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50 NOTATION The notation conforms to that of Section 5.3 of the AASHTO-LRFD Specifications; however, some new symbols are needed to describe terms used in various models and in several instances modifications are needed to the basic AASHTO-LRFD def- inition to better describe subsets of that term. Definitions for new terms and changes are shown in italics. Main Report Ac = area of concrete on flexural tension side of member Act = area of concrete in tension Acv = area of concrete resisting shear transfer Ag = gross area of concrete section Aps = area of prestressing steel on flexural tension side of member at ultimate load As = area of non-prestressed tension reinforcement on flexural tension side of member at ultimate load Av = area of transverse reinforcement within a distance s Av,min = area of minimum required transverse reinforcement ag = maximum aggregate size b = width of compression face of member bv = width of interface; web width including adjustment for presence of ducts bw = web width d = distance from compression face to centroid of tension reinforcement dv = effective shear depth Ec = modulus of elasticity of concrete Ep = modulus of elasticity of prestressing steel Es = modulus of elasticity of reinforcing bars f2 = stress in direction 2; principal compressive stress f â²c = concrete compressive strength fc1 = concrete stress in direction 1 fc2 = concrete stress in direction 2 fc2max = maximum value of concrete stress in direction 2 when there is tension in direction 1 fck = characteristic concrete cylinder compressive strength (EC2 method)(â 0.9f â²c) fcr = concrete stress at tensile cracking fct = concrete tensile stress fcx = concrete stress in direction x fd = stress due to unfactored dead load fpc = compressive stress in concrete after all prestress losses have occurred either at centroid of the cross-section resisting live load or at the junction of the web and flange when the centroid lies in the flange fpe = effective stress in the prestressing steel after losses; compressive stress in concrete due to effective prestress forces only at extreme fiber of section where tensile stress is caused by externally applied loads fpo = Ep times locked in difference in strain at ultimate load between the prestressing tendons and the surrounding concrete fps = stress in prestressing steel fpu = tensile strength of prestressing steel fsx = steel stress in direction x fsy = steel stress in direction y ft = tensile strength of concrete fv = shear stress; stress in shear reinforcement; vertical stress fx = stress in direction x fy = yield strength of reinforcing bars; stress in direction y h = overall thickness or depth of member
51 Ic = moment of inertia of uncracked concrete j = 1-k/3 K = coefficient to define prestress effect in ASBI shear strength evaluation method k = coefficient on d to define depth of compression zone for elastic behavior; parameter in EC2 (2003) and DIN shear strength evaluation method L = span of member center to center of supports M = moment Mcr = cracking moment Mmax = maximum factored moment at section due to externally applied loads Mn = nominal flexural resistance of section Mu = ultimate moment; factored moment at section Nu = factored axial force Nv = Vcotθ n = modular ratio s = spacing of bars of transverse reinforcement smax = maximum permitted spacing of transverse reinforcement sx = crack spacing parameter sxe = crack spacing parameter sz = crack spacing parameter sze = crack spacing parameter Tmin = minimum tensile capacity required for reinforcement on flexural tension side of member at dvcotθ from design section V = shear VAASHTO-LRFD = shear capacity evaluated using AASHTO-LRFD VACI = shear capacity evaluated using ACI 318 Vc = shear at inclined cracking; nominal shear resistance provided by concrete Vca = shear carried by aggregate interlock Vcc = shear in compression zone Vci = shear at flexure-shear cracking Vcode = nominal shear strength of member as evaluated by a specific code method or procedure Vcr = shear carried by residual tensile stresses in concrete Vcw = shear at web-shear cracking Vd = shear carried by dowel action; shear force at section due to unfactored dead load Vi = factored shear force at section due to externally applied loads occurring simultaneously with Mmax Vn = nominal shear resistance of section considered Vn,max = maximum allowable nominal shear capacity Vp = component in the direction of the applied shear of the effective prestressing force Vr = factored shear resistance = ÏVn Vs = shear resistance provided by transverse reinforcement Vtest = shear resistance measured at ultimate capacity in test Vu = factored shear force at section v = factored (design) shear stress vu = Vu/bvdv vutest = Vtest/bvdv or Vtest/bwd vxy = shear stress yt = distance from neutral axis to extreme tension fiber for uncracked section α = angle of inclination of transverse reinforcement to longitudinal axis of member αp = angle between prestressing force and longitudinal axis of member (JSCE 1986) β = factor relating effect of longitudinal strain on the shear capacity of concrete, as indicated by the ability of diagonally cracked concrete to transmit tension βd = depth effect parameter in JSCE shear strength evaluation procedure βn = coefficient to account for prestress and axial load in JSCE shear strength evaluation procedure βp = coefficient to account for longitudinal reinforcement ratio effect in JSCE shear strength evaluation method γxy = shear strain 1 = strain in concrete in direction 1; principal tensile strain 2 = strain in concrete in direction 2
52 t = strain at level of longitudinal reinforcement on tension side of member x = strain in direction x; longitudinal strain at mid-depth of section y = strain in direction y; strain at yield of reinforcing steel θ = angle of inclination of diagonal compressive stress ν = parameter determining maximum nominal shear capacity for EC2 method Ï = resistance factor Ïl = longitudinal reinforcement ratio = [As + Aps]/bwd Ïsx = steel ratio for direction x Ïsy = steel ratio for direction y Ïv = ratio of area of vertical shear reinforcement to area of gross concrete area of a horizontal section = Av/bws Ïw = As/bwd
