Canadian Standards Association Design of concrete structures Resistance factor-the factor, specified in Clause 8. 4 and applied to a specified material property or to the resistance of a member for the limit state under consideration, which takes into account the variability of dimensions, material properties, quality of work, type of failure, and uncertainty in the prediction of Ribbed shell-a spatial structure with material placed primarily along certain preferred rib lines, with the areas between the ribs filled with thin slabs or left open Sandwich panel-a panel consisting of two concrete layers or wythes separated by a layer of insulation least a six-bar-diameter extension at th o a seismic hook at one end and a hook not less than 90 with at mIC cPos stie- a single bar havin le other end. The hooks engage peripheral longitudinal bars. The 90 hooks of successive crossties engaging the same longitudinal bar are alternated end for end mic force resisting system-that part of the structural system that has been considered in the ign to provide the required resistance to the earthquake forces and effects in accordance with Clause 4.1.8 of the National Building Code of Canada Seismic hook -a hook with at least a 135 bend with a six- bar-diameter extension(but not less thar 100 mm) that engages the longitudinal reinforcement and is anchored in the confined core Slab band-a continuous extension of a drop panel between supports or between a support and another slab band Specified strength of concrete- the compressive strength of concrete used in the design and evaluated in accordance with Clause 4 Spiral-a helical tie complying with Clauses 7.6. 4 and 10.9.4 Spiral column -a column in which the longitudinal reinforcement is enclosed by a spiral Stirrup- reinforcement used to resist shear and torsion stresses in a structural member Note: The term"stirrups"is usually applied to lateral reinforcement in flexural members and the term ties"to lateral reinforcement in compression members. Structural diaphragm -a structural member, such as a floor or roof slab, that transmits forces to or between lateral-force-resisting members Tendon -a steel element such as a wire, bar or strand or a bundle of such elements that is used to impart prestress to concrete and complies with Clause 3. 1.4 Thin shell-a three-dimensional spatial structure made up of one or more curved slabs or folded plates whose thicknesses are small compared to their other dimensions Note: Thin shells are characterized by their three-dimensional load-carrying behaviour, which is determined by the Tie-a loop of reinforcing bar or wire enclosing longitudinal reinforcement. See also Stirrup Tilt-up wall panel - a reinforced concrete panel that is site-cast on a horizontal surface and subsequently tilted to a vertical orientation to form a vertical-and lateral-load-resisting building element Transfer- the act of transferring force in prestressing tendons from jacks or the pretensioning December 2004
© Canadian Standards Association Design of concrete structures December 2004 9 Resistance factor — the factor, specified in Clause 8.4 and applied to a specified material property or to the resistance of a member for the limit state under consideration, which takes into account the variability of dimensions, material properties, quality of work, type of failure, and uncertainty in the prediction of resistance. Ribbed shell — a spatial structure with material placed primarily along certain preferred rib lines, with the areas between the ribs filled with thin slabs or left open. Sandwich panel — a panel consisting of two concrete layers or wythes separated by a layer of insulation. Seismic crosstie — a single bar having a seismic hook at one end and a hook not less than 90° with at least a six-bar-diameter extension at the other end. The hooks engage peripheral longitudinal bars. The 90° hooks of successive crossties engaging the same longitudinal bar are alternated end for end. Seismic force resisting system — that part of the structural system that has been considered in the design to provide the required resistance to the earthquake forces and effects in accordance with Clause 4.1.8 of the National Building Code of Canada. Seismic hook — a hook with at least a 135° bend with a six-bar-diameter extension (but not less than 100 mm) that engages the longitudinal reinforcement and is anchored in the confined core. Slab band — a continuous extension of a drop panel between supports or between a support and another slab band. Specified strength of concrete — the compressive strength of concrete used in the design and evaluated in accordance with Clause 4. Spiral — a helical tie complying with Clauses 7.6.4 and 10.9.4. Spiral column — a column in which the longitudinal reinforcement is enclosed by a spiral. Stirrup — reinforcement used to resist shear and torsion stresses in a structural member. Note: The term “stirrups” is usually