Chapter 3 - Strength Design of Masonry

Chapter 3 - Strength Design of Masonry - l.l7.4.3 l l...

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Unformatted text preview: l.l7.4.3 l l BUILDING CODE REQUIREMENTS FOR MASONRY STRUCTURES C-37 CHAPTER 3 STRENGTH DESIGN OF MASONRY 3.1 —— General 3.1.1 Scope This Chapter provides minimum requirements for strength design of masonry. Masonry design by the strength design method shall comply with the requirements of Chapter 1, Section 3.1, and either Section 3.2 or 3.3. 3.1.2 Required strength Required strength shall be determined in accordance with the strength design load combinations of the legally adopted building code. When the legally adopted building code does not provide factored load combinations, structures and members shall be designed to resist the combination of loads specified in ASCE 7 for strength design. Members subject to compressive axial load shall be designed for the factored moment accompanying the factored axial load. The factored moment, Mu, shall include the moment induced by relative lateral displacement. 3.1.3 Design strength Masonry members shall be proportioned so that the design strength equals or exceeds the required strength. Design strength is the nominal strength multiplied by the strength-reduction factor, ¢, as specified in Section 3.1.4. 3.1.4 Strength-reduction factors 3.1.4.1 Combinations of flexure and axial load in reinforced masonry — The value of ¢ shall be taken as 0.90 for reinforced masonry subjected to flexure, axial load, or combinations thereof. 3.1.4.2 Combinations of flexure and axial load in unreinforced masonry — The value of 415 shall be taken as 0.60 for unreinforced masonry subjected to flexure, axial load, or combinations thereof. 3.1.4.3 Shear —- The value of ¢ shall be taken as 0.80 for masonry subjected to shear. 3.1.4.4 Anchor bolts —— For cases where the nominal strength of an anchor bolt is controlled by masonry breakout, by masonry crushing, or by anchor bolt pryout, ¢ shall be taken as 0.50. For cases where the nominal strength of an anchor bolt is controlled by anchor bolt steel, ¢ shall be taken as 0.90. For cases Where the nominal strength of an anchor bolt is controlled by anchor pullout, ¢ shall be taken as 0.65. 3.1.4.5 Bearing — For cases bearing on masonry, ¢ shall be taken as 0.60. involving 3.1.5 Deformation requirements 3.1.5.1 Deflection of unreinforced (plain) -1.17.2_4 masonry — Deflection calculations for unreinforced - (plain) masonry members shall be based on uncracked section properties. 3.1.5.2 Deflection of reinforced masonry — Deflection calculations for reinforced masonry members shall consider the effects of cracking and reinforcement I on member stiffness. The flexural and shear stiffness properties assumed for deflection calculations shall not exceed one-half of the gross section properties, unless a cracked—section analysis is performed. 3.1.6 Anchor bolts embedded in grout m 3.1.6.1 Design requirements — Anchor bolts shall be designed using either the provisions of 3.1.6.2 or, for headed and bent-bar anchor bolts, by the provisions of Section 3.1.6.3. 3.1.6.2 Nominal strengths determined by test 3.1.6.2.1 Anchor bolts shall be tested in accordance with ASTM E488, except that a minimum of five tests shall be performed. Loading conditions of the test shall be representative of intended use of the anchor bolt. 3.1.6.2.2 Anchor bolt nominal strengths used for design shall not exceed 65 percent of the average failure load from the tests. 3.1.6.3 Nominal strengths determined by calculation for headed and bent—bar anchor bolts — Nominal strengths of headed and bent—bar anchor bolts embedded in grout shall be determined in accordance with the provisions of Sections 3.1.6.3.1 through 3.1.6.3.3. 3.1.6.3.1 Nominal tensile strength of headed and bent—bar anchor bolts — The nominal axial tensile strength of headed anchor bolts shall be computed using the provisions of Sections 3.1.6.311. The nominal axial tensile strength of bent-bar anchor bolts shall be computed using the provisions of Section 3.1.6.3.1.2. 