CHAPTER 2 CHAPTER 2-NOTATION AND DEFINITIONS 21-Code notation 4 int in plane parallel to plane of reinforcement gener- The terms in this list are used in the code and as ating shear in the joint, mm, see 21.5.3.1 needed in the commentary Chapter 21 A,= total area of longitudinal reinforcement to a= depth of equivalent rectangular stress block as resist torsion, mm, Chapter 11 defined in 10.2.7.1, mm, Chapter 10 AL min =minimum area of longitudinal reinforcement to shear span, equal to distance from center of resist torsion, mm, see 11.6.5.3, Chapter 11 concentrated load to either(a) face of support A= area of reinforcement in bracket or corbel for continuous or cantilevered members, or(b) resisting tensile force Nuc, mm, see 11.9 center of support for simply supported mem- Chapter 11 bers, mm, Chapter 11, Appendix A nz= area of a face of a nodal zone or a section Ab= area of an individual bar or wire, mm2, Chap- through a nodal zone, mm, Appendix A ters 10. 12 Nc= projected concrete failure area of a single Abro= bearing area of the head of stud or anchor anchor or group of anchors, for calculation of dix D strength in tension, mm, see D.5.2.1, Appendix D area of concrete section resisting shear trans- ANco projected concrete failure area of fer, mm2, Chapter 11 anchor, for calculation of strength in tension if Act= larger gross cross-sectional area of the slab- not limited by edge distance or spacing, mm beam strips of the two orthogonal equivalent see D.5.2.1, Appendix D frames intersecting at a column of a two-way Ao= gross area enclosed by shear flow path, mm slab, mm,, Chapter 18 Chapter 11 Ach=cross-sectional area of a structural member Aoh=area enclosed by centerline of the outermost measured out-to-out of transverse reinforce- closed transverse torsional reinforcement ment, mm, Chapters 10, 21 mm, Chapter 11 area enclosed by outside perimeter of concrete ps= area of prestressing steel in flexural tension cross section mn e11.6.1, Chapter 11 Acs=cross-sectional area at one end of a strut in A zone, mm, Chapter 18, Appendix B area of nonprestressed longitudinal tension strut-and-tie model, taken perpendicular to the reinforcement, mm, Chapters 10-12, 14, 15 axis of the strut, mm2, Appendix A 18, Appendix B Aat= area of that part of cross section between the As= area of longitudinal compression reinforce- flexural tension face and center of gravity of ment, mm, Appendix A gross section, mm, Chapter 18 Asc= area of primary tension reinforcement in a cor- Ac=gross area of concrete section bounded by bel or bracket, mm, see 11.9.3.5, Chapter 11 web thickness and length of section in the direction of shear force considered. mm2 Ase= effective cross-sectional area of anchor, mm Appendix D Acw= area of concrete section of an individual pier, Ash= total cross-sectional area of transverse rein horizontal wall segment, or coupling beam forcement(including crossties) within spacing resisting shear, mm Chapter 21 s and perpendicular to dimension be, mm Af area of reinforcement in bracket or corbel Chapter 21 resisting factored moment, mm2, see 11.9 Asi= total area of surface reinforcement at spacing Si in the i-th layer crossing a strut, with rein- Ag= gross area of concrete section, mm For a hol- forcement at an angle a to the axis of the low section, Ag is the area of the concrete only strut,mm2, AppendⅸxA and does not include the area of the void(s) .min=minimum area of flexural reinforcement, mm2 see11.6.1, Chapters911,14-16,21 see 10.5, Chapter 10 Appendixes B, C Ast= total area of nonprestressed longitudinal rein Ah= total area of shear reinforcement parallel to forcement,(bars or steel shapes),mm primary tension reinforcement in a corbel Chapters 10, 21 bracket, mm, see 11.9, Chapter 11 Asx= area of structural steel shape, pipe, or tubing licene with Acl oduction of networking permitted without loene from H ACl 318 Building Not fis esek 11 182015mstary
CHAPTER 2 19 2.1 — Code notation The terms in this list are used in the code and as needed in the commentary. a = depth of equivalent rectangular stress block as defined in 10.2.7.1, mm, Chapter 10 av = shear span, equal to distance from center of concentrated load to either (a) face of support for continuous or cantilevered members, or (b) center of support for simply supported members, mm, Chapter 11, Appendix A Ab = area of an individual bar or wire, mm2, Chapters 10, 12 Abrg= bearing area of the head of stud or anchor bolt, mm2, Appendix D Ac = area of concrete section resisting shear transfer, mm2, Chapter 11 Acf = larger gross cross-sectional area of the slabbeam strips of the two orthogonal equivalent frames intersecting at a column of a two-way slab, mm2, Chapter 18 Ach = cross-sectional area of a structural member measured out-to-out of transverse reinforcement, mm2, Chapters 10, 21 Acp = area enclosed by outside perimeter of concrete cross section, mm2, see 11.6.1, Chapter 11 Acs = cross-sectional area at one end of a strut in a strut-and-tie model, taken perpendicular to the axis of the strut, mm2, Appendix A Act = area of that part of cross section between the flexural tension face and center of gravity of gross section, mm2, Chapter 18 Acv = gross area of concrete section bounded by web thickness and length of section in the direction of shear force considered, mm2, Chapter 21 Acw = area of concrete section of an individual pier, horizontal wall segment, or coupling beam resisting shear, mm2, Chapter 21 Af = area of reinforcement in bracket or corbel resisting factored moment, mm2, see 11.9, Chapter 11 Ag = gross area of concrete section, mm2 For a hollow section, Ag is the area of the concrete only and does not include the area of the void(s), see 