|a||=||depth of equivalent rectangular stress block, in.|
|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, in.|
|Ab||=||area of an individual bar or wire, in.2|
|Abrg||=||net bearing area of the head of stud, anchor bolt, or headed deformed bar, in.2|
|Ac||=||area of concrete section resisting shear transfer, in.2|
|Acf||=||greater gross cross-sectional area of the slab-beam strips of the two orthogonal equivalent frames intersecting at a column of a two-way slab, in.2|
|Ach||=||cross-sectional area of a member measured to the outside edges of transverse reinforcement, in.2|
|Acp||=||area enclosed by outside perimeter of concrete cross section, in.2|
|Acs||=||cross-sectional area at one end of a strut in a strut-and-tie model, taken perpendicular to the axis of the strut, in.2|
|Act||=||area of that part of cross section between the flexural tension face and centroid of gross section, in.2|
|Acv||=||gross area of concrete section bounded by web thickness and length of section in the direction of shear force considered in the case of walls, and gross area of concrete section in the case of diaphragms, not to exceed the thickness times the width of the diaphragm, in.2|
|Acw||=||area of concrete section of an individual pier, horizontal wall segment, or coupling beam resisting shear, in.2|
|Af||=||area of reinforcement in bracket or corbel resisting design moment, in.2|
|Ag||=||gross area of concrete section, in.2 For a hollow section, Ag is the area of the concrete only and does not include the area of the void(s)|
|Ah||=||total area of shear reinforcement parallel to primary tension reinforcement in a corbel or bracket, in.2|
|Aj||=||effective cross-sectional area within a joint in a plane parallel to plane of beam reinforcement generating shear in the joint, in.2|
|Aℓ||=||total area of longitudinal reinforcement to resist torsion, in.2|
|Aℓ,min||=||minimum area of longitudinal reinforcement to resist torsion, in.2|
|An||=||area of reinforcement in bracket or corbel resisting factored tensile force Nuc, in.2|
|Anz||=||area of a face of a nodal zone or a section through a nodal zone, in.2|
|ANa||=||projected influence area of a single adhesive anchor or group of adhesive anchors, for calculation of bond strength in tension, in.2|
|ANao||=||projected influence area of a single adhesive anchor, for calculation of bond strength in tension if not limited by edge distance or spacing, in.2|
|ANc||=||projected concrete failure area of a single anchor or group of anchors, for calculation of strength in tension, in.2|
|ANco||=||projected concrete failure area of a single anchor, for calculation of strength in tension if not limited by edge distance or spacing, in.2|
|Ao||=||gross area enclosed by torsional shear flow path, in.2|
|Aoh||=||area enclosed by centerline of the outermost closed transverse torsional reinforcement, in.2|
|Apd||=||total area occupied by duct, sheathing, and prestressing reinforcement, in.2|
|Aps||=||area of prestressed longitudinal tension reinforcement, in.2|
|Apt||=||total area of prestressing reinforcement, in.2|
|As||=||area of nonprestressed longitudinal tension reinforcement, in.2|
|As'||=||area of compression reinforcement, in.2|
|Asc||=||area of primary tension reinforcement in a corbel or bracket, in.2|
|Ase,N||=||effective cross-sectional area of anchor in tension, in.2|
|Ase,V||=||effective cross-sectional area of anchor in shear, in.2|
|Ash||=||total cross-sectional area of transverse reinforcement, including crossties, within spacing s and perpendicular to dimension bc, in.2|
|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, in.2|
|As,min||=||minimum area of flexural reinforcement, in.2|
|Ast||=||total area of nonprestressed longitudinal reinforcement including bars or steel shapes, and excluding prestressing reinforcement, in.2|
|Asx||=||area of steel shape, pipe, or tubing in a composite section, in.2|
|At||=||area of one leg of a closed stirrup, hoop, or tie resisting torsion within spacing s, in.2|
|Atp||=||area of prestressing reinforcement in a tie, in.2|
|Atr||=||total cross-sectional area of all transverse reinforcement within spacing s that crosses the potential plane of splitting through the reinforcement being developed, in.2|
|Ats||=||area of nonprestressed reinforcement in a tie, in.2|
|Av||=||area of shear reinforcement within spacing s, in.2|
|Avd||=||total area of reinforcement in each group of diagonal bars in a diagonally reinforced coupling beam, in.2|
|Avf||=||area of shear-friction reinforcement, in.2|
|Avh||=||area of shear reinforcement parallel to flexural tension reinforcement within spacing s2, in.2|
|Av,min||=||minimum area of shear reinforcement within spacing s, in.2|
|AVc||=||projected concrete failure area of a single anchor or group of anchors, for calculation of strength in shear, in.2|
|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, in.2|
|A1||=||loaded area for consideration of bearing strength, in.2|
|A2||=||area of the lower base of the largest frustum of a pyramid, cone, or tapered wedge contained wholly within the support and having its upper base equal to the loaded area. The sides of the pyramid, cone, or tapered wedge shall be sloped one vertical to two horizontal, in.2|
|b||=||width of compression face of member, in.|
|bc||=||cross-sectional dimension of member core measured to the outside edges of the transverse reinforcement composing area Ash, in.|
|bf||=||effective flange width of T section, in.|
|bo||=||perimeter of critical section for two-way shear in slabs and footings, in.|
|bs||=||width of strut, in.|
|bslab||=||effective slab width resisting γfMsc, in.|
|bt||=||width of that part of cross section containing the closed stirrups resisting torsion, in.|
|bv||=||width of cross section at contact surface being investigated for horizontal shear, in.|
|bw||=||web width or diameter of circular section, in.|
