Concrete masonry walls provide benefits such as structural integrity, fire resistance, thermal insulation and mass, low maintenance, and an aesthetic versatility unmatched by any other single building material. Structurally, concrete masonry walls for warehouses, foundations, loadbearing walls, retaining walls, etc. can carry vertical loads as well as lateral loads imposed by wind, soil, or earthquakes. Where these loads are high or walls are especially tall, the use of pilasters may be advantageous to allow thinner wall sections.
A pilaster is a strengthened section that is designed to provide lateral stability to the masonry wall. Pilasters can be the same thickness as the wall but most often project beyond one or both wall faces. A bonded pilaster may be constructed as an integral part of the wall or, where provisions for crack control are provided such as with control joints, they may be constructed as an unbonded structural member where lateral support is provided through the use of suitable connections. Typical construction details are provided in Figures 1 and 2 which show both bonded and unbonded pilasters. Other methods of providing load transfer across the control joint for the unbonded condition may be utilized than as detailed in this TEK. See CMU-TEC-009-23 (ref. 2) for more options.
DESIGN
Typically, pilasters are subject to little or no vertical load other than their own weight, and as such serve as flexural members. Pilasters required in this type of service must be able to resist bending while transferring the applied loads from the walls to the roof and foundation system. While the primary purpose of a pilaster is to provide lateral support, in many cases it may also be required to support vertical loads such as those imposed by beams or other framing members. When this occurs, pilasters are designed as columns and function as primarily as compression members. A chart for the selection of appropriate pilaster size and reinforcement for a variety of lateral loading conditions is presented in Table 1.
Table 1 is based on the provisions of Building Code Requirements For Masonry Structures (ref. 1). The values in the table include the capacity of the tensile reinforcement only. If lateral ties are provided in accordance with ref. 1, the capacity of the compressive reinforcement may also be considered as shown in Figure 3.
Pilaster spacing is a function of the wall thickness, the magnitude of lateral loads, and the distribution of the lateral load to the vertical and horizontal supports. A relationship exists between the ratio of pilaster spacing to wall height and load distribution. Figures illustrating this relationship are available in Designing Concrete Masonry Walls For Wind Loads (ref. 3). Once the wall panel dimensions have been determined, the lateral load which must be resisted by the pilasters may be calculated as follows:
DESIGN EXAMPLE
A warehouse requires 24 ft (7.3 m) of clear space between the floor and ceiling for storage. The applicable building code specifies a minimum design wind load of 15 psf (718 Pa). Determine the required pilaster size and spacing for an 8 in. (203 mm) hollow unreinforced concrete masonry wall, constructed with Type S portland cement/lime or mortar cement mortar.
Choose the next lower modular spacing for the pilasters, 15’ 4” (4.67 m). The lateral load that must be resisted by each pilaster is:
Assuming the pilaster is simply supported at top and bottom, the maximum shear and moment on the pilaster are:
From Table 1, choose a 16 x 16 in. (406 x 406 mm) pilaster reinforced with four #5 bars.
REFERENCES
Building Code Requirements for Masonry Structures, ACI 530-99/ASCE 5-99/TMS 402-99. Reported by the Masonry Standards Joint Committee, 1999.
Crack Control Strategies for Concrete Masonry Construction, CMU-TEC-009-23, Concrete Masonry & Hardscapes Association, 2023.
Designing Concrete Masonry Walls For Wind Loads, TEK 14-03A, Concrete Masonry & Hardscapes Association, 2008.
Weights and Section Properties of Concrete Masonry Assemblies, CMU-TEC-002-23, Concrete Masonry & Hardscapes Association, 2023.
The CMHA Masonry Anchor Bolt Design Calculator is a spreadsheet-based calculator tool to aid in the design of anchor bolts used in masonry construction. The spreadsheet can calculate both bent-bar and headed anchor bolts, either in top-mount or face-mount configuration. Design is based on the 2013 version of TMS 402/ACI 530/ASCE 5. Calculations for both allowable stress as well as strength design are provided.
Masonry is a versatile and robust structural system. The available variety of materials, shapes and strengths offers countless opportunities to create many types of masonry elements. Masonry’s versatility offers a continuous spectrum of systems from unreinforced to reinforced or post-tensioned. One example of such versatility is reinforced diaphragm walls. While not specifically mentioned in Building Code Requirements for Masonry Structures (ref. 1), reinforced diaphragm walls can be designed and constructed using criteria in that standard.
Diaphragm walls are cellular walls composed of two wythes of masonry with a large cavity or void; the wythes are bonded together with masonry ribs or crosswalls (see Figure 1). The ribs are connected to the wythes in such a way that the two wythes act compositely, thereby giving a fully composite section. This TEK covers the structural design of reinforced diaphragm walls. See TEK 03-15, Construction of Reinforced Concrete Masonry Diaphragm Walls, (ref. 2) for construction.
Figure 1 shows an example of a diaphragm wall constructed with concrete masonry units and its associated terminology. The reinforced wythes can be fully or partially grouted. The exterior face can be treated as the weathering side of the wall as shown in Figure 1, or a drainage cavity and anchored veneer can be used on the exterior face. The internal cavity (void) of the diaphragm wall is left open for utilities.
Figure 1—Typical Reinforced Diaphragm Wall
ADVANTAGES
Reinforced diaphragm walls present several opportunities for masonry design.
These include:
1. Diaphragm construction can efficiently create strong, stiff walls with individual units bonded together. Consider the economy of building a 24-in. (610-mm) thick wall with two 6 in. (152 mm) wythes and a 12 in. (305 mm) cavity rather than a solid 24 in. (610 mm) wall.
2. Thick diaphragm walls can be designed to span much further horizontally or vertically than single wythe walls or conventional composite walls. It is also possible to make very tall walls by virtue of the large sectional stiffness (ref. 3).
3. The greater thickness of diaphragm walls can also be used to replicate historic walls (buildings of Gothic style, monasteries, etc.) using modern methods.
4. The walls can have exposed, finished surfaces inside and out, and those finishes can be different because they are created by two individual wythes of masonry units.
5. The exterior wythe can be flashed and drained similar to the conventional back-up of an anchored veneer in cavity wall construction as detailed in TEK 19-05A, Flashing Details for Concrete Masonry Walls, or for single wythe walls per TEK 19-02B, Design for Dry SIngle-Wythe Concrete Masonry Walls, (refs. 4, 5).
6. The large interior voids allow for placement of insulation and utilities.
7. These walls can generate significant out-of-plane load capacity while supporting in-plane lateral loads.
8. The two distinct wythes provide a resilient system that can resist debris penetration from a high wind event and also provide great protection to potential blasts. With the high out-of-plane lateral load resistance, these walls can provide a good option for safe rooms or community rooms in tornado and hurricane regions.
HISTORICAL PERSPECTIVE
Unreinforced diaphragm walls have been used in Great Britain for decades. Many have been built using both concrete and clay masonry (Reference 3 provides wall diaphragm design criteria for concrete masonry assemblies used in Great Britain). The philosophy for unreinforced masonry in flexure is that the mortar controls the flexural tensile resistance and the composite of masonry and mortar controls both the compressive and shear stresses.
Valuable characteristics of unreinforced diaphragm walls are that the net section properties are easily calculated and they have a large moment of inertia. Given that they are thick, unreinforced diaphragm walls are effective at resisting out-of-plane loads and are inherently very stiff. However, unreinforced walls often crack before deflections control the performance. To further increase the bending resistance of unreinforced diaphragm walls, many walls in Great Britain have been posttensioned. The post-tensioning tendons are often placed in the void, unbounded and unrestrained, and protected from corrosion.
Unreinforced diaphragm walls have been used for sports halls, swimming pools, theaters, cinemas and other buildings that require tall walls. Other applications include tall freestanding walls, retaining walls, and replicating historical construction.
Figure 2 shows a fire station in Great Britain with posttensioned diaphragm sidewalls (arrows). These walls provide lateral stability for the building in both directions. As with traditional masonry buildings, the sidewalls are shear walls and resist loads acting on the front and rear of the building. In the transverse direction (plane of the overhead doors), the large openings leave short pier sections. Therefore, the diaphragm walls are designed to act as cantilever walls to provide the transverse building stability. This is a unique design solution because most masonry buildings do not depend upon the out-of-plane strength and stiffness of the walls to provide stability against lateral loads. Diaphragm walls, however, can be designed with sufficient thickness to develop the necessary out-of-plane strength and stiffness.
Figure 3 shows a cross-section of a bridge abutment and a photograph of the completed bridge where unreinforced post-tensioned brick diaphragm walls were used. Various bridges also use diaphragm walls for the cantilever wingwalls.
Unreinforced diaphragm walls have not been specifically addressed by name in codes and standards in the United States. Even the definition of a diaphragm wall does not exist. However, Building Code Requirements for Masonry Structures (the MSJC Code) includes design methodologies for unreinforced masonry using allowable stress design and strength design, as well as design criteria for composite assemblies. Therefore, unreinforced diaphragm walls can be designed using the existing standards, despite the fact that there is no specifically stated diaphragm wall criteria.
Figure 2—Fire Station With Diaphragm Wall (courtesy of Malcolm Phipps)
REINFORCED DIAPHRAGM WALLS
Even though unreinforced masonry is possible in areas of the United States, reinforced masonry is more widely adopted. Most regions require reinforcement for commercial masonry construction based upon the International Building Code (IBC) (ref. 6).
The MSJC provides design methodologies for reinforced masonry using allowable stress methods, post-tensioning, and strength design. These provisions can all be applied to reinforced concrete masonry diaphragm walls.
Design Detailing
Regardless of the design method utilized, there are some detailing criteria that apply equally to all reinforced diaphragm walls. These criteria are outlined below.
a) Spacing of Ribs
The ribs of the reinforced diaphragm wall act as webs for out-of-plane loads and connect the wythes structurally to create a composite section.
It is preferable that the ribs be spaced so that the flanges are fully effective in resisting applied loads. This is controlled by MSJC Section 5.1.1.2 which governs wall intersections. For reinforced walls where both flanges experience compression and tension, the MSJC requires the effective flange width on either side of the web to not exceed 6 times the flange thickness or 0.75 times the floor-to-floor height. In addition, the effective flange width must not extend past a control joint.
Therefore, the effective clear spacing between ribs is 12·twythe for walls without control joints (6·twythe from each rib), and the effective flange width is 12·twythe plus trib. Figure 4 illustrates how this effective flange width is smaller when a control joint is located at a rib. When placing a control joint between ribs, center the control joint and the effective flange remains 12·twythe plus trib.
b) Flange Thickness
The masonry unit selected for the flange wythe dictates the flange thickness (twythe). To accommodate reinforcement, a 6-in. (152-mm) concrete masonry unit is the smallest practical unit to be used. Larger units can be used to accommodate larger bars and provide larger compression areas.
c) Grouting
The choice of full vs. partial grouting is a function of design:
1. If the compression area required by out-of-plane design exceeds the face shell thickness of the wythe, the recommendation is to fully grout the flanges. Alternatively, the designer can use partial grouting and perform a T-beam analysis on the wall.
2. If the compression area does not exceed the face shell thickness of the wythe, either partial or full grouting can be used without using the more cumbersome T-beam analysis.
3. The ribs are often fully grouted, but they can also be designed with partial grouting.
d) Masonry Bond
TMS 402 Section 5.1.1.2.1 requires that intersecting walls be constructed in running bond for composite flanging action to occur. Therefore, reinforced diaphragm walls are always constructed in running bond.
e) Connecting the Ribs to the Wythes
MSJC Section 5.1.1.2.5 requires that the connection of intersecting walls conform to one of the following requirements:
1. At least fifty percent of the masonry units at the interface must interlock.
2. Walls must be anchored by steel connectors grouted into the wall and meeting the following requirements:
(a) Minimum size: 1/4 in. x 1-1/2 in. x 28 in. (6.4 x 38.1 x711 mm) including a 2-in. (50.8-mm) long, 90-degree bend at each end to form a U or Z shape. (b) Maximum spacing: 48 in. (1,219 mm).
3. Intersecting reinforced bond beams must be provided at a maximum spacing of 48 in. (1,219 mm) on center. The minimum area of reinforcement in each bond beam is 0.1 in.2 per ft (211 mm2/m) multiplied by the vertical spacing of the bond beams in feet (meters). Reinforcement is required to be developed on each side of the intersection.
The use of bond beams in requirement 3 above is one way of handling the interface shear requirement. However, the equations below can also be used for this purpose: For allowable stress design: fv = V/An TMS 402 Section 8.3.5.1.1 (Eqn. 8-21) where Fv is controlled by Section 8.3.5.1.2. For strength design, the shear strength, fv, is controlled by Sections 8.3.5.1.2 and 8.3.5.1.4.
f) Control (Movement) Joints
CMU-TEC-009-23, Crack Control Strategies for Concrete Masonry Construction (ref. 7) are the industry standards for determining control joint spacing. Both were developed for single wythe walls with and without horizontal reinforcement.
