A23.3-04 Canadian Standards Association Fic required tension force in longitudinal reinforcement on flexural compression side of member Fr required tension force in longitudinal reinforcement on flexural tension side of member Fr specified yield strength of structural steel section h overall thickness or height of member h height of effective embedment of tension tie(see Figure 11.3) hb distance from soffit of supporting beam to soffit of supported beam(see Figure 11.1) he clear vertical distance between successive floor slabs attached to the shear wall assembly ee Clause 14) dimension of concrete core of rectangular section measured perpendicular to the direction of the hoop bars to outside of peripheral hoop (see Clause 21) heol column dimension parallel to shear force in the joint hd overall thickness at a drop panel h3 overall thickness of slab; for slabs with drop panels, the overall thickness of the slab away from h unsupported vertical height of wall between horizontal supports hw vertical height of wall (see Clause 21) vertical height of wall above the section of maximum moment in the wall (see Clause 14) h maximum horizontal centre-to-centre spacing between longitudinal bars on all faces of the olumn that are laterally supported by seismic hoops or crosstie legs h1 overall height of supporting beam(see h2 = overall height of supported beam(see Figure 11.1) moment of inertia of section about centroidal axis lb = moment of inertia about centroidal axis of gross section of beam lcr moment of inertia of cracked section transformed to concrete le effective moment of inertia lec value of le at continuous end value of le at midspan le2 value of le at end 2 of a continuous beam span 9= moment of inertia of gross concrete section about centroidal axis, neglecting reinforcement Is= moment of inertia about centroidal axis of gross section of slab, equal to (2ahs/12 Ist= moment of inertia of reinforcement about centroidal axis of member cross-section h t moment of inertia of structural steel shape, pipe, or tubing about centroidal axis of composite member cross-section he earthquake importance factor of the structure, as specified in the National Building Code of Canada property of the critical shear section analogous to the polar moment of inertia effective length factor kn lting for the number of longitudinal reinforcing bars in a column k factor accounting for compression on column or wall (see Clause 21) factor for type of prestressing in Equation(18-1) bar location fa ctor k3 = concrete density factor ka bar size factor ks welded deformed wire fabric factor December 2004
A23.3-04 © Canadian Standards Association 14 December 2004 Flc = required tension force in longitudinal reinforcement on flexural compression side of member Flt = required tension force in longitudinal reinforcement on flexural tension side of member Fy = specified yield strength of structural steel section h = overall thickness or height of member ha = height of effective embedment of tension tie (see Figure 11.3) hb = distance from soffit of supporting beam to soffit of supported beam (see Figure 11.1) hc = clear vertical distance between successive floor slabs attached to the shear wall assembly (see Clause 14) = dimension of concrete core of rectangular section measured perpendicular to the direction of the hoop bars to outside of peripheral hoop (see Clause 21) hcol = column dimension parallel to shear force in the joint hd = overall thickness at a drop panel hs = overall thickness of slab; for slabs with drop panels, the overall thickness of the slab away from the drop panel hu = unsupported vertical height of wall between horizontal supports hw = vertical height of wall (see Clause 21) = vertical height of wall above the section of maximum moment in the wall (see Clause 14) hx = maximum horizontal centre-to-centre spacing between longitudinal bars on all faces of the column that are laterally supported by seismic hoops or crosstie legs h1 = overall height of supporting beam (see Figure 11.1) h2 = overall height of supported beam (see Figure 11.1) I = moment of inertia of section about centroidal axis Ib = moment of inertia about centroidal axis of gross section of beam Icr = moment of inertia of cracked section transformed to concrete Ie = effective moment of inertia Iec = value of Ie at continuous end Iem = value of Ie at midspan Ie1 = value of Ie at end 1 of a continuous beam span Ie2 = value of Ie at end 2 of a continuous beam span Ig = moment of inertia of gross concrete section about centroidal axis, neglecting reinforcement Is = moment of inertia about centroidal axis of gross section of slab, equal to A2ahs 3 / 12 Ist = moment of inertia of reinforcement about centroidal axis of member cross-section It = moment of inertia of structural steel shape, pipe, or tubing about centroidal axis of composite member cross-section IE = earthquake importance factor of the structure, as specified in the National Building Code of Canada J = property of the critical shear section analogous to the polar moment of inertia k = effective length factor kn = factor accounting for the number of longitudinal reinforcing bars in a column kp = factor accounting for compression on column or wall (see Clause 21) = factor for type of prestressing in Equation (18-1) k1 = bar location factor k2 = coating factor k3 = concrete density factor k4 = bar size factor k5 = welded deformed wire fabric factor
