Field Load Rating and Grillage Analysis Method for Skewed Steel Girder Highway Bridges

Acknowledgments

Notation

A_girder

cross-sectional area of the girder;

A_seq

equivalent shear area;

A₁

design load factor for dead load effect;

A₂

design load factor for live load effect;

a

distance between the girder and slab centers of gravity; equivalent to e_g in the LRFD Bridge Design Specifications (AASHTO 2020);

CF_A

analytical adjustment factor due to skew;

CF_E

experimental adjustment factor due to skew;

D

dead load effect on the bridge member;

DF_A

analytical live load distribution factor;

DF_E

experimental live load distribution factor;

(EI)_girder

girder flexural stiffness;

(EI)_slab

slab flexural stiffness;

F_y

minimum specified yield stress of steel;

$f_c^{\mathrm{\prime }}$

minimum specified compressive stress of concrete;

I

dynamic impact factor;

I_eq

equivalent moment of inertia;

I_girder

moment of inertia about the strong axis of the girder;

I_zz

moment of inertia of the cross section relative to the strong axis;

I_A

analytical dynamic impact factor;

I_E

experimental dynamic impact factor;

J_eq

equivalent torsion constant;

K_g

bridge longitudinal stiffness;

L

bridge span length;

LL

live load effect on the bridge member;

LL_A

analytical live load effect;

LL_E

experimental live load effect;

M

moment corresponding to $M_{\mathrm{TRK}\mathrm{\_}\mathrm{OS}}$ (M⁺ is the corresponding positive moment of $M_{\mathrm{TRK}\mathrm{\_}\mathrm{OS}}^{-}$, and M⁻ is the corresponding negative moment of $M_{\mathrm{TRK}}^{+}$);

$M_{\mathrm{design}\mathrm{\_}\mathrm{truck}}$

maximum analytical moment due to a standardized design truck;

$M_{\exp .}^{-}$

negative moment obtained experimentally;

M_experimental

moment corresponding to M_total ($M_{\mathrm{experimental}}^{+}$ is the corresponding positive moment of $M_{\mathrm{total}}^{-}$, and $M_{\mathrm{experimental}}^{-}$ is the corresponding negative moment of $M_{\mathrm{total}}^{+}$);

M_girder

internal moment due to live load in the noncomposite girder about its own axis;

$M_{\max }^{+}$

maximum positive moment at bridge outer span;

$M_{\mathrm{pier}}^{-}$

negative moment at the outer pier;

M_slab

internal moment due to live load in the slab about its own axis;

M_total

total internal moment due to live load ($M_{\mathrm{total}}^{+}$, total internal moment at the positive moment and $M_{\mathrm{total}}^{-}$, total internal moment at the negative moment);

M_HS20

maximum analytical moment due to the standardized HS20 design truck ($M_{\mathrm{HS}20}^{+}$, maximum positive analytical moment due to the standardized HS20 design truck and $M_{\mathrm{HS}20}^{-}$, maximum negative analytical moment due to the standardized HS20 design truck);

M_LE

elastic longitudinal adjustment moment;

M_TRK

maximum analytical moment due to the calibrated truck used in the field test ($M_{\mathrm{TRK}}^{+}$, maximum analytical moment due to the calibrated truck used in the field test at the positive moment);

$M_{\mathrm{TRK}\mathrm{\_}\mathrm{OS}}$

maximum analytical moment due to the calibrated truck used in the field test when the truck is at the outer span ($M_{\mathrm{TR}{\mathrm{K}}_{\mathrm{OS}}}^{-}$, maximum analytical moment due to the calibrated truck used in the field test when the truck is at the outer span at the negative moment);

m_A

analytical live load multipresence factor;

m_E

experimental live load multipresence factor;

N

axial force due to live load in the girder;

n

modular ratio between steel and concrete;

nr

number of lanes loaded (used for the calculation of DF_E);

R_n

capacity of the bridge member;

RF

rating factor;

RF_A

analytical rating factor;

RF_E

experimental rating factor;

S

spacing between girders;

S_girder

section modulus of the girder cross section;

STAT

total the statical moment;

STAT⁺

positive contribution of the statical moment;

STAT⁻

negative contribution of the statical moment;

t_s

bridge slab thickness;

θ

bridge skew angle;

σ_cg

total stress due to live load at the center of gravity of the girder;

σ₀

total stress due to live load at bottom of the bottom flange of the girder;

$\sum M_{\mathrm{total}}$

summation of the total internal moment due to live load in each girder;

$\sum \mathrm{STA}{\mathrm{T}}_A$

analytical statical moment;

$\sum \mathrm{STA}{\mathrm{T}}_{\mathrm{A}\mathrm{\_}\mathrm{SK}}$

statical moment based on the skewed bridge grillage model;

$\sum \mathrm{STA}{\mathrm{T}}_{\mathrm{A}\mathrm{\_}\mathrm{ST}}$

statical moment based on the nonskewed bridge grillage model; and

$\sum \mathrm{STA}{\mathrm{T}}_E$

experimental statical moment.

References