There is no specific research on shrinkage characteristics of reinforced diaphragm walls. The expectation is that the ribs restrain shrinkage movement of the wythes and the resulting spacing of control joints can be increased over what would be expected for a single wythe wall. Until research becomes available, however, the current recommendation is to use the existing industry crack control recommendations to space control joints for reinforced diaphragm walls.
Additional attention must be placed on the size of the corner control joints if the diaphragm walls are used to support out-ofplane loads (see Example 1).
Allowable Stress Design of Reinforced Diaphragm Walls
Reinforced masonry designed using allowable stress design (ASD) methods follows similar guidelines as that used for unreinforced masonry. The maximum wall height is controlled by the loadings and slenderness effects. The slenderness effects are based upon the h/r ratio and prevent the wall from buckling.
The design methodology for reinforced diaphragm walls is similar to reinforced single wythe wall design and is discussed in TEK 14-07C, ASD of Concrete Masonry (2012 IBC & 2011 MSJC) (ref. 8).
Strength Design of Reinforced Diaphragm Walls
The strength design method has no specific limit on h/t. However, it has design criteria that limit service load deflections and ultimate moment capacity for out-of-plane loads. The service load deflections cannot exceed 0.7 percent of the wall height. For a 30-ft (9.1 m) wall, that is 2.5 in. over 30 ft (64 mm over 9.1 m) for a simply supported wall.
There is an axial load capacity limitation when h/t exceeds 30: the factored axial load for these walls must be limited to 5 percent of f’m based upon the gross section properties.
The design methodology is similar to single wythe design and is discussed in CMHA TEK 14-11B, Strength Design of CM Walls for Axial Load & Flexure (ref. 9)
Reinforced Concrete Masonry Diaphragm Walls Using Post-tensioned Masonry Design
Post-tensioned masonry design of diaphragm walls is the same as single wythe design. However, the large void in diaphragm walls provides an opportunity for the tendons to be placed eccentrically as needed for the loadings. Placed inside the void, the tendons are generally unbonded and unrestrained.
Seismic Design
The MSJC Code and ASCE 7 (refs. 1, 11) provide additional criteria for seismic design of walls that need to be considered as for any other masonry wall. This includes the degree of grouting and the inclusion of prescriptive reinforcement.
Figure 3—Cross-Section of Diaphragm Walls for Abutment and Completed Bridge (courtesy of Malcolm Phipps)
Figure 4—Effective Flange Width, beffective
DESIGN EXAMPLE: WINGWALL DESIGN FOR A REINFORCED CONCRETE MASONRY MAINTENANCE STORAGE FACILITY
Figure 5 shows the basic building layout for the design example. The front and rear walls are perforated with 20 ft x 20 ft (6.1 x 6.1 m) overhead doors for vehicle access. Control joints are shown over the door openings; the pier sections are 6 ft (1.8 m) in length. The endwalls have personnel access openings. Because the front and rear walls are perforated, the pier sections may not have sufficient in-plane stiffness and strength. Therefore, the endwalls should be designed to brace the building in both directions.
Although the roof structure is not shown, long-span joists bear on the front and rear sidewalls (i.e., the walls with the large perforations); the endwalls are nonloadbearing. The roof diaphragm would be designed to distribute the frontrear lateral loads to the endwalls, which must be designed as conventional shear walls. Conventional shear wall design is covered by the Masonry Designer’s Guide (ref. 12) and is not covered here.
The roof diaphragm will not be used to brace the side-toside lateral forces. For this example, the out-of-plane design (the large red arrow in Figure 5 depicts the out-of-plane load) will treat the endwalls as diaphragm walls acting as cantilevers to brace the building for the side-to-side lateral loads similar to Figure 2. This decision exempts the roof diaphragm from the strength and stiffness requirements for lateral loads that are perpendicular to the plane of the roof trusses. These requirements are typically met by horizontal braces between roof trusses.
Input: Location: Coastal US, South Carolina Loadings: ASCE 7-16, Part 2 for wind design Masonry Standard: TMS 402, ASD method Because no bracing is used at the top of the wall, component and cladding loads will be used to design the wall.
1. Proposed wall section
Use 6-in. (152-mm) concrete masonry units for wythes and 8-in. (203-mm) for ribs (see Figure 1).
The three possible options are: a) Using CMU-TEC-009-23 (empirical method), space control joints at the lesser of 1.5h = 45 ft (13.7 m), max 25 ft (7.62 m). The 25 ft (7.62 m) criteria governs. The required horizontal reinforcement in the walls is 0.025 in.2/ft (CMUTEC-009-23, Table 1). This corresponds to two-wire W1.7 TEK 14-24 5 CONCRETE MASONRY & HARDSCAPES ASSOCIATION masonryandhardscapes.org (9 gauge, MW11) joint reinforcement at 16 in. (406 mm) on center vertically over the height of the wall (CMUTEC-009-23, Table 2).
b) Using CMU-TEC-009-23 (alternative engineered method), space control joints at the lesser of 2.5h = 75 ft or 25 ft (7.62 m). Again, the 25 ft (7.62 m) criteria governs. The required horizontal reinforcement in the walls is 0.0007An , which corresponds to 0.064 in2/ft or two-wire W1.7 (9 gauge, MW11) wire joint reinforcement at 24 in. (610 mm) on center vertically over the height of the wall (CMUTEC-009-23, Table 5).
c) Using CMU-TEC-009-23, space control joints at any length provided the horizontal reinforcement in the walls exceeds 0.002An (CMU-TEC-009-23). This corresponds to 0.183 in2/ft or two No. 6 (M#19) reinforcing bars in bond beams at 32 in. (813 mm) on center vertically over the height of the wall (CMU-TEC-009-23, Table 6 for fully grouted walls).
To minimize the possible number of control joints, select option c) with the horizontal bond beams. Provide control joints only at the corners (Figure 5). If the designer chooses to use horizontal joint reinforcement and not bond beams, the maximum control joint spacing would be 25 ft (7.62 m) using either options a) or b).
While the inner wythe will generally be exposed principally to shrinkage with only minor thermal effects, it is common to reinforce both wythes similarly.
3. Determine wind loads
From ASCE 7-16 Part 2, the suction load at the Exterior Zone (5) is calculated as 66.3 psf (3.17 kPa) (see Figure 6). In ASCE 7, wind loads are strength level. Roof dead load is ignored at the nonbearing wall.
4. Determine base of wall loads
Vu = 66.3 psf × 30 = 1,989 lb/ft of wall (29.0 kN/m) Mu = 66.3 x (30)2/2= 29,835 ft-lb/ft of wall (132 kN-m/m) Vser = 0.6 Vu = 1,193 lb/ft of wall (17.4 kN/m) Mser = 0.6 Mu = 17,901 ft-lb/ft of wall (79.6 kN-m/m) Note: 0.6 reduces Vu to ASD per ASCE 7.
5. Determine beffective
in field of wall (solid region away from openings): beffective = 12twythe + trib = 12(6 in.) + 8 in. = 80 in. (2,032 mm)
6. Determine minimum twall to satisfy shear capacity
Vrib = Vser × 80/12 = 7,953 lb (35.4 kN) fv = Vrib/Arib = 7,953/[(7.63 in.)·twall] (TMS 402, Equation 8-21) Fv ≤ 2 √f’m γg = 89 psi, assuming M/Vd > 1.0 and γg = 1.0 (MSJC Code, Equation 8-24) This produces twall ≥ 11.7 in. (297 mm) Checking M/Vd = 17,901/[1,193 x (<1 ft)] = 15.0 > 1.0 OK Shear is not an issue. The prescriptive requirements for the intersection of the ribs and flanges are sufficient.
7.Determine minimum twall due to moment capacity
Try a rib length of 1.5 courses of concrete masonry. twall = 15.625 in. unit + 0.375 in. mortar joint + 7.625 in. half unit = 23.63 in. (600 mm) d = 23.63 in. – (5.63 in./2) = 20.82 in. (529 mm) Ignoring axial load, As (estimated) = Mser /(2.16d) = (17,901/1,000)(2.16 x 20.82 in)(529 Mm) Try No. 8 at 24 in. o.c. (As = 0.40 in.2/ft) (M#25 at 610 mm o.c.)
8. Determine wall dead load at base of wall
From CMU-TEC-002-23 (ref. 16): wall weight of 125 pcf 6 in. fully grouted concrete masonry = 62 psf (303 kg/m2 )
125 pcf 8 in. fully grouted = 84 psf (411 kg/m2 ) Flange load: 2 wythes x 62 psf = 124 psf per ft Rib load: [23.63 in. – 2(5.63 in.)]/12 x 84 psf/80 in./12 = 13.0 psf/ft of wall
PDL = (124 + 13.0) x 30 ft = 4,110 lb/ft of wall (60 kN/m)
9. Load combination
0.6 PDL + 0.6W from ASCE 7-10 for ASD
Note: This one load combination is shown for this example. The designer must check all combinations required by ASCE 7. P = 0.6PDL = 0.6 (4,110) = 2,466 lb/ft (36 kN/m) M = 0.6 Mu, wind = Mser = 17,901 ft-lb/ft (79.6 kN-m/m)
10. Determine n
From MSJC Section 4.2.2: Es = 29,000,000 psi (200,000 MPa) Em = 900f’m = 1,800,000 psi (12,410 MPa) n = Es/Em = 16.1 For As = 0. 44 in.2 /ft (from 7 above),
nρ = nAs /bd = 16.1(0.4)/12(20.82) = 0.026 If P = 0, k = √ (nρ)2 + 2nρ – nρ = 0.204; j = 1- (k/3) = 0.932
kd = 4.25 > tface of 6-in. CMU but less than the wythe thickness. Axial load may increase kd. Therefore, grouting the full wythe is appropriate.
11. Design for PDL and M
(see Figure 7) From statics: P = C – T M = C x em + T (d – twall/2) Per foot: C = 1/2(kd)fm x 12 in. fm = Emεm T = As fs fs = Es εs em = twall/2 – kd/3
From strain compatibility: εm/kd = εs(d – kd) (fm /Em)/kd = (fs/Es)/(d – kd) → fs = n [(d – kd)/kd] fm Therefore, C = 6(kd)fm T = 0.4(16.1)((20.82 – kd)/kd)) fb = 6.44((20.82 – kd)/(kd)) fb Solving for P = C – T and M = C em + T (d – twall/2) gives kd = 4.65 in. (118 mm) and fb = 498 psi (3.4 MPa) Checking: C = 12,449 lb (55 kN) T = 10,030 lb (44 kN) P = 2,419 lb (10.7 kN) OK em = twall/2 – kd/3 = 10.27 in. (264 mm) M = Cem + T (d – twall/2) = 12,449(10.27)/12 + 10,030(20.82 – 23.63/2)/12 = 18,185 ft-lb approx. = M =17,901 ft-lb OK Check: fm = 498 psi < Fb = 0.45 f’m = 900 psi (6.2 MPa) OK (TMS 402 8.3.4.2.2) fs = 16.1((20.82 – 4.86)/4.86) 417 psi = 22,047 psi (152 MPa) fs < Fs = 32,000 psi (221 MPa) OK (MSJC 8.3.3.1)
MSJC Section 8.3.4.2.2 requires an additional check for fa alone. The design engineer is generally advised to perform this check. However, it rarely controls for diaphragm walls due to the stiff wall section. For this example, there is no applied axial load so the check is not required.
Therefore, this section checks using No. 8 bars at 24 in. on center (M#25 at 610 mm) in a fully grouted diaphragm wall. Note that this only applies to the end zone in suction. The design calculations should be repeated:
a. for pressure load on the end zone,
b. for pressure and suction over the interior zone,
c. over the height of the wall to reduce the amount of vertical reinforcement, and
d. the design should be checked adjacent to control joints and openings.
Using the walls to support of out-of-plane loads requires the foundations to be designed and detailed for the cantilever walls.
12. Check deflection at top of the wall for a cantilever
Using loads and section properties for beffective.
Provide the control joints between the sidewalls and the front/ rear walls. Construct with sealant that has a shear capacity of 50% of the joint thickness, the joint thickness should exceed 2 x 0.56 in. = 1.12 in. (28 mm). See white arrow on Figure 5.
Figure 5—Maintenance Facility for Design Example 1
Figure 6—Wall Sections
Figure 7—Force and Strain Diagrams
SUMMARY
Reinforced concrete masonry diaphragm walls provide opportunities for engineers to design a) very tall walls and b) brace walls using the diaphragm walls as cantilevers. For buildings, these are two unique options that are not normally available from traditional masonry walls.
