Guide for Heat-Straightening of Damaged Steel Bridge Members

Appendix II: Nomenclature

a,b,c = Dimensional constants

b_f = Flange width

b_s = Width of stiffening element

C = Temperature in degrees Celsius

c_d = Chord length across the yield zone of a curved beam

d = Depth of wide flange beam or primary plate element

d_s = Distance between the vee apex edge of the primary plate element and the stiffening element

d_v = Depth of vee in flat plate

E = Modulus of elasticity

f_a = Axial stress in a compression member due to live and dead loads

F_a = Stress factor for calculating plastic rotation in rolled shapes

F = Jacking load factor

F_s = Shape factor for calculating plastic rotation in rolled shapes

F_y = Yield stress

= Span length of flexural member

L, L_r = Lengths between offsets

L_u = Length of free edge of flange before localized damage

M_j = Moment produced by jacking forces

M_p = Plastic moment capacity of a member

M_r = Residual moment

M_y = Moment at initial yield

n = Number of single vee heats required to remove a specified amount of damage

P = Axial load in compression member

P_a = Total jacking force for an axially loaded member

P_ec = Additional jacking force required to cancel eccentric moments due to axial loads

P_j = Jacking force

P_n, P_f = Jacking force on near and far side of locally damaged flange

r = Radius of arbitrary circle on flange bulge

R = Actual radius of curvature

R = Jacking ratio M _j / M _p

R_y = Radius of curvature at initial yield

S = Section modulus

T = Heating temperature

t_w = Web thickness

V = Width at open end of vee

W = Primary plate element width

y_o = Initial out-of-straightness of compression member

y_r = Measured offsets at point r

y_max = Distance from centroid to extreme fiber

Z = Plastic section modulus

α = Coefficient of thermal expansion

δ_f, δ_n = Deflection of locally damaged flange on far and near side, respectively

a = Coefficient of thermal expansion

δ_max = Maximum deflection of laterally loaded beam

Δ = Lateral deflection of loaded member

ε = Actual strain

ε_e = Elastic strain at open end of vee

ε_max = Actual strain at extreme fiber of member

ε_y = Strain at initial yield of material

γ = Distribution factor for heated composite beam

μ = Ratio of maximum strain to yield strain, ε_max/ε_y

φ_b = Basic plate rotation factor

φ_c = Plastic rotation of composite girder

φ_d = Degree of damage

φ_p = Plastic rotation resulting from a single vee heat on a plate or rolled shape

θ = Vee angle

θ_f = Slope of flange on side away from impact for locally damaged member

θ_n = Slope of flange on impact side of locally damaged flange

θ_w = Slope of web for beam with local flange damage