An inforation series fro the national authority on concrete asonry technology ALLOWABLE STRESS DESIGN OF CONCRETE MASONRY BASED ON THE 2012 IBC & 2011 MSJC TEK 14-7C Structural (2013) INTRODUCTION Concrete asonry eleents can be designed by using one of several ethods in accordance with the International Building Code (IBC, ref. 2) and, by reference, Building Code Requireents for Masonry Structures (MSJC Code, ref. 1): allowable stress design, strength design, direct design, epirical design, or prestressed asonry. This TEK provides a basic overview of design criteria and requireents for concrete asonry asseblies designed using allowable stress design provisions. For asonry design in accordance with the strength design, prestressed or epirical provisions, the reader is referred to TEK 14-4B, Strength Design Provisions for Concrete Masonry (ref. 5), TEK 14-20A, Post-Tensioned Concrete Masonry Wall Design (ref. 10), and TEK 14-8B, Epirical Design of Concrete Masonry Walls (ref. 4), respectively. The content presented in this edition of TEK 14-7C is based on the requireents of the 2012 International Building Code (ref. 2a), which in turn references the 2011 edition of the MSJC Code (ref. 1a). For designs based on the 2006 or 2009 IBC (refs. 2b, 2c), which reference the 2005 and 2008 MSJC (refs. 1b, 1c), respectively, the reader is referred to TEK 14-7B (ref. 11). Significant changes were ade to the allowable stress design (ASD) ethod between the 2009 and 2012 editions of the IBC. In previous codes, the IBC included alternative load cobinations for ASD, and the MSJC ASD criteria allowed a one-third increase in allowable stresses for load cobinations that include wind or seisic. The one-third stress increase is not included in the 2011 MSJC. In addition, previous code versions allowed the use of strength-level load cobinations in ASD to copensate for the lack of service-level load cobinations in previously referenced versions of ASCE 7, Miniu Design Loads for Buildings and Other Structures (ref. 3). Currently, however, ASCE 7-10 includes both service level and strength level load cobinations, so this "pseudo-strength" procedure is no longer included in the current ASD ethod. This TEK provides a general review of the pertinent allowable stress design criteria contained within the 2011 MSJC. Allowable stress design is based on the following design principles and assuptions: Within the range of allowable stresses, asonry eleents satisfy applicable conditions of equilibriu and copatibility of strains. Stresses reain in the elastic range. Plane sections before bending reain plane after bending. Therefore, strains in asonry and reinforceent are directly proportional to the distances fro the neutral axis. Stress is linearly proportional to strain within the allowable stress range. For unreinforced asonry, the resistance of the reinforceent, if present, is neglected. For reinforced asonry design, all tensile stresses are resisted by the steel reinforceent. Masonry in tension does not contribute to axial or flexural strength. The units, ortar, grout, and reinforceent, if present, act copositely to resist applied loads. Based on these assuptions, the internal distribution of stresses and resulting equilibriu is illustrated in Figure 1 for unreinforced asonry and Figure 2 for reinforced asonry. Using allowable stress design, the calculated design stresses on a asonry eber (indicated by lowercase f) are copared to code-prescribed axiu allowable stresses (indicated by a capital F). The design is acceptable when the calculated applied stresses are less than or equal to the allowable stresses (f < F). DESIGN LOADS Utilizing ASD, asonry eleents are sized and proportioned such that the anticipated service level loads can be safely and econoically resisted using the specified aterial strengths. The specified strength of asonry and Related TEK: 12-4D, 14-1B, 14-4B, 14-5A, 14-7B, 14-8B, 14-19A, 14-20A Keywords: allowable loads, allowable stress, allowable stress design, axial strength, building code provisions, flexural strength, reinforced concrete asonry, shear strength, structural design, unreinforced concrete asonry NCMA TEK 14-7C 1