NOTATIONS
An = net cross-sectional area of a member, in.2 (mm2) As = area of nonprestressed longitudinal tension reinforcement, in.2(mm2) b = width of section, in. (mm) beffective = effective width of section, in. (mm) C = resultant compressive force, lb (N) c = distance from the fiber of maximum compressive strain to the neutral axis, in. (mm) d = distance from extreme compression fiber to centroid of tension reinforcement, in. (mm) Em = modulus of elasticity of masonry in compression, psi (MPa) Es = modulus of elasticity of steel, psi (MPa) em = eccentricity of axial load, in. (mm) Fm = allowable compressive stress, psi (MPa) fm = calculated compressive stress in masonry due to axial and flexure, psi (MPa) Fv = allowable shear stress, psi (MPa) Fs = allowable tensile or compressive stress in reinforcement, psi (MPa) fa = calculated compressive stress in masonry due to axial load only, psi (MPa) f’m = specified compressive strength of clay masonry or concrete masonry, psi (MPa) fr = modulus of rupture, psi (MPa) fs = calculated tensile or compressive stress in reinforcement, psi (MPa) fv = calculated shear stress in masonry, psi (MPa) fy = specified yield strength of steel for reinforcement and anchors, psi (MPa) h = effective height of wall, in. (mm) Icr = moment of inertia of cracked cross-sectional area of a member, in 4 (mm4) Ig = moment of inertia of gross cross-sectional area of a member,, in.4 (mm4) j = ratio of distance between centroid of flexural compressive forces and centroid of tensile forces to depth, d k = ratio of the distance between the compression face of an element and the neutral axis to the effective depth d M = maximum moment at the section under consideration, in.-lb (N-mm) Mcr = nominal cracking moment strength, in.-lb (N-mm) Mser = service moment at midheight of a member, in.-lb (N-mm) Mu = factored moment, magnified by second-order effects where required by the code, in.-lb (N-mm) n = modular ratio, Es/Em P = axial load, lb (N) PDL = axial load due to dead load, lb (N) Pu = factored axial load, lb (N) r = radius of gyration, in. (mm) Sg = section modulus of the gross cross-sectional area of a member, in.3(mm3) T = resultant tensile force, lb (N) t = nominal thickness of member, in. (mm) tface = specified thickness of masonry unit faceshell, in. (mm) trib = specified thickness of diaphragm wall rib, in. (mm) tsp = specified thickness of member, in. (mm) twall = specified thickness of wall, in. (mm) twythe = specified thickness of the masonry wythe, in. (mm) V = shear force, lb (N) Vrib = shear capacity (resisting shear) of diaphragm wall rib, lb (N) Vser = service level shear force, lb (N) Vu = factored shear force, lb (N) W = wind load, psf (kPa) γg = grouted shear wall factor δ = moment magnification factor εm = compressive strain of masonry εs = strain of steel f = strength reduction factor ρ = reinforcement ratio
References
Building Code Requirements for Masonry Structures, TMS 402-16, Reported by The Masonry Society 2016.
Construction of Reinforced Concrete Masonry Diaphragm Walls, TEK 03-15, Concrete Masonry & Hardscapes Association, 2017.
Aggregate Concrete Blocks: Unreinforced Masonry Diaphragm Walls, Data Sheet 10. Concrete Block Association of Great Britain, March 2003.
Flashing Details for Concrete Masonry Walls, TEK 19-05A, Concrete Masonry & Hardscapes Association, 2008.
Design for Dry Single-Wythe Concrete Masonry Walls, TEK 19-02B, Concrete Masonry & Hardscapes Association, 2012.
International Building Code. International Code Council, 2015/2018.
Crack Control Strategies for Concrete Masonry Construction, CMU-TEC-009-23, Concrete Masonry & Hardscapes Association, 2023.
TEK 14-07C, ASD of Concrete Masonry (2012 IBC & 2011 MSJC). Concrete Masonry & Hardscapes Association, 2013.
TEK 14-11B, Strength Design of CM Walls for Axial Load & Flexure. Concrete Masonry & Hardscapes Association, 2003.
Minimum Design Loads for Buildings and Other Structures, ASCE/SEI 7-10. American Society of Civil Engineers, 2010.
Masonry Designers’ Guide, Seventh Edition, MDG-7. The Masonry Society, 2013.
Standard Specification for Loadbearing Concrete Masonry Units, ASTM C90-14. ASTM International, Inc., 2014.
Standard Specification for Deformed and Plain CarbonSteel Bars for Concrete Reinforcement, ASTM A615/ A615M-14. ASTM International, Inc., 2014.
Standard Specification for Grout for Masonry, ASTM C476-10. ASTM International, Inc., 2010.
Standard Specification for Mortar for Unit Masonry ASTM C270-14. ASTM International, Inc., 2014.
Weights and Section Properties of Concrete Masonry Assemblies, CMU-TEC-002-23.Concrete Masonry & Hardscapes Association, 2023.
When selecting a building enclosure, concrete masonry cavity walls are considered to be one of the best solutions available for all types of buildings. From both an initial cost and life-cycle cost perspective, cavity wall construction is highly regarded as the prime choice in many applications.
Cavity walls typically consist of an inner wythe of concrete masonry units that are tied to an exterior wythe of architectural masonry units. The cavity space between the wythes is normally 2 to 4 ½ in. (51 to 114 mm) wide, easily accommodating rigid board insulation. The two wythes together provide a wall that is highly resistant to wind driven rain, absorbs and reflects sound, provides good thermal performance, and has excellent fire resistance characteristics.
Masonry walls constructed of two or more wythes can technically be classified in one of three ways, depending on how the wythes are designed and detailed. These wall types include composite, noncomposite and veneer assemblies. In noncomposite construction, covered in this TEK, each wythe is connected to the adjacent wythe with metal wall ties, but they are designed such that each wythe individually resists the loads imposed on it. Composite walls are designed so that the wythes act together as a single element to resist structural loads. This requires the masonry wythes to be connected by masonry headers or by a mortar- or grout-filled collar joint and wall ties (see ref. 4). In a veneer wall, the backup wythe is designed as the loadbearing system while the veneer provides a nonloadbearing architectural wall finish that transfers loads to the backup wythe through wall ties (see refs. 5, 6). Although Building Code Requirements for Masonry Structures (ref. 1) defines a cavity wall as a noncomposite masonry wall, the term cavity wall is also commonly used to describe a veneer wall with masonry backup.
This TEK illustrates the design of noncomposite concrete masonry walls based on Building Code Requirements for Masonry Structures (ref. 1), referred to here as the MSJC code. Each wythe of a noncomposite wall system can be designed to accommodate all types of loads, including gravity loads from roofs, walls and floors, as well as lateral loads from wind or earthquakes. The MSJC code design provisions are used to size these masonry walls.
STRUCTURAL DESIGN
The MSJC code includes noncomposite design provisions for both allowable stress design (Chapter 2) and empirical design (Chapter 5). The assumptions and relevant governing equations for each of these design approaches is given in references 2 and 3 respectively.
Concrete masonry cavity walls can be designed as either reinforced or unreinforced walls. For unreinforced design, flexural tensile stresses in masonry are resisted by bond developed between the masonry units and mortar; axial tension is not permitted (ref. 1). If direct axial tension is encountered in a design, reinforcement must be used. In reinforced masonry design, all tension is assumed to be resisted by reinforcement.
Empirical Design
Empirical design can be an expedient approach for typical loadbearing structures subjected to nominal wind loads (basic wind speed ≤ 110 mph, (177 km/h) (MSJC 5.1.2.2) and located in areas of low seismic risk, as it cannot be used for the design of seismic force resisting systems in SDC (Seismic Design Category) B or higher (MSJC 5.1.2.1). Empirical design utilizes prescriptive provisions, outlining criteria such as wall height to thickness ratios, minimum wall thickness and maximum building height.
References 1 and 3 contain maximum length-to-thickness or height-to-thickness ratios for empirically designed walls. When using these ratios for noncomposite multiwythe walls, the total wall thickness is taken as the sum of the nominal thicknesses of each wythe, neglecting the presence of any cavity thickness. Compressive stress is based on the gross cross-sectional area of all wythes, including hollow cells but not including the cavity between the wythes. When floor or roof loads are carried on only one wythe, only the gross cross-sectional area of that wythe is used to check the axial capacity. In addition, these walls must meet the following requirements for wall ties connecting the wythes:
wall ties of wire size W2.8 (3/16 in., MW 18), or metal wire of equivalent stiffness, spaced at a maximum of 24 in. (610 mm) o.c. vertically and 36 in. (914 mm) o.c. horizontally, with at least one wall tie for each 4½ ft² (0.42 m²) of wall area,
walls constructed with hollow units must use rectangular ties,
walls constructed with solid units must use Z-shaped ties with hooks at least 2 in. (51 mm) long,
wall ties may not have drips,
additional ties are required within 12 in. (305 mm) of all openings and must be spaced no more than 3 ft (914 mm) apart around the perimeter of the opening.
Requirements for bonding with joint reinforcement are the same as those for wall ties with the following exceptions: cross wire size may not be smaller than W1.7 (9 gage, MW 11) and the supported wall area per cross wire may not exceed 2⅔ ft² (0.25 m²). In addition, the longitudinal wires must be embedded in mortar.
Allowable Stress Design
Similar to empirical design, MSJC allowable stress design includes prescriptive requirements for bonding wythes of noncomposite walls via wall ties, adjustable ties and joint reinforcement.
For rectangular ties, Z ties (for use with other than hollow units) and ladder or tab-type joint reinforcement, ties or cross wires of joint reinforcement, ties must be placed with a maximum spacing of 36 in. (914 mm) horizontally and 24 in. (610 mm) vertically. The minimum number of ties is one per:
2⅔ ft² (0.25 m²) of wall for wire size W 1.7 (9 gage, MW 11), and
4½ ft² (0.42 m²) of wall for wire size W 2.8 (3/16 in., MW 18).
For adjustable ties, one tie must be provided for each 1.77 ft² (0.16 m²) of wall; maximum horizontal and vertical spacing is 16 in. (406 mm); misalignment of bed joints from one wythe to the other may not exceed 1 ¼ in. (31.8 mm); the maximum clearance between connecting parts of the tie is 1/16 in. (1.6 mm); and pintle ties must have at least two pintle legs of wire size W2.8 (3/16 in., MW 18) (see also Figure 1).
For noncomposite masonry walls, the following additional requirements apply.
Collar joints are not to contain headers, or be filled with mortar or grout.
Gravity loads from supported horizontal members are to be resisted by the wythe nearest the center of the span.
Bending moments about the weak axis of the wall and transverse loads are distributed to each wythe according to relative stiffness. This can be determined by: Wi = WT [EmIi/(EmIi+ EmI0)] Wo = WT [EmI0/(EmIi+ EmI0)]
Loads acting parallel to the wall are resisted by the wythe to which they are applied.
The cavity width between the wythes is limited to 4½ in. (114 mm) unless a detailed wall tie analysis is performed.
The following examples illustrate the use of noncomposite masonry employing empirical and allowable stress design methods. Although there are no specific provisions in MSJC for noncomposite wall design using strength design, strength design could be used provided the same load distribution principles as presented for allowable stress design are employed.
Empirical Design Design Example: Design the top story of a two-story noncomposite double wythe masonry wall system supported on continuous footings. Note that the design of the lower story, though not shown, is performed in the same manner, except that the floor live and dead loads from the upper story are also accounted for.
Given:
unsupported wall height
= 10 ft (3.01 m)
superimposed gravity dead load
= 220 plf (3.2 kN/m)
superimposed gravity live load
= 460 plf (6.7 kN/m)
net superimposed uplift from wind
= 120 plf (1.8 kN/m)
wind pressure
= 24 psf (1,149 Pa)
eccentricity of all gravity loads
= 0
f’m
= 1,500 psi (10.3 MPa)
Em
= 1,350 ksi (9,308 MPa)
Wall lateral support requirement: l/t or h/t < 18, so minimum required wall thickness = h/18 = 10 ft (12 in./ft)/18 = 6.7 in. (169 mm)
Try a 4-in. (102 mm) outer wythe and 6-in. (152 mm) inner wythe (providing a total nominal wall thickness of 10 in. (254 mm)), and check allowable axial compressive stress due to dead and live loads (gravity loads are carried by the inner wythe only):
dead:
roof
220 lb/ft
wythe = 10 ft x 26 psf (ref. 8)
260 lb/ft
live:
roof
460 lb/ft
total load:
940 lb/ft (13.7 kN/m)
Gross area of 6-in. (152-mm) wythe = 67.5 in.²/ft (ref. 7) fa = 940 lb/ft/(67.5 in.²/ft) = 13.9 psi (0.096 MPa) Fa = 75 psi (0.52 MPa) for Type M or S mortar, 70 psi (0.48 MPa) for Type N mortar (ref. 1) fa < Fa (OK for all mortar types)
Per MSJC code section 5.8.3.1, the net uplift on the roof must be resisted by an anchorage system. Use a bond beam at the top of the inner wythe with vertical reinforcement to the foundation to provide this resistance.
ASD Reinforced Design Example: Given:
unsupported wall height
= 18 ft (5.5 m)
wind load, w
= 36 psf (1,724 Pa)
net roof uplift at top of wall
= 400 plf (5.8 kN/m) )
eccentricity of all vertical loads
= 0
f’m
= 1,500 psi (0.0718 MPa )
unit density
= 115 pcf (1,842 kg/m³)
Grade 60 reinforcement
Note: The 36 psf (1,724 Pa) wind load is much higher than is generally applicable when using empirical design.