|b1||=||dimension of the critical section bo measured in the direction of the span for which moments are determined, in.|
|b2||=||dimension of the critical section bo measured in the direction perpendicular to b1, in.|
|Bn||=||nominal bearing strength, lb|
|Bu||=||factored bearing load, lb|
|c||=||distance from extreme compression fiber to neutral axis, in.|
|cac||=||critical edge distance required to develop the basic strength as controlled by concrete breakout or bond of a post-installed anchor in tension in uncracked concrete without supplementary reinforcement to control splitting, in.|
|ca,max||=||maximum distance from center of an anchor shaft to the edge of concrete, in.|
|ca,min||=||minimum distance from center of an anchor shaft to the edge of concrete, in.|
|ca1||=||distance from the center of an anchor shaft to the edge of concrete in one direction, in. If shear is applied to anchor, ca1 is taken in the direction of the applied shear. If tension is applied to the anchor, ca1 is the minimum edge distance. Where anchors subject to shear are located in narrow sections of limited thickness, see 220.127.116.11|
|ca2||=||distance from center of an anchor shaft to the edge of concrete in the direction perpendicular to ca1, in.|
|cb||=||lesser 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, in.|
|cc||=||clear cover of reinforcement, in.|
|cNa||=||projected distance from center of an anchor shaft on one side of the anchor required to develop the full bond strength of a single adhesive anchor, in.|
|ct||=||distance from the interior face of the column to the slab edge measured parallel to c1, but not exceeding c1, in.|
|c1||=||dimension of rectangular or equivalent rectangular column, capital, or bracket measured in the direction of the span for which moments are being determined, in.|
|c2||=||dimension of rectangular or equivalent rectangular column, capital, or bracket measured in the direction perpendicular to c1, in.|
|C||=||cross-sectional constant to define torsional properties of slab and beam|
|Cm||=||factor relating actual moment diagram to an equivalent uniform moment diagram|
|d||=||distance from extreme compression fiber to centroid of longitudinal tension reinforcement, in.|
|d'||=||distance from extreme compression fiber to centroid of longitudinal compression reinforcement, in.|
|da||=||outside diameter of anchor or shaft diameter of headed stud, headed bolt, or hooked bolt, in.|
|da'||=||value substituted for da if an oversized anchor is used, in.|
|dagg||=||nominal maximum size of coarse aggregate, in.|
|db||=||nominal diameter of bar, wire, or prestressing strand, in.|
|dp||=||distance from extreme compression fiber to centroid of prestressing reinforcement, in.|
|dpile||=||diameter of pile at footing base, in.|
|D||=||effect of service dead load|
|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, in.|
|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, in.; eN' is always positive|
|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, in.; eV' is always positive|
|E||=||effect of horizontal and vertical earthquake-induced forces|
|Ec||=||modulus of elasticity of concrete, psi|
|Ecb||=||modulus of elasticity of beam concrete, psi|
|Ecs||=||modulus of elasticity of slab concrete, psi|
|EI||=||flexural stiffness of member, in.2-lb|
|(EI)eff||=||effective flexural stiffness of member, in.2-lb|
|Ep||=||modulus of elasticity of prestressing reinforcement, psi|
|Es||=||modulus of elasticity of reinforcement and structural steel, excluding prestressing reinforcement, psi|
|f'c||=||specified compressive strength of concrete, psi|
|=||square root of specified compressive strength of concrete, psi|
|fci'||=||specified compressive strength of concrete at time of initial prestress, psi|
|=||square root of specified compressive strength of concrete at time of initial prestress, psi|
|fce||=||effective compressive strength of the concrete in a strut or a nodal zone, psi|
|fcm||=||measured average compressive strength of concrete, psi|
|fct||=||measured average splitting tensile strength of lightweight concrete, psi|
|fd||=||stress due to unfactored dead load, at extreme fiber of section where tensile stress is caused by externally applied loads, psi|
|fdc||=||decompression stress; stress in the prestressing reinforcement if stress is zero in the concrete at the same level as the centroid of the prestressing reinforcement, psi|
|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 where the centroid lies within the flange, psi. In a composite member, fpc is the resultant compressive stress at centroid of composite section, or at junction of web and flange where the centroid lies within the flange, due to both prestress and moments resisted by precast member acting alone|
|fpe||=||compressive stress in concrete due only to effective prestress forces, after allowance for all prestress losses, at extreme fiber of section if tensile stress is caused by externally applied loads, psi|
|fps||=||stress in prestressing reinforcement at nominal flexural strength, psi|
|fpu||=||specified tensile strength of prestressing reinforcement, psi|
|fpy||=||specified yield strength of prestressing reinforcement, psi|
|fr||=||modulus of rupture of concrete, psi|
|fs||=||tensile stress in reinforcement at service loads, excluding prestressing reinforcement, psi|
|f's||=||compressive stress in reinforcement under factored loads, excluding prestressing reinforcement, psi|
|fse||=||effective stress in prestressing reinforcement, after allowance for all prestress losses, psi|
|ft||=||extreme fiber stress in the precompressed tension zone calculated at service loads using gross section properties after allowance of all prestress losses, psi|
|futa||=||specified tensile strength of anchor steel, psi|
|fy||=||specified yield strength for nonprestressed reinforcement, psi|