3.1.6.3.1.1 Nominal axial tensile strength of headed anchor bolts — The nominal axial tensile strength, Ban, of headed anchor bolts embedded in grout shall be determined by Eq. (3—1) (nominal axial tensile strength governed by masonry breakout) or Eq. (3-2) (nominal axial tensile strength governed by steel yielding). The nominal axial tensile strength, BM, shall be the smaller of the values obtained from Eqs. (3-1) and (3-2). Banb : 4Apt Bans : Abfy (3-1) (3-2) C-38 1. 3.1.6.3.1.2 Nominal axial tensile strength of bent-bar anchor bolts — The nominal axial tensile strength, Ban, for bent-bar anchor bolts embedded in grout shall be determined by Eq. (3-3) (nominal axial tensile strength governed by masonry breakout), Eq. (3— 4) (nominal axial tensile strength governed by anchor bolt pullout), or Eq. (3—5) (nominal axial tensile strength governed by steel yielding). The nominal axial tensile strength, Ban, shall be the smallest of the values obtained from Eqs. (3-3), (3-4) and (3-5). B... =4Apn/E <3—3) B = 1.5 fjebdb + 300n(1,,+ e, + db)db (3-4) anp Ban. = Abfy (3-5) 3.1.6.3.2 Nominal shear strength of headed and bent-bar anchor bolts — The nominal shear strength, an, of headed and bent-bar anchor bolts shall be determined by Eq. (3-6) (nominal shear strength governed by masonry breakout), Eq. (3—7) (nominal shear strength governed by masonry crushing), Eq. (3-8) (nominal shear strength governed by anchor bolt pryout) or Eq. (3—9) (nominal shear strength governed by steel yielding). The nominal shear strength BM, shall be the smallest of the values obtained from Eqs. (3-6), (3-7), (3-8) and (3—9). anb : 4Apv BM 2 10504 f'm Ab (3-7) 3W = 208m = 8A.. 12'. (3-8) am = 0.6Abfy (3-9) 3.1.6.3.3 Combined axial tension and shear — Anchor bolts subjected to axial tension in combination with shear shall satisfy Eq. (3-10). b b “f + V :1 (3—10) ¢ Ban ¢an TMS 402-08/ACI 530-08/ASCE 5-08 3.1.7 Nominal bearing strength The nominal bearing strength of masonry shall be computed as 0.60 f ’m multiplied by the bearing area, Abr, as defined in Section 1.9.5. 3.1.8 Material properties 3.1.8.1 Compressive strength 3.1.8.1.1 Masonry compressive strength —— The specified compressive strength of masonry, f ’m , shall equal or exceed 1,500 psi (10.34 MPa). The value off 1,, used to determine nominal strength values in this chapter shall not exceed 4,000 psi (27.58 MPa) for concrete masonry and shall not exceed 6,000 psi (41.37 MPa) for clay masonry. 3.1.8.1.2 Grout compressive strength— For concrete masonry, the specified compressive strength of grout, f jg, shall equal or exceed the specified compressive strength of masonry, ’m, but shall not exceed 5,000 psi (34.47 MPa). For clay masonry, the specified compressive strength of grout, f 'g, shall not exceed 6,000 psi (41.37 MPa). 3.1.8.2 Masonry modulus of rupture— The modulus of rupture, f,, for masonry elements subjected to out-of-plane or in-plane bending shall be in accordance with the values in Table 3.1.8.2. For grouted stack bond masonry, tension parallel to the bed joints shall be assumed to be resisted only by the minimum cross-sectional area of continuous grout that is parallel to the bed joints. 3.1.8.3 Reinforcement strength —— Masonry design shall be based on a reinforcement strength equal to the specified yield strength of reinforcement, j}, which shall not exceed 60,000 psi (413.7 MPa). The actual yield strength shall not exceed 1.3 multiplied by the specified yield strength. The compressive resistance of steel reinforcement shall be neglected unless lateral reinforcement is provided in compliance with the requirements of Section 1.14.1.3. BUILDING CODE REQUIREMENTS FOR MASONRY STRUCTURES Table 3.1.8.2 — Modulus of rupture, f,, psi (kPa) Mortar types Portland cement/lime or mortar Masonry cement or air cement entrained