11.6.1, Chapters 9-11, 14-16, 21, 22, Appendixes B, C. Ah = total area of shear reinforcement parallel to primary tension reinforcement in a corbel or bracket, mm2, see 11.9, Chapter 11 Aj = effective cross-sectional area within a joint in a plane parallel to plane of reinforcement generating shear in the joint, mm2, see 21.5.3.1, Chapter 21 Al = total area of longitudinal reinforcement to resist torsion, mm2, Chapter 11 Al,min = minimum area of longitudinal reinforcement to resist torsion, mm2, see 11.6.5.3, Chapter 11 An = area of reinforcement in bracket or corbel resisting tensile force Nuc, mm2, see 11.9, Chapter 11 Anz = area of a face of a nodal zone or a section through a nodal zone, mm2, Appendix A ANc= projected concrete failure area of a single anchor or group of anchors, for calculation of strength in tension, mm2, see D.5.2.1, Appendix D ANco = projected concrete failure area of a single anchor, for calculation of strength in tension if not limited by edge distance or spacing, mm2, see D.5.2.1, Appendix D Ao = gross area enclosed by shear flow path, mm2, Chapter 11 Aoh= area enclosed by centerline of the outermost closed transverse torsional reinforcement, mm2, Chapter 11 Aps = area of prestressing steel in flexural tension zone, mm2, Chapter 18, Appendix B As = area of nonprestressed longitudinal tension reinforcement, mm2, Chapters 10-12, 14, 15, 18, Appendix B As ′ = area of longitudinal compression reinforcement, mm2, Appendix A Asc = area of primary tension reinforcement in a corbel or bracket, mm2, see 11.9.3.5, Chapter 11 Ase = effective cross-sectional area of anchor, mm2, Appendix D Ash = total cross-sectional area of transverse reinforcement (including crossties) within spacing s and perpendicular to dimension bc, mm2, Chapter 21 Asi = total area of surface reinforcement at spacing si in the i-th layer crossing a strut, with reinforcement at an angle αi to the axis of the strut, mm2, Appendix A As,min= minimum area of flexural reinforcement, mm2, see 10.5, Chapter 10 Ast = total area of nonprestressed longitudinal reinforcement, (bars or steel shapes), mm2, Chapters 10, 21 Asx = area of structural steel shape, pipe, or tubing CHAPTER 2 — NOTATION AND DEFINITIONS ACI 318 Building Code and Commentary Copyright American Concrete Institute Provided by IHS under license with ACI Licensee=Black & Veatch/5910842100 No reproduction or networking permitted without license from IHS Not for Resale, 11/28/2005 18:20:15 MST --`,,`,````````,,`,,`,,``,`,,,`-`-`,,`,,`,`,,`---
CHAPTER 2 in a composite section, mm, Chapter 10 in the direction of the span for which moments At area of one leg of a closed stirrup resisting tor- are determined, mm, Chapter 13 sion within spacing s, mm2, Chapter 11 b2= dimension of the critical section b, measured in Atp= area of prestressing steel in a tie, mm the direction perpendicular to b,, mm, Chapter Appendix A Atr= total cross-sectional of all transverse Bn= nominal bearing strength, N, Chapter 22 reinforcement within spacing s that crosses B factored bearing load, N, Chapter 22 the potential plane of splitting through the rein-c distance from extreme compression fiber to forcement being developed, mm, Chapter 12 neutral axis, mm, Chapters 9, 10, 14, 21 Ats= area of nonprestressed reinforcement in a tie, Cac= critical edge distance required to develop the mm, Appendix A basic concrete breakout strength of a post Av= area of shear reinforcement spacing s, mm installed anchor in uncracked concrete without Chapters 11, 17 supplementary reinforcement to control split Avc= projected concrete failure area of a single ting, mm, see D8.6, Appendix D anchor or group of anchors for calculation of Ca, mar maximum distance from center of an anchor strength in shear, mm, see D.6.2.1, Appendix D shaft to the edge of concrete, mm, Appendix D Avco: projected concrete failure area of a single a, min=minimum distance from center of an anchor anchor, for calculation of strength in shear, if not shaft to the edge of concrete, mm, Appendix D limited by corner influences, spacing, or mem- Cal= distance from the center of an anchor shaft to ber thickness, mm2, see D.6.2.1, Appendix D the edge of concrete in one direction, mm. If Ayd= total area of reinforcement in each group of shear is applied to anchor, ca1 is taken in the diagonal bars in a diagonally reinforced cou- applied to the anchor, Ca1 is the minimum Ay= area of shear-friction reinforcement, mm2, edge distance, Appendix D Ca2= distance from center of an anchor shaft to the Avh= area of shear reinforcement parallel to flexural dge of concrete in the direction perpendicu tension reinforcement within spacing S2, mm lar to c Chapter 11 Cb= smaller of (a) the distance from center of a bar Av.min minimum area of shear reinforcement within concre ete surface, and(b) spacing s, mm, see 11.5.6.3 and 11.5.6.4 one-half the center-to-center spacing of bars Chapter 11 or wires being developed, mm, Chapter 12 Al= loaded area, mm, Chapters 10, 22 c.= clear cover of reinforcement mm see 10. 6. 4 A2= area of the lower base of the largest frustum hapter tained wholly within the support and having for t= distance from the interior face of the column to of a pyramid, cone, or tapered wedge con the slab edge measured parallel to cl, but not its upper base the loaded area, and having xceeding Cr, mm, Chapter 2 side slopes of 1 vertical to 2 horizontal, mi C1= dimension of rectangular or equivalent rectan Chapters 10, 22 gular column, capital, or bracket measured in b width of compression face of member, mm, the direction of the span for which moments Chapter 10, Appendix B are being determined, mm, Chapters 11, 13, 21 bc= cross-sectional dimension of column c2=dimension of rectangular or equivalent rectangu measured center-to-center of outer legs of lar column, capital, or bracket measured in the transverse reinforcement comprising area direction perpendicular to cl, mm, Chapter 13 Ash, mm, Chapter 21 ctional constant to define torsional o perimeter of critical section for shear in slabs properties of slab and beam, see 13.6.4.2 and footings, mm, see 11.12. 