|fya||=||specified yield strength of anchor steel, psi|
|fyt||=||specified yield strength of transverse reinforcement, psi|
|F||=||effect of service lateral load due to fluids with well-defined pressures and maximum heights|
|Fnn||=||nominal strength at face of a nodal zone, lb|
|Fns||=||nominal strength of a strut, lb|
|Fnt||=||nominal strength of a tie, lb|
|Fun||=||factored force on the face of a node, lb|
|Fus||=||factored compressive force in a strut, lb|
|Fut||=||factored tensile force in a tie, lb|
|h||=||overall thickness, height, or depth of member, in.|
|ha||=||thickness of member in which an anchor is located, measured parallel to anchor axis, in.|
|hef||=||effective embedment depth of anchor, in.|
|hsx||=||story height for story x, in.|
|hu||=||laterally unsupported height at extreme compression fiber of wall or wall pier, in., equivalent to ℓu for compression members|
|hv||=||depth of shearhead cross section, in.|
|hw||=||height of entire wall from base to top, or clear height of wall segment or wall pier considered, in.|
|hx||=||maximum center-to-center spacing of longitudinal bars laterally supported by corners of crossties or hoop legs around the perimeter of the column, in.|
|H||=||effect of service load due to lateral earth pressure, ground water pressure, or pressure of bulk materials, lb|
|I||=||moment of inertia of section about centroidal axis, in.4|
|Ib||=||moment of inertia of gross section of beam about centroidal axis, in.4|
|Icr||=||moment of inertia of cracked section transformed to concrete, in.4|
|Ie||=||effective moment of inertia for calculation of deflection, in.4|
|Ig||=||moment of inertia of gross concrete section about centroidal axis, neglecting reinforcement, in.4|
|Is||=||moment of inertia of gross section of slab about centroidal axis, in.4|
|Ise||=||moment of inertia of reinforcement about centroidal axis of member cross section, in.4|
|Isx||=||moment of inertia of structural steel shape, pipe, or tubing about centroidal axis of composite member cross section, in.4|
|k||=||effective length factor for compression members|
|kc||=||coefficient for basic concrete breakout strength in tension|
|kcp||=||coefficient for pryout strength|
|kf||=||concrete strength factor|
|kn||=||confinement effectiveness factor|
|Ktr||=||transverse reinforcement index, in.|
|ℓ||=||span length of beam or one-way slab; clear projection of cantilever, in.|
|ℓa||=||additional embedment length beyond centerline of support or point of inflection, in.|
|ℓc||=||length of compression member, measured center-to-center of the joints, in.|
|ℓd||=||development length in tension of deformed bar, deformed wire, plain and deformed welded wire reinforcement, or pretensioned strand, in.|
|ℓdc||=||development length in compression of deformed bars and deformed wire, in.|
|ℓdb||=||debonded length of prestressed reinforcement at end of member, in.|
|ℓdh||=||development length in tension of deformed bar or deformed wire with a standard hook, measured from outside end of hook, point of tangency, toward critical section, in.|
|ℓdt||=||development length in tension of headed deformed bar, measured from the bearing face of the head toward the critical section, in.|
|ℓe||=||load bearing length of anchor for shear, in.|
|ℓext||=||straight extension at the end of a standard hook, in.|
|ℓn||=||length of clear span measured face-to-face of supports, in.|
|ℓo||=||length, measured from joint face along axis of member, over which special transverse reinforcement must be provided, in.|
|ℓsc||=||compression lap splice length, in.|
|ℓst||=||tension lap splice length, in.|
|ℓt||=||span of member under load test, taken as the shorter span for two-way slab systems, in. Span is the lesser 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|
|ℓtr||=||transfer length of prestressed reinforcement, in.|
|ℓu||=||unsupported length of column or wall, in.|
|ℓv||=||length of shearhead arm from centroid of concentrated load or reaction, in.|
|ℓw||=||length of entire wall, or length of wall segment or wall pier considered in direction of shear force, in.|
|ℓ1||=||length of span in direction that moments are being determined, measured center-to-center of supports, in.|
|ℓ2||=||length of span in direction perpendicular to ℓ1, measured center-to-center of supports, in.|
|L||=||effect of service live load|
|Lr||=||effect of service roof live load|
|Ma||=||maximum moment in member due to service loads at stage deflection is calculated, in.-lb|
|Mc||=||factored moment amplified for the effects of member curvature used for design of compression member, in.-lb|
|Mcr||=||cracking moment, in.-lb|
|Mcre||=||moment causing flexural cracking at section due to externally applied loads, in.-lb|
|Mmax||=||maximum factored moment at section due to externally applied loads, in.-lb|
|Mn||=||nominal flexural strength at section, in.-lb|
|Mnb||=||nominal flexural strength of beam including slab where in tension, framing into joint, in.-lb|
|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, in.-lb|
|Mo||=||total factored static moment, in.-lb|
|Mp||=||required plastic moment strength of shearhead cross section, in.-lb|
|Mpr||=||probable flexural strength of members, with or without axial load, determined using the properties of the member at joint faces assuming a tensile stress in the longitudinal bars of at least 1.25fy and a strength reduction factor ϕ of 1.0, in.-lb|
|Msa||=||maximum moment in wall due to service loads, excluding PΔ effects, in.-lb|
|Msc||=||factored slab moment that is resisted by the column at a joint, in.-lb|
|Mu||=||factored moment at section, in.-lb|
|Mua||=||moment at midheight of wall due to factored lateral and eccentric vertical loads, not including PΔ effects, in.-lb|
|Mv||=||moment resistance contributed by shearhead reinforcement, in.-lb|
|M1||=||lesser factored end moment on a compression member, in.-lb|