portland cement/lime 38(262) Direction of flexural tensile stress and masonry type Normal to bed joints in running or stack bond Sohdunfis 100(689) 75(517) 60(413) Hollow unitsl 63(431) 163(1124) 48(331) 158(1089) 38(262) 153(1055) 23(158) 145(1000) Ungrouted Fully grouted Parallel to bed joints in running bond Solid units 200 (1379) 150 (1033) 120 (827) 75 (517) Hollow units 125(862) 200(1379) 95(655) 150(1033) 75(517) 120(827) 48(331) 75(517) Ungrouted and partially grouted Fully grouted Parallel to bed joints in stack bond 250(1734) fiOUBQ 2m(NM) fiOUBQ Continuous grout section parallel to bed joints Other 0m) [email protected] mm mm 1 For partially grouted masonry, modulus of rupture values shall be determined on the basis of linear interpolation between fillly grouted hollow units and ungrouted hollow units based on amount (percentage) of grouting. C -39 C-39 0-40 3.2 —-—Unreinforced (plain) masonry 3.2.1 Scope The requirements of Section 3.2 are in addition to the requirements of Chapter 1 and Section 3.1 and govern masonry design in which masonry is used to resist tensile forces. 3.2.1.1 Strength for resisting loads ~— Unreinforced (plain) masonry members shall be designed using the strength of masonry units, mortar, and grout in resisting design loads. 3.2.1.2 Strength contribution from reinforcement —— Stresses in reinforcement shall not be considered effective in resisting design loads. 3.2.1.3 Design criteria — Unreinforced (plain) masonry members shall be designed to remain uncracked. 3.2.2 Flexural and axial strength of unreinforced (plain) masonry members 3.2.2.1 Design assumptions — The following assumptions shall apply when determining the flexural and axial strength of unreinforced (plain) masonry members: (a) Strength design of members for factored flexure and axial load shall be in accordance with principles of engineering mechanics. (b) Strain in masonry shall be directly proportional to the distance from the neutral axis. (c) Flexural tension in masonry shall be assumed to be directly proportional to strain. (d) Flexural compressive stress in combination with axial compressive stress in masonry shall be assumed to be directly proportional to strain. 3.2.2.2 Nominal strength — The nominal strength of unreinforced (plain) masonry cross—sections for combined flexure and axial loads shall be determined so that: (a) the compressive stress does not exceed 0.80 f ’m. (b) the tensile stress does not exceed the modulus of rupture determined from Section 3.1.8.2. 3.2.2.3 Nominal axial strength — The nominal axial strength, P", shall not be taken greater than the following: (a) For members having an h/r ratio not greater than 99: h 2 13,, = 0.80{0.80An fm [1—[140rj (b) For members having an h/r ratio greater than 99: 2 p, wits..." fig—r] ] (3-11) (3—12) TMS 402-08lACI 530-08lASCE 5-08 3.2.2.4 P-Delta effects 3.2.2.4.1 Members shall be designed for the factored axial load, Pu, and the moment magnified for the effects of member curvature, MC. 3.2.2.4.2 The magnified moment, MC, shall be determined either by a second—order analysis, or by a first-order analysis and Eqs. (3-13) and (3-14). Me = 6Mu (3-13) 6 — ——l———-——-—-— (3-14) _ Pu 1"““——2 Anfif'm 3.2.2.4.3 It shall be permitted to take 6 = 1 for members in which h / r S 45 . 3.2.2.4.4 It shall be permitted to take 6 = 1 for members in which 45 < h/r s 60, provided the nominal strength defined in Section 3.2.2.2 is reduced by 10 percent. 3.2.3 Axial tension — The tensile strength of unreinforced masonry shall be neglected in design when the masonry is subjected to axial tension forces. 3.2.4 Nominal shear strength — Nominal shear strength, V", shall be the smallest of (a), (b) and the applicable condition of (0) through (i): (a) 3.8A” M (b) 300A" (c) For running bond masonry not solidly grouted; 56A,, + 0.45Nu (d) For stack bond masonry with open end units and grouted solid; 56A,, +0.45Nu (e) For running bond masonry grouted solid; 90A,, + 0.45Nu (t) For stack bond other than open end units grouted solid; 23A ll BUILDING CODE REQUIREMENTS FOR MASONRY STRUCTURES 3.3 — Reinforced masonry 3.3.1 Scope The requirements of this Section are in addition to the requirements of Chapter 1 and Section 3.1 and govern masonry design in which reinforcement is used to resist tensile forces. 