1.2, Chapters 11 Chapter 13 Cm= factor relating actual moment diagram to an width of strut, mm, Appendix A equivalent uniform moment diagram, Chapter 10 width of that part of cross section containing the distance from extreme compression fiber to closed stirrups resisting torsion, mm, Chapter 11 centroid of longitudinal tension reinforcement, bv= width of cross section at contact surface being mm, Chapters 7, 9-12, 14, 17, 18, 21, Appen investigated for horizontal shear, mm, Chapter 17 dies B. c bw=web width, or diameter of circular section, d'=distance from extreme compression fiber mm, Chapters 10-12, 21, 22, Appendix B centroid of longitudinal compression reinforce- b,= dimension of the critical section bo measured ment, mm, Chapters 9, 18, Appendix C licene with Acl o reproducion of networking permitted without loene from H ACI 318 Building Cc Lc rseeesac 8 eatc5 93028042500
20 CHAPTER 2 ACI 318 Building Code and Commentary in a composite section, mm2, Chapter 10 At = area of one leg of a closed stirrup resisting torsion within spacing s, mm2, Chapter 11 Atp = area of prestressing steel in a tie, mm2, Appendix A Atr = total cross-sectional area of all transverse reinforcement within spacing s that crosses the potential plane of splitting through the reinforcement being developed, mm2, Chapter 12 Ats = area of nonprestressed reinforcement in a tie, mm2, Appendix A Av = area of shear reinforcement spacing s, mm2, Chapters 11, 17 AVc = projected concrete failure area of a single anchor or group of anchors, for calculation of strength in shear, mm2, see D.6.2.1, Appendix D AVco= projected concrete failure area of a single anchor, for calculation of strength in shear, if not limited by corner influences, spacing, or member thickness, mm2, see D.6.2.1, Appendix D Avd = total area of reinforcement in each group of diagonal bars in a diagonally reinforced coupling beam, mm2, Chapter 21 Avf = area of shear-friction reinforcement, mm2, Chapter 11 Avh = area of shear reinforcement parallel to flexural tension reinforcement within spacing s2, mm2, Chapter 11 Av,min= minimum area of shear reinforcement within spacing s, mm2, see 11.5.6.3 and 11.5.6.4, Chapter 11 A1 = loaded area, mm2, Chapters 10, 22 A2 = area of the lower base of the largest frustum of a pyramid, cone, or tapered wedge contained wholly within the support and having for its upper base the loaded area, and having side slopes of 1 vertical to 2 horizontal, mm2, Chapters 10, 22 b = width of compression face of member, mm, Chapter 10, Appendix B bc = cross-sectional dimension of column core measured center-to-center of outer legs of the transverse reinforcement comprising area Ash, mm, Chapter 21 bo = perimeter of critical section for shear in slabs and footings, mm, see 11.12.1.2, Chapters 11, 22 bs = width of strut, mm, Appendix A bt = width of that part of cross section containing the closed stirrups resisting torsion, mm, Chapter 11 bv = width of cross section at contact surface being investigated for horizontal shear, mm, Chapter 17 bw = web width, or diameter of circular section, mm, Chapters 10-12, 21, 22, Appendix B b1 = dimension of the critical section bo measured in the direction of the span for which moments are determined, mm, Chapter 13 b2 = dimension of the critical section bo measured in the direction perpendicular to b1, mm, Chapter 13 Bn = nominal bearing strength, N, Chapter 22 Bu = factored bearing load, N, Chapter 22 c = distance from extreme compression fiber to neutral axis, mm, Chapters 9, 10, 14, 21 cac = critical edge distance required to develop the basic concrete breakout strength of a postinstalled anchor in uncracked concrete without supplementary reinforcement to control splitting, mm, see D.8.6, Appendix D ca,max= maximum distance from center of an anchor shaft to the edge of concrete, mm, Appendix D ca,min= minimum distance from center of an anchor shaft to the edge of concrete, mm, Appendix D ca1 = distance from the center of an anchor shaft to the edge of concrete in one direction, mm. If shear is applied to anchor, ca1 is taken in the direction of the applied shear. If the tension is applied to the anchor, ca1 is the minimum edge distance, Appendix D ca2 = distance from center of an anchor shaft to the edge of concrete in the direction perpendicular to ca1, mm, Appendix D cb = smaller of (a) the distance from center of a bar or wire to nearest concrete surface, and (b) one-half the center-to-center spacing of bars or wires being developed, mm, Chapter 12 cc = clear cover of reinforcement, mm, see 10.6.4, Chapter 10 ct = distance from the interior face of the column to the slab edge measured parallel to c1, but not exceeding c1, mm, Chapter 21 c1 = dimension of rectangular or equivalent rectangular column, capital, or bracket measured in the direction of the span for which moments are being determined, mm, Chapters 11, 13, 21 c2 = dimension of rectangular or equivalent rectangular column, capital, or bracket measured in the direction perpendicular to c1, mm, Chapter 13 C = cross-sectional constant to define torsional properties of slab and beam, see 13.6.4.2, Chapter 13 Cm = factor relating actual moment diagram to an equivalent uniform moment diagram, Chapter 10 d = distance from extreme compression fiber to centroid of longitudinal tension reinforcement, mm, Chapters 7, 9-12, 14, 17, 18, 21, Appendixes B, C d ′ = distance from extreme compression fiber to centroid of longitudinal compression reinforcement, mm, Chapters 9, 18, Appendix C Copyright American Concrete Institute Provided by IHS under license with ACI Licensee=Black & Veatch/5910842100 No reproduction or networking permitted without license from IHS Not for Resale, 11/28/2005 18:20:15 MST --`,,`,````````,,`,,`,,``,`,,,`-`-`,,`,,`,`,,`---