reinforceent are in turn reduced by appropriate safety factors. Miniu design loads for allowable stress design are included in ASCE 7-10, Miniu Design Loads for Buildings and Other Structures, or obtained fro the IBC. UNREINFORCED MASONRY For unreinforced asonry, the asonry assebly (units, ortar, and grout if used) is designed to carry all applied stresses (see Figure 1). The additional capacity fro the inclusion of reinforcing steel, such as reinforceent added for the control of shrinkage cracking or prescriptively required by the code, is neglected. Because the asonry is intended to resist both tension and copression stresses resulting fro applied loads, the asonry ust be designed to reain uncracked. Unreinforced Out-of-Plane Flexure Allowable flexural tension values as prescribed in the 2011 MSJC Code vary with the direction of span, ortar type, bond pattern, and percentage of grouting as shown in Table 1. For asseblies spanning horizontally between supports, the code conservatively assues that asonry constructed in a bond pattern other than running bond cannot reliably transfer flexural tension stresses across the head joints. As such, the allowable flexural tension values parallel to the bed joints (perpendicular to the head joints) in these cases are assued to be zero. In cases where a continuous section of grout crosses the head joint, such as would occur with the use of open-ended units or bond bea units with recessed webs, tension resisted only by the iniu cross-sectional area of the grout ay be considered. Because the copressive strength of asonry is uch larger than its corresponding tensile strength, the capacity of unreinforced asonry subjected to net flexural stresses is alost always controlled by the flexural tension values of Table 1. For asonry eleents subjected to a bending oent, M, and a copressive axial force, P, the resulting flexural bending stress is deterined using Equation 1. Mt P fb = Eqn. 1 2I A n n TEK 14-1B, Section Properties of Concrete Masonry Walls (ref. 6) provides typical values for the net oent of inertia, I n, and cross-sectional area, A n, for various wall sections. If the value of the bending stress, f b, given by Equation 1 is positive, the asonry section is controlled by tension and the liiting values of Table 1 ust be satisfied. Conversely, if f b as given by Equation 1 is negative, the asonry section is in copression and the copressive stress liitation of Equation 2 ust be et. f b < F b = 1 / 3 f' Eqn. 2 Unreinforced Axial Copression and Flexure While unreinforced asonry can resist flexural tension stresses due to applied loads, unreinforced asonry is not peritted to be subjected to net axial tension, such as that due to wind uplift on a roof connected to a asonry wall or the overturning effects of lateral loads. While copressive stresses fro dead loads can be used to offset tensile stresses, reinforceent ust be incorporated to resist the resulting tensile forces when the eleent is subject to a net axial tension. When asonry eleents are subjected to copressive axial loads only, the calculated copressive stress due to ap- f b kd 1 3 kd d jd T kd 1 3 kd d jd T f b C f b C Wall width Masonry cover Bar diaeter Masonry cover Bar diaeter Wall width Wall width Figure 1 Unreinforced Masonry Stress Distribution 2A: Neutral 3Aaxis within the 2B: Neutral 3Baxis within copression face shell the core area Figure 2 Reinforced Masonry Stress Distribution 2 NCMA TEK 14-7C
plied load, f a, ust not exceed the allowable copressive stress, F a, as given by Equations 3 or 4, as appropriate. For eleents having h/r < 99: h fa Fa = f 2 1 ' 1 r Eqn. 3 4 140 For eleents having h/r > 99: 2 1 70r fa Fa = f ' h Eqn. 4 4 A further check for stability against an eccentrically applied axial load is included with Equation 5, whereby the axial copressive load, P, is liited to one-fourth the buckling load, P e. With Equation 5, the actual eccentricity of the applied load, e, is used to deterine P e. Moents on the assebly due to loads other than the eccentric load are not considered in Equation 5. EIn e P Pe = 2 3 1 1 π h 1 0. 