3.3.2 Design assumptions The following assumptions apply to the design of reinforced masonry: (a) There is strain continuity between the reinforcement, grout, and masonry so that loads are resisted in a composite manner. (b) The nominal strength of reinforced masonry cross- sections for combined flexure and axial load shall be based on applicable conditions of equilibrium. (0) The maximum usable strain, emu, at the extreme masonry compression fiber shall be assumed to be 0.0035 for clay masonry and 0.0025 for concrete masonry. (d) Strain in reinforcement and masonry shall be assumed to be directly proportional to the distance from the neutral axis. (e) Compression and tension stress in reinforcement shall be taken as E, multiplied by the steel strain, but not greater than fy . (f) The tensile strength of masonry shall be neglected in calculating flexural strength but shall be considered in calculating deflection. (g) The relationship between masonry compressive stress and masonry strain shall be assumed to be defined by the following: Masonry stress of 0.80 f 1,, shall be assumed uniformly distributed over an equivalent compression stress block bounded by edges of the cross section and a straight line located parallel to the neutral axis and located at a distance a = 0.80 c from the fiber of maximum compressive strain. The distance c from the fiber of maximum strain to the neutral axis shall be measured perpendicular to the neutral axis. 3.3.3 Reinforcement requirements and details 3.3.3.1 Reinforcing bar size limitations — Reinforcing bars used in masonry shall not be larger than No. 9 (M#29). The nominal bar diameter shall not exceed one-eighth of the nominal member thickness and shall not exceed one-quarter of the least clear dimension of the cell, course, or collar joint in which the bar is placed. The area of reinforcing bars placed in a cell or in a course of hollow unit construction shall not exceed 4 percent of the cell area. C-41 3.3.3.2 Standard hooks —— The equivalent embedment length to develop standard hooks in tension, 1,. , shall be determined by Eq. (3-15): 1,:13d, (345) 3.3.3.3 Development ——- The required tension or compression reinforcement shall be developed in accordance with the following provisions: The required development length of reinforcement shall be determined by Eq. (3-16), but shall not be less than 12 in. (305 mm). QBdfflJ lei—W K shall not exceed the smallest of the following: the minimum masonry clear cover, the clear spacing between adjacent reinforcement splices, and 5 d1, . y = 1.0 for No. 3 (M#lO) through No. 5 (M#16) bars; 7 = 1.3 for No. 6 (M#l9) through No. 7 (M#22) bars; @[email protected] and 7 = 1.5 for No. 8 (M#25) through No. 9 (M#29) bars. Development length of epoxy-coated reinforcing bars shall be taken as 150 percent of the length determined by Eq. (3—16). 3.3.3.3.1 Bars spliced by noncontact lap splices shall not be spaced farther apart than one-fifth the required length of lap nor more than 8 in. (203 mm). 3.3.3.3.2 Shear reinforcement shall extend the depth of the member less cover distances. 