|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, in.-lb|
|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, in.-lb|
|M2||=||greater factored end moment on a compression member. If transverse loading occurs between supports, M2 is taken as the largest moment occurring in member. Value of M2 is always positive, in.-lb|
|M2,min||=||minimum value of M2, in.-lb|
|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, in.-lb|
|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 analysis, in.-lb|
|n||=||number of items, such as, bars, wires, monostrand anchorage devices, anchors, or shearhead arms|
|nℓ||=||number of longitudinal bars around the perimeter of a column core with rectilinear hoops that are laterally supported by the corner of hoops or by seismic hooks. A bundle of bars is counted as a single bar|
|Na||=||nominal bond strength in tension of a single adhesive anchor, lb|
|Nag||=||nominal bond strength in tension of a group of adhesive anchors, lb|
|Nb||=||basic concrete breakout strength in tension of a single anchor in cracked concrete, lb|
|Nba||=||basic bond strength in tension of a single adhesive anchor, lb|
|Nc||=||resultant tensile force acting on the portion of the concrete cross section that is subjected to tensile stresses due to the combined effects of service loads and effective prestress, lb|
|Ncb||=||nominal concrete breakout strength in tension of a single anchor, lb|
|Ncbg||=||nominal concrete breakout strength in tension of a group of anchors, lb|
|Ncp||=||basic concrete pryout strength of a single anchor, lb|
|Ncpg||=||basic concrete pryout strength of a group of anchors, lb|
|Nn||=||nominal strength in tension, lb|
|Np||=||pullout strength in tension of a single anchor in cracked concrete, lb|
|Npn||=||nominal pullout strength in tension of a single anchor, lb|
|Nsa||=||nominal strength of a single anchor or individual anchor in a group of anchors in tension as governed by the steel strength, lb|
|Nsb||=||side-face blowout strength of a single anchor, lb|
|Nsbg||=||side-face blowout strength of a group of anchors, lb|
|Nu||=||factored axial force normal to cross section occurring simultaneously with Vu or Tu; to be taken as positive for compression and negative for tension, lb|
|Nua||=||factored tensile force applied to anchor or individual anchor in a group of anchors, lb|
|Nua,g||=||total factored tensile force applied to anchor group, lb|
|Nua,i||=||factored tensile force applied to most highly stressed anchor in a group of anchors, lb|
|Nua,s||=||factored sustained tension load, lb|
|Nuc||=||factored horizontal tensile force applied at top of bracket or corbel acting simultaneously with Vu, to be taken as positive for tension, lb|
|pcp||=||outside perimeter of concrete cross section, in.|
|ph||=||perimeter of centerline of outermost closed transverse torsional reinforcement, in.|
|Pc||=||critical buckling load, lb|
|Pn||=||nominal axial compressive strength of member, lb|
|Pn,max||=||maximum nominal axial compressive strength of a member, lb|
|Pnt||=||nominal axial tensile strength of member, lb|
|Pnt,max||=||maximum nominal axial tensile strength of member, lb|
|Po||=||nominal axial strength at zero eccentricity, lb|
|Ppu||=||factored prestressing force at anchorage device, lb|
|Ps||=||unfactored axial load at the design, midheight section including effects of self-weight, lb|
|Pu||=||factored axial force; to be taken as positive for compression and negative for tension, lb|
|PΔ||=||secondary moment due to lateral deflection, in.-lb|
|qDu||=||factored dead load per unit area, lb/ft2|
|qLu||=||factored live load per unit area, lb/ft2|
|qu||=||factored load per unit area, lb/ft2|
|Q||=||stability index for a story|
|r||=||radius of gyration of cross section, in.|
|R||=||cumulative load effect of service rain load|
|s||=||center-to-center spacing of items, such as longitudinal reinforcement, transverse reinforcement, tendons, or anchors, in.|
|si||=||center-to-center spacing of reinforcement in the i-th direction adjacent to the surface of the member, in.|
|so||=||center-to-center spacing of transverse reinforcement within the length ℓo, in.|
|ss||=||sample standard deviation, psi|
|sw||=||clear distance between adjacent webs, in.|
|s2||=||center-to-center spacing of longitudinal shear or torsional reinforcement, in.|
|S||=||effect of service snow load|
|Se||=||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 effects|
|Sm||=||elastic section modulus, in.3|
|Sn||=||nominal moment, shear, axial, torsional, or bearing strength|
|Sy||=||yield strength of connection, based on fy of the connected part, for moment, shear, or axial force, psi|
|t||=||wall thickness of hollow section, in.|
|tf||=||thickness of flange, in.|
|T||=||cumulative effects of service temperature, creep, shrinkage, differential settlement, and shrinkage-compensating concrete|
|Tcr||=||cracking torsional moment, in.-lb|
|Tt||=||total test load, lb|
|Tth||=||threshold torsional moment, in.-lb|
|Tn||=||nominal torsional moment strength, in.-lb|
|Tu||=||factored torsional moment at section, in.-lb|
|U||=||strength of a member or cross section required to resist factored loads or related internal moments and forces in such combinations as stipulated in this Code|
|vc||=||stress corresponding to nominal two-way shear strength provided by concrete, psi|
|vn||=||equivalent concrete stress corresponding to nominal two-way shear strength of slab or footing, psi|
|vs||=||equivalent concrete stress corresponding to nominal two-way shear strength provided by reinforcement, psi|
|vu||=||maximum factored two-way shear stress calculated around the perimeter of a given critical section, psi|
|vug||=||factored shear stress on the slab critical section for two-way action due to gravity loads without moment transfer, psi|
|Vb||=||basic concrete breakout strength in shear of a single anchor in cracked concrete, lb|
