Distribution of vehicular loads on bridge girders by the FEA using ADINA: modeling, simulation, and comparison

doi:10.1016/S0045-7949(99)00032-2

Computers & Structures

Volume 72, Issues 1–3, July–August 1999, Pages 127-139

https://doi.org/10.1016/S0045-7949(99)00032-2 Get rights and content

Abstract

This paper discusses how a general finite element (FE) code, such as ADINA, can be used to effectively and efficiently model the bridge superstructure system subjected to moving traffic loads and further to predict the accurate lateral distribution of such live loads on bridge longitudinal girders. An input generator suited for the ADINA Program was developed to facilitate the preparation of the tedious FE data as required, especially the varying movable loads. FE modeling techniques and features using the family of ADINA programs are presented and discussed in detail. Live-load distribution factors derived from the FE method are compared with those obtained by the other methods. Advantages of the FE method are also highlighted.

Introduction

Distribution of vehicular live loads is a vital issue concerning the safety and economy of highway bridges. Currently, for convenience and easiness the majority of bridge engineers still use the empirical formula or simplified method as specified in the bridge design codes [1], [2] to estimate the distribution of vehicular loads on main bridge girders. To understand the limitations and drawbacks of these practical design methods, a brief description of them is offered as follows.

The forever-used AASHTO’s empirical formula for estimating the distribution factor (g) for girders, after converting to the SI units, is [1] $g= S 3.35 on per wheel basis$ where S=(average) center-to-center transverse spacing between bridge girders (m), limited to 4.3 m.

Eq. (1) was intended for predicting the bending moment at the first interior girder of a nonskewed, simply-supported bridge. This empirical formula is generally too conservative in most cases, while it could result in unsafe girder designs in some situations. For exterior girders, the old design code [1] suggests that the simple beam theory be used to estimate the g factor. Furthermore, as a good bridge practice, the exterior girders should be designed to be no weaker than the interior girders regardless of which design code is used.

The improved but yet simplified method employs the following moment distribution factor formulae (on per wheel basis) for I-shaped interior girders in a nonskewed bridge [2].

For one design lane loaded, $g_{int} =0.06+ S 4300^{0.4} S L^{0.3} K_{g} Lt^{3}_{s}^{0.1}$ For two or more design lanes loaded, $g_{int} =0.075+ S 4300^{0.6} S L^{0.2} K_{g} Lt^{3}_{s}^{0.1}$ where S=center-to-center transverse spacing between girders (=1100–4900 mm), t_s=slab thickness (110–300 mm), L=bridge span length (6000–73000 mm), and K_g=a longitudinal stiffness parameter depending upon the materials and geometries of the deck and girders.

It should be noted that AASHTO LRFD multiple presence factor (live-load intensity reduction factor) (m) has been implicitly built in , . The m factors are: 1.2 (N_L=1), 1.0 (N_L=2), 0.85 (N_L=3), and 0.65 (N_L≥4), where N_L=number of loaded lanes [2]. In other words, there is no need to multiply an m factor when , is exercised.

For I-shaped exterior girders, the LRFD simplified method² adopts the following moment distribution factor formulae (on per wheel basis).

For one design lane loaded, g_ext is determined by the simple beam theory.

For two or more design lanes loaded, $g_{ext} = 0.6+ d_{e} 3000 g_{int}$ where g_int is obtained from Eq. (3),d_e=distance between the center of the exterior girder and the interior edge of parapet (=−300–1700 mm, d_e<0 if the parapet located inside of the exterior girder).

AASHTO LRFD Code [2] also states that for bridges with intermediate diaphragms g_ext shall be taken not less than that which would be obtained by assuming a ‘rigid’ cross-section. This mandatory special check on exterior girders is merely a safeguard, and is deemed too conservative as shown in the section of results and discussions. In general, the LRFD simplified method [2] also results in conservative girder designs though not as conservative as compared to the empirical formula, Eq. (1).

As can be understood, both the AASHTO empirical and LRFD simplified methods have certain applicability limits. They are generally intended for bridges with regular geometry and common dimensions. Since personal computers have become more and more powerful in terms of speed and memory, it is time to fully adopt a general finite element (FE) code, such as ADINA Program, to aid bridge designs in a more efficient and effective way. Besides, the new bridge design code [2] emphasizes the significance of using a refined analysis method. Nevertheless, most of the bridge engineers with B.S. degree are somewhat reluctant to employ a FE code partly because they are not familiar with the FE method itself. The main objective of this paper is therefore to describe the detailed FE methodology and modeling techniques using ADINA and further to demonstrate to bridge engineers how friendly they can be when used to perform a bridge superstructure analysis efficiently and effectively.

Section snippets

Finite element modeling and analysis

Bridge superstructure system generally consists of deck/slab, parapets/barriers, transverse diaphragms and longitudinal girders, as shown in Fig. 1. For prediction of the lateral distribution of vehicular loads (referred as live loads in bridge design codes) on longitudinal girders, results from the preliminary study indicate that it is not necessary to model all structural components in detail as long as the deck and girders are included in the FE model. A general FE model is shown in Fig. 2.

Computations of M_comp and g using the FEA results

Theoretically, the composite girder moment, M_comp, should be computed by: $M_{comp} =M′_{b} + ∫ 0 b_{e} M_{slab} d x$ where M′_b=girder moment referenced to a plane within the bridge deck/slab, b_e=effective slab width, and M_slab=moment in the slab.

However, Eq. (9) can be best approximated by $M_{comp} =σ_{comb} S_{b,c}$ where S_b,c=composite section modulus at the bottom of a girder, and σ_comb=combined stress at the center of gravity (c.g.) of a girder simply computed by $σ_{comb} = P A + M S_{b}$ where A=cross-sectional area of a girder, S_b

Selective bridge examples and results

For checking the validity of the modeling and analysis techniques described in Section 3, benchmark studies were first conducted using the existing examples and experimental results. As a verification case, Fig. 5 demonstrates the excellence between the FE results and field measurements. Total statics checks were also made to further confirm the accuracy of the FE model. Appendix D contains a typical total statics check.

Finally, a number of FE analyses covering a wide range of bridge cases were

Discussion

As implied in Table 3, the distribution of vehicular loads on bridge girders is a rather complex issue. The first interior girder would be controlled by three loaded lanes, while the exterior girder could be governed by two loaded lanes, depending upon the system parameters (span length, deck overhang, deck width, girder type, girder spacing, configuration of vehicles, …). As shown in Table 4, Table 5, clearly the out-of-date AASHTO method [1] is the most conservative approach, while the FE

Conclusions and recommendations

This limited numerical study related to bridge superstructure analysis proves the following points:

•
The live-load distribution factors derived from the FE results are the lowest for all study cases, as compared to those obtained from the code-specified empirical formulae (See Table 4, Table 5). This implies a significant cost saving in girder construction if the FE method is employed. The cost for the FEA is merely a fraction of the total project cost.
•
It was interesting to note that the

Acknowledgements

The author wishes to express his gratitude to Professor A. Aswad and Professor J. Mays for assisting the development of the bridge input generator ‘BRGEN’.

References (6)

AASHTO. Standard Specifications for Highway Bridges. Washington, DC: American Association of State Highway and...
AASHTO. LRFD Bridge Design Specifications. Washington, DC: American Association of State Highway and Transportation...
M.E. Mabsout
Finite-element analysis of steel girder highway bridges
ASCE J Bridge Engineering
(1997)

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