3.3.3.3.2.1 Except at wall intersections, the end of a horizontal reinforcing bar needed to satisfy shear strength requirements of Section 3.3.4.1.2 shall be bent around the edge vertical reinforcing bar with a 180- degree hook. The ends of single-leg or U-stirrups shall be anchored by one of the following means: (a) A standard hook plus an effective embedment of [4/2. The effective embedment of a stirrup leg shall be taken as the distance between the mid-depth of the member, d/2, and the start of the hook (point of tangency). (b) For No. 5 (M #16) bars and smaller, bending around longitudinal reinforcement through at least 135 degrees plus an embedment of [4/3. The M3 embedment of a stirrup leg shall be taken as the distance between mid-depth of the member, d/2, and the start of the hook (point of tangency). (0) Between the anchored ends, each bend in the continuous portion of a transverse U-stirrup shall enclose a longitudinal bar. c-41 C-42 C-42 3.3.3.3.2.2 At wall intersections, horizontal reinforcing bars needed to satisfy shear strength requirements of Section 3.3.4.1.2 shall be bent around the edge vertical reinforcing bar with a 90—degree standard hook and shall extend horizontally into the intersecting wall a minimum distance at least equal to the development length. 3.3.3.4 Splices — Reinforcement splices shall comply with one of the following: (a) The minimum length of lap for bars shall be 12 in. (305 mm) or the development length determined by Eq. (3-16), whichever is greater. (b) A welded splice shall have the bars butted and welded to develop at least 125 percent of the yield strength, 1; , of the bar in tension or compression, as required. (c) Mechanical splices shall have the bars connected to develop at least 125 percent of the yield strength, fy, of the bar in tension or compression, as required. 3.3.3.5 Maximum area of flexural tensile reinforcement 3.3.3.5.1 For masonry members where Mu/Vudvz 1, the cross-sectional area of flexural tensile reinforcement shall not exceed the area required to maintain axial equilibrium under the following conditions: (a) A strain gradient shall be assumed, corresponding to a strain in the extreme tensile reinforcement equal to 1.5 multiplied by the yield strain and a maximum strain in the masonry as given by 3.3.2(c). (b) The design assumptions of Section 3.3.2 shall apply. (c) The stress in the tension reinforcement shall be taken as the product of the modulus of elasticity of the steel and the strain in the reinforcement, and need not be taken as greater than j}. ((1) Axial forces shall be taken from the loading combination given by D + 0.75L + 0.525QE. (e) The effect of compression reinforcement, with or without lateral restraining reinforcement, shall be permitted to be included for purposes of calculating maximum flexural tensile reinforcement. 3.3.3.5.2 For intermediate reinforced masonry shear walls subject to in-plane loads where Mu/Vudv 2 1, a strain gradient corresponding to a strain in the extreme tensile reinforcement equal to 3 multiplied by the yield strain and a maximum strain in the masonry as given by 3.3.2(c) shall be used. For intermediate reinforced masonry shear walls subject to out-of-plane loads, the provisions of Section 3.3.3.5.1 shall apply. 3.3.3.5.3 For special reinforced masonry shear walls subject to in-plane loads where Mu/Vud 2 l, a strain gradient corresponding to a strain in the extreme tensile reinforcement equal to 4 multiplied by the yield TMS 402-08IACI 530-08IASCE 5-08 strain and a maximum strain in the masonry as given by 3.3.2(c) shall be used. For special reinforced masonry shear walls subject to out-of-plane loads, the provisions of Section 3.3.3.5.1 shall apply. 3.3.3.5.4 For masonry members where Mu/Vudv S 1 and when designed using R S 1.5, there is no upper limit to the maximum flexural tensile reinforcement. For masonry members where Mu/Vudv S l and when designed using R 2 1.5, the provisions of Section 3.3.3.5.1 shall apply. 3.3.3.6 Bundling of reinforcing bars — Reinforcing bars shall not be bundled. 3.3.4 Design of beams, piers, and columns Member design forces shall be based on an analysis that considers the relative stiffness of structural members. The calculation of lateral stiffness shall include the contribution of all beams, piers, and columns. The effects of cracking on member stiffness shall be considered. 