|Vc||=||nominal shear strength provided by concrete, lb|
|Vcb||=||nominal concrete breakout strength in shear of a single anchor, lb|
|Vcbg||=||nominal concrete breakout strength in shear of a group of anchors, lb|
|Vci||=||nominal shear strength provided by concrete where diagonal cracking results from combined shear and moment, lb|
|Vcp||=||nominal concrete pryout strength of a single anchor, lb|
|Vcpg||=||nominal concrete pryout strength of a group of anchors, lb|
|Vcw||=||nominal shear strength provided by concrete where diagonal cracking results from high principal tensile stress in web, lb|
|Vd||=||shear force at section due to unfactored dead load, lb|
|Ve||=||design shear force for load combinations including earthquake effects, lb|
|Vi||=||factored shear force at section due to externally applied loads occurring simultaneously with Mmax, lb|
|Vn||=||nominal shear strength, lb|
|Vnh||=||nominal horizontal shear strength, lb|
|Vp||=||vertical component of effective prestress force at section, lb|
|Vs||=||nominal shear strength provided by shear reinforcement, lb|
|Vsa||=||nominal shear strength of a single anchor or individual anchor in a group of anchors as governed by the steel strength, lb,|
|Vu||=||factored shear force at section, lb|
|Vua||=||factored shear force applied to a single anchor or group of anchors, lb|
|Vua,g||=||total factored shear force applied to anchor group, lb|
|Vua,i||=||factored shear force applied to most highly stressed anchor in a group of anchors, lb|
|Vuh||=||factored shear force along contact surface in composite concrete flexural member, lb|
|Vus||=||factored horizontal shear in a story, lb|
|wc||=||density, unit weight, of normalweight concrete or equilibrium density of lightweight concrete, lb/ft3|
|wu||=||factored load per unit length of beam or one-way slab, lb/in.|
|w/cm||=||water-cementitious material ratio|
|W||=||effect of wind load|
|x||=||shorter overall dimension of rectangular part of cross section, in|
|y||=||longer overall dimension of rectangular part of cross section, in|
|yt||=||distance from centroidal axis of gross section, neglecting reinforcement, to tension face, in.|
|α||=||angle defining the orientation of reinforcement|
|αc||=||coefficient defining the relative contribution of concrete strength to nominal wall shear strength|
|αf||=||ratio of flexural stiffness of beam section to flexural stiffness of a width of slab bounded laterally by centerlines of adjacent panels, if any, on each side of the beam|
|αfm||=||average value of αf for all beams on edges of a panel|
|αf1||=||αf in direction of ℓ1|
|αf2||=||αf in direction of ℓ2|
|αi||=||angle between the axis of a strut and the bars in the i-th layer of reinforcement crossing that strut|
|αs||=||constant used to calculate Vc in slabs and footings|
|αv||=||ratio of flexural stiffness of shearhead arm to that of the surrounding composite slab section|
|α1||=||orientation of distributed reinforcement in a strut|
|α2||=||orientation of reinforcement orthogonal to α1 in a strut|
|β||=||ratio of long to short dimensions: clear spans for two-way slabs, sides of column, concentrated load or reaction area; or sides of a footing|
|βb||=||ratio of area of reinforcement cut off to total area of tension reinforcement at section|
|βdns||=||ratio used to account for reduction of stiffness of columns due to sustained axial loads|
|βds||=||the ratio of maximum factored sustained shear within a story to the maximum factored shear in that story associated with the same load combination|
|βn||=||factor used to account for the effect of the anchorage of ties on the effective compressive strength of a nodal zone|
|βs||=||factor used to account for the effect of cracking and confining reinforcement on the effective compressive strength of the concrete in a strut|
|βt||=||ratio of torsional stiffness of edge beam section to flexural stiffness of a width of slab equal to span length of beam, center-to-center of supports|
|β1||=||factor relating depth of equivalent rectangular compressive stress block to depth of neutral axis|
|γf||=||factor used to determine the fraction of Msc transferred by slab flexure at slab-column connections|
|γp||=||factor used for type of prestressing reinforcement|
|γs||=||factor used to determine the portion of reinforcement located in center band of footing|
|γv||=||factor used to determine the fraction of Msc transferred by eccentricity of shear at slab-column connections|
|δ||=||moment magnification factor used to reflect effects of member curvature between ends of a compression member|
|δs||=||moment magnification factor used for frames not braced against sidesway, to reflect lateral drift resulting from lateral and gravity loads|
|δu||=||design displacement, in.|
|Δcr||=||calculated out-of-plane deflection at midheight of wall corresponding to cracking moment Mcr, in.|
|Δn||=||calculated out-of-plane deflection at midheight of wall corresponding to nominal flexural strength Mn, in.|
|Δo||=||relative lateral deflection between the top and bottom of a story due to Vus, in.|
|Δfp||=||increase in stress in prestressing reinforcement due to factored loads, psi|
|Δfps||=||stress in prestressing reinforcement at service loads less decompression stress, psi|
|Δr||=||residual deflection measured 24 hours after removal of the test load. For the first load test, residual deflection is measured relative to the position of the structure at the beginning of the first load test. For the second load test, residual deflection is measured relative to the position of the structure at the beginning of the second load test, in.|
|Δs||=||out-of-plane deflection due to service loads, in.|
|Δu||=||calculated out-of-plane deflection at midheight of wall due to factored loads, in.|
|Δx||=||design story drift of story x, in.|