CHAPTER 2 db nominal diameter of bar, wire, or prestressing of concrete at time of initial prestress, MPa, strand, mm, Chapters 7, 12, 21 Chapter 18 do outside diameter of anchor or shaft diameter fcr= required average compressive strength of of headed stud, headed bolt or hooked bolt concrete used as the basis for selection of mm, see D8.4, Appendix D concrete proportions, MPa, Chapter 5 do value substituted for do when an oversized average splitting tensile strength of lightweight anchor is used, mm, see D8.4, Appendix D distance from extreme compression fiber to concrete, MPa, Chapters 5, 9, 11, 12, 22 fd stress due to unfactored dead load at centroid of prestressing steel, mm, Chapter extreme fiber of section where tensile stress is 11, 18, Appendix B caused by externally applied loads, MPa, diameter of pile at footing base, mm, Chapter 15 di = distance from extreme compression fiber to fac decompression stress; stress in the prestress centroid of extreme layer of longitudinal ten- ing steel when stress is zero in the concrete at sion steel, mm, Chapters 9, 10, Appendix C ame D dead loads, or related internal moments and stressing steel, MPa, Chapter 18 forces, Chapters 8, 9, 20, 21, Appendix C compressive stress in concrete(after allow- e= base of Napierian logarithms, Chapter 18 ance for all prestress losses) at centroid of eh= distance from the inner surface of the shaft of a cross section resisting externally applied J-or L-bolt to the outer tip of the J-or L-bolt, mm, loads or at junction of web and flange when the centroid lies within the flange, MPa(In a en= distance between resultant tension load on a composite member, foc is the resultant group of anchors loaded in tension and the compressive stress at centroid of composite centroid of the group of anchors loaded in ten section, or at junction of web and flange when sion, mm; e w is always positive, Appendix D the centroid lies within the flange, due to both e'v= distance between resultant shear load on a prestress and moments resisted by precast group of anchors loaded in shear in the same member acting alone), Chapter 11 direction, and the centroid of the group of fpe= compressive stress in concrete due to effec- anchors loaded in shear in the same directio tive prestress forces only(after allowance for mm;ey is always positive, Appendix D all prestress losses)at extreme fiber of section E= load effects of earthquake, or related internal where tensile stress is caused by externally moments and forces, Chapters 9, 21, Appen dix C fps= stress in prestressing steel at nominal flexural Ec modulus of elasticity of concrete, MPa, see strength, MPa, Chapters 12, 18 8.51, Chapters810,14,19 pu=specified tensile strength of prestressing steel Ecb= modulus of elasticity of beam concrete, MPa, MPa, Chapters 11, 18 Chapter 13 Pey=specified yield strength of prestressing steel Ecs= modulus of elasticity of slab concrete, MP fr= modulus of rupture of concrete, MPa,see N-mm2. see 10.12.3, Chapter 10 h member El= flexural stiffness of compressio 9.5.2.3, Chapters 9, 14, 18, Appendix B calculated tensile stress in reinforcement at modulus of elasticity of prestressing steel service loads, MPa, Chapters 10, 18 MPa, see 8.5.3, Chapter 8 fs stress in compression reinforcement under Es modulus of elasticity of reinforcement and struc factored loads, MPa, Appendix A tural steel, MPa, see 8.5.2, Chapters 8, 10, 14 fse effective stress in prestressing steel(after fc=specified compressive strength of concrete, allowance for all prestress losses), MPa MPa, Chapters4,5,8-12,14,18,19,21,22, Chapters 12, 18, Appendix A ft extreme fiber stress in tension in the precom- Wc=square root of specified compressive strength pressed tensile zone calculated at service of concrete, MPa, Chapters 8, 9, 11, 12, 18 loads using gross section properties, MPa 19,21,22, Appen dix D effective compressive strength of the concrete futa= specified tensile strength of anchor steel in a strut or a nodal zone, MPa, Chapter 15 MPa, Appendix D Appendix A fy specified yield strength of reinforcement, MPa fci= specified compressive strength of concret Chapters3,7,9-12,14,17-19,21, Appen time of initial prestress, MPa, Chapters 7, dies A-C ci= square root of specified compressive strength fya = specified yield strength of anchor steel, MPa licene with Acl ACI 318 Building Nor censeenBlack Veatch5910842100 oduction of networking permitted without loene from H ot for Resale, 11/28/2005 182015ural