Design the inside wythe first, as it must resist the uplift in addition to the flexural loads. Try two 6-in. (152 mm) wythes with No. 5 (M #16) reinforcement at 32 in. (813 mm) o.c.
Determine reinforcement needed for uplift at midheight: uplift = 400 lb/ft – 34 lb/ft² (18 ft/2) = 94 lb/ft (1.37 kN/m) (ref. 8) reinforcement needed = [(94 lb/ft)(32 in.)/(12 in./ft)]/[1.333(24,000 psi)] = 0.0078 in.² As available for flexure = 0.31 – 0.0078 = 0.3022 in.² Ms = FsAsjd = 1.333 (24,000 psi) (0.3022 in.²)(0.894)(2.813 in.) = 24,313 lb-in. for 32 in. width = 9,117 lb-in./ft (3,378 N⋅m/m) > 8,996 lb-in./ft (3,333 N⋅m/m), therefore Mm controls
Determine applied moment: Since the wythes are identical, each would carry ½ the lateral load or ½ (36 psf) = 18 psf (124 kPa) Mmax = wl²/8 = (18 psf)(18 ft)²(12 in./ft)/8 = 8,748 lb-in./ft (3,241 N⋅m/m) < 8,996 lb-in./ft (3,333 N⋅m/m) OK
A quick check of the outside wythe shows that the same reinforcement schedule will work for it as well. Therefore, use two 6-in. (152-mm) wythes with No. 5 (M #16) vertical reinforcement at 32 in. (813 mm) o.c.
This wall could be designed using an unreinforced 4-in. (102 mm) outside wythe and a reinforced 8-in. (203-mm) inside wythe, with lateral loads distributed to each wythe according to the uncracked stiffness per MSJC section 1.9.2. Experience has shown, however, that the design would be severely limited by the capacity of the unreinforced outside wythe. Additionally, such a design could be used only in SDC A or B since 4-in. (102 mm) concrete masonry does not have cores large enough to reinforce.
Another alternative would be to design this system treating the 4 in. (102 mm) outer wythe as a nonloadbearing veneer. Designing this wall as a 4-in. (102 mm) veneer with an 8-in. (203 mm) reinforced structural backup wythe would result in No. 5 bars at 16 in. (M #16 at 406 mm) on center. This is the same amount of reinforcement used in the example above (two 6-in. (152 mm) wythes with No. 5 (M #16) at 32 in. (813 mm) on center). However, because the 6-in. (152 mm) units have smaller cores, 30% less grout is required.
The design using two 6-in. (152-mm) reinforced wythes has the following advantages over veneer with structural backup:
no limitation on SDC as when a veneer or an unreinforced outer wythe is used,
no limitation on wind speed as with a veneer,
equal mass on both sides of the wall permitting the use of the prescriptive energy tables for integral insulation, and
the flexibility of using units with different architectural finishes on each side.
NOMENCLATURE
As = effective cross-sectional area of reinforcement, in.²(mm²) b = width of section, in. (mm) d = distance from extreme compression fiber to centroid of tension reinforcement, in. (mm) Em = modulus of elasticity of masonry, psi (MPa) Es = modulus of elasticity of steel, psi (MPa) Fa = allowable compressive stress due to axial load only, psi (kPa) Fb = allowable compressive stress due to flexure only, psi (kPa) Fs = allowable tensile or compressive stress in reinforcement, psi (kPa) Fv = allowable shear stress in masonry, psi (MPa) fa = calculated compressive stress in masonry due to axial load only, psi (kPa) f’m = specified compressive strength of masonry, psi (kPa) h = effective height, in. (mm) fv = calculated shear stress in masonry, psi (MPa) Ii = average moment of inertia of inner wythe, in.4/ft (m4/m) Io = average moment of inertia of outer wythe, in.4/ft (m4/m) j = ratio of distance between centroid of flexural compressive forces and centroid of tensile forces to depth d k = ratio of distance between compression face of wall and neutral axis to depth d l = clear span between supports, in. (mm) M = moment at the section under consideration, in.-lb/ft (N⋅m/m) Mm = flexural capacity (resisting moment) when masonry controls, in.-lb/ft (N⋅m/m) Mmax = maximum moment at the section under consideration, in.-lb/ft (N⋅m/m) Ms = flexural capacity (resisting moment) when reinforcement controls, in.-lb/ft (N⋅m/m) t = nominal thickness of a member, in. (mm) Vmax = maximum shear at the section under consideration, lb/ft (kN/m) Wi = percentage of transverse load on inner wythe Wo = percentage of transverse load on outer wythe WT = total transverse load w = wind pressure, psf (Pa) ρ = reinforcement ratio
REFERENCES
Building Code Requirements for Masonry Structures, ACI 530-02/ASCE 5-02/TMS 402-02. Reported by the Masonry Standards Joint Committee, 2002.
ASD of Concrete Masonry (2012 IBC & 2011 MSJC), TEK 14-07C, Concrete Masonry & Hardscapes Association, 2004.
Empirical Design of Concrete Masonry Walls, TEK 1408B, Concrete Masonry & Hardscapes Association, 2003
Structural Design of Unreinforced Composite Masonry, TEK 16-02B, Concrete Masonry & Hardscapes Association, 2001.
Reinforced composite concrete masonry walls can provide geometric diversity. Composite walls consist of multiple wythes of masonry connected such that they act as a single structural member. There are prescriptive requirements in both the International Building Code (ref. 1) and Building Code Requirements for Masonry Structures (ref. 2) for connecting the wythes. General information on composite walls is included in TEK 16-01A, Multi-Wythe Concrete Masonry Walls (ref. 3) which is intended to be used in conjunction with this TEK.
Reinforced composite masonry walls are designed by the same procedures as all reinforced masonry walls. They must meet the same construction requirements for reinforcing placement, tolerances, grout placement, and workmanship as all reinforced concrete masonry walls.
Although composite walls can be reinforced or unreinforced, this TEK discusses the requirements for reinforced composite walls. Unreinforced composite walls are discussed in TEK 1602B, Structural Design of Unreinforced Composite Masonry (ref. 4).
DESIGN CONSIDERATIONS
Composite masonry is defined as “multicomponent masonry members acting with composite action” (ref. 2). For a multiwythe wall section to act compositely, the wythes of masonry must be adequately connected. Provisions for properly bonding the wythes are discussed in TEK 16-01A. When wall ties are used, the collar joint – the vertical space between the two wythes of masonry – must be filled solid with grout or mortar (refs. 1, 2). However, when reinforcement is placed in the collar joint, grout must be used to fill the collar joint.
Considerations When Choosing a Cross Section
Unlike single wythe walls, where the geometric cross section is set by the product as manufactured, the cross section of a composite wall is determined by the combination of units and collar joint which can theoretically be any thickness. Practically speaking, code, structural and architectural requirements will narrow the options for wall sections. In addition to structural capacity, criteria specific to cross-section selection for reinforced composite walls include:
• location of reinforcement in collar joint or in unit cores;
• collar joint thickness;
• unit selection for each wythe.
Structural Reinforcement Location
The engineer has the option of locating the structural reinforcing steel in the collar joint or in one or both wythes. While there is no direct prohibition against placing reinforcement in both the collar joint and the unit cores, practically speaking there is rarely a structural reason to complicate the cross section with this configuration.
With some units, it may be easier to install reinforcement in the collar joint, such as when both wythes are solid or lack sufficient cell space for reinforcing bars. Depending on the units selected, the collar joint may or may not provide the option to center the reinforcement within the wall cross section. For example, when the units are not the same thickness, the collar joint does not necessarily span the center of the section.
Conversely, if off-set reinforcing is preferred, perhaps to accommodate unbalanced lateral loads, it may be benefi cial to place the vertical bars in the unit cores. Placing reinforcement in the unit cores permits a thinner collar joint and possibly a thinner overall cross-section. Unit cores may provide a larger and less congested opening for the reinforcing bars and grout since the collar joint will be crossed with connecting wall ties. There is also the possibly that for a given geometry, centered reinforcement does end up in a core space.
Reinforcement can also be placed in the cells of each wythe, providing a double curtain of steel to resist lateral loads from both directions, as in the case of wind pressure and suction.
Collar Joint Width
There are no prescriptive minimums or maximums explicit to collar joint thickness in either Building Code Requirements for Masonry Structures or the International Building Code, however there are some practical limitations for constructability and also code compliance in reinforcing and grouting that effect the collar joint dimension. Many of these are covered in TEK 16-01A but a few key points from the codes that are especially relevant for reinforced composite masonry walls included below:
Wall tie length: Noncomposite cavity walls have a cavity thickness limit of 4½ in. (114 mm) unless a wall tie analysis is performed. There is no such limitation on width for filled collar joints in composite construction since the wall ties can be considered fully supported by the mortar or grout, thus eliminating concern about local buckling of the ties. Practically speaking, since cavity wall construction is much more prevalent, the availability of standard ties may dictate collar joint thickness maximums close to 4½ in. (114 mm).
Pour and lift height: Since the collar joint must be fi lled, the width of the joint infl uences the lift height. Narrow collar joints may lead to low lift or pour heights which could impact cost and construction schedule. See Table 1 in TEK 03-02A, Grouting Concrete Masonry Walls (ref. 5) for more detailed information.
Course or fine grout: Codes require a minimum clear distance of ¼-in. (6.3-mm) for fine grout and ½-in. (13-mm) for coarse grout between reinforcing bars and any face of the masonry unit.
Course or fine grout: Codes require a minimum clear distance of ¼-in. (6.3-mm) for fine grout and ½-in. (13-mm) for coarse grout between reinforcing bars and any face of the masonry unit.
Grout or mortar fill: Although codes permit collar joints to be filled with either mortar or grout, grout is preferred because it helps ensure complete filling of the collar joint without creating voids. Note that collar joints less than ¾ in. (19 mm), unless otherwise required, are to be filled with mortar as the wall is built. Increasing the slump of the mortar to achieve a solidly filled joint is preferred. This effectively requires a ¾-in. (19-mm) minimum on collar joints with structural reinforcing since it is also a code requirement that reinforcing bars be placed in grout, not mortar.
Reinforcing bar diameter: The reinforcing bar diameter cannot exceed one-half the least clear dimension of the collar joint.
Horizontal bond beams: Bond beams may be required to meet prescriptive code requirements such as seismic detailing. The collar joint then must be wide enough to accommodate the horizontal and vertical reinforcement along with the accompanying clearances for embedment in grout.
Unit Selection for Each Wythe
Aesthetic criteria may play a primary role in unit selection for reinforced composite walls. Designing the composite wall to match modular dimensions may make detailing of interfaces much easier. Window and door frames, foundations, connectors and other accessories may coordinate better if typical masonry wall thicknesses are maintained. Additional criteria that influence the selection of units for reinforced composite walls include:
Size and number of reinforcing bars to be used and the cell space required to accommodate them.
Cover requirements (see ref. 6) may come into play when reinforcement is placed in the cells off-center. Cover requirements could affect unit selection, based on the desired bar placement; face shell thickness and cell dimensions.
If double curtains of vertical reinforcement are used, it is preferable to use units of the same thickness to produce a symmetrical cross section.
Structural Considerations
Some structural considerations were addressed earlier in this TEK during the discussion of cross section determination. Since reinforced composite masonry by definition acts as one wall to resist loads, the design procedures are virtually the same as for all reinforced masonry walls. TEK 14-07C, ASD of Concrete Masonry (2012 IBC & 2011 MSJC) (ref. 7) details design procedures. A few key points should be stressed, however:
Analysis: Empirical design methods are not permitted to be used for reinforced multiwythe composite masonry walls.
Section properties: Section properties must be calculated using the transformed section method described in TEK 1601A (ref. 3).
Shear stresses: Shear stress in the plane of interface between wythes and collar joint is limited to 5 psi (34.5 kPa) for mortared collar joints and 10 psi (68.9 kPa) for grouted collar joints.
DESIGN TABLES
Design tables for select reinforced composite walls are included below. The tables include maximum bending moments and shear loads that can be sustained without exceeding the allowable stresses defined in the International Building Code and Building Code Requirements for Masonry Structures. These can be compared to Tables 1 and 2 of TEK 14-19B, ASD Tables for Reinforced CM Walls (2012 IBC & 2011 MSJC) (ref. 8) for wall subjected to uniform lateral loads to ensure the wall under consideration is not loaded beyond its design capacity. The examples are based on the following criteria:
The examples are based on the following criteria:
• Allowable stresses:
In addition to these tables, it is important to check all code requirements governing grout space dimensions and maximum reinforcement size to ensure that the selected reinforcing bar is not too large for the collar joint. The designer must also check shear stress at the unit/grout interface to ensure it does not exceed the code allowable stress for the design loading.
Table 2—Two 4-in. (102-mm) Wythes, Reinforcement Centered in Collar Joint
CONSTRUCTION AND DETAILING REQUIREMENTS
With composite wall construction, the two masonry wythes are not required to be built at the same time unless the collar joint is less than ¾ in. (19 mm), as the code mandates that those collar joints be mortared as the wall is built. Practically speaking it is easier to build both wythes at the same time to facilitate placing either the grout or the mortar in the collar joint at the code required pour heights.