3.3.4.1 Nominal strength 3.3.4.1.1 Nominal axial and flexural strength ~ The nominal axial strength, P” , and the nominal flexural strength, M", of a cross section shall be determined in accordance with the design assumptions of Section 3.3.2 and the provisions of Section 3.3.4.1. Using the slendemess- dependent modification factors of Eq. (3—17) [l—(h/140r)2)] and Eq. (3-18) (70r/h)2, as appropriate, the nominal axial strength shall be modified for the effects of slendemess. The nominal flexural strength at any section along a member shall not be less than one—fourth of the maximum nominal flexural strength at the critical section. The nominal axial compressive strength shall not exceed Eq. (3-17) or Eq. (3—18), as appropriate. (a) For members having an h/r ratio not greater than 99: h 2 = . . ' _ _ - 7 P" 080[0 80fm(An As,)+fyAS,][1 (14%] 1(3 1 ) (b) For members having an h/r ratio greater than 99: 2 P" = 0.8o[0.80f,;,(A,, —As,)+ fyAS, (3—18) 3.3.4.1.2 Nominal shear strength — Nominal shear strength, V", shall be computed using Eq. (3-19) and either Eq. (3-20) or Eq. (3-21), as appropriate. V" = Vnm + Vm (3-19) where V" shall not exceed the following: (a) Where Mu/Vu a", S 0.25: V, 3 6A,, J7; (3—20) BUILDING CODE REQUIREMENTS FOR MASONRY STRUCTURES (b) Where Mu/Vu d, 2 1.00 V,smydff (c) The maximum value of V,, for Mu/Vu dv between 0.25 and 1.0 shall be permitted to be linearly interpolated. 3.3.4.1.2.1 Nominal masonry shear strength — Shear strength provided by the masonry, Vnm , shall be computed using Eq. (3-22): M . Vnm = [4.0—1.75{V 6: HA" ‘lfm +0.25Pu (3—22) M,/( V" d.) need not be taken greater than 1.0. 3.3.4.1.2.2 The value of Mu/(Vu dv) shall be taken as a positive number. 3.3.4.1.2.3 Nominal shear strength provided by reinforcement —— Nominal shear strength provided by shear reinforcement, V”, shall be computed as follows: (3-21) AV S (3-23) tgs=05£ Jfgdv 3.3.4.2 Beams ~ Design of beams shall meet the requirements of Section 1.13 and the additional requirements of Section 3.3.4.2. 3.3.4.2.1 Members designed primarily to resist flexure shall comply with the requirements of Section 3.3.4.2. The factored axial compressive force on a beam shall not exceed 0.05 A, f ’m . 3.3.4.2.2 Longitudinal reinforcement 3.3.4.2.2.1 The variation in longitudinal reinforcing bars in a beam shall not be greater than one bar size. Not more than two bar sizes shall be used in a beam. 3.3.4.222 The nominal flexural strength of a beam shall not be less than 1.3 multiplied by the nominal cracking moment of the beam, M6,. The modulus of rupture, f,, for this calculation shall be determined in accordance with Section 3.1.8.2. 3.3.4.2.2.3 The requirements of Section 3.3.4.222 need not be applied if at every section the area of tensile reinforcement provided is at least one-third greater than that required by analysis. 3.3.4.2.3 Transverse reinforcement — Transverse reinforcement shall be provided where V" exceeds ¢ Vnm. The factored shear, V”, shall include the effects of lateral load. When transverse reinforcement is required, the following provisions shall apply: (a) Transverse reinforcement shall be a single bar with a l80—degree hook at each end. 043 (b) Transverse reinforcement shall be hooked around the longitudinal reinforcement. (c) The minimum area of transverse reinforcement shall be 0.0007 bdv. (d) The first transverse bar shall not be located more than one- fourth of the beam depth, dv , from the end of the beam. (e) The maximum spacing shall not exceed one-half the depth of the beam nor 48 in. (1219 mm). 3.3.4.2.4 Construction — Beams shall be grouted solid. 3.3.4.2.5 Dimensional limits — The nominal depth of a beam shall not be less than 8 in. (203 mm). 3.3.4.3 Piers 3.3.4.3.1 The factored axial compression force on piers shall not exceed 0.3 A” f 'm . 