Field Load Rating and Grillage Analysis Method for Skewed Steel Girder Highway Bridges
Publication: Journal of Bridge Engineering
Volume 26, Issue 11
Abstract
An innovative load rating method for skewed highway bridges with steel girders is proposed in this paper. In the proposed method, a field test coupled with a grillage analysis is used to determine the actual safe load-carrying capacity of a bridge and the key factors that contribute to the capacity. Because the actual behavior of the bridge is incorporated via the field test, the method provides a justifiable evaluation of system behavior. The effect of additional system stiffness due to bridge skew is determined using a grillage analysis. The proposed method allows the factors that contribute to the load rating, such as critical span adjustment, longitudinal and lateral load distribution, unintended composite action, slab flexure, and additional system stiffness, to be quantified and qualified. The proposed method is illustrated using a case study of a symmetric steel girder bridge with a 43° skew angle. The case study demonstrates that the proposed method provides an accurate determination of the skew effect, compared to approximate methods of analysis, because the location of the girder and moment under consideration, the cross frames and parapets, and the location of the applied loading are explicitly incorporated.
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Acknowledgments
This study was funded by the Wyoming Department of Transportation (WYDOT) and the Federal Highway Administration (FHWA) under Grant No. RS06216. The first author was also supported through a graduate teaching assistantship provided by the State of Wyoming. The authors recognize Paul G. Cortez, WYDOT Assistant State Bridge Engineer, Operations, Randy Ringstmeyer, WYDOT Bridge Inspection Engineer, and WYDOT District 3 personnel for their assistance in the field tests. The views expressed in this paper are those of the authors and do not necessarily reflect the views of those acknowledged.
Notation
The following symbols are used in this paper:
- Agirder
- cross-sectional area of the girder;
- Aseq
- 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 eg in the LRFD Bridge Design Specifications (AASHTO 2020);
- CFA
- analytical adjustment factor due to skew;
- CFE
- experimental adjustment factor due to skew;
- D
- dead load effect on the bridge member;
- DFA
- analytical live load distribution factor;
- DFE
- experimental live load distribution factor;
- (EI)girder
- girder flexural stiffness;
- (EI)slab
- slab flexural stiffness;
- Fy
- minimum specified yield stress of steel;
- minimum specified compressive stress of concrete;
- I
- dynamic impact factor;
- Ieq
- equivalent moment of inertia;
- Igirder
- moment of inertia about the strong axis of the girder;
- Izz
- moment of inertia of the cross section relative to the strong axis;
- IA
- analytical dynamic impact factor;
- IE
- experimental dynamic impact factor;
- Jeq
- equivalent torsion constant;
- Kg
- bridge longitudinal stiffness;
- L
- bridge span length;
- LL
- live load effect on the bridge member;
- LLA
- analytical live load effect;
- LLE
- experimental live load effect;
- M
- moment corresponding to (M+ is the corresponding positive moment of , and M− is the corresponding negative moment of );
- maximum analytical moment due to a standardized design truck;
- negative moment obtained experimentally;
- Mexperimental
- moment corresponding to Mtotal ( is the corresponding positive moment of , and is the corresponding negative moment of );
- Mgirder
- internal moment due to live load in the noncomposite girder about its own axis;
- maximum positive moment at bridge outer span;
- negative moment at the outer pier;
- Mslab
- internal moment due to live load in the slab about its own axis;
- Mtotal
- total internal moment due to live load (, total internal moment at the positive moment and , total internal moment at the negative moment);
- MHS20
- maximum analytical moment due to the standardized HS20 design truck (, maximum positive analytical moment due to the standardized HS20 design truck and , maximum negative analytical moment due to the standardized HS20 design truck);
- MLE
- elastic longitudinal adjustment moment;
- MTRK
- maximum analytical moment due to the calibrated truck used in the field test (, maximum analytical moment due to the calibrated truck used in the field test at the positive moment);
- maximum analytical moment due to the calibrated truck used in the field test when the truck is at the outer span (, 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);
- mA
- analytical live load multipresence factor;
- mE
- 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 DFE);
- Rn
- capacity of the bridge member;
- RF
- rating factor;
- RFA
- analytical rating factor;
- RFE
- experimental rating factor;
- S
- spacing between girders;
- Sgirder
- 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;
- ts
- bridge slab thickness;
- θ
- bridge skew angle;
- σcg
- 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;
- summation of the total internal moment due to live load in each girder;
- analytical statical moment;
- statical moment based on the skewed bridge grillage model;
- statical moment based on the nonskewed bridge grillage model; and
- experimental statical moment.
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Received: Sep 23, 2020
Accepted: Jul 27, 2021
Published online: Aug 25, 2021
Published in print: Nov 1, 2021
Discussion open until: Jan 25, 2022
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