Canadian Standards Association Design of concrete structures panel bending stiffness at factored loads panel bending stiffness at service loads flexural stiffness of column; moment per unit rotation K flexural stiffness of equivalent column; moment per unit rotation K torsional stiffness of member; moment per unit rotation transverse reinforcement index ecuve pan additional embedment length at support or at point of inflection(see Clause 12) length of effective bearing area for strut anchored by reinforcement(see Figure 11.3) length of bearing(see Figure 11.3) ec = length of a compression member in a frame, measured from centre-to-centre of the joints in the frame(see Clause 10) length of the outermost compression segment of a coupled wall(see Clause 21) the lesser of h and w(see Clause 14) vertical clear distance between supports or unsupported length of the drilled pile (see Clause 22) horizontal distance between centroids of walls on either side of coupling beam fcc development length of reinforcement basic development length levelopment length of standard hook in tension, measured from critical section to outside end of hook(straight embedment length between critical section and start of hook [point of tangency] plus radius of bend and one bar diameter)(see Clauses 12 and 21) basic development length of standard hook in tension dimension of joint in the direction of reinforcement passing through the joint clear span(see Clauses 9 and 16) length of clear span in the direction that moments are being determined, measured face-to-face of supports ( minimum length measured from the face of the joint along the axis of the structural member, 。( over which transverse reinforcement needs to be provided(see Clause 21) overall length of tendon between anchors(see Clause 18) length of attached torsional member, equal to the smaller of lla or l2a of spans adjacent to the clear span or unsupported length between floors or other effective horizontal lines of lateral support(see Clause 21) unsupported length of compression member (see Clause 10) horizontal length of wall length of span in the direction that moments are being determined, measured centre-to-centre of supports average l, for spans adjacent to a column G2 = length of span transverse to l1 measured centre-to-centre of supports L2a =average l2 for the adjacent spans transverse to L1 distance from edge to panel centreline for spans along an edge L variable load due to intended use and occupancy, including loads due to cranes, pressure of liquids in containers, or related moments or forces bending moment per unit length on section perpendicular to th e x-axIs total design moment per unit length on section perpendicular to the x-axis torsional moment per unit length on section December 2004 5
© Canadian Standards Association Design of concrete structures December 2004 15 Kbf = panel bending stiffness at factored loads Kbs = panel bending stiffness at service loads Kc = flexural stiffness of column; moment per unit rotation Kec = flexural stiffness of equivalent column; moment per unit rotation Kt = torsional stiffness of member; moment per unit rotation Ktr = transverse reinforcement index A = effective panel height Aa = additional embedment length at support or at point of inflection (see Clause 12) = length of effective bearing area for strut anchored by reinforcement (see Figure 11.3) Ab = length of bearing (see Figure 11.3) Ac = length of a compression member in a frame, measured from centre-to-centre of the joints in the frame (see Clause 10) = length of the outermost compression segment of a coupled wall (see Clause 21) = the lesser of hc and wc (see Clause 14) = vertical clear distance between supports or unsupported length of the drilled pile (see Clause 22) Acg = horizontal distance between centroids of walls on either side of coupling beam Ad = development length of reinforcement Adb = basic development length Adh = development length of standard hook in tension, measured from critical section to outside end of hook (straight embedment length between critical section and start of hook [point of tangency] plus radius of bend and one bar diameter) (see Clauses 12 and 21) Ahb = basic development length of standard hook in tension Aj = dimension of joint in the direction of