Manual Estimation of Elastic Lateral Torsional Buckling Resistance of I-Section Members with Cross-Section Transitions

Data Availability Statement

Notation

b₂

second smallest flange width in the respective flange along the length of the member, mm;

b_eff

effective flange width, mm;

b_fc

compression flange width, mm;

b_ft

tension flange width, mm;

b_small

smallest flange width in the respective flange along the length of the member, mm;

C_b

lateral-torsional buckling modification factor for nonuniform member stress;

D

web height, mm;

D_sb

distance of the shear center to the bottom of the web depth, mm;

d_Smax

maximum shift in the shear center due to a step in cross-section geometry, mm;

E

modulus of elasticity, MPa;

F_nc

compression flange stress at the LTB strength limit, MPa;

F_y

specified minimum yield strength, MPa;

f_bu

factored compressive flexural stress, MPa;

h_o

distance between flange centroids, mm;

I_y

moment of inertia about y-axis of the cross-section, m⁴;

I_y.bot

moment of inertia about y-axis of the bottom flange, m⁴;

I_y.top

moment of inertia about y-axis of the top flange, m⁴;

J

St Venant’s torsional constant, m⁴;

L_b

length between points that are braced against lateral displacement of compression flanges or braced against twist of the cross-section, m;

M_cr1

elastic lateral-torsional buckling strength under uniform bending, kN·m;

M_L

internal moment at the left end of the unbraced length, kN·m;

M_M

internal moment at the middle of the unbraced length, kN·m;

M_n

moment at the LTB strength limit, kN·m;

M_R

internal moment at the right end of the unbraced length, kN·m;

M_u

LRFD required flexural strength, kN·m;

q

uniformly distributed load, kN/m;

R_m

moment gradient modification factor for reverse-curvature bending;

r_t

radius of gyration of the flange in flexural compression plus one-third of the web area in compression due to the application of major axis bending moment alone, mm;

S_xc

elastic section modulus referenced to compression flange, m³;

t_fc

compression flange thickness, mm;

t_ft

tension flange thickness, mm;

t_w

web thickness, mm;

x_inf

distance between the inflection point and the braced end corresponding to the smaller end moment, m;

x_small

fraction of the unbraced length consisting of the small section, mm;

α

ratio of the end moments;

χ

nonprismatic geometry factor;

γ_eLTB

ratio of the elastic lateral-torsional buckling moment to the required moment of a member;

ρ_top.base

monosymmetry of the smaller section before effective plate dimensions are used;

ρ

monosymmetry parameter; and

ζ

nondimensional measure of the nonlinearity of the moment diagrams.

References