It can be more complex to grout composite walls. Consider that a composite wall may have requirements to grout the collar joint for the full wall height and length but the cores of the concrete masonry units may only need to be partially grouted at reinforcing bar locations. Installing reinforcement and grout in the collar joint space can also be more time-consuming because of congestion due to the wall ties.
Nonmodular composite wall sections may cause diffi culty at points where they interface with modular elements such as window and door frames, bonding at corners and bonding with modular masonry walls.
NOTATIONS
As = effective cross-sectional area of reinforcement, in.²/ft (mm²/m) d = distance from extreme compression fiber to centroid of tension reinforcement, in. (mm) Eg = modulus of elasticity of grout, psi (MPa) Em = modulus of elasticity of masonry in compression, psi (MPa) Es = modulus of elasticity of steel, psi (MPa) Fb = allowable compressive stress due to flexure only, psi (MPa) Fs = allowable tensile or compressive stress in reinforcement, psi (MPa) Fv = allowable shear stress in masonry, psi (MPa) f’g = specified compressive strength of grout, psi (MPa) f’m = specified compressive strength of masonry, psi (MPa) Mr = resisting moment of wall, in.-lb/ft (kNm/m) Vr = resisting shear of wall, lb/ft (kN/m)
REFERENCES
International Building Code 2003. International Code Council, 2003.
Building Code Requirements for Masonry Structures, ACI 530-05/ASCE 5-05/TMS 402-05. Reported by the Masonry Standards Joint Committee, 2005.
Lintels and beams are horizontal structural members designed to carry loads above openings. Although lintels may be constructed of grouted and reinforced concrete masonry units, precast or cast-in-place concrete, or structural steel, this TEK addresses reinforced concrete masonry lintels only. Concrete masonry lintels have the advantages of easily maintaining the bond pattern, color, and surface texture of the surrounding masonry and being placed without need for special lifting equipment.
Concrete masonry lintels are sometimes constructed as a portion of a continuous bond beam. This construction provides several benefits: it is considered to be more advantageous in high seismic areas or areas where high winds may be expected to occur; control of wall movement due to shrinkage or temperature differentials is more easily accomplished; and lintel deflection may be substantially reduced.
The content presented in this TEK is based on the requirements of the 2012 IBC (ref. 1a), which in turn references the 2011 edition of the MSJC Code (ref. 2a).
Significant changes were made to the allowable stress design (ASD) method between the 2009 and 2012 editions of the IBC. These are described in detail in TEK 14-07C, ASD of Concrete Masonry (2012 IBC & 2011 MSJC) (ref. 3), along with a detailed presentation of all of the allowable stress design provisions of the 2012 IBC.
DESIGN LOADS
Vertical loads carried by lintels typically include:
distributed loads from the dead weight of the lintel, the dead weight of the masonry above, and any floor and roof loads, dead and live loads supported by the masonry; and
concentrated loads from floor beams, roof joists, or other beams framing into the wall. Axial load carried by lintels is negligible.
Most of these loads can be separated into the four types illustrated in Figure 1: uniform load acting over the effective span; triangular load with apex at mid-span acting over the effective span; concentrated load; and uniform load acting over a portion of the effective span.
The designer calculates the effects of each individual load and then combines them using superposition to determine the overall effect, typically by assuming the lintel is a simply supported beam.
Figure 1—Typical Lintel Load Components
A Effective span length is the center-to-center distance between supports.
Arching Action
For some configurations, the masonry will distribute applied loads in such a manner that they do not act on the lintel. This is called arching action of masonry. Arching action can be assumed when the following conditions are met (see also Figure 2):
masonry wall laid in running bond,
sufficient wall height above the lintel to permit formation of a symmetrical triangle with base angles of 45° from the horizontal as shown in Figure 2,
at least 8 in. (203 mm) of wall height above the apex of the 45° triangle,
minimum end bearing (4 in. (102 mm) typ.) is maintained,
control joints are not located adjacent to the lintel, and
sufficient masonry on each side of the opening to resist lateral thrust from the arching action.
Figure 2—Arching Action
Lintel Loading
The loads supported by a lintel depend on whether or not arching action can occur. When arching is not present, the lintel self-weight, the full weight of the wall section above the lintel and superimposed loads are considered. Self weight is a uniform load based on lintel weight (see Table 1).
When arching occurs, the wall weight supported by the lintel is taken as the wall weight within the triangular area below the apex (see Figure 2 and Table 2). This triangular load has a base equal to the effective span length of the lintel and a height of half the effective span. Any superimposed roof and floor live and dead loads outside this triangle are neglected, since they are assumed to be distributed to the masonry on either side of the lintel. Loads applied within the triangle need to be considered, however.
Concentrated loads are assumed to be distributed as illustrated in Figure 3. The load is then resolved onto the lintel as a uniform load, with a magnitude determined by dividing the concentrated load by this length. In most cases, this results in a uniform load acting over a portion of the lintel span.
The MSJC (ref. 2) does not address how to apply uniform loads that are applied within the 45° triangle. There are two schools of thought (see Figure 4):
Apply the full uniform load directly to the lintel without further distribution just as though there was no arching for those loads.
Distribute the portions of uniform loads that are applied within the 45o triangle to the lintel. These uniform loads within the 45o triangle may be dispersed and distributed at a 45o angle onto the lintel (ref. 5).
Lintels are required to be designed to have adequate stiffness to limit deflections that would adversely affect strength or serviceability. In addition, the deflection of lintels supporting unreinforced masonry is limited to the clear lintel span divided by 600 to limit damage to the supported masonry (ref. 2).
Table 1—Lintel Weights per Foot, D(lintel), lb/ft (kN/m) (A)
A Face shell mortar bedding. Unit weights: grout = 140 pcf (2,242 kg/m³); lightweight masonry units = 100 pcf (1602 kg/m³); normal weight units = 135 pcf (2,162 kg/m³).
Figure 3—Distribution of Concentrated Load for Running Bond Construction
Figure 4—Methods of Applying Uniform Loads that Occur Within the 45° Triangle
DESIGN TABLES
Tables 3 and 4 present allowable shear and moment, respectively, for various concrete masonry lintels, with various amounts of reinforcement and bottom cover based on a specified compressive strength of masonry, f’m = 1,500 psi (10.3 MPa) and the allowable stress design provisions of the 2011 MSJC (ref. 2a) and the 2012 IBC (ref.1a).
Table 3—Allowable Shear Capacities for Concrete Masonry LintelsA
Table 4
Table 4 continued
DESIGN EXAMPLE
Design a lintel for a 12 in. (305 mm) normal weight concrete masonry wall laid in running bond with vertical reinforcement at 48 in. (1.2 m) o.c. The wall configuration is shown in Figure 5.
Case 1—Arching Action
Check for Arching Action. Determine the height of masonry required for arching action. Assuming the lintel has at least 4 in. (102 mm) bearing on each end, the effective span is:
L = 5.33 + 0.33 = 5.67 ft (1.7 m).
The height of masonry above the lintel necessary for arching to occur in the wall (from Figure 2) is h + 8 in. (203 mm) = L/2 + 8 in. = 3.5 ft (1.1 m). Based on an 8-in. (203-mm) high lintel, there is 18.0 – (3.33 + 4.0 + 0.67) = 10.0 ft (3.0 m) of masonry above the lintel. Therefore, arching is assumed and the superimposed uniform load is neglected.
Design Loads. Because arching occurs, only the lintel and wall dead weights are considered. Lintel weight, from Table 1, for 12 in. (305 mm) normal weight concrete masonry units assuming an 8 in. (203 mm) height is Dlintel = 88 lb/ft (1.3 kN/m).
For wall weight, only the triangular portion with a height of 3.5 ft (1.1 m) is considered. From Table 2, wall dead load is:
Dwall = 63 lb/ft² (3.5 ft) = 221 lb/ft (3.2 kN/m) at the apex.
Maximum moment and shear are determined using simply supported beam relationships. The lintel dead weight is considered a uniform load, so the moment and shear are,
Because the maximum moments for the two loading conditions occur in the same locations on the lintel (as well as the maximum shears), the moments and shears are superimposed and summed:
Lintel Design. From Tables 3 and 4, a 12 x 8 lintel with one No. 4 (M#13) bar and 3 in. (76 mm) or less bottom cover has adequate strength (Mall = 22,356 lb-in. (2.53 kN-m) and Vall = 2,152 lb (9.57 kN)). In this example, shear was conservatively computed at the end of the lintel. However, Building Code Requirements for Masonry Structures (ref. 2) allows maximum shear to be calculated using a distance d/2 from the face of the support.
Case 2—No Arching Action
Using the same example, recalculate assuming a 2 ft (0.6 m) height from the bottom of the lintel to the top of the wall. For ease of construction, the entire 2 ft (0.6 m) would be grouted solid, producing a 24 in. (610 mm) deep lintel.
Because the height of masonry above the lintel is less than 3.5 ft (1.1 m), arching cannot be assumed, and the superimposed load must be accounted for.
Dlintel = 264 lb/ft (3.9 kN/m), from Table 1. Because the lintel is 24 in. (610 mm) deep, there is no additional dead load due to masonry above the lintel.
From Tables 3 and 4, a 12 x 24 lintel with one No. 4 (M#13) reinforcing bar and 3 in. (76 mm) or less bottom cover is adequate (Mall = 122,872 lb-in. (13.88 kN-m) and Vall = 10,256 lb (45.62 kN).
Figure 5—Wall Configuration for Design Example
NOTATIONS
b = width of lintel, in. (mm) Dlintel = lintel dead load, lb/ft (kN/m) Dwall = wall dead load, lb/ft (kN/m) d = distance from extreme compression fiber to centroid of tension reinforcement, in. (mm) f’m = specified compressive strength of masonry, psi (MPa) h = half of the effective lintel span, L/2, ft (m) L = effective lintel span, ft (m) Mall = allowable moment, in.-lb (N⋅m) Mlintel = maximum moment due to lintel dead load, in.-lb (N⋅m) Mmax = maximum moment, in.-lb (N⋅m) Mwall = maximum moment due to wall dead load moment, in.-lb (N⋅m) Vall = allowable shear, lb (N) Vlintel = maximum shear due to lintel dead load, lb (N) Vmax = maximum shear, lb (N) Vwall = maximum shear due to wall dead load, lb (N) Wtotal = total uniform live and dead load, lb/ft (kN/m) w = uniformly distributed load, lb/in. (N/mm)
REFERENCES
International Building Code. International Code Council.
2012 Edition
Building Code Requirements for Masonry Structures. Reported by the Masonry Standards Joint Committee. a. 2011 Edition: TMS 402-11/ACI 530-11/ASCE 5-11
ASD of Concrete Masonry (2012 IBC & 2011 MSJC), TEK 14-07C, Concrete Masonry & Hardscapes Association, 2011.
Weights and Section Properties of Concrete Masonry Assemblies, CMU-TEC-002-23, Concrete Masonry & Hardscapes Association, 2023.
Openings in Concrete Masonry Walls (Part 1), Masonry Chronicles Winter 2008-09, Concrete Masonry Association of California and Nevada, 2009.
Using concrete masonry in retaining walls, abutments and other structural components designed primarily to resist lateral pressure permits the designer and builder to capitalize on masonry’s unique combination of structural and aesthetic features—excellent compressive strength; proven durability; and a wide selection of colors, textures and patterns. The addition of reinforcement to concrete masonry greatly increases the tensile strength and ductility of a wall, providing higher load resistance.
In cantilever retaining walls, the concrete base or footing holds the vertical masonry wall in position and resists overturning and sliding caused by lateral soil loading. The reinforcement is placed vertically in the cores of the masonry units to resist the tensile stresses developed by the lateral earth pressure.
DESIGN
Retaining walls should be designed to safely resist overturning and sliding due to the forces imposed by the retained backfill. The factors of safety against overturning and sliding should be no less than 1.5 (ref. 7). In addition, the bearing pressure under the footing or bottom of the retaining wall should not exceed the allowable soil bearing pressure.
Recommended stem designs for reinforced cantilever retaining walls with no surcharge are contained in Tables 1 and 2 for allowable stress design and strength design, respectively. These design methods are discussed in detail in ASD of Concrete Masonry (2012 IBC & 2011 MSJC), TEK 14-07C, and Strength Design Provisions for Concrete Masonry, TEK 14-04B (refs. 5, 6).
Figure 2—Reinforced Cantilever Retaining Wall Design Example
DESIGN EXAMPLE
The following design example briefly illustrates some of the basic steps used in the allowable stress design of a reinforced concrete masonry cantilever retaining wall.
Example: Design the reinforced concrete masonry cantilever retaining wall shown in Figure 2. Assume level backfill, no surcharge or seismic loading, active earth pressure and masonry laid in running bond. The coefficient of friction between the footing and foundation soil, k1, is 0.25, and the allowable soil bearing pressure is 2,000 psf (95.8 kPa) (ref. 7).