CHAPTER 2 21 ACI 318 Building Code and Commentary db = nominal diameter of bar, wire, or prestressing strand, mm, Chapters 7, 12, 21 do = outside diameter of anchor or shaft diameter of headed stud, headed bolt, or hooked bolt, mm, see D.8.4, Appendix D do ′ = value substituted for do when an oversized anchor is used, mm, see D.8.4, Appendix D dp = distance from extreme compression fiber to centroid of prestressing steel, mm, Chapters 11,18, Appendix B dpile= diameter of pile at footing base, mm, Chapter 15 dt = distance from extreme compression fiber to centroid of extreme layer of longitudinal tension steel, mm, Chapters 9, 10, Appendix C D = dead loads, or related internal moments and forces, Chapters 8, 9, 20, 21, Appendix C e = base of Napierian logarithms, Chapter 18 eh = distance from the inner surface of the shaft of a J- or L-bolt to the outer tip of the J- or L-bolt, mm, Appendix D e′ N = distance between resultant tension load on a group of anchors loaded in tension and the centroid of the group of anchors loaded in tension, mm; e′ N is always positive, Appendix D e′ V = distance between resultant shear load on a group of anchors loaded in shear in the same direction, and the centroid of the group of anchors loaded in shear in the same direction, mm; e′ V is always positive, Appendix D E = load effects of earthquake, or related internal moments and forces, Chapters 9, 21, Appendix C Ec = modulus of elasticity of concrete, MPa, see 8.5.1, Chapters 8-10, 14, 19 Ecb = modulus of elasticity of beam concrete, MPa, Chapter 13 Ecs = modulus of elasticity of slab concrete, MPa, Chapter 13 EI = flexural stiffness of compression member, N⋅mm2, see 10.12.3, Chapter 10 Ep = modulus of elasticity of prestressing steel, MPa, see 8.5.3, Chapter 8 Es = modulus of elasticity of reinforcement and structural steel, MPa, see 8.5.2, Chapters 8, 10, 14 fc′ = specified compressive strength of concrete, MPa, Chapters 4, 5, 8-12, 14, 18, 19, 21, 22, Appendixes A-D = square root of specified compressive strength of concrete, MPa, Chapters 8, 9, 11, 12, 18, 19, 21, 22, Appendix D fce = effective compressive strength of the concrete in a strut or a nodal zone, MPa, Chapter 15, Appendix A fci ′ = specified compressive strength of concrete at time of initial prestress, MPa, Chapters 7, 18 = square root of specified compressive strength of concrete at time of initial prestress, MPa, Chapter 18 f cr ′ = required average compressive strength of concrete used as the basis for selection of concrete proportions, MPa, Chapter 5 fct = average splitting tensile strength of lightweight concrete, MPa, Chapters 5, 9, 11, 12, 22 fd = stress due to unfactored dead load, at extreme fiber of section where tensile stress is caused by externally applied loads, MPa, Chapter 11 fdc = decompression stress; stress in the prestressing steel when stress is zero in the concrete at the same level as the centroid of the prestressing steel, MPa, Chapter 18 fpc = compressive stress in concrete (after allowance for all prestress losses) at centroid of cross section resisting externally applied loads or at junction of web and flange when the centroid lies within the flange, MPa. (In a composite member, fpc is the resultant compressive stress at centroid of composite section, or at junction of web and flange when the centroid lies within the flange, due to both prestress and moments resisted by precast member acting alone), Chapter 11 fpe = compressive stress in concrete due to effective prestress forces only (after allowance for all prestress losses) at extreme fiber of section where tensile stress is caused by externally applied loads, MPa, Chapter 11 fps = stress in prestressing steel at nominal flexural strength, MPa, Chapters 12, 18 fpu = specified tensile strength of prestressing steel, MPa, Chapters 11, 18 fpy = specified yield strength of prestressing steel, MPa, Chapter 18 fr = modulus of rupture of concrete, MPa, see 9.5.2.3, Chapters 9, 14, 18, Appendix B fs = calculated tensile stress in reinforcement at service loads, MPa, Chapters 10, 18 fs ′ = stress in compression reinforcement under factored loads, MPa, Appendix A fse = effective stress in prestressing steel (after allowance for all prestress losses), MPa, Chapters 12, 18, Appendix A ft = extreme fiber stress in tension in the precompressed tensile zone calculated at service loads using gross section properties, MPa, see 18.3.3, Chapter 18 futa = specified tensile strength of anchor steel, MPa, Appendix D fy = specified yield strength of reinforcement, MPa, Chapters 3, 7, 9-12, 14, 17-19, 21, Appendixes A-C fya = specified yield strength of anchor steel, MPa, fc ′ fci′ Copyright American Concrete Institute Provided by IHS under license with ACI Licensee=Black & Veatch/5910842100 No reproduction or networking permitted without license from IHS Not for Resale, 11/28/2005 18:20:15 MST --`,,`,````````,,`,,`,,``,`,,,`-`-`,,`,,`,`,,`---
CHAPTER 2 Appendix D bers, Chapters 10, 14 specified yield strength ty of transverse rein- kc =coefficient for basic concrete breakout forcement, MPa, Chapters 10-12, strength in tension, Appendix D loads due to weight and pressures of kcp= coefficient for pryout strength, Appendix D with well-defined densities and contro maximum heights, or related internal K wobble friction coefficient per meter of tendon moments and forces, Chapter 9, Appendix C Chapter 18 Fn= nominal strength of a strut, tie, or noda\ nne, t- transverse reinforcement index, see 12.2.3, Chapter 12 N, Appendix A e= span length of beam or one-way slab; clear Fnn= nominal strength at face of a nodal zone, N, projection of cantilever, mm, see 8.7, Chapter 9 Appendix A additional embedment length beyond center- F nominal strength of a strut, N, Appendix A line of support or point of inflection, mm, Fnt= nominal strength of a tie, N, Appendix A Chapter 12 Fu= factored force acting in a strut, tie, bearing ec =length of compression member in a frame, area. or nodal zone in a strut-and-tie model measured center-to-center of the joints in the N, Appendix A frame, mm, Chapters 10, 14, 22 h= overall thickness or height of member, mm, ed=development length in tension of deformed Chapters 9-12, 14, 17, 18, 20-22, Appendixes bar, deformed wire, plain and deformed welded wire reinforcement, or pretensioned h thickness of member in which an anchor is strand, mm, Chapters 7, 12, 19, 2 located, measured parallel to anchor