15.4.1.3— The forces typically acting on a wall are illustrated in Fig. R15.4.1.3. 127

128 129

Fig. R15.4.1.3—In-plane and out-of-plane forces. 130

131

132

15.4.2 — Factored axial force and moment 133

134

15.4.2.1 — Walls shall be designed for the maximum factored moment that can accompany the 135

factored axial force for each applicable load combination. The factored axial force Pu at given 136

eccentricity shall not exceed Pn,max where Pn,max shall be as given in 9.4.3.1 and strength 137

reduction factor shall be that for compression-controlled sections in Table 9.4.2.1 . The 138

maximum factored moment Mu shall be magnified for slenderness effects in accordance with 139

8.6.4, 8.7, or 8.8.<10.3.7> 140

141

142

15.4.3 — Factored shear 143

144


6

15.4.3.1 — Walls shall be designed for the maximum factored in-plane and out-of-plane shear 145

Vu. <~> 146

147

15.5 — Design strength 148

149

15.5.1 — General 150

151

15.5.1.1 — Design strength at all wall sections shall be in accordance with (a), (b), and (c) for 152

each applicable factored load combination. <9.1.1> <10.3.6> <14.2.1> <11.1.1> 153

154

(a) Pn ≥ Pu 155

(b) Mn ≥ Mu 156

(c) Vn ≥ Vu 157

158

Interaction between axial load and moment shall be considered. 159

160

15.5.2 — Axial load and in-plane or out-of-plane flexure 161

162

15.5.2.1 —For bearing walls, Pn and Mn (in-plane or out-of-plane) shall be calculated in 163

accordance with 9.4. Alternatively, out-of-plane flexure shall be permitted to be considered 164

using 15.5.3. <14.2.2> <14.4> <10.3.6><10.3.7> <14.5.1> 165

166

<<Commentary repeats the code.>> 167

R15.4.1.3 — Design is to be carried out in accordance with 14.4 unless the wall meets the requirements 168

of 14.5.1. <R14.2> 169

170

171

15.5.2.2 — For nonbearing walls, Mn shall be calculated in accordance with 9.3. 172

173

R15.5.2.2 — Nonbearing walls, by definition, are not subject to any significant axial force; and, 174

therefore, flexural strength is not a function of axial force. 175

176

15.5.3 — Axial load and out-of-plane flexure – simplified design method 177


7

178

15.5.3.1 —If the resultant of all factored loads is located within the middle third of the thickness 179

of a solid wall with a rectangular cross section, Pn shall be permitted to be calculated by: 180

<14.4> <14.5.1> <14.5.2> 181

182

(15.5.3.1) 183

184

15.5.3.2 — Effective length factor k for use with Eq. (15.5.3.1) shall be in accordance with Table 185

15.5.3.2. <14.5.2> 186

187

Table 15.5.3.2 — Effective length factor k for walls 188

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)

(b) Unrestrained against rotation at both ends

0.8

1.0

Walls not braced against lateral translation 2.0

189

15.5.3.3 — Strength reduction factor in Eq. (15.5.3.1) shall be that for compression-190

controlled sections in Table 9.4.2.1. <9.3.2.2> 191

192

15.5.3.4 —Wall reinforcement shall not be less than that required by 15.6. 193

194

R15.5.3.1 — The empirical simplified design method applies only to solid rectangular cross sections; . 195

and all other shapes should be designed according to 14.4 15.5.2. 196

197

Eccentric axial loads and moments due to lateralout-of-plane forces are used to determine the maximum 198

total eccentricity of the factored axial force Pu. When the resultant axial force for all applicable load 199

combinations falls within the middle third of the wall thickness (eccentricity not greater than h/6) at all 200

sections along the length of the undeformed wall, no tension is induced in the wall and the simplified design 201


8

method may be used. The design is then carried out considering Pu as a concentric axial force. The 202

factored axial force Pu should be less than or equal to the design axial strength ΦPn calculated by Eq. 203