|Δ1||=||maximum deflection, during first load test, measured 24 hours after application of the full test load, in.|
|Δ2||=||maximum deflection, during second load test, measured 24 hours after application of the full test load. Deflection is measured relative to the position of the structure at the beginning of the second load test, in.|
|εt||=||net tensile strain in extreme layer of longitudinal tension reinforcement at nominal strength, excluding strains due to effective prestress, creep, shrinkage, and temperature|
|εty||=||value of net tensile strain in the extreme layer of longitudinal tension reinforcement used to define a compression-controlled section|
|θ||=||angle between axis of strut, compression diagonal, or compression field and the tension chord of the members|
|λ||=||modification factor to reflect the reduced mechanical properties of lightweight concrete relative to normalweight concrete of the same compressive strength|
|λa||=||modification factor to reflect the reduced mechanical properties of lightweight concrete in certain concrete anchorage applications|
|λΔ||=||multiplier used for additional deflection due to long-term effects|
|µ||=||coefficient of friction|
|ξ||=||time-dependent factor for sustained load|
|ρ||=||ratio of As to bd|
|ρ'||=||ratio of As' to bd|
|ρℓ||=||ratio of area of distributed longitudinal reinforcement to gross concrete area perpendicular to that reinforcement|
|ρp||=||ratio of Aps to bdp|
|ρs||=||ratio of volume of spiral reinforcement to total volume of core confined by the spiral, measured out-to-out of spirals|
|ρt||=||ratio of area of distributed transverse reinforcement to gross concrete area perpendicular to that reinforcement|
|ρv||=||ratio of tie reinforcement area to area of contact surface|
|ρw||=||ratio of As to bwd|
|ϕ||=||strength reduction factor|
|τcr||=||characteristic bond stress of adhesive anchor in cracked concrete, psi|
|τuncr||=||characteristic bond stress of adhesive anchor in uncracked concrete, psi|
|ψc||=||factor used to modify development length based on cover|
|ψc,N||=||factor used to modify tensile strength of anchors based on presence or absence of cracks in concrete|
|ψc,P||=||factor used to modify pullout strength of anchors based on presence or absence of cracks in concrete|
|ψc,V||=||factor used to modify shear strength of anchors based on presence or absence of cracks in concrete and presence or absence of supplementary reinforcement|
|ψcp,N||=||factor used to modify tensile strength of post-installed anchors intended for use in uncracked concrete without supplementary reinforcement to account for the splitting tensile stresses due to installation|
|ψcp,Na||=||factor used to modify tensile strength of adhesive anchors intended for use in uncracked concrete without supplementary reinforcement to account for the splitting tensile stresses due to installation|
|ψe||=||factor used to modify development length based on reinforcement coating|
|ψec,N||=||factor used to modify tensile strength of anchors based on eccentricity of applied loads|
|ψec,Na||=||factor used to modify tensile strength of adhesive anchors based on eccentricity of applied loads|
|ψec,V||=||factor used to modify shear strength of anchors based on eccentricity of applied loads|
|ψed,N||=||factor used to modify tensile strength of anchors based on proximity to edges of concrete member|
|ψed,Na||=||factor used to modify tensile strength of adhesive anchors based on proximity to edges of concrete member|
|ψed,V||=||factor used to modify shear strength of anchors based on proximity to edges of concrete member|
|ψh,V||=||factor used to modify shear strength of anchors located in concrete members with ha < 1.5ca1|
|ψr||=||factor used to modify development length based on confining reinforcement|
|ψs||=||factor used to modify development length based on reinforcement size|
|ψt||=||factor used to modify development length for casting location in tension|
|ψw||=||factor used to modify development length for welded deformed wire reinforcement in tension|
|Ωo||=||amplification factor to account for overstrength of the seismic-force-resisting system determined in accordance with the general building code|
adhesive—chemical components formulated from organic polymers, or a combination of organic polymers and inorganic materials that cure if blended together.
aggregate—granular material, such as sand, gravel, crushed stone, and iron blast-furnace slag, used with a cementing medium to form concrete or mortar.
aggregate, lightweight—aggregate meeting the requirements of ASTM C330 and having a loose bulk density of 70 lb/ft3 or less, determined in accordance with ASTM C29.
anchor, adhesive—a post-installed anchor, inserted into hardened concrete with an anchor hole diameter not greater than 1.5 times the anchor diameter, that transfers loads to the concrete by bond between the anchor and the adhesive, and bond between the adhesive and the concrete.
anchor, undercut—post-installed anchor that develops its tensile strength from the mechanical interlock provided by undercutting of the concrete at the embedded end of the anchor. Undercutting is achieved with a special drill before installing the anchor or alternatively by the anchor itself during its installation.
anchor pullout strength—the strength corresponding to the anchoring device or a major component of the device sliding out from the concrete without breaking out a substantial portion of the surrounding concrete.
anchorage zone—in post-tensioned members, portion of the member through which the concentrated prestressing force is transferred to concrete and distributed more uniformly across the section; its extent is equal to the largest dimension of the cross section; for anchorage devices located away from the end of a member, the anchorage zone includes the disturbed regions ahead of and behind the anchorage device.
