1. Vietnam Institute for Building Science and Technology (IBST)
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

2. This morning
Slender columns
Walls
High-strength concrete

3. Walls (Chapters 14, 10, and 11)

4. Outline
Overview
Notation
General design requirements
Minimum reinforcement
Reinforcement around openings
Design of bearing walls (3 methods)
Design of shear walls

5. Walls can be categorized based on
Construction Design
method loading
Cast-in-place Axial load, flexure,
Precast and out-of-plane shear
Tilt-up In-plane shear

6. Types of Walls Cast-in-place Precast Tilt-up
Before we begin our discussion on the analysis methods for walls, we would like to briefly describe the different types of concrete wall systems.

7. As the name suggests, cast-in-place concrete walls are cast on site utilizing formwork that is also built on site. After the forms have been erected, the required reinforcing bars are set in the forms at the proper location, and then the concrete is subsequently deposited into the forms.

8. Precast concrete walls are manufactured in a precasting plant under controlled conditions and are subsequently shipped to the site for erection. Such walls are reinforced with either nonprestressed or prestressed reinforcement. We will be covering the design of precast walls with nonprestressed reinforcement in this module.

9. Tilt-up concrete walls are cast in a horizontal position at the jobsite and then tilted up into their final position in the structure. According to ACI 318, tilt-up concrete construction is a form of precast concrete. In this module, we will be discussing the design methods for these three types of walls after the walls are in their final positions within the structure. In the case of precast and tilt-up concrete walls, design methods for handling or erection are not covered, as they are beyond the scope of this module.

10. Walls can be categorized based on
Construction Design
method loading
Cast-in-place Axial load, flexure,
Precast and out-of-plane shear
Tilt-up In-plane shear
Bearing walls*
Shear walls*

11. Notation and Abbreviation
l = Vertical reinforcement ratio t = Horizontal reinforcement ratio lc = Height of wall measured center-to-center of supports h = Wall thickness hw = Total height of wall lw = Length of wall Mcr = Cracking moment WWR = welded wire reinforcement

12. 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

14. 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)

15. Minimum reinforcement
Vertical reinforcement ratio l  Reduce to for bar sizes  No. 16 and fy  420 MPa or for WWR reinforcement sizes  16 mm Horizontal reinforcement ratio t  Reduce to for bar sizes  No. 16 and

16. Walls more than 250 mm thick (except basement walls):
Must have two layers of reinforcement parallel with the faces
1/2 to 2/3 of reinforcement in each direction located between 50 mm and 1/3 of wall thickness from exterior surface
balance of reinforcement in each direction located between 20 mm and 1/3 of wall thickness from interior surface

17. Vertical and horizontal reinforcement spaced ≤ 3h ≤ 450 mm Ties not required around vertical reinforcement when l ≤ 0.01

18. 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

19. Reinforcement around openings

20. Design of bearing walls
Axial load and flexure Shear perpendicular to the wall
14.2 Design Methods

21. 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)
According to Section 14.4, walls subjected to axial load or combined flexure and axial load are to be designed as compression members in accordance with specific sections of Chapter 10 and Chapter 14 of the code. The design assumptions, general principles and requirements, and the provisions for slenderness effects of Chapter 10 are applicable to the design of walls. Sections 14.2 and 14.3 give general and minimum reinforcement requirements that must be satisfied for any wall section, respectively.

22. Walls designed as compression members
Design as column, including slenderness requirements
Also meet general and minimum reinforcement requirements for walls
Wall design is further complicated by the fact that slenderness is a consideration in practically all cases. A second-order analysis, which takes into account variable wall stiffness, as well as the effects of member curvature and lateral drift, duration of the loads, shrinkage and creep, and interaction with the supporting foundation is specified in Section In lieu of that procedure, the approximate evaluation of slenderness effects prescribed in Section may be used.

23. Empirical Design Method
Limitations
Thickness of solid rectangular cross section
h  (lc or lw between supports)/25
 100 mm for bearing walls
 190 mm for exterior basement and foundation walls
The provisions for the Empirical Design Method are given in Section This method may be used for the design of walls with solid rectangular cross-sections if the resultant of all applicable factored loads falls within the middle third of the wall thickness. Also, the thickness h of the wall must be greater than or equal to the unsupported height lc or length lw, whichever is shorter, divided by 25. In no case shall the wall be less than 4 inches in thickness for bearing walls. For exterior basement walls and foundation walls, the minimum thickness is 7.5 inches.