F.S. (overturning) = total resisting moment about toe/overturning moment = 14,670/5,966 = 2.4 > 1.5 O.K.
e. Pressure on footing
f. Determine size of key
Passive lateral soil resistance = 150 psf/ft of depth and may be increased 150 psf for each additional foot of depth to a maximum of 15 times the designated value (ref. 7). The average soil pressure under the footing is: ½ (1,356 + 404) = 880 psf (42.1 kPa).
Equivalent soil depth: 880 psf/120 pcf = 7.33 ft (2.23 m)
Pp = (150 psf/ft)(7.33 ft) = 1,100 psf (52.7 kPa)
For F.S. (sliding) = 1.5, the required total passive soil resistance is: 1.5(1,851 lb/ft) = 2,776 lb/ft (41 kN/m)
The shear key must provide for this value minus the frictional resistance: 2,776 – 1,248 = 1,528 lb/ft (22 kN/m).
Depth of shear key = (1,528 lb/ft)/(1,100 psf) = 1.39 ft (0.42 m), try 1.33 ft (0.41 m).
At 1.33 ft, lateral resistance = (1,100 psf) + (150 psf/ft)(1.33 ft) = 1,300 lb/ft (19 kN/m) Depth = (1,528 lb/ft)/[½ (1,100 + 1,300)] = 1.27 ft (0.39 m) < 1.33 ft (0.41 m) O.K.
g. Design of masonry
Tables 1 and 2 can be used to estimate the required reinforcing steel based on the equivalent fluid weight of soil, wall thickness, and wall height. For this example, the equivalent fluid weight = (Ka)(º) = 0.33 x 120 = 40 pcf (6.2 kN/m³).
Using allowable stress design (Table 1) and the conservative equivalent fluid weight of soil of 45 pcf (7.1 kN/m³), this wall requires No. 6 bars at 16 in. o.c. (M #19 at 406 mm o.c.). Using strength design (Table 2), this wall requires No. 5 bars at 16 in. o.c. (M #16 at 406 mm o.c.).
h. Design of footing
The design of the reinforced concrete footing and key should conform to American Concrete Institute requirements. For guidance, see ACI Standard 318 (ref. 2) or reinforced concrete design handbooks.
Table 1—Allowable Stress Design: Vertical Reinforcement for Cantilever Retaining Walls
Table 2—Strength Design: Vertical Reinforcement for Cantilever Retaining Walls
CONSTRUCTION
Materials and construction practices should comply with applicable requirements of Specification for Masonry Structures (ref. 4), or applicable local codes.
Footings should be placed on firm undisturbed soil, or on adequately compacted fill material. In areas exposed to freezing temperatures, the base of the footing should be placed below the frost line. Backfilling against retaining walls should not be permitted until the masonry has achieved sufficient strength or the wall has been adequately braced. During backfilling, heavy equipment should not approach closer to the top of the wall than a distance equal to the height of the wall. Ideally, backfill should be placed in 12 to 24 in. (305 to 610 mm) lifts, with each lift being compacted by a hand tamper. During construction, the soil and drainage layer, if provided, also needs to be protected from saturation and erosion.
Provisions must be made to prevent the accumulation of water behind the face of the wall and to reduce the possible effects of frost action. Where heavy prolonged rains are anticipated, a continuous longitudinal drain along the back of the wall may be used in addition to through-wall drains.
Climate, soil conditions, exposure and type of construction determine the need for waterproofing the back face of retaining walls. Waterproofing should be considered: in areas subject to severe frost action; in areas of heavy rainfall; and when the backfill material is relatively impermeable. The use of integral and post-applied water repellents is also recommended. The top of masonry retaining walls should be capped or otherwise protected to prevent water entry.
REFERENCES
Building Code Requirements for Masonry Structures, ACI 530-05/ASCE 5-05/TMS 402-05. Reported by the Masonry Standards Joint Committee, 2005.
Building Code Requirements for Structural Concrete and Commentary, ACI 318-02. Detroit, MI: American Concrete Institute, 2002.
Das, B. M. Principles of Foundation Engineering. Boston, MA: PWS Publishers, 1984.
Specification for Masonry Structures, ACI 530.1-05/ASCE 6-05/TMS 602-05. Reported by the Masonry Standards Joint Committee, 2005.
ASD of Concrete Masonry (2012 IBC & 2011 MSJC), TEK 14-07C, Concrete Masonry & Hardscapes Association, 2004.
Strength Design Provisions for Concrete Masonry, TEK 14-04B, Concrete Masonry & Hardscapes Association, 2008.
2003 International Building Code. International Code Council, 2003.
NOTATIONS
a length of footing toe, in. (mm) B width of footing, ft (m) d distance from extreme compression fiber to centroid of tension reinforcement, in. (mm) e eccentricity, in. (mm) F.S. factor of safety f’m specified compressive strength of masonry, psi (MPa) H total height of backfill, ft (m) I moment of inertia, ft4 (m4) Ka active earth pressure coefficient k1 coefficient of friction between footing and foundation soil M maximum moment in section under consideration, ft-lb/ft (kN⋅m/m) Pa resultant lateral load due to soil, lb/ft (kN/m) Pp passive earth pressure, lb/ft (N/m) p pressure on footing, psf (MPa) T thickness of wall, in. (mm) t thickness of footing, in. (mm) W vertical load, lb/ft (N/m) x location of resultant force, ft (m) º density of soil, pcf (kg/m³) ¤ angle of internal friction of soil, degreesDisclaimer: Although care has been taken to ensure the enclosed information is as accurate and complete as possible, NCMA does not assume responsibility for errors or omissions resulting from the use of this TEK.
Retaining walls support soil and other materials laterally. That is, retaining walls “retain” earth, keeping it from sliding. Retaining walls must resist overturning and sliding, and the pressure under the toe (front bottom edge of footing) should not exceed the bearing capacity of the soil. Finally, the wall must be strong enough to prevent failure at any point in its height due to the pressure of the retained material. Concrete masonry retaining walls meet these requirements admirably.
Three different types of concrete masonry retaining walls are illustrated in Figure 1. They are the simple unreinforced vertical face gravity retaining wall, the steel reinforced cantilever retaining wall, and the segmental retaining wall. This TEK addresses unreinforced gravity retaining walls only. Each of these retaining wall systems has its advantages, and the choice may depend on a number of factors including aesthetics, constructibility, cost, and suitability for a particular project. The gravity wall is much simpler in design and construction, and can be an effective choice for smaller projects. It is thicker at the base than cantilever and segmental walls, and hence could cost more to construct on larger projects. Gravity retaining walls resist sliding by means of their large mass, whereas cantilever retaining walls are designed to resist sliding by using reinforcement. Because of their large mass, gravity retaining walls may not be appropriate for use on soils with low bearing capacities.
An engineer who is familiar with local conditions can assist in the choice of retain ing wall type. Where especially unfavorable soil conditions occur or where piling is required under a retaining wall, the assistance of an engineer is essential for design and construction.
Figure 1—Concrete Masonry Retaining Walls
DESIGN
The primary force acting on a retaining wall is the pressure exerted by the retained material at the back of the wall and on the heel of the footing. The magnitude and direction of this pressure depends on the height and shape of the surface and on the nature and properties of the backfill. One common method of estimating backfill pressure is the equivalent fluid pressure method. In this method, it is assumed that the retained earth will act as a fluid in exerting pressure on the wall. Assumed equivalent fluid pressures vary with the type of soil. Representative soil types with their equivalent fluid pressures are shown in Table 1.
Since the stability of the gravity type retaining wall depends mainly on its weight, the thickness required at its base will increase with height of backfill, or wall height. Uplift pressure at the back of the wall (the heel) is avoided by designing the gravity retaining wall thick enough at the base so that the resultant of all forces (overturning force and vertical loads) falls within a zone called the kern, which is the middle one third of the base. The eccentricity of the resultant force is equal to or less than one-sixth of the base width. When the eccentricity, e, is equal to one-sixth the base width exactly, the maximum footing pressure on the soil at the front edge of the base (toe) will be twice the average pressure on the soil.
The horizontal force of the retained material causes the overturning moment on the gravity retaining wall. For a given wall height, the required thickness at the base will depend not only on height, but also on the magnitude of the equivalent fluid pressure of the retained soil. The two forces act in opposition; the horizontal force tends to overturn the wall, while the vertical forces tend to stabilize it via gravity. The ratio of wall height to base width will vary with the ratio of vertical pressure to horizontal pressure. More properly, the relationship between thickness of base and wall height can be expressed:
where: H = height of gravity retaining wall, in. (mm) L = width of gravity retaining wall at base, in. (mm) Q = equivalent fluid pressure of retained material acting horizontally as overturning moment, pcf (kg/m³) W = average weight of masonry, soil and other material acting vertically to retain soil, pcf (kg/m³)
This relationship between wall height and base width for gravity retaining walls is shown in Figure 2 for different ratios of horizontal to vertical unit loads. The relationship shown in Figure 2 is employed in the selection of dimensions for gravity retaining walls up to eight ft (1.8 to 2.4 m) high.
Having selected the height-base proportions from Figure 2, the trial design is analyzed for safety against overturning and sliding, bearing pressure on the soil, and flexural and shear stress in the wall.
Figure 2—Relationship of Gravity Retaining Wall Height to Width at Base
CONSTRUCTION AND MATERIALS
Each course of the retaining wall should be constructed with full-size concrete masonry units, with an overlapping bond pattern between courses, as shown in Figure 3.
Hollow or solid concrete masonry units used in gravity retaining walls should meet the requirements of ASTM C 90 (ref. 2) and preferably have an oven-dry density of 125 lb/ft³ (2002 kg/m³) or more. Cores of hollow units are typically filled to increase the weight of the wall. The fill should be granular in areas subject to freezing. Bond is important to ensure sufficient shear resistance to withstand the pressure exerted by the retained earth. Type M or S mortars complying to ASTM C 270 (ref. 3) are recommended.
Concrete footings should be placed on firm undisturbed soil. In areas where freezing is expected, the base of the footing should be placed below the frost line. If the soil under the footing consists of soft or silty clay, it is usually advisable to place 4 to 6 in. (102 to 152 mm) of well compacted sand or gravel under the footing before pouring the concrete. It is usually not necessary to reinforce the footing.
If heavy equipment is employed for backfilling, it should not be allowed to approach closer to the top of the wall than a distance equal to the wall height. Care should also be taken to avoid large impact forces on the wall as could occur by a large mass of moving earth.
Provision should be made to pre vent water accumulation behind the retaining wall. Accumulated water causes increased pressure, seep age, and in areas subject to frost action, an expansive force of considerable magnitude near the top of the wall. In most instances, weep holes located at 5 to 10 foot (1.5 to 3 m) spacing along the base of the wall are sufficient.
From Figure 2, the base of the wall is 24 in. (610 mm), which can be accomplished using three 8-inch (203 mm) block. Note that the footing weight was not included in the calculation of average unit weight of the materials acting vertically, so that the width determined from Figure 2 would be the width of the masonry wall at its base.
Determine overturning moment: pressure at the base of the wall, p = total soil height x equivalent fluid pressure of soil p = (4.67 ft)(30 pcf) = 140 lb/ft² (6703 Pa) resultant pressure, P = ½ (p)(total soil height) P = ½ (140 lb/ft²)(4.67 ft) = 327 lb/ft (4.8 kN/m)
Determine resisting moment (about the toe): First, determine the weight of each element, then determine the resisting moment of each weight, then sum the resisting moments to determine the total resisting moment.
Element:
Weight
S1
(0.67 ft)(1.33 ft)(100 pcf)
= 89 lb (396 N)
S2
(0.67 ft)(2.67 ft)(100 pcf)
= 179 lb (796 N)
S3
(0.33 ft)(4.0 ft)(100 pcf)
= 132 lb (587 N)
M1
(0.67 ft)(4.0 ft)(120 pcf)
= 322 lb (1432 N)
M2
(0.67 ft)(2.67 ft)(120 pcf)
= 214 lb (952 N)
M3
(0.67 ft)(1.33 ft)(120 pcf)
= 107 lb (476 N)
F
(2.67 ft)(0.67 ft)(150 pcf)
= 268 lb (1192 N)
Element:
Weight, lb (N) x
Arm, ft (m) =
Moment, ft-lb (N-m)
S1
89 (396)
1.33 (0.41)
118.5 (161)
S2
179 (796)
2.00 (0.61)
357.8 (485)
S3
132 (587)
2.50 (0.76)
330.0 (447)
M1
322 (1432)
0.67 (0.20)
215.5 (292)
M2
214 (952)
1.33 (0.41)
285.5 (387)
M3
107 (476)
2.00 (0.61)
213.9 (290)
F
268 (1192)
1.33 (0.41)
356.4 (483)
Total
1311 (5832)
1878 (2546)
Determine the overturning moment about the base, M: M = (P)(⅓ x total height of soil) M = (327 lb/ft)(⅓ x 4.67 ft) = 509 ft-lb/ft (2.28 kN-m/m)
Check safety factors: overturning moment safety factor = 1878/509 = 3.7 3.7 > 2 OK sliding safety factor = (1311 lb)(0.55)/(327 lb/ft) = 2.2 2.2 > 1.5 OK
Check pressure on soil:
Since the concrete masonry used in this example is assumed solid or fully grouted, the calculations do not include a check of shear stresses and flexural stresses in the wall. Flexural and shear stresses are checked in the second design example, and it is seen that the magnitudes are very low. Flexural and shear stresses in gravity retaining walls will almost always be of minor importance.