3.3.4.3.2 Longitudinal reinforcement v A pier subjected to in-plane stress reversals shall be reinforced symmetrically about the neutral axis of the pier. Longitudinal reinforcement of piers shall comply with the following: (a) At least, one bar shall be provided in each end cell. (b) The minimum area of longitudinal reinforcement shall be 0.0007 bd. 3.3.4.3.3 Dimensional limits w Dimensions shall be in accordance with the following: (a) The nominal thickness of a pier shall not exceed 16 in. (406 mm). (b) The distance between lateral supports of a pier shall not exceed 25 multiplied by the nominal thickness of a pier except as provided for in Section 3.3.4.3.3(c). (c) When the distance between lateral supports of a pier exceeds 25 multiplied by the nominal thickness of the pier, design shall be based on the provisions of Section 3.3.5. (d) The nominal length of a pier shall not be less than three multiplied by its nominal thickness nor greater than six multiplied by its nominal thickness. The clear height of a pier shall not exceed five multiplied by its nominal length. Exception: When the factored axial force at the location of maximum moment is less than 0.05 f ’,,, Ag, the length of a pier shall be permitted to be equal to the thickness of the pier. 3.3.4.4 Columns — Design of columns shall meet the requirements of Section 1.14 and the additional requirements of Section 3.3.4.4. 3.3.4.4.] Construction — Columns shall be solid grouted. 1.9.6 C-44 3.3.4.4.2 Dimensional limits —— Dimensions shall be in accordance with the following: (a) The distance between lateral supports of a colurrm shall not exceed 30 multiplied by its nominal width. (b) The nominal depth of a column shall not be less than 8 in. (203 mm) and not be greater than three multiplied by its nominal width. 3.3.5 Wall design for out-of-plane loads 3.3.5.1 Scope —— The requirements of Section 3.3.5 are for the design of walls for out-of-plane loads. 3.3.5.2 Moment and deflection calculations — Moment and deflection calculations in Sections 3.3.5.3 and 3.3.5.4 are based on simple support conditions top and bottom. For other support and fixity conditions, moments and deflections shall be calculated using established principles of mechanics. 3.3.5.3 Walls with factored axial stress of 0.20 f ’m or less — The procedures set forth in this Section shall be used when the factored axial load stress at the location of maximum moment satisfies the requirement computed by Eq. (3-24). P [ “ J3 0.20f,;, A8 When the slenderness ratio, h/t, exceeds 30, the factored axial stress shall not exceed 0.05f’m. (3—24) Factored moment and axial force shall be determined at the midheight of the wall and shall be used for design. The factored moment, Mu, at the midheight of the wall shall be computed using Eq. (3-25). wu h 2 eu Mu = 8 + Puf 7 + Pu 6“ (3-25) Where Pu = PW + Pu] (3—26) The deflection due to factored loads (6“) shall be obtained using Eq. (3-31) and (3-32) and replacing Mm with Mu and dwith 6“. The design strength for out-of-plane wall loading shall be in accordance with Eq. (3-27). Mu s ¢Mn (3-27) The nominal moment shall be calculated using Eqs. (3-28) and (3-29) if the reinforcing steel is placed in the center of the wall. Mn = (Asfy +Pu(d—%] (3-28) TMS 402-08lACI 530-08/ASCE 5-08 Pu + As a = ( 0.80 f?) (3'29) The nominal shear strength shall be determined by Section 3.3.4.1.2. 3.3.5.4 Deflections — The horizontal midheight deflection, 8, , under service lateral and service axial loads (without load factors) shall be limited by the relation: 53 S 0.007 h (3-30) P-delta effects shall be included in deflection calculation. The midheight deflection shall be computed using either Eq. (3-31) or Eq. (3-32), as applicable. (a) Where Mm < MC, 5M h2 as = (3-31) 48Em1g (b) Where MC, < M5,, < Mn 2 _ 2 65 = SMcrh + 5 (Mser MCI‘) h 48Emlg 485mg, The cracking moment of the wall shall be computed using the modulus of rupture, fr, taken from Table 3.1.8.2. 3.3.6 Wall design for in-plane loads 3.3.6.1 Scope — The requirements of Section 3.3.6 are for the design of walls to resist in-plane loads. 