A | Cross sectional area |
Ae | Effective cross sectional area |
AISI | American Iron and Steel Institute |
Area | Cross sectional area |
ASCE | American Society of Civil Engineers |
ASD | Allowable Strength Design |
B | Required bimoment strength |
Ba | Allowable bimoment strength |
ϕBn | Design bimoment strength |
b/t | Ratio of flange width to thickness |
Cbx | Bending coefficient dependent on moment gradient for bending about the X axis |
Cby | Bending coefficient dependent on moment gradient for bending about the Y axis |
Cmx | Moment coefficient in interaction formula for bending about the X axis |
Cmy | Moment coefficient in interaction formula for bending about the Y axis |
Cw | Torsional warping constant |
D/t | Ratio of outside diameter to thickness |
D/w | Ratio of lip overall depth to flange flat width |
d/t | Ratio of lip flat width to thickness |
d₀/b₀ | Ratio of lip outside width to flange outside width |
E | Modulus of elasticity (initial modulus for stainless steel) |
ex | Axial load eccentricity in the X direction, measured from the origin with positive to the right |
ey | Axial load eccentricity in the Y direction, measured from the origin with positive up |
Fu | Longitudinal ultimate tensile strength |
Fy | Yield strength |
h | Height of the flat portion of a web |
h/t | Ratio of web flat width to thickness |
I₁ | Moment of inertia about the major axis |
I₂ | Moment of inertia about the minor axis |
Ic | Polar moment of inertia about the centroid |
I₀ | Polar moment of inertia about the shear center |
Ix | Moment of inertia about the X axis |
Ixe | Effective moment of inertia about the X axis |
Ixy | Product of inertia about the X and Y axes |
Iy | Moment of inertia about the Y axis |
Iye | Effective moment of inertia about the Y axis |
J | St. Venant torsion constant |
jx | Asymmetry property for lateral-torsional buckling:
(∫x³dA + ∫xy²dA)/2Iy - x₀ |
jy | Asymmetry property for lateral-torsional buckling:
(∫y³dA + ∫yx²dA)/2Ix - y₀ |
KL/r | Slenderness ratio of a compressive member |
Kx | Effective length factor for buckling about the X axis ( in the Y direction) |
Ky | Effective length factor for buckling about the Y axis ( in the X direction) |
Kt | Effective length factor for torsional buckling |
k | Plate buckling coefficient |
kϕ | Rotational stiffness provided to a flange by attachment to deck or sheathing |
LRFD | Load and Resistance Factor Design |
LSD | Limit States Design |
Lm | Distance between discrete distortional buckling restraints |
Lx | Unbraced length for buckling about the X axis (in the Y direction) |
Ly | Unbraced length for buckling about the Y axis (in the X direction) |
Lt | Unbraced length for torsional buckling |
Max | Allowable moment strength about the X axis |
Maxo | Allowable moment strength about the X axis, based on yielding and local buckling (fully braced) |
May | Allowable moment strength about the Y axis |
Mayo | Allowable moment strength about the Y axis, based on yielding and local buckling (fully braced) |
ϕMnx | Design moment strength about the X axis |
ϕMnxo | Design moment strength about the X axis, based on yielding and local buckling (fully braced) |
ϕMny | Design moment strength about the Y axis |
ϕMnyo | Design moment strength about the Y axis, based on yielding and local buckling (fully braced) |
Mx | Applied moment about the X axis, positive moment has compression above the X axis |
My | Applied moment about the Y axis, positive moment has compression to the right of the Y axis |
N | Bearing length for web crippling check |
n | Modified Ramberg-Osgood Equation coefficient, indicating the linearity of the stress-strain curve. |
P | Applied compressive force |
Pa | Allowable compressive strength |
Pa | Allowable web crippling strength for an element, perpendicular to the bearing flange |
Pao | Allowable compressive strength, based on initiation of yielding (fully braced) |
Pax | Allowable web crippling strength for an element, in the X direction |
Pay | Allowable web crippling strength for an element, in the Y direction |
ϕPn | Design axial compressive strength |
ϕPn | Design web crippling strength for an element, perpendicular to the bearing flange |
ϕPno | Design axial compressive strength, based on initiation of yielding (fully braced) |
ϕPnx | Design web crippling strength for an element, in the X direction |
ϕPny | Design web crippling strength for an element, in the Y direction |
R | Moment reduction factor for beam with braced tension flange |
R/t | Ratio of inside bend radius to thickness |
r₁ | Radius of gyration about the major axis |
r₂ | Radius of gyration about the minor axis |
rc | Polar radius of gyration about the centroid |
r₀ | Polar radius of gyration about the shear center |
rx | Radius of gyration about the X axis |
ry | Radius 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 |
t | Design thickness of the material |
Ta | Allowable tensile strength |
ϕTn | Design axial tensile strength |
Tsv | Internal St. Venant (pure) torque |
Tw | Internal warping torque |
Vax | Allowable shear strength in the horizontal direction |
Vay | Allowable shear strength in the vertical direction |
ϕVnx | Design shear strength in the horizontal direction |
ϕVny | Design shear strength in the vertical direction |
Vx | Applied shear force in the horizontal direction |
Vy | Applied shear force in the vertical direction |
Wt. | Weight per unit length for a section |
w | Width of the flat portion of an element |
w/t | Width to thickness ratio for an element |
X | Horizontal axis or dimension in the plane of the cross section, positive is to the right |
x₀ | Horizontal 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 |
Y | Vertical axis or dimension in the plane of the cross section, positive is up |
y₀ | Vertical 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 |
Zx | Plastic section modulus about the X axis |
Zy | Plastic section modulus about the Y axis |
α | Angle of the major axis with respect to the X axis, counter-clockwise is positive. |