axis, edc= development length in compression of deformed mm, AppendⅸxD bars and deformed wire, mm, Chapter 12 Def= effective embedment depth of anchor, mm ldh= development length in tension of deformed bar D85, AppendⅸxD or deformed wire with a standard hook. mea- hy= depth of shearhead cross section, mm, sured from critical section to outside end of Chapter 11 hook (straight embedment length between height of entire wall from base to top or height critical section and start of hook [point of tan the segment of wall considered, mm, Chap- gency] plus inside radius of bend and one bar ters 11 21 diameter), mm, see 12.5 and 21.5.4, Chapters h x= maximum center-to-center horizontal spacing of crossties or hoop legs on all faces of the le load bearing length of anchor for shear, mm column, mm, Chapter 21 see D.6.2.2, Appendix D H= loads due to weight and pressure of soil, water en length of clear span measured face-to-face of in soil. or other materials or related internal of supports, mm, Chapters 8-11, 13, 16, 18, 21 moments and forces, Chapter 9, Appendix C eo length, measured from joint face along axis of I= moment of inertia of section about centroidal structural member, over which special trans- axis, mm, Chapters 10, 11 verse reinforcement must be provided, mm, centroidal axis, mm, see 13.2.4, Chapter 1 out b b= moment of inertia of gross section of beam ab Chapter 21 ' px= distance from jacking end of prestressing steel Ii moment of inertia of cracked section trans- lement to point under consideration, m, see formed to concrete, mm", Chapters 9, 14 18.6.2, Chapter 18 le effective moment of inertia for computation of .t span of member under load test, taken as the deflection. mm see 9.5.2.3, Chapters 9, 14 shorter span for two-way slab systems, mm g= moment of inertia of gross concrete section Span is the smaller of(a) distance between about centroidal axis, neglecting reinfor centers of supports, and(b)clear distance ment, mm", Chapters 9, between supports plus thickness h of mem- Is= moment of inertia of gross section of slab ber. Span for a cantilever shall be taken as about centroidal axis defined for calculating af twice the distance from face of support to can- and Bt mm4, Chapter 13 tilever end, Chapter 20 Ise moment of inertia of reinforcement about cent- lu unsupported length of compression member, roidal axis of member cross section mm, Wv mm, see 10.11. 3.1, Chapter 10 Chapter 10 length of shearhead arm from centroid of con Iv= moment of inertia of structural steel centrated load or reaction, mm, Chapter 11 pipe, or tubing about centroidal axis lw length of entire wall or length of segment of wall considered in direction of shear force effective length factor for compression mem- mm, Chapters 11, 14, 21 licene with Acl oduction of networking permitted without loene from H ACI 318 Building CcNot fos gesake 12e2oo5 18920415
22 CHAPTER 2 ACI 318 Building Code and Commentary Appendix D fyt = specified yield strength fy of transverse reinforcement, MPa, Chapters 10-12, 21 F = loads due to weight and pressures of fluids with well-defined densities and controllable maximum heights, or related internal moments and forces, Chapter 9, Appendix C Fn = nominal strength of a strut, tie, or nodal zone, N, Appendix A Fnn = nominal strength at face of a nodal zone, N, Appendix A Fns = nominal strength of a strut, N, Appendix A Fnt = nominal strength of a tie, N, Appendix A Fu = factored force acting in a strut, tie, bearing area, or nodal zone in a strut-and-tie model, N, Appendix A h = overall thickness or height of member, mm, Chapters 9-12, 14, 17, 18, 20-22, Appendixes A, C ha = thickness of member in which an anchor is located, measured parallel to anchor axis, mm, Appendix D hef = effective embedment depth of anchor, mm, see D.8.5, Appendix D hv = depth of shearhead cross section, mm, Chapter 11 hw = height of entire wall from base to top or height of the segment of wall considered, mm, Chapters 11, 21 hx = maximum center-to-center horizontal spacing of crossties or hoop legs on all faces of the column, mm, Chapter 21 H = loads due to weight and pressure of soil, water in soil, or other materials, or related internal moments and forces, Chapter 9, Appendix C I = moment of inertia of section about centroidal axis, mm4, Chapters 10, 11 Ib = moment of inertia of gross section of beam about centroidal axis, mm4, see 13.2.4, Chapter 13 Icr = moment of inertia of cracked section transformed to concrete, mm4, Chapters 9, 14 Ie = effective moment of inertia for computation of deflection, mm4, see 9.5.2.3, Chapters 9, 14 Ig = moment of inertia of gross concrete section about centroidal axis, neglecting reinforcement, mm4, Chapters 9, 10 Is = moment of inertia of gross section of slab about centroidal axis defined for calculating αf and βt, mm4, Chapter 13 Ise = moment of inertia of reinforcement about centroidal axis of member cross section, mm4, Chapter 10 Isx = moment of inertia of structural steel shape, pipe, or tubing about centroidal axis of composite member cross section, mm4, Chapter 10 k = effective length factor for compression members, Chapters 10, 14 kc = coefficient for basic concrete breakout strength in tension, Appendix D kcp = coefficient for pryout strength, Appendix D K = wobble friction coefficient per meter of tendon, Chapter 18 Ktr = transverse reinforcement index, see 12.2.3, Chapter 12 l = span length of beam or one-way slab; clear projection of cantilever, mm, see 8.7, Chapter 9 la = additional embedment length beyond centerline of support or point of inflection, mm, Chapter 12 lc = length of compression member in a frame, measured center-to-center of the joints in the frame, mm, Chapters 