applied to lateral reinforcement in flexural members and the term “ties” to lateral reinforcement in compression members. Structural diaphragm — a structural member, such as a floor or roof slab, that transmits forces to or between lateral-force-resisting members. Tendon — a steel element such as a wire, bar, or strand, or a bundle of such elements, that is used to impart prestress to concrete and complies with Clause 3.1.4. Thin shell — a three-dimensional spatial structure made up of one or more curved slabs or folded plates whose thicknesses are small compared to their other dimensions. Note: Thin shells are characterized by their three-dimensional load-carrying behaviour, which is determined by the geometry of their form, the manner in which they are supported, and the nature of the applied load. Tie — a loop of reinforcing bar or wire enclosing longitudinal reinforcement. See also Stirrup. Tilt-up wall panel — a reinforced concrete panel that is site-cast on a horizontal surface and subsequently tilted to a vertical orientation to form a vertical- and lateral-load-resisting building element. Transfer — the act of transferring force in prestressing tendons from jacks or the pretensioning anchorage to the concrete member
A23.3-04 o Canadian Standards Associatio Tributary width- the width of a panel attracting vertical and horizontal loads that the design width Wall-a vertical element in which the horizontal length, lw, is at least six times the thickness, t, and at least one-third the clear height of the element. Bearing wall-a wall that supports ) factored in-plane vertical loads exceeding 0. 10 CA (b) weak axis moments about a horizontal axis in the plane of the wall; and (c)the shear forces necessary to equilibrate the moments specified in Item(b) Flexural shear wall-a shear wall that resists in-plane lateral loads by flexural action. Flexural shear walls have a height, hw, above the section of maximum moment in the walls that is greater than 20 Non-bearing wall-a wall that supports factored in-plane vertical loads less than or equal to 0.10 Aa and, in some cases, moments about a horizontal axis in the plane of the wall and the shear forces necessary to equilibrate those moments Shear wall-a wall or an assembly of interconnected walls considered to be part of the lateral-load- resisting system of a building or structure. Shear walls support (a) vertical loads (b) moments about horizontal axes perpendicular to the plane of the wall(strong axis bending); and (c) shear forces acting parallel to the plane of the wall Weak axis bending can also be present Squat shear wall-a shear wall with a height, hw, above the section of maximum moment in the wall that does not exceed 2(w Wobble friction- friction caused by the unintended deviation of prestressing sheath or duct from its specified profile Yield strength -the specified minimum yield strength or yield point of reinforcement. 2.3 Symbols The following symbols apply in this Standarc depth of equivalent rectangular stress block specified nominal maximum size of coarse aggregate area of that part of cross-section between flexural tension face and centroid of gross section (see Clause 18) effective tension area of concrete surrounding the flexural tension reinforcement and extending from the extreme tension fibre to the centroid of the flexural tension reinforcement and an equal distance past that centroid, divided by the number of bars or wires. When the flexural reinforcement consists of different bar or wire sizes the number of bars or wires used to compute a is to be taken as the total area of reinforcement divided by the area of the largest bar or wire used(see Clause 10) A area of an individual bar Ac area enclosed by outside perimeter of concrete cross-section, including area of holes(if any) (see Clause 11) area of core of spirally reinforced compression member measured to outside diameter of spiral (see Clause 10) cross-sectional area of core of a structural member 10 December 2004
A23.3-04 © Canadian Standards Association 10 December 2004 Tributary width — the width of a panel attracting vertical and horizontal loads that the design width must support. Wall — a vertical element in which the horizontal length, Aw , is at least six times the thickness, t, and at least one-third the clear height of the element. Bearing wall — a wall that supports (a) factored in-plane vertical loads exceeding 0.10 fc ’Ag ; (b) weak axis moments about a horizontal axis in the plane of the wall; and (c) the shear forces necessary to equilibrate the moments specified in Item (b). Flexural shear wall — a shear wall that resists in-plane lateral loads by flexural action. Flexural shear walls have a height, hw , above the section of maximum moment in the walls that is greater than 2Aw . Non-bearing wall — a wall that supports factored in-plane vertical loads less than or equal to 0.10 fc ’Ag and, in some cases, moments about a horizontal