6-foot (1.8 m) high gravity retaining wall equivalent fluid pressure of soil = 40 pcf (7.1 kN/m³) soil weight = 100 pcf (15.7 kN/m³) soil friction coefficient = 0.55 soil bearing capacity = 2000 lb/ft² (0.096 MPa) hollow concrete masonry units, 130 pcf (20.4 kN/m³), units will be filled with sand, resulting in a combined weight of 115 pcf (18.1 kN/m³) f’m = 1500 psi (10.3 MPa)
Type S portland cement-lime mortar concrete footing, 150 pcf (23.6 kN/m³)
First, determine the width of the wall base:
From Figure 2, try a base width of 42 in. (1067 mm), with a footing width of 50 in. (1270 mm)
Determine overturning moment: p = (6.67 ft)(40 pcf) = 267 lb/ft² (0.013 MPa) P = ½ (267 lb/ft²)(6.67 ft) = 890 lb/ft (13 kN/m) M = (890 lb/ft)(⅓ x 6.67 ft) = 1978 ft-lb/ft (8.81 kN-m/m)
Element:
Weight, lb (N) x
Arm, ft (m) =
Moment, ft-lb (N-m)
S1
22 (98)
1.50 (0.46)
33 (45)
S2
44 (196)
1.83 (0.56)
80 (108)
S3
66 (294)
2.17 (0.66)
143 (194)
S4
88 (391)
2.50 (0.76)
220 (298)
S5
110 (489)
2.83 (0.86)
311 (422)
S6
132 (587)
3.17 (0.97)
418 (566)
S7
154 (685)
3.50 (1.07)
539 (731)
S8
176 (783)
3.83 (1.17)
674 (914)
S9
198 (881)
4.17 (1.27)
826 (1120)
M1
690 (3070)
0.83 (0.25)
575 (780)
M2
202 (899)
1.50 (0.46)
303 (411)
M3
177 (787)
1.83 (0.56)
325 (441)
M4
152 (676)
2.17 (0.66)
329 (446)
M5
126 (560)
2.50 (0.76)
316 (428)
M6
101 (449)
2.83 (0.86)
287 (389)
M7
76 (338)
3.17 (0.97)
241 (327)
M8
50 (222)
3.50 (1.07)
177 (240)
M9
25 (111)
3.83 (1.17)
97 (132)
F
419 (1864)
2.08 (0.63)
872 (1182)
Total
3008 (13,380)
6766 (9173)
Check safety factors: overturning moment safety factor = 6766/1978 = 3.4 3.4 > 2 OK sliding safety factor = (3008 lb)(0.55)/(890 lb/ft) = 1.9 1.9 > 1.5 OK
Check pressure on soil: location of P and eccentricity, e:
Check flexural stresses: At 6 ft (1.8 m) depth: P = ½ (6 ft)(40 pcf)(6 ft) = 720 lb (3203 N) M = (720 lb)(⅓ x 6 ft) = 1440 ft-lb (1952 N-m)
Assume mortar bed is 50% of gross area:
Check shear stresses:
REFERENCES
Building Code Requirements for Masonry Structures, ACI 530-95/ASCE 5-95/TMS 402-95. Reported by the Masonry Standards Joint Committee, 1995.
Standard Specification for Load-Bearing Concrete Masonry Units, ASTM C 90-94. American Society for Testing and Materials, 1994.
Standard Specification for Mortar for Unit Masonry, ASTM C 270-92a. American Society for Testing and Materials, 1992.
Basements provide: economical living, working and storage areas; convenient spaces for mechanical equipment; safe havens during tornadoes and other violent storms; and easy access to plumbing and ductwork. Concrete masonry is well suited to basement and foundation wall construction due to its inherent durability, compressive strength, economy, and resistance to fire, termites, and noise.
Traditionally, residential basement walls have been constructed of plain (unreinforced) concrete masonry, often designed empirically. Walls over 8 ft (2.4 m) high or with larger soil loads are typically designed using reinforced concrete masonry or using design tables included in building codes such as the International Building Code (ref. 4).
DESIGN LOADS
Soil imparts a lateral load on foundation walls. For design, the load is traditionally assumed to increase linearly with depth resulting in a triangular load distribution. This lateral soil load is expressed as an equivalent fluid pressure, with units of pounds per square foot per foot of depth (kPa/m). The maximum force on the wall depends on the total wall height, soil backfill height, wall support conditions, soil type, and the existence of any soil surcharges. For design, foundation walls are typically assumed to act as simple vertical beams laterally supported at the top and bottom.
Foundation walls also provide support for the structure above, transferring vertical loads to the footing. When foundations span vertically, this vertical compression counteracts flexural tension, increasing the wall’s resistance to flexure. In low-rise construction, these vertical loads are typically small in relation to the compressive strength of concrete masonry. Further, if the wall spans horizontally, vertical compression does not offset the flexural tension. Vertical load effects are not included in the tables and design example presented in this TEK (references 2 and 3 include vertical load effects).
EMPIRICAL DESIGN
The empirical design method uses historical experience to proportion and size masonry elements. Empirical design is often used to design concrete masonry foundation walls due to its simplicity and history of successful performance.
Table 1 lists the allowable backfill heights for 8, 10 and 12-inch (203, 254 and 305 mm) concrete masonry foundation walls. Table 1 may be used for foundation walls up to 8 feet (2.4 m) high under the following conditions (ref. 1):
terrain surrounding the foundation wall is graded to drain surface water away from foundation walls,
backfill is drained to remove ground water away from foundation walls,
tops of foundation walls are laterally supported prior to backfilling,
the length of foundation walls between perpendicular masonry walls or pilasters is a maximum of 3 times the foundation wall height,
the backfill is granular and soil conditions in the area are non-expansive,
masonry is laid in running bond using Type M or S mortar, and
units meet the requirements of ASTM C 90 (ref. 6).
Where these conditions cannot be met, the wall must be engineered using either an allowable stress design (see following section) or strength design procedure (see ref. 5).
Table 1—Empirical Foundation Wall Design (ref. 1)
WALL DESIGN
Tables 2 through 4 of this TEK have been rationally designed in accordance with the allowable stress design provisions of Building Code Requirements for Masonry Structures (ref. 1) and therefore meet the requirements of the International Building Code even though the latter limits reinforcment spacing to 72 in. (1829 mm) when using their tables. Additional reinforcement alternatives may be appropriate and can be verified with an engineering analysis.
Tables 2, 3 and 4 list reinforcement options for 8, 10 and 12-in. (203, 254 and 305-mm) thick walls, respectively. The effective depths of reinforcement, d, (see Table notes) used are practical values, taking into account variations in face shell thickness, a range of bar sizes, minimum required grout cover, and construction tolerances for placing the reinforcing bars.
Tables 2 through 4 are based on the following:
no surcharges on the soil adjacent to the wall and no hydrostatic pressure,
negligible axial loads on the wall,
wall is simply supported at top and bottom,
wall is grouted only at reinforced cells,
section properties are based on minimum face shell and web thicknesses in ASTM C 90 (ref. 6),
specified compressive strength of masonry, f’m, is 1,500 psi (10.3 MPa),
reinforcement yield strength, fy, is 60,000 psi (414 MPa),
modulus of elasticity of masonry, Em, is 1,350,000 psi (9,308 MPa),
modulus of elasticity of steel, Es, is 29,000,000 psi (200,000 MPa),
maximum width of compression zone is six times the wall thickness (where reinforcement spacing exceeds this distance, the ability of the plain masonry outside the compression zone to distribute loads horizontally to the reinforced section was verified assuming two-way plate action),
allowable tensile stress in reinforcement, Fs, is 24,000 psi (165 MPa),
allowable compressive stress in masonry, Fb, is ⅓f’m (500 psi, 3.4 MPa),
grout complies with ASTM C 476 (2,000 psi (14 MPa) if property spec is used) (ref. 7), and
masonry is laid in running bond using Type M or S mortar and face shell mortar bedding.
Table 2—Vertical Reinforcement for 8 in. (203 mm) Concrete Masonry Foundation Walls
Table 3—Vertical Reinforcement for 10 in. (254 mm) Concrete Masonry Foundation Walls
Table 4—Vertical Reinforcement for 12 in. (305 mm) Concrete Masonry Foundation Walls
DESIGN EXAMPLE
Wall: 12-inch (305 mm) thick, 12 feet (3.7 m) high.
Loads: equivalent fluid pressure of soil is 45 pcf (7.07 kPa/ m), 10 foot (3.1 m) backfill height. No axial, seismic, or other loads.
Using Table 4, #8 bars at 40 in. (M 25 at 1016 mm) o.c. are sufficient.
CONSTRUCTION ISSUES
This section is not a complete construction guide, but rather discusses those issues directly related to structural design assumptions. Figures 1 and 2 illustrate typical wall support conditions, drainage, and water protection.
Before backfilling, the floor diaphragm must be in place or the wall must be properly braced to resist the soil load. In addition to the absence of additional dead or live loads following construction, the assumption that there are no surcharges on the soil also means that heavy equipment should not be operated close to basement wall systems that are not designed to carry the additional load. In addition, the backfill materials should be placed and compacted in several lifts, taking care to prevent wall damage. Care should also be taken to prevent damaging the drainage, waterproofing, or exterior insulation systems, if present.
Figure 1—Typical Base of Foundation Wall
Figure 2—Typical Top of Foundation Wall
REFERENCES
Building Code Requirements for Masonry Structures, ACI 530-99/ASCE 5-99/TMS 402-99. Reported by the Masonry Standards Joint Committee, 1999.
International Building Code. International Code Council, 2000.
Strength Design of Reinforced CM Foundation Walls, TEK 15-02B, Concrete Masonry & Hardscapes Association, 2004.
Standard Specification for Loadbearing Concrete Masonry Units, ASTM C 90-01. American Society for Testing and Materials, 2001.
Standard Specification for Grout Masonry, ASTM C476- 01. American Society for Testing and Materials, 2001.
Construction of masonry wall systems is possible without the use of mortar. The use of standard CMU units laid dry and subsequently surface bonded with fiber reinforced surfaced bonding cement has been well documented in the past. (ref. 16) With the use of specially fabricated concrete masonry units known as “dry-stack units,” construction of these mortarless systems is simple, easy and cost effective. This TEK describes the construction and engineering design of such mortarless wall systems.
The provisions of this TEK apply to both specialty units manufactured specifically for dry-stack construction and conventional concrete masonry units with the following system types:
Grouted, partially grouted or surface bonded
Unreinforced, reinforced, or prestressed
Note that dry-stacked prestressed systems are available that do not contain grout or surface bonding. The provisions of this TEK do not apply to such systems due to a difference in design section properties (ref 8).
Specially designed units for dry-stack construction are available in many different configurations as shown in Figure 1. The latest and most sophisticated designs incorporate face shell alignment features that make units easier and faster to stack plumb and level. Other units are fabricated with a combination of keys, tabs or slots along both horizontal and vertical faces as shown in Figure 1 so that they may interlock easily when placed. Physical tolerances of dry-stack concrete units are limited to ±1/16 in. (1.58 mm.) which precludes the need for mortaring, grinding of face shell surfaces or shimming to even out courses during construction. Interlocking units placed in running bond resist flexural and shear stresses resulting from out-of-plane loads as a result of the keying action: (a) at the top of a web with the recess in the web of the unit above, (b) at two levels of bearing surface along each face shell at the bed joint, and (c) between adjacent blocks along the head joint. The first of these two interlocking mechanisms also ensures vertical alignment of blocks.
The interlocking features of dry-stack units improve alignment and leveling, reduce the need for skilled labor and reduce construction time. Floor and roof systems can be supported by mortarless walls with a bond beam at the top of the wall which expedites the construction process.
Wall strength and stability are greatly enhanced with grouting which provides the necessary integrity to resist forces applied parallel, and transverse to, the wall plane. Vertical alignment of webs ensures a continuous grout column even when the adjacent cell is left ungrouted. Grouting is necessary to develop flexural tensile stress normal to the bed joints, which is resisted through unit-mortar bond for traditional masonry construction. Strength of grouted dry-stack walls may also be enhanced by traditional reinforcement, prestressing, post-tensioning or with external fiber-reinforced surface coatings (surface bonding) as described in the next section.
Typical applications for mortarless concrete masonry include basement walls, foundation walls, retaining walls, exterior above-grade walls, internal bearing walls and partitions. Dry-stack masonry construction can prove to be a cost-effective solution for residential and low-rise commercial applications because of it’s speed and ease of construction, strength and stability even in zones of moderate and high seismicity. More information on design and construction of dry-stack masonry can be found in Reference 5.