577 2 r Eqn. 5 4 4 When unreinforced asonry eleents are subjected to a cobination of axial load and flexural bending, a unity equation is used to proportion the available allowable stresses to the applied loads per Equation 6. This check ensures that the critical sections reain uncracked under design loads. fa fb + 1 Eqn. 6 F F a b Table 1 Allowable Flexural Tensile Stresses, psi (kpa) (ref. 1a) Direction of flexural Mortar types tensile stress and asonry type Noral to bed joints: Solid units Hollow units A Ungrouted Fully grouted Parallel to bed joints in running bond: Solid units Hollow units Ungrouted & partially grouted Fully grouted Parallel to bed joints in asonry not laid in running bond: Continuous grout section parallel to bed joints Other Portland ceent/ lie or ortar ceent Masonry ceent or air-entrained portland ceent/lie M or S N M or S N 53 (366) 33 (228) 86 (593) 106 (731) 66 (455) 106 (731) 133 (917) 0 (0) 40 (276) 25 (172) 84 (579) 80 (552) 50 (345) 80 (552) 133 (917) 0 (0) 32 (221) 20 (138) 81 (559) 64 (441) 40 (276) 64 (441) 133 (917) 0 (0) 20 (138) 12 (83) 77 (531) 40 (276) 25 (172) 40 (276) 133 (917) 0 (0) A For partially grouted asonry, allowable stresses are deterined on the basis of linear interpolation between fully grouted hollow units and ungrouted hollow units based on aount (percentage) of grouting. Unreinforced Shear Shear stresses on unreinforced asonry eleents are calculated using the net cross-sectional properties of the asonry in the direction of the applied shear force using the following relation: VQ fv = Eqn. 7 Ib n Equation 7 is applicable to deterining both in-plane and out-of-plane shear stresses. Because unreinforced asonry is designed to reain uncracked, it is not necessary to perfor a cracked section analysis to deterine the net cross-sectional area of the asonry. The theoretical distribution of shear stress, f v, along the length of the shear wall (Figure 3) for in-plane loads, or perpendicular to any wall for out-of-plane loads, is parabolic in shape for a rectangular cross-section. The calculated shear stress due to applied loads, f v, as given by Equation 7 cannot exceed any of the code-prescribed allowable shear stresses, F v, as follows: a) 15. f ' psi ( 0. 125 f ' MPa) b) 120 psi (827 kpa) b P M Figure 3 Unreinforced Masonry Shear Walls V Copressive stress, f b Shear stress, f v NCMA TEK 14-7C 3
c) For running bond asonry not fully grouted: 37 psi + 0.45N v /A n (255 + 0.45N v /A n kpa) d) For asonry not laid in running bond, constructed of open-end units and fully grouted: 37 psi + 0.45N v /A n (255 + 0.45N v /A n kpa) e) For running bond asonry fully grouted: 60 psi + 0.45N v /A n (414 + 0.45N v /A n kpa) f) For asonry not laid in running bond, constructed of other than open-end units and fully grouted: 15 psi (103 kpa) The MSJC Code defines the above allowable shear stresses as being applicable to in-plane shear stresses only: allowable shear stresses for out-of-plane loads are not provided. In light of this absence, Coentary on Building Code Requireents for Masonry Structures suggests using these sae values for out-of-plane shear design. REINFORCED MASONRY Reinforced asonry design in accordance with the MSJC Code neglects the tensile resistance provided by the asonry units, ortar and grout in deterining the strength of the asonry asseblage. Thus, for design purposes, the portion of asonry subjected to net tensile stresses is assued to have cracked, transferring all tensile forces to the reinforceent. (While the deterination of the reinforced asonry eleent strength conservatively assues the portion of the asonry subjected to net tensile stresses has cracked, this should be verified when calculating the stiffness and deflection of a reinforced asonry eleent.) Reinforceent The tensile stress in the reinforceent due to applied load, f s, is calculated as the product of the strain in the steel (which increases linearly in proportion to the distance fro the neutral axis) and its odulus of elasticity, E s. The odulus of elasticity, E s, of ild steel reinforceent is assued to be 29,000,000 psi (200 GPa). The code-prescribed allowable steel stresses are as follows (ref. 1a): For Grade 60 bar reinforceent in tension: F s = 32,000 psi (220.7 MPa) For Grade 40 and 50 bar reinforceent in tension: F s = 20,000 psi (137.9 MPa) For wire joint reinforceent in tension: F s = 30,000 psi (206.9 MPa) Unless ties or stirrups laterally confine bar reinforceent as required by the MSJC Code, the reinforceent is assued not to contribute copressive resistance to axially loaded eleents. When