axis in the plane of the wall and the shear forces necessary to equilibrate those moments. Shear wall — a wall or an assembly of interconnected walls considered to be part of the lateral-load-resisting system of a building or structure. Shear walls support (a) vertical loads; (b) moments about horizontal axes perpendicular to the plane of the wall (strong axis bending); and (c) shear forces acting parallel to the plane of the wall. Weak axis bending can also be present. Squat shear wall — a shear wall with a height, hw , above the section of maximum moment in the wall that does not exceed 2Aw. Wobble friction — friction caused by the unintended deviation of prestressing sheath or duct from its specified profile. Yield strength — the specified minimum yield strength or yield point of reinforcement. 2.3 Symbols The following symbols apply in this Standard: a = depth of equivalent rectangular stress block ag = specified nominal maximum size of coarse aggregate A = area of that part of cross-section between flexural tension face and centroid of gross section (see Clause 18) = effective tension area of concrete surrounding the flexural tension reinforcement and extending from the extreme tension fibre to the centroid of the flexural tension reinforcement and an equal distance past that centroid, divided by the number of bars or wires. When the flexural reinforcement consists of different bar or wire sizes, the number of bars or wires used to compute A is to be taken as the total area of reinforcement divided by the area of the largest bar or wire used (see Clause 10) Ab = area of an individual bar Ac = area enclosed by outside perimeter of concrete cross-section, including area of holes (if any) (see Clause 11) = area of core of spirally reinforced compression member measured to outside diameter of spiral (see Clause 10) Ach = cross-sectional area of core of a structural member
Canadian Standards Association Design of concrete structures area of concrete in strips along exposed side faces of beams(see Clause 10) effective cross-sectional area of concrete compressive strut(see Clause 11) Act area of concrete on flexural tension side of member(see Figure 11.2) Ac area of concrete section resisting shear transfer(see Clause 11) net area of concrete section bounded by web thickness and length of section in the direction of lateral forces considered(see Clause 21) Af area of flange Ag gross area of section gross area of a boundary element A minimum cross-sectional area within a joint in a plane parallel to the axis of the reinforcement generating the shear in the joint, equal to the lesser of Ag of the column or 2bwhcol Ao= area enclosed by shear flow path, including area of holes(if any) Aoh area enclosed by centreline of exterior closed transverse torsion reinforcement, including area of holes(if any) Ap area of prestressing tendons(see Clause 10) area of prestressing tendons in tension zone(see Clause 18) area of tendons on the flexural tension side of the member(see Clause 11) As= area of longitudinal reinforcement on the flexural tension side of the member(see Clause 11) area of non-prestressed tension reinforcement (see Clauses 12, 13, 18, and 23) A area of compression reinforceme A minimum area of bottom reinforcement crossing one face of the periphery of a column and connecting the slab to the column or support to provide structural integrity effective area of tension reinforcement Ash= total cross-sectional area of transverse reinforcement(including crossties)within spacing s and perpendicular to dimension h minimum area of tension reinfo area of reinforcement in compression strut area of reinforcement in tension tie(see Clause 11 total area of longitudinal reinforcement (see Clause 10) A. area of one leg of closed transverse torsion reinforcement (see Clause 11) area of structural steel shape, pipe, or tubing in a composite section(see Clause 10 A total cross-sectional area of reinforcement that is within spacing s and crosses the potential plane of bond splitting through the reinforcement being developed A.= area of shear reinforcement within a distance s Ave effective shear cross-section area of coupling beam to be used for analysis A area of shear-friction reinforcement cross-sectional area of headed shear reinforcement on a line parallel to the perimeter of the area of an individual wire to be developed or spliced Axe effective axial cross-section area to be used for analysis Al loaded area A2 area of the lower base of the largest frustum of a pyramid, cone, or tapered wedge contained wholly within the support, having for its upper base the loaded area and having side slopes of vertical to 2 horizonta b width of compression face of member(see Clauses 9, 10, and 21) width of compression face of panel within design width(see Clause 23) width of member(see Clause 22) December 2004