10, 14, 22 ld = development length in tension of deformed bar, deformed wire, plain and deformed welded wire reinforcement, or pretensioned strand, mm, Chapters 7, 12, 19, 21 ldc = development length in compression of deformed bars and deformed wire, mm, Chapter 12 ldh = development length in tension of deformed bar or deformed wire with a standard hook, measured from critical section to outside end of hook (straight embedment length between critical section and start of hook [point of tangency] plus inside radius of bend and one bar diameter), mm, see 12.5 and 21.5.4, Chapters 12, 21 le = load bearing length of anchor for shear, mm, see D.6.2.2, Appendix D ln = length of clear span measured face-to-face of of supports, mm, Chapters 8-11, 13, 16, 18, 21 lo = length, measured from joint face along axis of structural member, over which special transverse reinforcement must be provided, mm, Chapter 21 lpx = distance from jacking end of prestressing steel element to point under consideration, m, see 18.6.2, Chapter 18 lt = span of member under load test, taken as the shorter span for two-way slab systems, mm. Span is the smaller of (a) distance between centers of supports, and (b) clear distance between supports plus thickness h of member. Span for a cantilever shall be taken as twice the distance from face of support to cantilever end, Chapter 20 lu = unsupported length of compression member, mm, see 10.11.3.1, Chapter 10 lv = length of shearhead arm from centroid of concentrated load or reaction, mm, Chapter 11 lw = length of entire wall or length of segment of wall considered in direction of shear force, mm, Chapters 11, 14, 21 Copyright American Concrete Institute Provided by IHS under license with ACI Licensee=Black & Veatch/5910842100 No reproduction or networking permitted without license from IHS Not for Resale, 11/28/2005 18:20:15 MST --`,,`,````````,,`,,`,,``,`,,,`-`-`,,`,,`,`,,`---
CHAPTER 2 G1= length of span in direction that moments are due to factored lateral and eccentric vertical being determined, measured center-to-center loads, N.mm, Chapter 14 of supports, mm, Chapter 13 M moment resistance contributed by shearhead e2 =length of span in direction perpendicular to G1 reinforcement, N-mm, Chapter 11 measured center-to-center of supports, mm, M,= smaller factored end moment on a compre see 13.6.2.3 and 13.6.2. 4, Chapter 13 sion member, to be taken as positive if mem L= live loads. or related internal moments and ber is bent in single curvature, and negative forces, Chapters 8, 9, 20, 21, Appendix C bent in double curvature, N-mm, Chapter 10 roof live load, or related internal moments and Mins= factored end moment on a compression mem- forces, Chapter 9 ber at the end at which M, acts, due to load M maximum unfactored moment due to service that cause no appreciable sidesway, calcu- loads, including P4 effects, N-mm, Chapter 14 lated using a first-order elastic frame analysis, 1a maximum unfactored moment in member at Nmm, Chapter 10 stage deflection is computed, N-mm, Chapters Mis= factored end moment on compression mem- 9.14 ber at the end at which M, acts, due to loads Mc= factored moment amplified for the effects of that cause appreciable sidesway, calculated member curvature used for design of compres- using a first-order elastic frame analysis mber, N-mm, see 10. 12.3, Chapter 10 N.mm, Chapter 10 Mer= cracking moment, N- mm, see 9.5.2.3, Chap- M2= larger factored end moment on compression member, always positive, N- mm, Chapter 10 Mere= moment causing flexural cracking at section due M2. min=minimum value of M2, N-mm, Chapter 10 to externally applied loads, N-mm, Chapter 11 Mans= factored end moment on compression M= factored moment modified to account for effect ber at the end at which M acts, due to loads of axial compression, N-mm, see 11.3.2.2 that cause no appreciable sidesway, calcu lated using a first-order elastic frame analysis, Amax= maximum factored moment at section due to N-mm, Chapter 10 externally applied loads, N- mm, Chapter 11 Mas= factored end moment on compression member M nominal flexural strength at section, N-mm, at the end at which M2 acts, due to loads that Chapters11,12,14,18,21,22 cause appreciable sidesway, calculated using a Mnb= nominal flexural strength of beam including first-order elastic frame, N mm, Chapter 10 slab where in tension, framing into joint, n= number of items, such as strength tests, bars, N.mm, see 21.4.2.2, Chapter 21 wires, monostrand anchorage devices Mnc= nominal flexural strength of column framing anchors, or shearhead arms, Chapters 5, 11 into joint, calculated for factored axial force, consistent with the direction of lateral forces Nb basic concrete breakout strength in tension of considered, resulting in lowest flexural a single anchor in cracked concrete, N, see strength, N mm, see 21 4.2.2, Chapter 21 D 5.2.2, Appendix D Mo= total factored static moment, N-mm, Chapter 13 Nc= tension force in concrete due to unfactored M,= required plastic moment strength of shea dead load plus live load, N, Chapter 18 head cross section, N-mm, Chapter 11 Ncb= nominal concrete breakout strength in tension Mpr= probable flexural strength of members, with or of a single anchor, N, see D.5.2.1, Appendix without axial load, determined using the prop Ncbg nominal concrete breakout strength in tension erties of the member at the joint faces assum- ing a tensile stress in the longitudinal bars of of a group of anchors, N, see D.5.2.1, Appe at least 1.25fy and a strength reduction factor, No= nominal strength in tension, N, Appendix D Ms= factored moment due to loads causing appre- Np=pullout strength in tension of a single anchor in. ciable sway, N-mm, Chapter 10 cracked concrete N. see D.5.3.4 and D.5.3.5 Msa= maximum unfactored applied moment due to A service loads, not including PA effects, N mm, Non= nominal pullout strength in tension of a single Chapter 14 anchor, N, see D 5.3.1, Appendix Mslab- portion of slab factored moment balanced by Nsa= nominal strength of a single anchor or group of support moment, N-mm, Chapter 21 anchors in tension as governed by the steel Mu= factored moment at section, N- mm, Chapters strength, N, see D 5.1.1 and D.5.1.2, Appendix D 10,11,13,14,21,22 Nsb= side-face blowout strength of a single anchor, Mua= moment at the midheight section of the wall N, Appendix D licene with Acl censeenBlack Veatch5910842100 o reproducion of networking permitted without loene from H ACI 318 Building Nor ot for Resale, 11/28/2005 182015ural