reinforceent is confined as prescribed, stresses are liited to the values listed above. Additional inforation on ild reinforcing steel can be found in TEK 12-4D, Steel Reinforceent for Concrete Masonry (ref. 7). Reinforced Out-of-Plane Flexure The allowable copressive stress in asonry, F b, due to flexure or due to a cobination of flexure and axial load is liited by Equation 8. When axial loads are not present, or are conservatively neglected as ay be appropriate in soe cases, there are several circustances to consider in deterining the flexural capacity of reinforced asonry asseblies. f b < F b = 0.45 f' Eqn. 8 For a fully grouted eleent, a cracked transfored section approach is used, wherein the reinforceent area is transfored to an equivalent area of concrete asonry using the odular ratio. Partially grouted asseblies are analyzed in the sae way, but with the additional consideration of the ungrouted cores. For partially grouted asonry there are two types of behavior to consider. 1. The first case applies when the neutral axis (the location of zero stress) lies within the copression face shell, as shown in Figure 2A. In this case, the asonry is analyzed and designed using the procedures for a fully grouted assebly. 2. The second type of analysis occurs when the neutral axis lies within the core area rather than the copression face shell, as shown in Figure 2B. For this case, the portion of the ungrouted cells ust be deducted fro the area of asonry capable of carrying copression stresses. The neutral axis location depends on the relative oduli of elasticity of the asonry and steel, n, as well as the reinforceent ratio, ρ, and the distance between the reinforceent and extree copression fiber, d. When analyzing partially grouted asseblies, it is typically assued that the neutral axis lies within the copression face shell, as the analysis is ore straightforward. Based on this assuption, the resulting value of k and the location of the neutral axis (kd) is calculated. If it is deterined that the neutral axis lies outside the copression face shell, the ore rigorous tee bea analysis is perfored. Otherwise, the rectangular bea analysis is carried out. A coplete discussion and derivation of this procedure is contained in Concrete Masonry Design Tables (ref. 8). For design purposes, the effective width of the copression zone per bar is liited to the sallest of: six ties the wall thickness, the center-to-center spacing of the reinforceent, or 72 in. (1,829 ). This requireent applies to asonry laid in running bond and to asonry not laid in running bond and containing bond beas spaced no farther than 48 in. (1,219 ) on center. Where the center-to-center spacing of the reinforceent does not control the effective width of the copression zone, the resulting resisting oent or resisting shear is proportioned over the width corresponding to the effective width of the copression zone as deterined above. Rectangular Bea Analysis For fully grouted asonry eleents and for partially grouted asonry eleents with the neutral axis in the copression face shell, the resisting flexural capacity, M r, is calculated as follows: n = E s /E Eqn. 9 ρ = A s bd Eqn. 10 4 NCMA TEK 14-7C
2 k = 2ρn+( ρn) ρn Eqn. 11 j = 1 - k/3 Eqn. 12 M = 1 / 2 F b k j b d 2 Eqn. 13 M s = A s F s j d Eqn. 14 Where the resisting flexural capacity, M r, is taken as the lesser of M and M s. Tee Bea Analysis For partially grouted asonry asseblies where the neutral axis is located within the cores (i.e., when kd > t fs ), the resisting flexural capacity, M r, is calculated using the neutral axis coefficient k given by Equation 15 and either Case A or Case B as follows: tfs b bw Asn k = ( ) + db w 2 ( tfs ( b bw)+ Asn) + bw( t 2 fs( b bw)+ 2Asnd) db w Eqn. 15 (A) For cases where the asonry strength controls the design capacity: 1 k fs = nfb k Eqn. 16 If f s as deterined using Equation 16 is greater than the allowable steel stress, F s, then the steel controls the strength and the design is carried out using procedure (B) below. Otherwise, the internal copression force, C, and oent capacity are coputed as follows: C = 1 / 2 F b b k d Eqn. 17 M r = Cjd Eqn. 18 (B) For cases where the steel strength controls: T = A s F s Eqn. 19 M r = Tjd Eqn. 20 Reinforced Axial Copression Axial loads acting through the axis of a eber are distributed over the net cross-sectional area of the effective copression zone, or, for concentrated loads, 4t plus the bearing width. The allowable axial copressive force is based on the copressive strength of asonry and the slenderness ratio of the eleent in accordance with the following: For eleents having h/r < 99, the allowable copressive force, P a, is deterined as follows: h Pa = ( f An + AsFs ) 2 025. ' 065. 