24. 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
The second limitation of this method is illustrated here for the case of an axial load acting on the wall section. Axial loads with an eccentricity less than or equal the thickness of the wall h divided by 6 act within the middle third of the section. Note that in addition to any eccentric axial loads, the effect of any lateral loads on the wall must be included to determine the total eccentricity of the resultant load. Primary application of this method is for relatively short walls subjected to vertical loads. Application becomes extremely limited when lateral loads need to be considered, since the total eccentricity must not exceed h/6. Walls not meeting these criteria must be designed as compression members for flexure and axial load by the provisions of Chapter 10, which were previously discussed, or, if applicable, by the Alternate Design Method of Section 14.8, which will be covered shortly.

25. Design axial strength f = 0.65
The design axial strength fPn of a wall satisfying the limitations of this method is determined by Eq. (14-1), which is shown here. This design strength must be greater than or equal to the factored axial force Pu acting on the wall. This equation takes into consideration both load eccentricity and slenderness effects. The eccentricity factor 0.55 was originally selected to give strengths comparable to those given by Chapter 10 for members with axial load applied at an eccentricity of h/6. The strength reduction factor f corresponds to compression-controlled sections in accordance with Section Thus, f will typically be equal to 0.65 for wall sections.
f = 0.65

26. 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
In earlier editions of the code, the wall strength equation was based on the assumption that the top and bottom ends of the wall are restrained against lateral movement, and that rotation restraint exists at one end. These assumptions imply an effective length factor between 0.8 and 0.9. Axial load strength values based on this effective length factor could be unconservative for pinned-pinned end conditions, which can exist in certain walls, especially those in precast and tilt-up applications. Axial strength could also be overestimated where the top end of the wall is free and not braced against translation. To circumvent these situations, effective length factors are given in Section for the cases listed here. Selection of the proper k for a particular set of support end conditions is left to the judgment of the engineer. Figure R14.5 in the Commentary shows a comparison of the strengths obtained from the Empirical Design Method and Section 14.4 for members loaded at the middle third of the wall thickness with different end conditions. We will now move on to the last of the three design methods for walls.

27. 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
Lateral Load
Alternate Design of Slender Walls reworked in ACI ’08 – Alternate design allows for bypassing the moment magnification calculations in Section (loads = axial, end moments, or lateral loads)

28. Distribution of load within wall
Fifth, concentrated gravity loads applied to the wall above the design flexural section, which is at mid-height, must be distributed over widths equal to those shown in the figure for loads near the edge and at the interior of the wall. In the figure, W is the bearing length at the top of the wall, S is the spacing between concentrated gravity loads, and E is the distance from the edge of bearing to the edge of the wall.

29. Provisions cover
Factored moment Mu Out-of-plane service load deflection s

30. Factored moment Mu P e
By iteration By direct solution c u wu

31. + = Factored moment Mu by iteration u Solve by iteration e Mua Puu
Account for P-Delta Effects – Solution for Mu is Iterative.
Solve by iteration

32. Icr = moment of inertia of cracked section

33. Factored moment Mu by direct solution= + Pu
Mua
Puu u
Account for P-Delta Effects – Alternate Direct Solution, Es/Ec >= 6, h = thickness of wall, d = depth to steel, c = dist to neutral axis, lw = length of wall

34. Out-of-plane service load deflection
Service Deflection Limit P e
s  c / 150 c s
Loading
D + 0.5L + Wa or
D + 0.5L + 0.7E
(per ACI Commentary and
ASCE 7-10)
Service load Behavior – need to calculate Delta service Wa = service load wind, E = strength-based earthquake loading

35. Service Load DeflectionsMn Ma s
Mcr
(2/3)cr
(2/3)Mcr Ma s
Calculation delta service
cr n

36. Service load deflections for Ma  (2/3)McrP e
Ma = Service load moment at midheight including P-D c s
Calculation delta service
Service deflection
Find Ma by iteration

37. Service load deflections for Ma > (2/3)McrP e c s
Calculation delta service
Service deflection
Find Ma and Icr by iteration

38. Design of shear walls Shear parallel to the wall  in-plane shear
14.2 Design Methods

39. Shear wall

40. Design loading
Design for bending, axial load, and in-plane shear Bending and axial load: design as beam or column If hw  2lw, design is permitted using a strut-and-tie model (Appendix A)

41. Shear design

42. Effective depth d

44. Alternatively, use the lesser of

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

47. Horizontal shear reinforcement

48. Vertical shear reinforcement

49. Summary
Design of walls
Notation
General design requirements
Minimum reinforcement
Reinforcement around openings
Design of bearing walls (3 methods)
Design of shear walls

51. Figures copyright  2010 by McGraw-Hill Companies, Inc
Figures copyright  2010 by McGraw-Hill Companies, Inc Avenue of the America New York, NY 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

52. 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 Engineering
2142 Learned Hall
Lawrence, Kansas,
(785) Fax: (785)