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
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