1 r Eqn. 21 140 For eleents having h/r > 99, the allowable copressive force, P a, is deterined as follows: r Pa = ( f An + AsFs ) 2 70 025. ' 0. 65 h Eqn. 22 Note that Equations 21 and 22 apply only if copression reinforceent is provided. Such reinforceent requires ties or stirrups to laterally confine the reinforceent. Reinforced Axial Copression and Flexure Often, loading conditions result in both axial load and flexure on a asonry eleent. Superiposing the stresses resulting fro axial copression and flexural copression produces the cobined stress. Mebers are proportioned so that this axiu cobined stress does not exceed the allowable stress liitation iposed by Equation 8 and the calculated copressive stress due to the axial load coponent f a, ust not exceed the allowable copressive stress, F a, as given by Equation 3 or 4 as appropriate if no copression reinforceent is provided. If copression reinforceent is provided, liitations are per Equation 8 and either Equation 21 or 22, as appropriate. In cases where the cobined copressive stresses are relatively large, design econoy ay be realized by increasing the specified asonry copressive strength, f, which in turn can result in thinner wall crosssections, reduced aterial usage, and increased construction productivity. Several design approaches are available for cobined axial copression and flexure, ost coonly using either coputer progras to perfor the necessary iterative calculations or using interaction diagras to graphically deterine the required reinforceent for a given condition. One such software progra is Structural Masonry Design Syste (ref. 9), which is described in TEK 14-17A, Software for the Structural Design of Concrete Masonry (ref. 12). Reinforced Shear Under the 2011 MSJC Code, the shear resistance provided by the asonry is added to the shear resistance provided by the shear reinforceent. This is a change fro previous versions of the Code, and provides a better prediction of shear strength. Note that additional requireents apply to special reinforced asonry shear walls. There are two checks to be ade for reinforced shear. First, as for all ASD design, the calculated shear stress ust be less than or equal to the allowable shear stress (f v < F v ). Secondly, when the calculated shear stress is greater than the allowable shear stress resisted by the asonry (f v > F v ), shear reinforceent ust be provided. These calculations are presented below. The applied shear stress on the asonry eber is calculated as follows: V fv = Eqn. 23 A nv The allowable shear stress, F v, is deterined using Equation 24 and Equation 25 or 26, as appropriate. F v = F v +F vs Eqn. 24 Where M/Vd < 0.25: F 3 f ' v Where M/Vd is > 1.0: F 2 f ' v Eqn. 25 Eqn. 26 NCMA TEK 14-7C 5
When the ratio M/Vd falls between 0.25 and 1.0, the axiu value of F v ay be linearly interpolated using Equations 25 and 26. The values of F v and F vs are deterined using Equations 27 and 28. When calculating F v, M/Vd ust be taken as a positive nuber and need not exceed 1. 1 M P Fv = f 40. 175. Vd ' 2 + 0. 25 Eqn. 27 An AFd v s Fvs = 05. As Eqn. 28 n In addition, when f v > F v, shear reinforceent ust be provided in accordance with the following requireents: the shear reinforceent ust be oriented parallel to the direction of the shear force, the shear reinforceent spacing ust not exceed the lesser of d/2 or 48 in. (1,219 ), and reinforceent ust also be provided perpendicular to the shear reinforceent. This prescriptive reinforceent ust have an area of at least one-third A v, ust be uniforly distributed, and ay not be spaced farther apart than 8 ft (2,438 ). 6 NCMA TEK 14-7C