CHAPTER 2 23 ACI 318 Building Code and Commentary l1 = length of span in direction that moments are being determined, measured center-to-center of supports, mm, Chapter 13 l2 = length of span in direction perpendicular to l1, measured center-to-center of supports, mm, see 13.6.2.3 and 13.6.2.4, Chapter 13 L = live loads, or related internal moments and forces, Chapters 8, 9, 20, 21, Appendix C Lr = roof live load, or related internal moments and forces, Chapter 9 M = maximum unfactored moment due to service loads, including P∆ effects, N⋅mm, Chapter 14 Ma = maximum unfactored moment in member at stage deflection is computed, N⋅mm, Chapters 9, 14 Mc = factored moment amplified for the effects of member curvature used for design of compression member, N⋅mm, see 10.12.3, Chapter 10 Mcr = cracking moment, N⋅mm, see 9.5.2.3, Chapters 9, 14 Mcre= moment causing flexural cracking at section due to externally applied loads, N⋅mm, Chapter 11 Mm = factored moment modified to account for effect of axial compression, N⋅mm, see 11.3.2.2, Chapter 11 Mmax= maximum factored moment at section due to externally applied loads, N⋅mm, Chapter 11 Mn = nominal flexural strength at section, N⋅mm, Chapters 11, 12, 14, 18, 21, 22 Mnb= nominal flexural strength of beam including slab where in tension, framing into joint, N⋅mm, see 21.4.2.2, Chapter 21 Mnc= nominal flexural strength of column framing into joint, calculated for factored axial force, consistent with the direction of lateral forces considered, resulting in lowest flexural strength, N⋅mm, see 21.4.2.2, Chapter 21 Mo = total factored static moment, N⋅mm, Chapter 13 Mp = required plastic moment strength of shearhead cross section, N⋅mm, Chapter 11 Mpr = probable flexural strength of members, with or without axial load, determined using the properties of the member at the joint faces assuming a tensile stress in the longitudinal bars of at least 1.25fy and a strength reduction factor, φ, of 1.0, N⋅mm, Chapter 21 Ms = factored moment due to loads causing appreciable sway, N⋅mm, Chapter 10 Msa = maximum unfactored applied moment due to service loads, not including P∆ effects, N⋅mm, Chapter 14 Mslab= portion of slab factored moment balanced by support moment, N⋅mm, Chapter 21 Mu = factored moment at section, N⋅mm, Chapters 10, 11, 13, 14, 21, 22 Mua= moment at the midheight section of the wall due to factored lateral and eccentric vertical loads, N⋅mm, Chapter 14 Mv = moment resistance contributed by shearhead reinforcement, N⋅mm, Chapter 11 M1 = smaller factored end moment on a compression member, to be taken as positive if member is bent in single curvature, and negative if bent in double curvature, N⋅mm, Chapter 10 M1ns= factored end moment on a compression member at the end at which M1 acts, due to loads that cause no appreciable sidesway, calculated using a first-order elastic frame analysis, N⋅mm, Chapter 10 M1s= factored end moment on compression member at the end at which M1 acts, due to loads that cause appreciable sidesway, calculated using a first-order elastic frame analysis, N⋅mm, Chapter 10 M2 = larger factored end moment on compression member, always positive, N⋅mm, Chapter 10 M2,min =minimum value of M2, N⋅mm, Chapter 10 M2ns= factored end moment on compression member at the end at which M2 acts, due to loads that cause no appreciable sidesway, calculated using a first-order elastic frame analysis, N⋅mm, Chapter 10 M2s= factored end moment on compression member at the end at which M2 acts, due to loads that cause appreciable sidesway, calculated using a first-order elastic frame, N⋅mm, Chapter 10 n = number of items, such as strength tests, bars, wires, monostrand anchorage devices, anchors, or shearhead arms, Chapters 5, 11, 12, 18, Appendix D Nb = basic concrete breakout strength in tension of a single anchor in cracked concrete, N, see D.5.2.2, Appendix D Nc = tension force in concrete due to unfactored dead load plus live load, N, Chapter 18 Ncb = nominal concrete breakout strength in tension of a single anchor, N, see D.5.2.1, Appendix D Ncbg= nominal concrete breakout strength in tension of a group of anchors, N, see D.5.2.1, Appendix D Nn = nominal strength in tension, N, Appendix D Np = pullout strength in tension of a single anchor in cracked concrete, N, see D.5.3.4 and D.5.3.5, Appendix D Npn= nominal pullout strength in tension of a single anchor, N, see D.5.3.1, Appendix D Nsa = nominal strength of a single anchor or group of anchors in tension as governed by the steel strength, N, see D.5.1.1 and D.5.1.2, Appendix D Nsb = side-face blowout strength of a single anchor, N, Appendix D Copyright American Concrete Institute Provided by IHS under license with ACI Licensee=Black & Veatch/5910842100 No reproduction or networking permitted without license from IHS Not for Resale, 11/28/2005 18:20:15 MST --`,,`,````````,,`,,`,,``,`,,,`-`-`,,`,,`,`,,`---