Building Code Requirements for Structural Concrete (ACI 318M-11)

Design of Wall Structures by ACI 318

David Darwin

Vietnam Institute for Building Science and Technology (IBST)

Hanoi and Ho Chi Minh City

December 12-16, 2011

This morning

Slender columns

Walls

High-strength concrete

Walls (Chapters 14, 10, and 11)

Outline

OverviewNotationGeneral design requirementsMinimum reinforcementReinforcement around openingsDesign of bearing walls (3 methods)Design of shear walls

Walls can be categorized based on

Construction Design

method loadingCast-in-place Axial load, flexure,

Precast and out-of-plane shear

Tilt-up In-plane shear

Types of Walls

Cast-in-place

Precast

Tilt-up

Walls can be categorized based on

Construction Design

method loadingCast-in-place Axial load, flexure,

Precast and out-of-plane shear

Tilt-up In-plane shear

Bearing walls*

Shear walls*

Notation and Abbreviation

l = Vertical reinforcement ratio

t = Horizontal reinforcement ratio

c = Height of wall measured center-to-center of supports

h = Wall thickness

hw = Total height of wall

w = Length of wall

Mcr = Cracking moment

WWR = welded wire reinforcement

General design requirements in ACI 318

Design for axial, eccentric, lateral, shear and other loads to which the wall is subjected

Walls must be anchored to intersecting structural elements (floors, roofs, columns…)

Horizontal length of a wall considered effective for each concentrated load

≤ center-to center spacing of loads

≤ bearing width + 4 wall thickness h

Outer limits of compression member built integrally with a wall ≤ 40 mm from outside of spiral or ties

Minimum reinforcement and reinforcement based on the Empirical Method may be waived if analysis shows adequate strength and stability

Transfer force to footing at base of wall in accordance with Chapter 15 (Footings)

Minimum reinforcement

Vertical reinforcement ratio l 0.0015

Reduce to 0.0012 for bar sizes No. 16 and

fy 420 MPa

or for WWR reinforcement sizes 16 mm

Horizontal reinforcement ratio t 0.0025

Reduce to 0.0020 for bar sizes No. 16 and

fy 420 MPa

or for WWR reinforcement sizes 16 mm

Walls more than 250 mm thick (except basement walls):

Must have two layers of reinforcement parallel with the faces

(a)1/2 to 2/3 of reinforcement in each direction located between 50 mm and 1/3 of wall thickness from exterior surface

(b) balance of reinforcement in each direction located between 20 mm and 1/3 of wall thickness from interior surface

Vertical and horizontal reinforcement spaced

≤ 3h

≤ 450 mm

Ties not required around vertical reinforcement when l ≤ 0.01

Reinforcement around openings

At least 2 No. 16 bars in walls with 2 layers of reinforcement in both directions

At least 1 No. 16 bar in walls with 1 layer of reinforcement in both directions

Anchored to develop fy

Reinforcement around openings

Design of bearing walls

Axial load and flexure

Shear perpendicular to the wall

Design of walls for axial load and flexure

Design options:

Wall Designed as Compression Members (subjected to P & M design as columns)

Empirical Design Method (some limitations)

Alternative Design of Slender Walls (some limitations)

Walls designed as compression members

Design as column, including slenderness requirements

Also meet general and minimum reinforcement requirements for walls

Empirical Design Method

Limitations

Thickness of solid rectangular cross section

h (cor w between supports)/25

100 mm for bearing walls

190 mm for exterior basement and foundation walls

Resultant of all factored loads

must be located within the

middle third of the overall

wall thickness

h

Pu

e h/6

h/6

Wall cross section

Design axial strength

= 0.65

2

0 55 132

cn c g u

kP . f A P

h

Effective length factor, k

Walls braced at top and bottom against lateral translation

Restrained against rotation at one or both ends…k = 0.8

Unrestrained against rotation at both ends …k = 1.0

Walls not braced against lateral translation…k = 2.0

Alternative Design of Slender Walls

When flexural tension controls the out-of-plane design, the requirements of this procedure are considered to satisfy the slenderness requirements for compression members