(14-1 15.5.3.1). 204

205

<Historical.> 206

With the 1980 Code supplement, Eq. (14-1) was revised to reflect the general range of end conditions 207

encountered in wall designs. The wall strength equation in the 1977 Code was based on the assumption of 208

a wall with top and bottom fixed against lateral movement, and with moment restraint at one end 209

corresponding to an effective length factor between 0.8 and 0.9. Axial strength values determined from 210

the original equation were unconservative when compared to test results14.1 for walls with pinned 211

conditions at both ends, as occurs with some precast and tilt-up applications, or when the top of the wall 212

is not effectively braced against translation, as occurs with free-standing walls or in large structures where 213

significant roof diaphragm deflections occur due to wind and seismic loads. Equation (14-1) gives the 214

same results as the 1977 Code for walls braced against translation and with reasonable base restraint 215

against rotation.14.2 Values of effective length factors k are given for commonly occurring wall end 216

conditions. The end condition “restrained against rotation” required for a k of 0.8 implies attachment to a 217

member having flexural stiffness EI/ℓ at least as large as that of the wall. 218

219

The slenderness portion of Eq. (14-1 15.5.3.1) results in relatively comparable strengths by 14.4 15.5.2 220

for members loaded at the middle third of the thickness with different braced and restrained end 221

conditions. See Fig. R14.5 R15.5.3.1. 222

223

Fig. R14.5 R15.5.3.1—Simplified design of walls, Eq. (14-1 15.5.3.1) versus 14.4 15.5.2. <R14.5> 224

Note to ACI staff: Section nos. inside figure need to be updated. 225

226

227


9

15.5.4 — In-plane shear <14.2.3> 228

229

15.5.4.1 — Vn shall be calculated in accordance with 15.5.4.2 through 15.5.4.67. Alternatively, 230

for walls with hw ≤ 2ℓw, it shall be permitted to design for in-plane shear in accordance with the 231

strut-and-tie procedure of 18.5. In all cases, 15.6, 15.7.2, and 15.7.3 shall apply. <11.9.1> 232

233

R15.5.4.1 — Shear in the plane of the wall is primarily of importance for shearstructural walls with a 234

small height-to-length ratio. The design of taller walls, particularly walls with uniformly distributed 235

reinforcement, will likely be controlled by flexural considerations. <R11.9.1> Possible exceptions may 236

occur in tall shearstructural walls subject to high seismicstrong earthquake excitation. 237

238

239

15.5.4.2 — Strength reduction factor shall be as given in Section 9.5.2.1. <~> 240

241

15.5.4.3 —For in-plane shear design, h is thickness of wall and d shall be taken equal to 0.8ℓw. 242

A larger value of d, equal to the distance from extreme compression fiber to center of force of all 243

reinforcement in tension, shall be permitted to be used if determined by a strain compatibility 244

analysis. <11.9.4> 245

246

15.5.4.4 —Vn at any horizontal section shall not exceed 10'

cf hd . <11.9.3> <11.9.3> 247

248

R15.5.4.4 — This limit is imposed to control cracking under service loads and guard against diagonal 249

compression failure in shear walls. 250

251

252

15.5.4.5 —Vn shall be calculated by <11.1.1> 253

254

Vn = Vc + Vs (15.5.4.5) 255

256

15.5.4.6 — Unless a more detailed calculation is made in accordance with 15.5.4.7, Vc shall not 257

be taken greater than 2λ√fc’ hd for walls subject to axial compression or greater than the value 258

given in 9.5.8 for walls subject to axial tension. <11.9.2><11.9.5> 259


10

260

15.5.4.67 — It shall be permitted to calculate Vc in accordance with Table 15.5.4.67, where Nu 261

is positive for compression and negative for tension and the quantity Nu/Ag is expressed in psi. 262

<11.9.5> <11.2.1.2> <11.9.6>> <11.1.1> <11.2.2.3> <11.9.1> <11.9.2> <11.9.5> 263

264

265

Table 15.5.4.67 — Vc : nonprestressed and prestressed walls 266

267

Calculation

Option Axial Force Vc

Simplified

Compression hdf'c2 (a)

Tension Greater

of:

hdfA

N 'c

g

u

50012 (b)

0 (c)

Detailed Tension or

Compression

Lesser

of:

w

u'c

dNhdf.

433 (d)

hd

V

M

h

N.f.

f.w

u

u

w

u'cw

'c

2

20251

60

(e)*

Notes: *Equation (e) shall not apply if (Mu /Vu - ℓw/2) is negative.