B-region—portion of a member in which it is reasonable to assume that strains due to flexure vary linearly through section.
base of structure—level at which horizontal earthquake ground motions are assumed to be imparted to a building. This level does not necessarily coincide with the ground level.
beam—member subjected primarily to flexure and shear, with or without axial force or torsion; beams in a moment frame that forms part of the lateral-force-resisting system are predominantly horizontal members; a girder is a beam.
building official—term used to identify the Authority having jurisdiction or individual charged with administration and enforcement of provisions of the building code. Such terms as building commissioner or building inspector are variations of the title, and the term "building official" as used in this Code, is intended to include those variations, as well as others that are used in the same sense.
cementitious materials—materials that have cementing value if used in concrete either by themselves, such as portland cement, blended hydraulic cements, and expansive cement; or such materials in combination with fly ash, other raw or calcined natural pozzolans, silica fume, and slag cement.
collector—element that acts in axial tension or compression to transmit forces between a diaphragm and a vertical element of the lateral-force-resisting system.
column—member, usually vertical or predominantly vertical, used primarily to support axial compressive load, but that can also resist moment, shear, or torsion. Columns used as part of a lateral-force-resisting system resist combined axial load, moment, and shear. See also moment frame.
composite concrete flexural members—concrete flexural members of precast or cast-in-place concrete elements, constructed in separate placements but connected so that all elements respond to loads as a unit.
compression-controlled strain limit—net tensile strain at balanced strain conditions.
concrete, all-lightweight—lightweight concrete containing only lightweight coarse and fine aggregates that conform to ASTM C330.
concrete, nonprestressed—reinforced concrete with at least the minimum amount of nonprestressed reinforcement and no prestressed reinforcement; or for two-way slabs, with less than the minimum amount of prestressed reinforcement.
concrete strength, specified compressive, (fc')—compressive strength of concrete used in design and evaluated in accordance with provisions of this Code, psi; wherever the quantity fc' is under a radical sign, the square root of numerical value only is intended, and the result has units of psi.
construction documents—written and graphic documents and specifications prepared or assembled for describing the location, design, materials, and physical characteristics of the elements of a project necessary for obtaining a building permit and construction of the project.
contraction joint—formed, sawed, or tooled groove in a concrete structure to create a weakened plane and regulate the location of cracking resulting from the dimensional change of different parts of the structure.
crosstie—a continuous reinforcing bar having a seismic hook at one end and a hook not less than 90 degrees with at least a 6db extension at the other end. The hooks shall engage peripheral longitudinal bars. The 90-degree hooks of two successive crossties engaging the same longitudinal bars shall be alternated end for end.
DESIGN DISPLACEMENT. Total lateral displacement expected for the design-basis earthquake, as specified by Section 12.8.6 of ASCE 7.
design story drift ratio—relative difference of design displacement between the top and bottom of a story, divided by the story height.
DETAILED PLAIN CONCRETE STRUCTURAL WALL. A wall complying with the requirements of Chapter 14, including 14.6.2.
discontinuity—abrupt change in geometry or loading.
durability—ability of a structure or member to resist deterioration that impairs performance or limits service life of the structure in the relevant environment considered in design.
effective depth of section—distance measured from extreme compression fiber to centroid of longitudinal tension reinforcement.
effective embedment depth—overall depth through which the anchor transfers force to or from the surrounding concrete; effective embedment depth will normally be the depth of the concrete failure surface in tension applications; for cast-in headed anchor bolts and headed studs, the effective embedment depth is measured from the bearing contact surface of the head.
embedments—items embedded in concrete, excluding reinforcement as defined in Chapter 20 and anchors as defined in Chapter 17. Reinforcement or anchors welded, bolted or otherwise connected to the embedded item to develop the strength of the assembly, are considered to be part of the embedment.
embedments, pipe—embedded pipes, conduits, and sleeves.
equilibrium density—density of lightweight concrete determined in accordance with ASTM C567 after exposure to a relative humidity of 50 ± 5 percent and a temperature of 73.5 ± 3.5°F for a period of time sufficient to reach constant density.
expansion sleeve—outer part of an expansion anchor that is forced outward by the center part, either by applied torque or impact, to bear against the sides of the predrilled hole. See also anchor, expansion.
finite element analysis—a numerical modeling technique in which a structure is divided into a number of discrete elements for analysis.
five percent fractile—statistical term meaning 90 percent confidence that there is 95 percent probability of the actual strength exceeding the nominal strength.
headed deformed bars—deformed bars with heads attached at one or both ends.
headed stud—a steel anchor conforming to the requirements of AWS D1.1 and affixed to a plate or similar steel attachment by the stud arc welding process before casting; also referred to as a welded headed stud.
headed shear stud reinforcement—reinforcement consisting of individual headed studs or groups of studs, with anchorage provided by a head at each end, or by a head at one end and a common base rail consisting of a steel plate or shape at the other end.
hoop—closed tie or continuously wound tie, made up of one or several reinforcement elements, each having seismic hooks at both ends. A closed tie shall not be made up of interlocking headed deformed bars. See 25.7.4.
inspection—observation, verification, and required documentation of the materials, installation, fabrication, erection, or placement of components and connections to determine compliance with construction documents and referenced standards.
isolation joint—separation between adjoining parts of a concrete structure, usually a vertical plane at a designed location such as to interfere least with performance of the structure, yet such as to allow relative movement in three directions and avoid formation of cracks elsewhere in the concrete, and through which all or part of the bonded reinforcement is interrupted.
joint—portion of structure common to intersecting members
licensed design professional—an individual who is licensed to practice structural design as defined by the statutory requirements of the professional licensing laws of the state or jurisdiction in which the project is to be constructed, and who is in responsible charge of the structural design.
load—forces or other actions that result from the weight of all building materials, occupants, and their possessions, environmental effects, differential movement, and restrained dimensional changes; permanent loads are those loads in which variations over time are rare or of small magnitude; all other loads are variable loads.
load, dead—(a) the weights of the members, supported structure, and permanent attachments or accessories that are likely to be present on a structure in service; or (b) loads meeting specific criteria found in the general building code; without load factors.
load, live—(a) load that is not permanently applied to a structure, but is likely to occur during the service life of the structure (excluding environmental loads); or (b) loads meeting specific criteria found in the general building code; without load factors.
load, roof live—a load on a roof produced: (a) during maintenance by workers, equipment, and materials, and (b) during the life of the structure by movable objects, such as planters or other similar small decorative appurtenances that are not occupancy related; or loads meeting specific criteria found in the general building code; without load factors.
load path—sequence of members and connections designed to transfer the factored loads and forces in such combinations as are stipulated in this Code, from the point of application or origination through the structure to the final support location or the foundation.