reinforcement passing through the joint An = clear span (see Clauses 9 and 16) = length of clear span in the direction that moments are being determined, measured face-to-face of supports (see Clause 13) Ao = minimum length measured from the face of the joint along the axis of the structural member, over which transverse reinforcement needs to be provided (see Clause 21) = overall length of tendon between anchors (see Clause 18) At = length of attached torsional member, equal to the smaller of A1a or A2a of spans adjacent to the joint Au = clear span or unsupported length between floors or other effective horizontal lines of lateral support (see Clause 21) = unsupported length of compression member (see Clause 10) Aw = horizontal length of wall A1 = length of span in the direction that moments are being determined, measured centre-to-centre of supports A1a = average A1 for spans adjacent to a column A2 = length of span transverse to A1, measured centre-to-centre of supports A2a = average A2 for the adjacent spans transverse to A1 = distance from edge to panel centreline for spans along an edge L = variable load due to intended use and occupancy, including loads due to cranes, pressure of liquids in containers, or related moments or forces mx = bending moment per unit length on section perpendicular to the x-axis = total design moment per unit length on section perpendicular to the x-axis mxy = torsional moment per unit length on section
A23.3-04 Canadian Standards Association ending moment per unit length on section perpendicular to the y-axis total design moment per unit length on section perpendicular to the y-axis Ma maximum moment in member at load stage at which deflection is computed or at any revIous Mb= maximum factored moment in panel at load stage at which deflection is computed, not ncluding P△ effects maximum moment in panel due to service loads at load stage at which deflection is computed not including P-A effects M magnified factored moment to be used for design of compression member Mar cracking moment Mdc of a prestressed members qual to the moment when the compressive stress on the tensile face decompression moment e M, factored moment at interior support resisted by elements above and below the slab factored moment, including P-A effects(see Clause 23) moment due to factored loads(see Clauses 10, 11, 18, and 20) unbalanced moment about the centroid of the critical shear section(see Equation(13-9)) Ms factored strong axis moment acting on a shear wall M ak axis moment acting on a she Mnc nominal flexural resistance of a column total factored static moment probable flexural resistance of a beam factored moment resistance factored end moment on a compression member due to loads that result in appreciable sway, calculated using a first-order elastic frame analysis(see Clause 10) maximum moment due to service loads, including P-A effects(see Clause 23) moment due to specified loads(see Clause 18) portion of slab moment balanced by support moment(see Clause 21) M,= smaller factored end moment on a compression member associated with the same loading case as M2(positive if member is bent in single curvature, negative if bent in double curvature) MI factored end moment on a compression member at the end at which M, acts, due to loads that cause no appreciable sway, calculated using a first-order elastic frame analysis Mis factored end moment on a compression member at the end at which M, acts, due to loads that cause appreciable sway, calculated using a first-order elastic frame analysis M2 larger factored end moment on a compression member(always positive) M2 factored end moment on a compression member at the end at which M2 acts, due to loads that cause no appreciable sway, calculated using a first-order elastic frame analysis factored end moment on a compression member at the end at which M2 acts, due to loads that cause appreciable sway, calculated using a first-order elastic frame analysis n number of bars or wires being spliced or developed along the potential plane of bond splitting total number of longitudinal bars in the column cross-section that are laterally supported by the corner of hoops or by hooks of seismic crossties unfactored permanent compressive load perpendicular to the shear plane(see Clause 11) N= tensile force in concrete N, = factored axial load normal to the cross-section occurring simultaneously with Vf, including effects of tension due to creep and shrinkage(taken as positive for tension and negative for compression 16 December 2004