268

R15.5.4.67 —Equations (11-27) and (11-28) Expressions (d) and(a) through (e) in Table 15.5.4.76 may 269

be used to determine Vc at any section through a shear wall. Equation (11-27) Expression (d) corresponds 270

to the occurrence of web shear cracking at a principal tensile stress of approximately 4λ√fc′ at the centroid 271

of the shear wall cross section. Equation (11-28) Expression(e) corresponds approximately to the 272

occurrence of flexure-shear cracking at a flexural tensile stress of 6λ√fc′ at a section ℓw/2 above the section 273

being investigated. As the term 274

Note to ACI staff: lw in equation needs to be consistent with ℓw elsewhere. 275

decreases, Eq. (11-27) (ed) will control; before this term becomes negative. When this term becomes 276

negative, Eq. (11-27) (d) should be used even when this term becomes negative. <R11.9.5 and R11.9.56> 277


11

278

279

15.5.4.78 — Sections located closer to the wall base than a distance ℓw/2 or one-half the wall 280

height, whichever is less, shall be permitted to be designed for the same value of Vc calculated 281

using the detailed calculation options in Table 15.5.4.67 at a distance ℓw/2 or one-half the wall 282

height, whichever is less. <11.9.7> 283

284

285

R15.5.4.78 — The values of Vc calculated from Eq. (11-27) and (11-28) (d) and (e) in Table 15.5.4.67 at 286

a section located a distance above the base of ℓw/2 or hw/2, whichever is lesser, apply to that section and all 287

sections between it and the base. However, the maximum factored shear force Vu at any section, including 288

the base of the wall, is limited to the upper bound on Vn in accordance with 11.9.3 15.5.4.4. <R11.9.7> 289

290

291

15.5.4.89 — Vs shall be provided by transverse shear reinforcement, where Vs shall be 292

calculated by <11.9.9.1> 293

294

s

dfAV

ytv

s

(15.5.4.9) 295

296

R15.5.4.89 — Equation (11-29) (15.5.4.9) is presented in terms of shear strength Vs provided by the 297

horizontal shear reinforcement for direct application in (11-1) (11-2) 15.5.4.5. 298

299

Vertical shear reinforcement should also be provided in accordance with 11.9.9.4 15.6 and the spacing 300

limitation of 11.9.9.5 15.7.2. <R11.9.9> 301

302

303

15.5.5 — Out-of-plane shear <14.2.3> 304

305

15.5.5.1 — Vn shall be calculated in accordance with 9.5. 306

307

15.5.5.2 — Strength reduction factor shall be as given in Section 9.5.2.1 or 9.6.2.1. <~> 308

309


12

310

15.6 — Reinforcement limits 311

312

15.6.1 — If in-plane Vu ≤ 0.5Vc, minimum ρℓ and minimum ρt shall be in accordance with Table 313

15.6.1. These limits need not apply if structural analysis shows adequate strength and stability 314

without less than the specified minimum reinforcement.<11.9.8> <14.3.1> <14.3.2> 315

<14.3.3><16.4.1> <16.4.2><14.2.7><18.11.2.1> <18.11.2.3> 316

317

Table 15.6.1 — Minimum reinforcement for walls with in-plane Vu ≤ 0.5Vc 318

Wall type

Type of

nonprestressed

reinforcement

Minimum

Longitudinal†, ρℓ

Minimum

Transverse, ρt Bar/wire

size fy, psi

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*

Deformed bars or

welded wire

reinforcement

Any Any 0.0010 0.0010

*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.

†Prestressed walls with an average effective compressive stress of at least 225 psi need not meet

the requirement for minimum longitudinal reinforcement, ρℓ.

319

320

R15.6.1 — Both horizontal and vertical shear reinforcement are required for all walls. <Historical>The 321

notation used to identify the direction of the distributed shear reinforcement in walls was updated in 2005 322

to eliminate conflicts between the notation used for ordinary structural walls in Chapters 11 and 14 and 323

the notation used for special structural walls in Chapter 21. The distributed reinforcement is identified as 324

being oriented parallel to either the longitudinal or transverse axis of the wall. Therefore, for vertical wall 325


13

segments, the notation used to describe the horizontal distributed reinforcement ratio is ρt, and the 326

notation used to describe the vertical distributed reinforcement ratio is ρℓ. <R11.9.9> 327

328

<Now that the provisions of Chapter 11 and 14 are combined, this paragraph is no longer needed.> 329

The requirements of 14.3 are similar to those in previous codes. These apply to walls designed according 330

to 14.4, 14.5, or 14.8. For walls resisting horizontal shear forces in the plane of the wall, reinforcement 331

designed according to 11.9.9.2 and 11.9.9.4 may exceed the minimum reinforcement in 14.3. 332