© Canadian Standards Association Design of concrete structures December 2004 11 Acs = area of concrete in strips along exposed side faces of beams (see Clause 10) = effective cross-sectional area of concrete compressive strut (see Clause 11) Act = area of concrete on flexural tension side of member (see Figure 11.2) Acv = area of concrete section resisting shear transfer (see Clause 11) = net area of concrete section bounded by web thickness and length of section in the direction of lateral forces considered (see Clause 21) Af = area of flange Ag = gross area of section Agb = gross area of a boundary element Aj = minimum cross-sectional area within a joint in a plane parallel to the axis of the reinforcement generating the shear in the joint, equal to the lesser of Ag of the column or 2bwhcol Ao = area enclosed by shear flow path, including area of holes (if any) Aoh = area enclosed by centreline of exterior closed transverse torsion reinforcement, including area of holes (if any) Ap = area of prestressing tendons (see Clause 10) = area of prestressing tendons in tension zone (see Clause 18) = area of tendons on the flexural tension side of the member (see Clause 11) As = area of longitudinal reinforcement on the flexural tension side of the member (see Clause 11) = area of non-prestressed tension reinforcement (see Clauses 12, 13, 18, and 23) As ’ = area of compression reinforcement Asb = minimum area of bottom reinforcement crossing one face of the periphery of a column and connecting the slab to the column or support to provide structural integrity As,eff = effective area of tension reinforcement Ash = total cross-sectional area of transverse reinforcement (including crossties) within spacing s and perpendicular to dimension hc As,min = minimum area of tension reinforcement Ass = area of reinforcement in compression strut Ast = area of reinforcement in tension tie (see Clause 11) = total area of longitudinal reinforcement (see Clause 10) At = area of one leg of closed transverse torsion reinforcement (see Clause 11) = area of structural steel shape, pipe, or tubing in a composite section (see Clause 10) Atr = total cross-sectional area of reinforcement that is within spacing s and crosses the potential plane of bond splitting through the reinforcement being developed Av = area of shear reinforcement within a distance s Ave = effective shear cross-section area of coupling beam to be used for analysis Avf = area of shear-friction reinforcement Avs = cross-sectional area of headed shear reinforcement on a line parallel to the perimeter of the column Aw = area of an individual wire to be developed or spliced Axe = effective axial cross-section area to be used for analysis A1 = loaded area A2 = area of the lower base of the largest frustum of a pyramid, cone, or tapered wedge contained wholly within the support, having for its upper base the loaded area and having side slopes of 1 vertical to 2 horizontal b = width of compression face of member (see Clauses 9, 10, and 21) = width of compression face of panel within design width (see Clause 23) = width of member (see Clause 22)
A23.3-04 o Canadian Standards Associatio b band width of reinforced concrete slab extending a distance 1. 5hd or 1.5h, past the sides of the column or column capital (see Clauses 13 and 21) bearing width for concentrated load(see Figure 23. 2) b design width(see Figure 23. 2) br width of flange bo perimeter of critical section for shear in slabs and footings b s width of support reaction(see Figure 23. 2) b. tributary width(see Clause 23) width of tension zone of section (see Clause 10) b width of cross-section at contact surface being investigated for longitudinal shear beam web width or diameter of circular section or wall thickness(see Clause 21) minimum effective web width(see Clause 11) width of web(see Clause 10) b, width of the critical section for shear(see Clause 13)measured in the direction of the span for which moments are determined b2 width of the critical section for shear(see Clause 13)measured in the direction perpendicular to by cohesion stress (see Clause 11) depth of the neutral axis, with the axial loads Pn, Pns, and P measured from the compression edge of a wall section(see Clause 21) distance from extreme compression fibre to neutral axis(see Clauses 9 and 10) distance from extreme compression fibre to neutral axis calculated using factored material strengths and assuming a tendon force of d A pr(see Clause 18) distance from extreme compression fibre to neutral axis computed for the cracked transformed section(see Clause 23) dimension equal to the distance from the interior face of the edge column to the slab edge sy distance from extreme compression fibre to neutral axis calculated using factored material strengths and assuming a tendon force of d A py size of rectangular or equivalent rectangular column, capital, or bracket measured in the direction of the span for which moments are being determined size of rectangular or equivalent rectangular column, capital, or bracket measured in the direction perpendicular to Gr cross-sectional constant used in the definition of torsional properties Cm factor relating actual moment diagram to an equivalent uniform moment diagram distance from extreme compression fibre to centroid of longitudinal tension reinforcement, but need not be less than 0. 