A23.3-04 © Canadian Standards Association 16 December 2004 my = bending moment per unit length on section perpendicular to the y-axis = total design moment per unit length on section perpendicular to the y-axis Ma = maximum moment in member at load stage at which deflection is computed or at any previous load stage Mb = maximum factored moment in panel at load stage at which deflection is computed, not including P-∆ effects Mbs = maximum moment in panel due to service loads at load stage at which deflection is computed, not including P-∆ effects Mc = magnified factored moment to be used for design of compression member Mcr = cracking moment Mdc = decompression moment, equal to the moment when the compressive stress on the tensile face of a prestressed member is zero Mf = factored moment at interior support resisted by elements above and below the slab (see Equation (13-24)) = factored moment, including P-∆ effects (see Clause 23) = moment due to factored loads (see Clauses 10, 11, 18, and 20) = unbalanced moment about the centroid of the critical shear section (see Equation (13-9)) Mfs = factored strong axis moment acting on a shear wall Mfw = factored weak axis moment acting on a shear wall Mnc = nominal flexural resistance of a column Mo = total factored static moment Mpb = probable flexural resistance of a beam Mr = factored moment resistance Ms = factored end moment on a compression member due to loads that result in appreciable sway, calculated using a first-order elastic frame analysis (see Clause 10) = maximum moment due to service loads, including P-∆ effects (see Clause 23) = moment due to specified loads (see Clause 18) = portion of slab moment balanced by support moment (see Clause 21) M1 = smaller factored end moment on a compression member associated with the same loading case as M2 (positive if member is bent in single curvature, negative if bent in double curvature) M1ns = factored end moment on a compression member at the end at which M1 acts, due to loads that cause no appreciable sway, calculated using a first-order elastic frame analysis M1s = factored end moment on a compression member at the end at which M1 acts, due to loads that cause appreciable sway, calculated using a first-order elastic frame analysis M2 = larger factored end moment on a compression member (always positive) M2ns = factored end moment on a compression member at the end at which M2 acts, due to loads that cause no appreciable sway, calculated using a first-order elastic frame analysis M2s = factored end moment on a compression member at the end at which M2 acts, due to loads that cause appreciable sway, calculated using a first-order elastic frame analysis n = number of bars or wires being spliced or developed along the potential plane of bond splitting nA = total number of longitudinal bars in the column cross-section that are laterally supported by the corner of hoops or by hooks of seismic crossties N = unfactored permanent compressive load perpendicular to the shear plane (see Clause 11) Nc = tensile force in concrete Nf = factored axial load normal to the cross-section occurring simultaneously with Vf, including effects of tension due to creep and shrinkage (taken as positive for tension and negative for compression)
Canadian Standards Association Design of concrete structures N factored resistance in tension outside perimeter of the concrete cross-section perimeter of the centreline of the closed transverse torsion reinforcement mPPP critical axial load factored axial load(see Clauses 10 and 20) factored load at mid-height of panel (see Clause 23) maximum factored axial load for earthquake loading cases(see Clause 21) earthquake-induced transfer force resulting from interaction between elements of a linked or oupled wall system, taken as the sum of the end shears corresponding to the nominal flexural resistance in the coupling beams above the section nominal net force on a cross-section for the direction being considered due to yielding in tension or compression of concentrated and distributed reinforcement during plastic hinge formation(positive for tension) Po nominal axial resistance at zero eccentricity earthquake-induced transfer force resulting from interaction between elements of a linked or coupled wall system, taken as the sum of the end shears corresponding to the probable flexural resistance in the coupling beams above the section factored axial load resistance of wall P maximum axial load resistance calculated using Equations(10-8)and(10-9) factored axial load resistance at zero eccentricity Ps axial force at section resulting from factored dead load plus factored live load using earthquake load factors(see Clause 21) service load at mid-height of panel (see Clause 23) factored load from tributary roof or floor area Pts service load from tributary roof or floor area Pw factored weight of panel tributary to and above design section Pws unfactored weight of panel tributary to and above design section Q stability index for a storey r radius of gyration of cross-section of a compression member Ra ductility-related force modification factor, as specified in the National Building Code of Canada Ro