333

<This commentary is a repeat of R11.9.9 which is shown above.> 334

The notation used to identify the direction of the distributed reinforcement in walls was updated in 2005 335

to eliminate conflicts between the notation used for ordinary structural walls in Chapters 11 and 14 and 336

the notation used for special structural walls in Chapter 21. The distributed reinforcement is now 337

identified as being oriented parallel to either the longitudinal or transverse axis of the wall. Therefore, for 338

vertical wall segments, the notation used to describe the horizontal distributed reinforcement ratio is ρt, 339

and the notation used to describe the vertical distributed reinforcement ratio is ρℓ. <R14.3> 340

341

Transverse reinforcement is not required in precast, prestressed walls equal to or less than 12 ft in width 342

because thisThe 12 ft width is less than that in which shrinkage and temperature stresses can build up to a 343

magnitude requiring transverse reinforcement. In addition, much of the shrinkage occurs before the 344

members are connected into the structure. Once in the final structure, the members are usually not as 345

rigidly connected transversely as monolithic concrete; thus the transverse restraint stresses due to both 346

shrinkage and temperature change are significantly reduced. 347

348

349

This The minimum area of wall reinforcement for precast walls, instead of the minimum values in 14.3, 350

has been used for many years and is recommended by PCI 16.4 and the Canadian Concrete Design 351

Standard.16.20 Reduced minimum reinforcement and greater spacings in 15.7.2.2 are allowed recognizing 352

that precast wall panels have very little restraint at their edges during early stages of curing and develop 353

less shrinkage stress than comparable cast-in-place walls. <R16.4.2> 354

355

<This commentary repeats the code language.> 356

The minimum amounts of reinforcement in 14.3 need not apply to prestressed concrete walls, provided 357

the average compressive stress in concrete due to effective prestress force only is 225 psi or greater and a 358


14

structural analysis is performed to show adequate strength and stability with lower amounts of 359

reinforcement. <R18.11.2.3> 360

361

362

15.6.2 — If in-plane Vu ˃ 0.5Vc, (a) and (b) shall apply: 363

364

a) minimum ρℓ shall be the greater of the value calculated by Eq. (15.6.2) and 0.0025, but need 365

not exceed ρt required by 15.5.4.9. 366

367

368

ρℓ ≥ 0.0025 + 0.5 (2.5 - hw/ℓw) (ρt - 0.0025) (15.6.2) 369

370

b) minimum t shall be 0.0025. <11.9.9.4> <11.9.8><11.9.9.2> 371

372

373

R15.6.2 — For monotonically loaded walls with low height-to-length ratios, test data11.58

indicate 374

that horizontal shear reinforcement becomes less effective for shear resistance than vertical 375

reinforcement. This change in effectiveness of the horizontal versus vertical reinforcement is 376

recognized in Eq. (11-30) (15.6.2); if hw/ℓw is less than 0.5, the amount of vertical reinforcement 377

is equal to the amount of horizontal reinforcement. If hw/ℓw is greater than 2.5, only a minimum 378

amount of vertical reinforcement is required (0.0025sh). <R11.9.9> 379

380

381

15.7 — Reinforcement detailing 382

383

15.7.1 — General 384

385

15.7.1.1 — Concrete cover for reinforcement shall be in accordance with 6.11.1. <~> 386

387

15.7.1.2 — Development lengths of deformed and prestressed reinforcement shall be calculated 388

in accordance with 21.4. <~> 389

390


15

15.7.1.3 — Splice lengths of deformed reinforcement shall be calculated in accordance with 391

21.5. <~> 392

393

15.7.2 — Spacing of longitudinal reinforcement 394

395

15.7.2.1— Maximum spacing, s, of longitudinal bars in cast-in-place walls shall be the lesser of 396

3h and 18 in. If shear reinforcement is required for in-plane strength, spacing of longitudinal 397

reinforcement shall not exceed ℓw / 3. <7.6.5> <11.9.9.5> <14.3.5> 398

399

15.7.2.2 — Maximum spacing, s, of longitudinal bars in precast walls shall be the lesser of: 400

401

(a) 5h and 402

(b) 18 in. for exterior walls or 30 in. for interior walls. 403

404

If shear reinforcement is required for in-plane strength, spacing of longitudinal reinforcement 405

shall not exceed the smallest of 3h, 18 in., and ℓw / 3.<7.6.5> <10.6.4> <11.9.9.5> <14.3.5> 406