NOTATION A n = net cross-sectional area of a eber, in. 2 ( 2 ) A nv = net shear area, in. 2 ( 2 ) A s = area of nonprestressed longitudinal reinforceent, in. 2 ( 2 ) A v = cross-sectional area of shear reinforceent, in. 2 ( 2 ) b = width of section, in. () b w = for partially grouted walls, width of grouted cell plus each web thickness within the copression zone, in. () C = resultant copressive force, lb (N) d = distance fro extree copression fiber to centroid of tension reinforceent, in. () E = odulus of elasticity of asonry in copression, psi (MPa) E s = odulus of elasticity of steel, psi (MPa) e = eccentricity of axial load, lb (N) F a = allowable copressive stress available to resist axial load only, psi (MPa) F b = allowable copressive stress available to resist flexure only, psi (MPa) F s = allowable tensile or copressive stress in reinforceent, psi (MPa) F v = allowable shear stress, psi (MPa) F v = allowable shear stress resisted by the asonry, psi (MPa) F vs = allowable shear stress resisted by the shear reinforceent, psi (MPa) f a = calculated copressive stress in asonry due to axial load only, psi (MPa) f b = calculated flexural bending stress in asonry, psi (MPa) f = specified copressive strength of asonry, psi (MPa) f s = calculated tensile or copressive stress in reinforceent, psi (MPa) f v = calculated shear stress in asonry, psi (MPa) h = effective height of asonry eleent, in. () I n = oent of inertia of net cross-sectional area of a eber, in. 4 ( 4 ) j = ratio of distance between centroid of flexural copressive forces and centroid of tensile forces to depth, d k = ratio of distance between copression face of eleent and neutral axis to the effective depth d M = axiu calculated bending oent at section under consideration, in.-lb, (N-) M = flexural strength (resisting oent) when asonry controls, in.-lb (N-) M r = flexural strength (resisting oent), in.-lb (N-) M s = flexural strength (resisting oent) when reinforceent controls, in.-lb (N-) N v = copressive force acting noral to shear surface, lb (N) n = odular ratio, E s /E P = axial copression load, lb (N) P a = allowable axial copressive force in a reinforced eber, lb (N) P e = Euler buckling load, lb (N) Q = first oent of inertia about the neutral axis of an area between the extree fiber and the plane at which the shear stress is being calculated, in. 3 ( 3 ) r = radius of gyration, in. () s = spacing of shear reinforceent, in. () T = resultant tensile force, lb (N) t = noinal thickness of asonry eber, in. () t fs = concrete asonry unit face shell thickness, in. () V = shear force, lb (N) V r = shear capacity (resisting shear) of asonry, lb (N) ρ = reinforceent ratio NCMA TEK 14-7C 7
REFERENCES 1. Building Code Requireents for Masonry Structures, Reported by the Masonry Standards Joint Coittee. a. 2011 Edition: TMS 402-11/ACI 530-11/ASCE 5-11 b. 2008 Edition: TMS 402-08/ACI 530-08/ASCE 5-08 c. 2005 Edition: ACI 530-05/ASCE 5-05/TMS 402-05 2. International Building Code. International Code Council. a. 2012 Edition b. 2009 Edition c. 2006 Edition 3. Miniu Design Loads for Buildings and Other Structures, ASCE 7-10. Aerican Society of Civil Engineers, 2010. 4. Epirical Design of Concrete Masonry Walls, TEK 14-8B. National Concrete Masonry Association, 2008. 5. Strength Design Provisions for Concrete Masonry, TEK 14-4B. National Concrete Masonry Association, 2008. 6. Section Properties of Concrete Masonry Walls, TEK 14-1B. National Concrete Masonry Association, 2007. 7. Steel Reinforceent for Concrete Masonry, TEK 12-4D. National Concrete Masonry Association, 2007. 8. Concrete Masonry Design Tables, TR121. National Concrete Masonry Association, 2000. 9. Structural Masonry Design Syste Software, CMS10V5. National Concrete Masonry Association, 2010. 10. Post-Tensioned Concrete Masonry Wall Design, TEK 14-20A. National Concrete Masonry Association, 2002. 11. Allowable Stress Design of Concrete Masonry, TEK 14-7B. National Concrete Masonry Association, 2009. 12. Software for the Structural Design of Concrete Masonry, TEK 14-17A. National Concrete Masonry Association, 2010. NCMA and the copanies disseinating this technical inforation disclai any and all responsibility and liability for the accuracy and the application of the inforation contained in this publication. NATIONAL CONCRETE MASONRY ASSOCIATION 13750 Sunrise Valley Drive, Herndon, Virginia 20171 www.nca.org To order a coplete TEK Manual or TEK Index, contact NCMA Publications (703) 713-1900 8 NCMA TEK