8h for prestressed members and circular sections(see Clauses 11 and 18) distance from extreme compression fibre to centroid of tension reinforcement(see Clauses 9, 0,12,13,21,and23) distance from extreme compression fibre to centroid of tension reinforcement for entire d depth of compression strut(see Figure 11.3) db diameter of bar, wire, or prestressing strand distance from extreme tension fibre to centre of the longitudinal bar or wire located closest to 2 December 2004
A23.3-04 © Canadian Standards Association 12 December 2004 bb = band width of reinforced concrete slab extending a distance 1.5hd or 1.5hs past the sides of the column or column capital (see Clauses 13 and 21) = bearing width for concentrated load (see Figure 23.2) bd = design width (see Figure 23.2) bf = width of flange bo = perimeter of critical section for shear in slabs and footings bs = width of support reaction (see Figure 23.2) bt = tributary width (see Clause 23) = width of tension zone of section (see Clause 10) bv = width of cross-section at contact surface being investigated for longitudinal shear bw = beam web width or diameter of circular section or wall thickness (see Clause 21) = minimum effective web width (see Clause 11) = width of web (see Clause 10) b1 = width of the critical section for shear (see Clause 13) measured in the direction of the span for which moments are determined b2 = width of the critical section for shear (see Clause 13) measured in the direction perpendicular to b1 c = cohesion stress (see Clause 11) = depth of the neutral axis, with the axial loads Pn , Pns, and Psmeasured from the compression edge of a wall section (see Clause 21) = distance from extreme compression fibre to neutral axis (see Clauses 9 and 10) = distance from extreme compression fibre to neutral axis calculated using factored material strengths and assuming a tendon force of φ pApfpr (see Clause 18) = distance from extreme compression fibre to neutral axis computed for the cracked transformed section (see Clause 23) ct = dimension equal to the distance from the interior face of the edge column to the slab edge measured parallel to c1, but not exceeding c1 cy = distance from extreme compression fibre to neutral axis calculated using factored material strengths and assuming a tendon force of φpApfpy c1 = size of rectangular or equivalent rectangular column, capital, or bracket measured in the direction of the span for which moments are being determined c2 = size of rectangular or equivalent rectangular column, capital, or bracket measured in the direction perpendicular to c1 C = cross-sectional constant used in the definition of torsional properties Cm = factor relating actual moment diagram to an equivalent uniform moment diagram d = distance from extreme compression fibre to centroid of longitudinal tension reinforcement, but need not be less than 0.8h for prestressed members and circular sections (see Clauses 11 and 18) = distance from extreme compression fibre to centroid of tension reinforcement (see Clauses 9, 10, 12, 13, 21, and 23) = distance from extreme compression fibre to centroid of tension reinforcement for entire composite section (see Clause 17) da = depth of compression strut (see Figure 11.3) db = diameter of bar, wire, or prestressing strand dc = distance from extreme tension fibre to centre of the longitudinal bar or wire located closest to it
Canadian Standards Association Design of concrete structures the smaller of (a)the distance from the closest concrete surface to the centre of the bar being developed; or (b) two-thirds of the centre-to-centre spacing of the bars being developed ile shaft diameter(see Clauses 15 and 22) distance from extreme compression fibre to centroid of the prestressing tendons see d effective shear depth, taken as the greater of 0. 9d or 0.72h distance from centroid of section for critical shear to point where shear stress is being eccentricity of Pr parallel to axis measured from the centroid of the section(see Clause 23) Ep= modulus of elasticity of prestressing tendons Es modulus of elasticity of non-prestressed reinforcement El= flexural stiffness of compression member f ified compres ive strength of concrete c specified compressive strength of concrete in columns fce compression stress in the concrete due to effective prestress only(after allowance for all prestress losses)at the extreme fibre of a section where tensile stresses are caused by applied ce effective compressive strength of concrete in columns a compressive strength of concrete at time of prestress transfer all prestress losses). For slabs and footings, tp