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

This morning Slender columns Walls High-strength concrete

Walls (Chapters 14, 10, and 11)

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

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

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.

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.

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.

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.

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*

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

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

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

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 14.2 Design Methods

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.

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 10.10.1. In lieu of that procedure, the approximate evaluation of slenderness effects prescribed in Section 10.11 may be used.

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 14.5. 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.

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.

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 9.3.2.2. Thus, f will typically be equal to 0.65 for wall sections. f = 0.65

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 14.5.2 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.

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 10.10 (loads = axial, end moments, or lateral loads)

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.

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

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

+ = 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

Icr = moment of inertia of cracked section

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

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

Service Load Deflections Mn Ma s Mcr (2/3)cr (2/3)Mcr Ma s Calculation delta service cr n

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

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

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

Shear wall

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)

Shear design

Effective depth d

Alternatively, use the lesser of

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

Horizontal shear reinforcement

Vertical shear reinforcement

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

Figures copyright  2010 by McGraw-Hill Companies, Inc 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 Engineering 2142 Learned Hall Lawrence, Kansas, 66045-7609 (785) 864-3827 Fax: (785) 864-5631 daved@ku.edu