3.3.6.2 Reinforcement — Reinforcement shall be provided perpendicular to the shear reinforcement and shall be at least equal to one—third Av. The reinforcement shall be uniformly distributed and shall not exceed a spacing of 8 ft (2.44 m). 3.3.6.3 Flexural and axial strength —— The nominal flexural and axial strength shall be determined in accordance with Section 3.3.4.1.1. 3.3.6.4 Shear strength —- The nominal shear strength shall be computed in accordance with Section 3.3.4.1.2. ‘ 3.3.6.5 The maximum reinforcement requirements of Section 3.3.3.5 shall not apply if a shear wall is designed to satisfy the requirements of 3.3.6.5.1 through 3.3.6.5.5. 3.3.6.5.1 Special boundary elements need not be provided in shear walls meeting the following conditions: 1. PuSOJOAgf ’m for geometrically symmetrical wall sections Pu S 0.05 Agf C" for geometrically unsymmetrical wall sections; and either BUILDING CODE REQUlREMENTS FOR MASONRY STRUCTURES 01‘ 3. V, sum/f," and Mu S 3.0 Vulw 3.3.6.5.2 The need for special boundary elements at the edges of shear walls shall be evaluated in accordance with Section 3.3.6.5.3 or 3.3.6.54. The requirements of Section 3.3.6.5.5 shall also be satisfied. 3.3.6.5.3 This Section applies to walls bending in single curvature in which the flexural limit state response is governed by yielding at the base of the wall. Walls not satisfying those requirements shall be designed in accordance with Section 3.3.6.5.4 (a) Special boundary elements shall be provided over portions of compression zones where: c 2 _J__ 600 (Cdan, /hw) and c is calculated for the PM given by ASCE 7 Strength Design Load Combination 5 (1.2D + 1.0E + L + 0.25) or the corresponding strength design load combination of the legally adopted building code, and the corresponding nominal moment strength, Mn , at the base critical section. The load factor on L in Combination 5 is reducible to 0.5, as per exceptions to Section 2.3.2 of ASCE 7. (b) Where special boundary elements are required by Section 3.3.6.5.3 (a), the special boundary element reinforcement shall extend vertically from the critical section a distance not less than the larger of [w or Mu/4 Vu. C-45 3.3.6.5.4 Shear walls not designed by Section 3.3.6.5.3 shall have special boundary elements at boundaries and edges around openings in shear walls where the maximum extreme fiber compressive stress, corresponding to factored forces including earthquake effect, exceeds 0.2 f ’m. The special boundary element shall be permitted to be discontinued where the calculated compressive stress is less than 0.15 f ’m. Stresses shall be calculated for the factored forces using a linearly elastic model and gross section properties. For walls with flanges, an effective flange width as defined in Section 1.9.4.2.3 shall be used. 3.3.6.5.5 Where special boundary elements are required by Section 3.3.6.5.3 or 3.3.6.5.4, requirements (a) through (d) in this section shall be satisfied and tests shall be performed to verify the strain capacity of the element: (a) The special boundary element shall extend horizontally from the extreme compression fiber a distance not less than the larger of (c - 0.11,,) and c/2. (b) In flanged sections, the special boundary element shall include the effective flange width in compression and shall extend at least 12 in. (305 mm) into the web. (0) Special boundary element transverse reinforcement at the wall base shall extend into the support a minimum of the development length of the largest longitudinal reinforcement in the boundary element unless the special boundary element terminates on a footing or mat, where special boundary element transverse reinforcement shall extend at least 12 in. (305 mm) into the footing or mat. (d) Horizontal shear reinforcement in the wall web shall be anchored to develop the specified yield strength, fy , within the confined core of the boundary element. ...
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Chapter 3 - Strength Design of Masonry - l.l7.4.3 l l...

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