<16.4.2> 407

408

R15.7.2.2 — See R15.6.1 for a discussion ofn the increased maximum reinforcement spacing for 409

precast walls. 410

411

15.7.2.3 — For walls with h greater than 10 in., except basement walls and cantilever retaining 412

walls, distributed reinforcement for each direction shall be placed in two layers parallel with wall 413

faces in accordance with (a) and (b): <14.3.4> 414

415

(a) One layer consisting of not less than ½ and not more than 2/3 of total reinforcement 416

required for each direction shall be placed not less than 2 in. nor more than h/3 from the 417

exterior surface; 418

419

(b) The other layer, consisting of the balance of required reinforcement in that direction, 420

shall be placed not less than 3/4 in. nor more than h/3 from the interior surface. 421

422

15.7.2.4 — Flexural tension reinforcement shall be well distributed and placed as close as 423

practicable to the tension face. <18.8.3> <18.9.2.1> <10.6.3> 424


16

425

15.7.3 — Spacing of transverse reinforcement 426

427

15.7.3.1 — Maximum spacing, s, of transverse reinforcement in cast-in-place walls shall be the 428

lesser of 3h and 18 in If shear reinforcement is required for in-plane strength, spacing of 429

transverse reinforcement shall not exceed ℓw / 5. <7.6.5> <11.9.9.3> <14.3.5> 430

431

15.7.3.2— Maximum spacing, s, of transverse bars in precast walls shall be the lesser of: 432

433

(a) 5h and 434

(b) 18 in. for exterior walls or 30 in. for interior walls. 435

436

If shear reinforcement is required for in-plane strength, spacing of transverse reinforcement 437

shall not exceed the smallest of 3h,18 in., and ℓw / 5 <7.6.5> <11.9.9.3> <14.3.5> <16.4.2> 438

439

R15.7.3.2 — See R15.6.1 for a discussion ofn the increased maximum reinforcement spacing for 440

precast walls. 441

15.7.4 — Lateral support of longitudinal reinforcement 442

443

15.7.4.1 — Longitudinal reinforcement, if required as compression reinforcement or if Ast 444

exceeds 0.01Ag, shall be laterally supported by transverse ties. <14.3.6> 445

446

447

15.7.5 — Reinforcement around openings 448

449

15.7.5.1 — In addition to the minimum reinforcement required by 15.6, a minimum of two No. 5 450

bars in walls having two layers of reinforcement in both directions and one No. 5 bar in walls 451

having a single layer of reinforcement in both directions shall be provided around window, door, 452

and similarly sized openings. Such bars shall be anchored to develop fy in tension at the corners 453

of the openings. <14.3.7> 454

455

15.8 — Alternate method for out-of-plane slender wall analysis 456

457

15.8.1 — General 458


17

459

15.8.1.1 — It shall be permitted to analyze out-of-plane slenderness effects using the 460

requirements of this section for walls satisfying (a) through (e). <14.8.2> 461

462

(a) Cross section is constant over the height of the wall.<14.8.2.2> 463

464

(b) Wall is tension-controlled for out-of-plane flexural effects. <14.8.2.3> <14.8.1> 465

466

(c) Reinforcement provides a design strength Mn not less than Mcr, where Mcr is calculated 467

using fr as provided in 5.2.3. <14.8.2.4> 468

469

(d) Pu at the midheight section does not exceed 0.06f′cAg. <14.8.2.6> 470

471

(e) Calculated out-of-plane deflection due to service loads, Δs, including PΔ effects, does not 472

exceed c/150 <14.8.4> 473

474

475

R15.8.1.1 — Section 14.8 15.8 was introduced in the 1999 edition and the provisions are based on 476

requirements in the 1997 Uniform Building Code (UBC)14.3 and experimental research.14.4 Changes were 477

included in the 2008 edition to reduce differences in the serviceability provisions and ensure that the 478

intent of the UBC provisions is included in future editions of this Code and the International Building 479

Code. 480

481

The procedure is presented as an alternative to the requirements of 10.10 15.4.1.2 for the out-of-plane 482

design of slender wall panels, where the panels are restrained against overturning at the top. 483

484

Panels that have windows or other large openings are not considered to have constant cross section over 485

the height of the panel. Such walls are to be designed taking into account the effects of openings. 486

487

Many aspects of the design of tilt-up walls and buildings are discussed in References 14.5 and 14.6. 488

<R14.8> Staff to update reference nos. 489

490


18

This The previous requirement that the reinforcement ratio should not exceed 0.6ρbal was replaced in the 491