Figure 1–– Dry-Stack Masonry Units
CONSTRUCTION
Dry-stack concrete masonry units can be used to construct walls that are grouted or partially grouted; unreinforced, reinforced or prestressed; or surface bonded. With each construction type, walls are built by first stacking concrete masonry units.
For unreinforced construction as shown in Figure 2a, grouting provides flexural and shear strength to a wall system. Flexural tensile stresses due to out-of-plane bending are resisted by the grout cores. Grout cores also interlace units placed in running bond and thus provide resistance to in-plane shear forces beyond that provided by friction developed along horizontal joints. Grout cores can also be reinforced to increase flexural strength.
Reinforcement can be placed vertically, in which case only those cells containing reinforcement may be grouted as shown in Figure 2b, as well as horizontally, in which case the masonry must be fully grouted. Another version is to place vertical prestressing tendons in place of reinforcement. Vertical axial compressive stress, applied via the tendons, increases flexural and shear capacity. Tendons may be bonded to grout, or unbonded, based upon the design. Placement of grout may be optional. Horizontally reinforced bond beam lintels can be created using a grout stop beneath the unit to contain grout.
As an alternative to reinforcing or prestressing, wall surfaces may be parged (coated) with a fiber-reinforced surface bonding cement/stucco per ASTM C887(ref. 14) as illustrated in Figure 2c. This surface treatment, applied to both faces of a wall, bonds concrete units together without the need for grout or internal reinforcement. The parging material bridges the units and fills the joints between units to provide additional bonding of the coating to the units through keying action. The compressive strength of the parging material should be equal to or greater than that of the masonry units.
Figure 2–– Basic Dry-Stack Masonry Wall Types
Laying of Units
The first course of dry-stack block should be placed on a smooth, level bearing surface of proper size and strength to ensure a plumb and stable wall. Minor roughness and variations in level can be corrected by setting the first course in mortar. Blocks should be laid in running bond such that cells will be aligned vertically.
Grout and Reinforcement
Grout and grouting procedures should be the same as used in conventional masonry construction (ref. 1, 10) except that the grout must have a compressive strength of at least 2600 psi (190 MPa) at 28 days when tested in accordance with ASTM C 1019 (ref.12). Placement of grout can be accomplished in one lift for single-story height walls less than 8 ft (2.43 m). Grout lifts must be consolidated with an internal vibrator with a head size less than 1 in. (25 mm).
Vertical Reinforcing
As for conventional reinforced masonry construction, good construction practice should include placement of reinforcing bars around door and window openings, at the ends, top and bottom of a wall, and between intersecting walls. Well detailed reinforcement such as this can help enhance nonlinear deformation capacity, or ductility, of masonry walls in building systems subjected to earthquake loadings – even for walls designed as unreinforced elements. Additional information on conventional grouting and reinforced masonry wall can be found in TEK 09-04A and TEK 03-03B (refs. 9 & 6).
Pre-stressed Walls
Mortarless walls can also be prestressed by placing vertical tendons through the cores. Tendons can be anchored within the concrete foundation at the base of a wall or in a bottom bond beam and are tensioned from the top of a wall.
Surface Bonded Walls
For walls strengthened with a surface bonding, a thin layer of portland cement surface bonding material should be troweled or sprayed on to a wall surface. The thickness of the surface coating should be at least ⅛ in. (3.2 mm.) or as required by the material supplier.
ENGINEERING PROPERTIES
Walls constructed with mortarless masonry can be engineered using conventional engineering principles. Existing building code recommendations such as that produced by the building code (ref. 1) can serve as reference documents, but at the time of this printing it does not address mortarless masonry directly. It is thus considered an alternate engineered construction type. The International Building Code (ref. 7) does list allowable stresses based on gross-cross-sectional area for dry-stacked, surface-bonded concrete masonry walls. These values are the same as presented in TEK 03-05A (ref. 16). Suggested limits on wall or building height are given in Table 1.
Test data (refs. 2, 3 and 4) have shown that the strength of drystack walls exceeds the strength requirements of conventional masonry, and thus the recommended allowable stress design practices of the code can be used in most cases. When designing unreinforced, grouted masonry wall sections, it is important to deduct the thickness of the tension side face shell when determining the section properties for flexural resistance.
Table 1 –– Summary of Wall Heights for 8” (203 mm) Dry-stacked Units (ref. 5)
* Laterally supported at each floor
Unit and Masonry Compressive Strength
Units used for mortarless masonry construction are made of the same concrete mixes as used for conventional masonry units. Thus, compressive strength of typical units could vary between 2000 psi (13.79MPa) and 4000 psi. (27.58 MPa) Standard Methods of Sampling and Testing Concrete Masonry Units (ref. 11) can be referred to for determining strength of dry-stack units.
Masonry compressive strength f’m can conservatively be based on the unit-strength method of the building code (ref . 15), or be determined by testing prisms in accordance with ASTM C1314 (ref. 4). Test prisms can be either grouted or ungrouted depending on the type of wall construction specified.
Because no mortar is used to resist flexural tension as for conventional masonry construction, flexural strength of mortarless masonry is developed through the grout, reinforcement or surface coating. For out-of-plane bending of solid grouted walls allowable flexural strength can be estimated based on flexural tensile strength of the grout per Equation 1.
Consideration should be given to the reduction in wall thickness at the bed joints when estimating geometrical properties of the net effective section.
Correspondingly, flexural strength based on masonry compressive stress should be checked, particularly for walls resisting significant gravity loads, using the unity equation as given below.
Buckling should also be checked. (Ref. 8)
In-Plane Shear Strength
Shear strength for out-of-plane bending is usually not a concern since flexural strength governs design for this case. For resistance to horizontal forces applied parallel to the plane of a wall, Equation 3 may be used to estimate allowable shear strength.
Fv is the allowable shear strength by the lesser of the three values given in Equation 4.
Grouted, Reinforced Construction
Mortarless masonry that is grouted and reinforced behaves much the same as for conventional reinforced and mortared construction. Because masonry tensile strength is neglected for mortared, reinforced construction, flexural mechanisms are essentially the same with or without the bed joints being mortared provided that the units subjected to compressive stress are in good contact. Thus, allowable stress design values can be determined using the same assumptions and requirements of the MSJC code. (ref.1)
Axial and flexural tensile stresses are assumed to be resisted entirely by the reinforcement. Strains in reinforcement and masonry compressive strains are assumed to vary linearly with their distance from the neutral axis. Stresses in reinforcement and masonry compressive stresses are assumed to vary linearly with strains. For purposes of estimating allowable flexural strengths, full bonding of reinforcement to grout are assumed such that strains in reinforcement are identical to those in the adjacent grout.
For out-of-plane loading where a single layer of vertical reinforcement is placed, allowable flexural strength can be estimated using the equations for conventional reinforcement with the lower value given by Equations 5 or 6.
In-Plane Shear Strength
Though the MSJC code recognizes reinforced masonry shear walls with no shear, or horizontal reinforcement, it is recommended that mortarless walls be rein- forced with both vertical and horizontal bars. In such case, allowable shear strength can be determined based on shear reinforcement provisions (ref. 1) with Equations 7, 8 and 9.
Where Fv is the masonry allowable shear stress per Equations 8 or 9.
Solid Grouted, Prestressed Construction
Mortarless masonry walls that are grouted and pre- stressed can be designed as unreinforced walls with the prestressing force acting to increase the vertical compres- sive stress. Grout can be used to increase the effective area of the wall. Flexural strength will be increased because of the increase in the fa term in Equation 1. Shear strength will be increased by the Nv term in Equation 4.
Because the prestressing force is a sustained force, creep effects must be considered in the masonry. Research on the long-term behavior of dry-stacked masonry by Marzahn and Konig (ref. 8) has shown that creep effects may be accentuated for mortarless masonry as a result of stress concentrations at the contact points of adjacent courses. Due to the roughness of the unit surfaces, high stress concentrations can result which can lead to higher non-proportional creep deformations. Thus, the creep coefficient was found to be dependent on the degree of roughness along bed-joint surfaces and the level of applied stress. As a result, larger losses in prestressing force is probable for dry-stack masonry.
Surface-Bonded Construction
Dry-stack walls with surface bonding develop their strength through the tensile strength of small fiberglass fibers in the 1/8” (3.8mm) thick troweled or surface bonded cement-plaster coating ASTM C-887(Ref. 14). Because no grouting is necessary, flexural tension and shear strength are developed through tensile resistance of fiberglass fibers applied to both surfaces of a wall. Test data has shown that surface bonding can result in a net flexural tension strength on the order of 300 psi.(2.07 MPa) Flexural capacity, based on this value, exceeds that for conventional, unreinforced mortared masonry construction, therefore it is considered conservative to apply the desired values of the code (ref. 1) for allowable flexural capacity for portland cement / lime type M for the full thickness of the face shell.
Out-of-Plane and In-Plane Flexural Strength
Surface-bonded walls can be considered as unreinforced and ungrouted walls with a net allowable flexural tensile strength based on the strength of the fiber-reinforcement. Flexural strength is developed by the face shells bonded by the mesh. Allowable flexural strength can be determined using Equation 1 with an Ft value determined on the basis of tests provided by the surface bonding cement supplier. Axial and flexural compressive stresses must also be checked per Equation 2 considering again only the face shells to resist stress.
Surface Bonded In-Plane Shear Strength
In-plane shear strength of surface-bonded walls is attributable to friction developed along the bed joints resulting from vertical compressive stress in addition to the diagonal tension strength of the fiber coating. If the enhancement in shear strength given by the fiber reinforced surface parging is equal to or greater than that provided by the mortar-unit bond in conventional masonry construction, then allowable shear strength values per the MSJC code (ref. 1) may be used. In such case, section properties used in Equation 3 should be based on the cross-section of the face shells.
Figure 3 – A Mortarless Garden Wall Application
Figure 4 – A Residential, Mortarless, Single-Family Basement – Part of a 520 Home Development
REFERENCES
Building Code Requirements for Masonry Structures), ACI 530-02/ ASCE 5-02/TMS 402-02. Reported by the Masonry Standards Joint Committee (MSJC), 2002.
Drysdale, R.G., Properties of Dry-Stack Block, Windsor, Ontario, July 1999.
Drysdale, R.G., Properties of Surface-Bonded Dry-Stack Block Construction, Windsor, Ontario, January 2000.
Drysdale, R.G., Racking Tests of Dry-Stack Block, Windsor, Ontario, October 2000.
Drysdale, R.G., Design and Construction Guide for Azar Dry-Stack Block Construction, JNE Consulting, Ltd., February 2001.
Grout for Concrete Masonry, TEK 09-04A, Concrete Masonry & Hardscapes Association, 2002.
2000 International Building Code, Falls Church, VA. International Code Council, 2000.
Marzahn, G. and G. Konig, Experimental Investigation of Long-Term Behavior of Dry-Stacked Masonry, Journal of The Masonry Society, December 2002, pp. 9-21.
Hybrid Concrete Masonry Construction Details, TEK 0303B. Concrete Masonry & Hardscapes Association, 2009.
Specification for Masonry Structures, ACI 530.1-02/ASCE 6-02/ TMS 602-02. Reported by the Masonry Standards Joint Committee (MSJC), 2002.
Standard Methods of Sampling and Testing Concrete Masonry Units, ASTM C140-02a, ASTM International, Inc. , Philadelphia, 2002.
Standard Method of Sampling and Testing Grout, ASTM C1019-02, ASTM International, Inc., Philadelphia, 2002.
Standard Specification for Grout for Masonry, ASTM C 476-02. ASTM International, Inc., 2002
Standard Specification for Packaged, Dry, Combined Materials for Surface Bonding Mortar, ASTM C 887-79a (2001). ASTM International, Inc., 2001.
Standard Test Method for Compressive Strength of Masonry Assem blages, ASTM C1314-02a, ASTM International, Inc., Philadelphia, 2002.
An net cross-sectional area of masonry, in² (mm²) As effective cross-sectional area of reinforcement, in2 (mm2) b width of section, in. (mm) d distance from extreme compression fiber centroid of tension reinforcement, in. (mm) Fa allowable compressive stress due to axial load only, psi (MPa) Fb allowable compressive stress due to ß exure only, psi (MPa) Fs allowable tensile or compressive stress in reinforcement, psi (MPa) Ft flexural tensile strength of the grout, psi(MPa) Fv allowable shear stress in masonry psi (MPa) fa calculated vertical compressive stress due to axial load, psi (MPa) fb calculated compressive stress in masonry due to ß exure only, psi (MPa) f’ specified compressive strength of masonry, psi (MPa) I moment of inertia in.4 (mm4) j ratio of distance between centroid of flexural compressive forces and centroid of tensile forces to depth, d k ratio of the distance between compression face of the wall and neu tral axis to the effective depth d M maximum moment at the section under consideration, in.-lb (N-mm) Nv compressive force acting normal to the shear surface, lb (N) Q first moment about the neutral axis of a section of that portion of the cross section lying between the neutral axis and extreme fiber in.³ (mm³) Sg section modulus of uncracked net section in.³ (mm³) V shear force, lb (N)