Manufacturer's Printed Installation Instructions (MPII)—published instructions for the correct installation of an adhesive anchor under all covered installation conditions as supplied in the product packaging.
modulus of elasticity—ratio of normal stress to corresponding strain for tensile or compressive stresses below proportional limit of material.
moment frame—frame in which beams, slabs, columns, and joints resist forces predominantly through flexure, shear, and axial force; beams or slabs are predominantly horizontal or nearly horizontal; columns are predominantly vertical or nearly vertical.
pedestal—member with a ratio of height-to-least lateral dimension less than or equal to 3 used primarily to support axial compressive load; for a tapered member, the least lateral dimension is the average of the top and bottom dimensions of the smaller side.
plastic hinge region—length of frame element over which flexural yielding is intended to occur due to earthquake design displacements, extending not less than a distance h from the critical section where flexural yielding initiates.
Seismic Design Category—classification assigned to a structure based on its occupancy category and the severity of the design earthquake ground motion at the site, as defined by the general building code. Also denoted by the abbreviation SDC.
seismic hook—hook on a stirrup, hoop, or crosstie having a bend not less than 135 degrees, except that circular hoops shall have a bend not less than 90 degrees; hooks shall have an extension of at least 6db, but not less than 3 in. The hooks shall engage the longitudinal reinforcement and the extension shall project into the interior of the stirrup or hoop.
shear cap—projection below the slab used to increase the slab shear strength.
sheathing—material encasing prestressing reinforcement to prevent bonding of the prestressing reinforcement with the surrounding concrete, to provide corrosion protection, and to contain the corrosion-inhibiting coating.
side-face blowout strength, concrete—strength of anchors with deep embedment and thin side-face cover such that spalling occurs on the side face around the embedded head without breakout occurring at the top concrete surface.
spacing, clear—least dimension between the outermost surfaces of adjacent items.
span length—distance between supports.
specialty insert—predesigned and prefabricated cast-in anchors specifically designed for attachment of bolted or slotted connections.
SPECIAL STRUCTURAL WALL. A cast-in-place or precast wall complying with the requirements of 18.2.4 through 18.2.8, 18.10 and 18.11, as applicable, in addition to the requirements for ordinary reinforced concrete structural walls or ordinary precast structural walls, as applicable. Where ASCE 7 refers to a "special reinforced concrete structural wall," it shall be deemed to mean a "special structural wall."
steel element, brittle—element with a tensile test elongation of less than 14 percent, or reduction in area of less than 30 percent at failure.
steel element, ductile—element with a tensile test elongation of at least 14 percent and reduction in area of at least 30 percent; steel element meeting the requirements of ASTM A307 shall be considered ductile; except as modified by for earthquake effects, deformed reinforcing bars meeting the requirements of ASTM A615, A706, or A955 shall be considered as ductile steel elements.
stirrup—reinforcement used to resist shear and torsion forces in a member; typically deformed bars, deformed wires, or welded wire reinforcement either single leg or bent into L, U, or rectangular shapes and located perpendicular to, or at an angle to, longitudinal reinforcement. See also tie.
strength, nominal—strength of a member or cross section calculated in accordance with provisions and assumptions of the strength design method of this Code before application of any strength reduction factors.
structural diaphragm—member, such as a floor or roof slab, that transmits forces acting in the plane of the member to vertical elements of the lateral-force-resisting system. A structural diaphragm may include chords and collectors as part of the diaphragm.
structural integrity—ability of a structure through strength, redundancy, ductility, and detailing of reinforcement to redistribute stresses and maintain overall stability if localized damage or significant overstress occurs.
structural system—interconnected members designed to meet performance requirements.
strut-and-tie model—truss model of a member or of a D-region in such a member, made up of struts and ties connected at nodes and capable of transferring the factored loads to the supports or to adjacent B-regions.
tendon—in post-tensioned members, a tendon is a complete assembly consisting of anchorages, prestressing reinforcement, and sheathing with coating for unbonded applications or ducts filled with grout for bonded applications.
tendon, unbonded—tendon in which prestressed reinforcement is prevented from bonding to the concrete. The prestressing force is permanently transferred to the concrete at the tendon ends by the anchorages only.
tie—(a) loop of reinforcing bar or wire enclosing longitudinal reinforcement; a continuously wound transverse bar or wire in the form of a circle, rectangle, or other polygonal shape without reentrant corners enclosing longitudinal reinforcement; see also stirrup, hoop; (b) tension element in a strut-and-tie model.
two-way construction—members designed to be capable of supporting loads through bending in two directions; some slabs and foundations are considered two-way construction. See also one-way construction.
wall pier—a vertical wall segment within a structural wall, bounded horizontally by two openings or by an opening and an edge, with ratio of horizontal length to wall thickness (ℓw/bw) less than or equal to 6.0, and ratio of clear height to horizontal length (hw/ℓw) greater than or equal to 2.0.
yield strength—specified minimum yield strength or yield point of reinforcement; yield strength or yield point shall be determined in tension according to applicable ASTM standards as modified by this Code.