2005 Code by the requirement that the wall be tension-controlled, resulting in approximately the same 492

reinforcement ratio. <R14.8.2.3> 493

494

495

496

15.8.2 — Modeling 497

498

15.8.2.1 —The wall shall be analyzed as a simply-supported, axially-loaded member subject to 499

an out-of-plane uniformly distributed lateral load, with maximum moments and deflections 500

occurring at midheight. <14.8.2.1> 501

502

15.8.2.2 — Concentrated gravity loads applied to the wall above any section shall be assumed 503

to be distributed over a width equal to the bearing width, plus a width on each side that 504

increases at a slope of 2 vertical to 1 horizontal, but not extending beyond (a) or (b): <14.8.2.5> 505

506

(a) the spacing of the concentrated loads, 507

508

(b) the edges of the wall panel. 509

510

15.8.3 — Factored moment 511

512

15.8.3.1 — Mu at midheight of wall due to combined flexure and axial loads shall include the 513

effects of wall deflection in accordance with (a) or (b): <14.8.3> 514

515

(a) By iterative calculation using: 516

517

Mu = Mua + PuΔu (15.8.3.1a) 518

519

where Mua is the maximum factored moment at midheight of wall due to lateral and 520

eccentric vertical loads, not including PΔ effects. 521

522

Δu shall be calculated by: 523

524


19

(15.8.3.1b) 525

526

where Icr shall be calculated by: 527

528

(15.8.3.1c) 529

530

and the value of s cE / E shall not be taken less than 6. 531

532

(b) By direct calculation using: 533

(15.8.3.1d) 534

535

R15.8.3.1 — 536

537

The neutral axis depth, c, in Eq. (14-7 15.8.3.1c) corresponds to the following effective area of 538

longitudinal reinforcement-:. <R14.8.3> 539

,

/ 2u

se w s

y

P hA A

f d

540

Note to staff: Add notation to Ch.2. 541

542

543

15.8.4 — Out-of-plane deflection – service loads 544

545

15.8.4.1 — Out-of-plane deflection due to service loads, Δs, shall be calculated in accordance 546

with Table 15.8.4.1, where Ma is calculated by 15.8.4.2. <14.8.4> 547

548


20

Table 15.8.4.1 — Calculation of s 549

Ma s

2 3cr

M Δ Δas cr

cr

M

M

2 3cr

M

2 3

2 3 2 32 3

a cr

s cr n cr

n cr

M M

M M

550

551

552

R15.8.4.1 —Test data14.4 demonstrated that out-of-plane deflections increase rapidly when the service-553

level moment exceeds 2/3Mcr. A linear interpolation between Δcr and Δn is used to determine Δs to 554

simplify the design of slender walls if Ma > 2/3Mcr. 555

556

Service-level load combinations are not defined in Chapter 9 7 of ACI 318, but they are discussed in 557

Appendix C of ASCE/SEI 7-10.14.7 Unlike ACI 318, however, appendicxes to ASCE/SEI 7 are not 558

considered to be mandatory parts of that standard. For calculating service-level lateral deflections of 559

structures, Appendix C of ASCE/SEI 7-10 recommends using the following load combination 560

561

D + 0.5L + Wa 562

563

in which Wa is wind load based on serviceability wind speeds provided in the commentary to Appendix C 564

of ASCE/SEI 7-10. If the slender wall is designed to resist earthquake effects, E, and E is based on 565

strength-level earthquake effects, the following load combination is considered to be appropriate for 566

evaluating the service-level lateral deflections 567

568

D + 0.5L + 0.7E 569

<R14.8.4> 570

571

572

15.8.4.2 — The maximum moment Ma at midheight of wall due to service lateral and eccentric 573

vertical loads, including PsΔs effects, shall be calculated by Eq. (15.8.4.2) with iteration of 574

deflections <14.8.4> 575


21

576

M M Pa sa s s (15.8.4.2) 577

578

15.8.4.3 — Δcr and Δn shall be calculated using Eq. (15.8.4.3a) and Eq. (15.8.4.3b). <14.8.4> 579

580

(15.8.4.3a) 581

(15.8.4.3b) 582

583

15.8.4.4 — Icr shall be calculated by Eq. 15.8.3.1c. <14.8.3> 584

585

CHAPTER 15 — WALLS - American Concrete Institute · PDF file1 CHAPTER 15 — WALLS 2 ... (tilt-up) 16 17 15.1.2 — ... 141 15.5.4.23 —For in-plane shear design, h is...

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