overstrength-related force modification factor, as specified in the National Building Code of Canada Re reduction factor on two-way shear stress as a function of interstorey deflection factor for creep deflections under sustained loads(see Clause 9) maximum centre-to-centre spacing of transverse reinforcement within a(see Clause 12) spacing of headed shear reinforcement or stirrups measured perpendicular to bo see Clause 13) spacing of shear or torsion reinforcement measured parallel to the longitudinal axis of the member (see Clause 11) spacing of transverse reinforcement measured along the longitudinal axis of the structural member(see Clause 21) spacing of wire to be developed or spliced longitudinal spacing of transverse reinforcement S2=crack spacing parameter dependent on crack control characteristics of longitudinal reinforcement(see Figure 11.2) equivalent value of s, that allows for influence of aggregate size s variable loads due to ice, rain, and snow(including associated rain) December 2004
© Canadian Standards Association Design of concrete structures December 2004 17 Nr = factored resistance in tension pc = outside perimeter of the concrete cross-section ph = perimeter of the centreline of the closed transverse torsion reinforcement Pc = critical axial load Pf = factored axial load (see Clauses 10 and 20) = factored load at mid-height of panel (see Clause 23) = maximum factored axial load for earthquake loading cases (see Clause 21) Pn = earthquake-induced transfer force resulting from interaction between elements of a linked or coupled wall system, taken as the sum of the end shears corresponding to the nominal flexural resistance in the coupling beams above the section Pns = nominal net force on a cross-section for the direction being considered due to yielding in tension or compression of concentrated and distributed reinforcement during plastic hinge formation (positive for tension) Po = nominal axial resistance at zero eccentricity Pp = earthquake-induced transfer force resulting from interaction between elements of a linked or coupled wall system, taken as the sum of the end shears corresponding to the probable flexural resistance in the coupling beams above the section Pr = factored axial load resistance of wall Pr,max = maximum axial load resistance calculated using Equations (10-8) and (10-9) Pro = factored axial load resistance at zero eccentricity Ps = axial force at section resulting from factored dead load plus factored live load using earthquake load factors (see Clause 21) = service load at mid-height of panel (see Clause 23) Ptf = factored load from tributary roof or floor area Pts = service load from tributary roof or floor area Pwf = factored weight of panel tributary to and above design section Pws = unfactored weight of panel tributary to and above design section Q = stability index for a storey r = radius of gyration of cross-section of a compression member Rd = ductility-related force modification factor, as specified in the National Building Code of Canada Ro = overstrength-related force modification factor, as specified in the National Building Code of Canada RE = reduction factor on two-way shear stress as a function of interstorey deflection s = factor for creep deflections under sustained loads (see Clause 9) = maximum centre-to-centre spacing of transverse reinforcement within Ad (see Clause 12) = spacing of headed shear reinforcement or stirrups measured perpendicular to bo (see Clause 13) = spacing of shear or torsion reinforcement measured parallel to the longitudinal axis of the member (see Clause 11) = spacing of transverse reinforcement measured along the longitudinal axis of the structural member (see Clause 21) sw = spacing of wire to be developed or spliced sx = longitudinal spacing of transverse reinforcement sz = crack spacing parameter dependent on crack control characteristics of longitudinal reinforcement (see Figure 11.2) sze = equivalent value of sz that allows for influence of aggregate size S = variable loads due to ice, rain, and snow (including associated rain)
A23.3-04 Canadian Standards Association S.(0. 2)=damped spectral response acceleration for a period of 0.2 s, as specified in the National Building moment, shear, or axial force at connection corresponding to development of probable strength at intended yield locations, based on the governing mechanism of inelastic lateral deformation, considering both gravity and earthquake load erects S, factored flexural, shear or axial resistance of a connection wall thickness(see Clauses 14 and 22) wall thickness of box section (see Clause 11) effects of imposed deformations due to moisture changes, shrinkage, creep, temperature, and ground settlement or combinations thereof pure torsional cracking resistance T factored torsional moment factored torsional resistance provided by circulatory