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Guide for Heat-Straightening of Damaged Steel Bridge Members

Appendix II: Nomenclature

a,b,c = Dimensional constants

bf = Flange width

bs = Width of stiffening element

C = Temperature in degrees Celsius

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

d = Depth of wide flange beam or primary plate element

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

dv = Depth of vee in flat plate

E = Modulus of elasticity

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

Fa = Stress factor for calculating plastic rotation in rolled shapes

Fl = Jacking load factor

Fs = Shape factor for calculating plastic rotation in rolled shapes

Fy = Yield stress

L = Span length of flexural member

L, Lr = Lengths between offsets

Lu = Length of free edge of flange before localized damage

Mj = Moment produced by jacking forces

Mp = Plastic moment capacity of a member

Mr = Residual moment

My = Moment at initial yield

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

P = Axial load in compression member

Pa = Total jacking force for an axially loaded member

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

Pj = Jacking force

Pn, Pf = Jacking force on near and far side of locally damaged flange

r = Radius of arbitrary circle on flange bulge

R = Actual radius of curvature

Rl = Jacking ratio M j / M p

Ry = Radius of curvature at initial yield

S = Section modulus

T = Heating temperature

tw = Web thickness

V = Width at open end of vee

W = Primary plate element width

yo = Initial out-of-straightness of compression member

yr = Measured offsets at point r

ymax = Distance from centroid to extreme fiber

Z = Plastic section modulus

α = Coefficient of thermal expansion

δf, δn = Deflection of locally damaged flange on far and near side, respectively

a = Coefficient of thermal expansion

δmax = Maximum deflection of laterally loaded beam

Δ = Lateral deflection of loaded member

ε = Actual strain

εe = Elastic strain at open end of vee

εmax = Actual strain at extreme fiber of member

εy = Strain at initial yield of material

γ = Distribution factor for heated composite beam

μ = Ratio of maximum strain to yield strain, εmaxy

φb = Basic plate rotation factor

φc = Plastic rotation of composite girder

φd = Degree of damage

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

θ = Vee angle

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

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

θw = Slope of web for beam with local flange damage

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Updated: 07/23/2013
Federal Highway Administration | 1200 New Jersey Avenue, SE | Washington, DC 20590 | 202-366-4000