is the average of fep for the two direction or average compressive stress in concrete due to effective prestress force only (after allowane (see Clause 18) compressive stress in concrete(after allowance for all prestress losses)at the centroid of the cross-section resisting externally applied loads or at the junction of the web and flange whet the centroid lies within the flange(in a composite member, tcp is the resultant compressive stress at the centroid of the composite section or at the junction of the web and flange when the centroid lies within the flange, due to both prestress and moments being resisted by the precast member acting alone)(see Clause 11) as specified compressive strength of concrete in slab feu limiting compressive stress in concrete strut f specified compressive strength of concrete in the wall fe effective stress in prestressing tendons after allowance for all prestress losses fpo stress in prestressing tendons when strain in the surrounding concrete is zero(may be taken as 0.7f.u for bonded tendons outside the transfer length and fe for unbonded tendons per stress in prestressing tendons at factored resistance pu =specified tensile strength of prestressing tendons yield strength of prestressing tendons modulus of rupture of concrete calculated stress in reinforcement at specified loads f specified yield strength of non-prestressed reinforcement or anchor steel specified yield strength of compression non-prestressed reinforcement specified yield strength of hoop reinforcement specified yield strength of transverse reinforcement fy specified yield strength of headed shear reinforcement Fa acceleration-based site coefficient, as specified in the National Building Code of Canada December 2004
© Canadian Standards Association Design of concrete structures December 2004 13 dcs = the smaller of (a) the distance from the closest concrete surface to the centre of the bar being developed; or (b) two-thirds of the centre-to-centre spacing of the bars being developed dp = pile shaft diameter (see Clauses 15 and 22) = distance from extreme compression fibre to centroid of the prestressing tendons (see Clause 18) dv = effective shear depth, taken as the greater of 0.9d or 0.72h e = distance from centroid of section for critical shear to point where shear stress is being calculated (see Clause 13) = eccentricity of Ptf parallel to axis measured from the centroid of the section (see Clause 23) Ec = modulus of elasticity of concrete Ep = modulus of elasticity of prestressing tendons Es = modulus of elasticity of non-prestressed reinforcement EI = flexural stiffness of compression member fc ’ = specified compressive strength of concrete fc ’ c = specified compressive strength of concrete in columns fce = compression stress in the concrete due to effective prestress only (after allowance for all prestress losses) at the extreme fibre of a section where tensile stresses are caused by applied loads fc ’ e = effective compressive strength of concrete in columns fc ’ i = compressive strength of concrete at time of prestress transfer fcp = average compressive stress in concrete due to effective prestress force only (after allowance for all prestress losses). For slabs and footings, fcp is the average of fcp for the two directions (see Clause 18) = compressive stress in concrete (after allowance for all prestress losses) at the centroid of the cross-section resisting externally applied loads or at the junction of the web and flange when the centroid lies within the flange (in a composite member, fcp is the resultant compressive stress at the centroid of the composite section or at the junction of the web and flange when the centroid lies within the flange, due to both prestress and moments being resisted by the precast member acting alone) (see Clause 11) fc ’ s = specified compressive strength of concrete in slab fcu = limiting compressive stress in concrete strut fc ’ w = specified compressive strength of concrete in the wall fpe = effective stress in prestressing tendons after allowance for all prestress losses fpo = stress in prestressing tendons when strain in the surrounding concrete is zero (may be taken as 0.7fpu for bonded tendons outside the transfer length and fpe for unbonded tendons) fpr = stress in prestressing tendons at factored resistance fpu = specified tensile strength of prestressing tendons fpy = yield strength of prestressing tendons fr = modulus of rupture of concrete fs = calculated stress in reinforcement at specified loads fy = specified yield strength of non-prestressed reinforcement or anchor steel fy ’ = specified yield strength of compression non-prestressed reinforcement fyh = specified yield strength of hoop reinforcement fyt = specified yield strength of transverse reinforcement fyv = specified yield strength of headed shear reinforcement Fa = acceleration-based site coefficient, as specified in the National Building Code of Canada