Pu/Ag 0.06f’c at midheight

Wall must be tension-controlled

Mn ≥ Mcr

P

Lat

eral

Lo

ad

Distribution of load within wall

Provisions cover

Factored moment Mu

Out-of-plane service load deflection s

Factored moment Mu

By iteration

By direct solution

c u

P

e

wu

Solve by iteration

Factored moment Mu by iteration

2

8u c

u u u

wM Pe P

25

0 75 48u c

uc cr

M

. E I

u ua u uM M P

u = +

Pu

Mua Puu

e

Icr = moment of inertia of cracked section

32

2 3s u w

cr sc y

E P h cI A d c

E f d

not taken < 6s

c

E

E

Factored moment Mu by direct solution

251

0 75 48

uau

u c

c cr

MM

P. E I

u = +

Pu

Mua Puu

e

Out-of-plane service load deflection

Loading

D + 0.5L + Wa or

D + 0.5L + 0.7E

(per ACI Commentary and

ASCE 7-10)

s c / 150

c s

P

e

Service Deflection Limit

Service Load Deflections

35(2/3)cr

(2/3)Mcr

n

Mn

Ma

ss

Mcr

Ma

cr

Ma = Service load moment at midheight including P-

Service deflection

Find Ma by iteration

Service load deflections for Ma (2/3)Mcr

c s

P

e

25

48

as cr

cr

cr ccr

c cr

M

M

M

E I

Service load deflections for Ma > (2/3)Mcr

Service deflection

Find Ma and Icr by iteration

c s

P

e

2

2 32 3 2 3

2 3

5

48

a crs cr n cr

n cr

n cn

c cr

M / M/ /

M / M

M

E I

Design of shear walls

Shear parallel to the wall in-plane shear

Shear wall

Design loading

Design for bending, axial load, and in-plane shear

Bending and axial load: design as beam or column

If hw 2w, design is permitted using a strut-and-tie model (Appendix A)

Shear design

0 83

u n

n c s

n c

V V

V V V

V . f hd

Effective depth d

0 8

Larger value equal to the distance from

extreme compression fiber to center of

force of all reinforcement in tension permitted

when determined by strain compatibility

wd . h

For walls subject to vertical compression,

0 17

For walls subject to vertical tension ,

0 29 0 17 1

is negative for tension

lightweight concrete factor

c c

u

uc c

g

u

V . f hd

N

. NV . f hd

A

N

Alternatively, use the lesser of

0 274

or

0 1 0 20 05

2

When 2 is negative, second

equation is not applicable

uc c

w

w c u w

c cu u w

u u w

N dV . f hd

. f . N hV . f hd

M V

M V

First equation corresponds to a principal tensile

stress of about 0 33 at centroid of shear-wall

cross section.

Second equation corresponds to a flexural tensile

stress of about 0 50 at a section

c

c

. f

. f 2 above

the section being investigated

w

Horizontal sections closer to the wall base than w /2 or hw/2, whichever is less, may be designed for the same Vc as computed

at w /2 or hw/2

Where Vu Vc/2, minimum wall reinforcement may be used

Where Vu Vc/2, wall reinforcement must meet the requirements described next

Horizontal shear reinforcement

v y u c

s vy

A f d V V sV A

s f d

0 0025

5, 3 , 450 mm

vt

w

A.

hs

s h

Vertical shear reinforcement

1

1

0 0025 0 5 2 5 0 0025

0 0025

3, 3 , 450 mm

h wt

w

w

A h. . . .

hs

.

s h

Summary

Design of wallsNotationGeneral design requirementsMinimum reinforcementReinforcement around openingsDesign of bearing walls (3 methods)Design of shear walls

50

Figures copyright 2010 by

McGraw-Hill Companies, Inc.

1221 Avenue of the America

New York, NY 10020 USA

Duplication authorized for use with this presentation only.

Photographs and figures on bearing wall design provided courtesy of the Portland Cement Association, Skokie, Illinois, USA

The University of

Kansas

David Darwin, Ph.D., P.E.Deane E. Ackers Distinguished Professor Director, Structural Engineering & Materials Laboratory

Dept. of Civil, Environmental & Architectural Engineering2142 Learned HallLawrence, Kansas, 66045-7609(785) 864-3827 Fax: (785) 864-5631

daved@ku.edu