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OCR for page 50
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
fc = 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)( 0.9f c )
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
OCR for page 51
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 = Vcot
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 dvcot 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 = Vn
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/bv dv
vutest = Vtest/bv dv or Vtest/bw d
vxy = shear stress
yt = distance from neutral axis to extreme tension fiber for uncracked section
= angle of inclination of transverse reinforcement to longitudinal axis of member
p = angle between prestressing force and longitudinal axis of member (JSCE 1986)
= factor relating effect of longitudinal strain on the shear capacity of concrete, as indicated by the ability of diagonally
cracked concrete to transmit tension
d = depth effect parameter in JSCE shear strength evaluation procedure
n = coefficient to account for prestress and axial load in JSCE shear strength evaluation procedure
p = coefficient to account for longitudinal reinforcement ratio effect in JSCE shear strength evaluation method
xy = shear strain
1 = strain in concrete in direction 1; principal tensile strain
2 = strain in concrete in direction 2
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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
= angle of inclination of diagonal compressive stress
= parameter determining maximum nominal shear capacity for EC2 method
= resistance factor
l = longitudinal reinforcement ratio = [As + Aps]/bw d
sx = steel ratio for direction x
sy = steel ratio for direction y
v = ratio of area of vertical shear reinforcement to area of gross concrete area of a horizontal section = Av/bw s
w = As/bw d