shear flow factored shear stress resistance provided by the concrete Vr factored shear stress resistance(see Clauses 13 and 18) factored shear stress resistance of shear plane(see Clause 1 factored shear stress resistance provided by shear reinforcement Ve shear resistance attributed to the concrete factored by pc factored horizontal shear in a storey(see Clause 10) factored shear force(see Clauses 11, 12, 13, 17, 20, and 22) factored shear force through a beam-column joint acting parallel to beam bars component in the direction of the applied shear of the effective prestressing force factored by dpi for variable depth members, the sum of the component of the effective prestressing force and the components of flexural compression and tension in the direction of the applied shear positive if resisting applied shear, factored by dp v factored shear resistance factored longitudinal shear resistance maximum possible factored shear resistance Vs shear resistance provided by shear reinforcement factored by os shear transmitted to column or column capital due to specified loads, but not less than the shear corresponding to twice the self-weight of the slab wh width of a bearing for a concentrated vertical load acting on a wall clear horizontal distance between adjacent shear wall webs, if webs are present factored dead load per unit area factored load per unit area(see Clause 13) factored load per unit length of beam or per unit area of slab(see Clause 9) factored uniformly distributed lateral load(see Clause 23) factored live load per unit area service uniformly distributed lateral load anchorage length of tension tie(see Clause 11) entroidal x-axis of a critical section (see Clause 13) direction of coordinates in elastic plate theory(see Clause 13.6.4) shorter overall dimension of rectangular part of cross-section(see Clause 13) dimension from face of column to edge of drop panel (see Figure 13.1) 18 December 2004
A23.3-04 © Canadian Standards Association 18 December 2004 Sa(0.2) = damped spectral response acceleration for a period of 0.2 s, as specified in the National Building Code of Canada Sp = moment, shear, or axial force at connection corresponding to development of probable strength at intended yield locations, based on the governing mechanism of inelastic lateral deformation, considering both gravity and earthquake load effects Sr = factored flexural, shear, or axial resistance of a connection t = wall thickness (see Clauses 14 and 22) = wall thickness of box section (see Clause 11) T = effects of imposed deformations due to moisture changes, shrinkage, creep, temperature, and ground settlement or combinations thereof Tcr = pure torsional cracking resistance Tf = factored torsional moment Tr = factored torsional resistance provided by circulatory shear flow vc = factored shear stress resistance provided by the concrete vf = factored shear stress vr = factored shear stress resistance (see Clauses 13 and 18) = factored shear stress resistance of shear plane (see Clause 11) vs = factored shear stress resistance provided by shear reinforcement Vc = shear resistance attributed to the concrete factored by φ c Vf = factored horizontal shear in a storey (see Clause 10) = factored shear force (see Clauses 11, 12, 13, 17, 20, and 22) Vfb = factored shear force through a beam-column joint acting parallel to beam bars Vp = component in the direction of the applied shear of the effective prestressing force factored by φ p; for variable depth members, the sum of the component of the effective prestressing force and the components of flexural compression and tension in the direction of the applied shear, positive if resisting applied shear, factored by φ p Vr = factored shear resistance VrA = factored longitudinal shear resistance Vr,max = maximum possible factored shear resistance Vs = shear resistance provided by shear reinforcement factored by φ s Vse = shear transmitted to column or column capital due to specified loads, but not less than the shear corresponding to twice the self-weight of the slab wb = width of a bearing for a concentrated vertical load acting on a wall wc = clear horizontal distance between adjacent shear wall webs, if webs are present wdf = factored dead load per unit area wf = factored load per unit area (see Clause 13) = factored load per unit length of beam or per unit area of slab (see Clause 9) = factored uniformly distributed lateral load (see Clause 23) wlf = factored live load per unit area ws = service uniformly distributed lateral load x = anchorage length of tension tie (see Clause 11) = centroidal x-axis of a critical section (see Clause 13) = direction of coordinates in elastic plate theory (see Clause 13.6.4) = shorter overall dimension of rectangular part of cross-section (see Clause 13) xd = dimension from face of column to edge of drop panel (see Figure 13.1)