Symbols and Abbreviations

ACross sectional area
AeEffective cross sectional area
AISIAmerican Iron and Steel Institute
AreaCross sectional area
ASCEAmerican Society of Civil Engineers
ASDAllowable Strength Design
BRequired bimoment strength
BaAllowable bimoment strength
ϕBnDesign bimoment strength
b/tRatio of flange width to thickness
CbxBending coefficient dependent on moment gradient for bending about the X axis
CbyBending coefficient dependent on moment gradient for bending about the Y axis
CmxMoment coefficient in interaction formula for bending about the X axis
CmyMoment coefficient in interaction formula for bending about the Y axis
CwTorsional warping constant
D/tRatio of outside diameter to thickness
D/wRatio of lip overall depth to flange flat width
d/tRatio of lip flat width to thickness
d₀/b₀Ratio of lip outside width to flange outside width
EModulus of elasticity (initial modulus for stainless steel)
exAxial load eccentricity in the X direction, measured from the origin with positive to the right
eyAxial load eccentricity in the Y direction, measured from the origin with positive up
FuLongitudinal ultimate tensile strength
FyYield strength
hHeight of the flat portion of a web
h/tRatio of web flat width to thickness
I₁Moment of inertia about the major axis
I₂Moment of inertia about the minor axis
IcPolar moment of inertia about the centroid
I₀Polar moment of inertia about the shear center
IxMoment of inertia about the X axis
IxeEffective moment of inertia about the X axis
IxyProduct of inertia about the X and Y axes
IyMoment of inertia about the Y axis
IyeEffective moment of inertia about the Y axis
JSt. Venant torsion constant
jxAsymmetry property for lateral-torsional buckling: (∫xdA + ∫xydA)/2Iy - x₀
jyAsymmetry property for lateral-torsional buckling: (∫ydA + ∫yxdA)/2Ix - y₀
KL/rSlenderness ratio of a compressive member
KxEffective length factor for buckling about the X axis ( in the Y direction)
KyEffective length factor for buckling about the Y axis ( in the X direction)
KtEffective length factor for torsional buckling
kPlate buckling coefficient
Rotational stiffness provided to a flange by attachment to deck or sheathing
LRFDLoad and Resistance Factor Design
LSDLimit States Design
LmDistance between discrete distortional buckling restraints
LxUnbraced length for buckling about the X axis (in the Y direction)
LyUnbraced length for buckling about the Y axis (in the X direction)
LtUnbraced length for torsional buckling
MaxAllowable moment strength about the X axis
MaxoAllowable moment strength about the X axis, based on yielding and local buckling (fully braced)
MayAllowable moment strength about the Y axis
MayoAllowable moment strength about the Y axis, based on yielding and local buckling (fully braced)
ϕMnxDesign moment strength about the X axis
ϕMnxoDesign moment strength about the X axis, based on yielding and local buckling (fully braced)
ϕMnyDesign moment strength about the Y axis
ϕMnyoDesign moment strength about the Y axis, based on yielding and local buckling (fully braced)
MxApplied moment about the X axis, positive moment has compression above the X axis
MyApplied moment about the Y axis, positive moment has compression to the right of the Y axis
NBearing length for web crippling check
nModified Ramberg-Osgood Equation coefficient, indicating the linearity of the stress-strain curve.
PApplied compressive force
PaAllowable compressive strength
PaAllowable web crippling strength for an element, perpendicular to the bearing flange
PaoAllowable compressive strength, based on initiation of yielding (fully braced)
PaxAllowable web crippling strength for an element, in the X direction
PayAllowable web crippling strength for an element, in the Y direction
ϕPnDesign axial compressive strength
ϕPnDesign web crippling strength for an element, perpendicular to the bearing flange
ϕPnoDesign axial compressive strength, based on initiation of yielding (fully braced)
ϕPnxDesign web crippling strength for an element, in the X direction
ϕPnyDesign web crippling strength for an element, in the Y direction
RMoment reduction factor for beam with braced tension flange
R/tRatio of inside bend radius to thickness
r₁Radius of gyration about the major axis
r₂Radius of gyration about the minor axis
rcPolar radius of gyration about the centroid
r₀Polar radius of gyration about the shear center
rxRadius of gyration about the X axis
ryRadius of gyration about the Y axis
Sx(b)Section modulus about the X axis for the extreme bottom fiber
Sxe(b)Effective section modulus about the X axis for the extreme bottom fiber
Sx(t)Section modulus about the X axis for the extreme top fiber
Sxe(t)Effective section modulus about the X axis for the extreme top fiber
Sy(l)Section modulus about the Y axis for the extreme left fiber
Sye(l)Effective section modulus about the Y axis for the extreme left fiber
Sy(r)Section modulus about the Y axis for the extreme right fiber
Sye(r)Effective section modulus about the Y axis for the extreme right fiber
tDesign thickness of the material
TaAllowable tensile strength
ϕTnDesign axial tensile strength
TsvInternal St. Venant (pure) torque
TwInternal warping torque
VaxAllowable shear strength in the horizontal direction
VayAllowable shear strength in the vertical direction
ϕVnxDesign shear strength in the horizontal direction
ϕVnyDesign shear strength in the vertical direction
VxApplied shear force in the horizontal direction
VyApplied shear force in the vertical direction
Wt.Weight per unit length for a section
wWidth of the flat portion of an element
w/tWidth to thickness ratio for an element
XHorizontal axis or dimension in the plane of the cross section, positive is to the right
x₀Horizontal coordinate of the shear center relative to the centroid
x(l)Horizontal distance from the centroid of the section to the extreme left fiber
x(r)Horizontal distance from the centroid of the section to the extreme right fiber
YVertical axis or dimension in the plane of the cross section, positive is up
y₀Vertical coordinate of the shear center relative to the centroid
y(b)Vertical distance from the centroid of the section to the extreme bottom fiber
y(t)Vertical distance from the centroid of the section to the extreme top fiber
ZxPlastic section modulus about the X axis
ZyPlastic section modulus about the Y axis
αAngle of the major axis with respect to the X axis, counter-clockwise is positive.