This article notes that the truss bridge contains the potential for achieving a high degree of re... more This article notes that the truss bridge contains the potential for achieving a high degree of redundancy if properly designed and if trusses, floorbeams, and the longitudinal stringer elements are properly interconnected. The effectiveness of such design relies on the adequacy of the analysis method used to quantify the level of redundancy. Although such an assessment is generally very difficult, it is relatively straightformward in the case of the highway truss bridge where the primary and alternate load paths are generally well defined. It is pointed out that the acceptability of the highway truss bridge is highly dependent upon the analysis method which quantifies structural redundancy levels in the design and evluation of the highway bridge system.
A discussion of a paper with the aforementioned title by Hsu, Fu, and Schelling, published in thi... more A discussion of a paper with the aforementioned title by Hsu, Fu, and Schelling, published in this journal (Volume 121, Number 3, March 1995), is presented. Discussers Cortinez and Piovan report that the EBEF method for the distortional analysis of box girder bridges proposed by the authors is more versatile than the traditional beam on elastic foundation (BEF) analysis because it can be applied with great simplicity to more complex problems, such as varied sections and multispan beams. Cortinez and Piovan present an alternative finite-element (FE) formulation, based on exact solution, that is more convenient, for some situations, than the authors' approach. Discussion is followed by closure from the authors.
The effect of steel bridge diaphragms, with partial warping restraint, on the torsional behavior ... more The effect of steel bridge diaphragms, with partial warping restraint, on the torsional behavior of the grid model is presented. The element stiffness matrix is developed from thin-walled beam theory and can be easily implemented into a computer program, which will make the analytical process more practical and efficient. A numerical example that shows the effect of partial warping is also presented. The results of the example clearly exhibits that the warping boundary condition provided by the diaphragm elements can increase the torsional constants of the main girder.
Journal of Performance of Constructed Facilities, 2004
ABSTRACT This paper reports the bridge damage in the Chi Chi earthquake. Damage to bridge structu... more ABSTRACT This paper reports the bridge damage in the Chi Chi earthquake. Damage to bridge structures may occur in the superstructure, the substructure, or the approaches. Typical types of damage are discussed and illustrated in this paper. A review of the design specifications in Taiwan is also presented to give the background on the seismic design of highway bridges in Taiwan.
In this paper, a method for designing a statistically valid sample of bridges is proposed. The ne... more In this paper, a method for designing a statistically valid sample of bridges is proposed. The need for such a sampling procedure arises from the impracticality of a detailed analysis of the structural effects of new candidate truck configurations on the whole bridge inventory. In this study, a set of bridges from the national inventory was determined for the purpose of selecting a bridge sample. This set of bridges is referred to as the population. The selection of bridges for inclusion in the population was based on the status of the bridge, type of service, structural material, structural system type and functional class. The stratified sampling method was used in the determination of the required sample sizes. According to this method, the population was first divided into sub‐populations, or strata. These sub‐populations were non‐overlapping. In turn, each strata was divided into sub‐strata. The characteristics of each sub‐stratum were estimated and combined to determine the ch...
Contained herein are the results of research which quantifies the effects that various existing a... more Contained herein are the results of research which quantifies the effects that various existing and projected truck configurations have as live loadings upon bridges which currently exist on the National Bridge Inventory (NBI). The truck configurations were determined from those actual or proposed vehicles which exhibit the highest GVW and which either are causing or are perceived to cause the highest levels of overstress on bridge superstructure elements.In order to simulate most accurately the actual field conditions, a criterion was defined which contained three major requirements: 1) The bridges utilized within the study shall be defined as being a statistically significant sample and be actual bridges taken from the NBI; 2) The analysis method shall be consistent with those actually used by engineers in designing and rating bridges, and; 3) The criteria utilized in evaluating the various bridge structures under the defined loadings shall be consistent with current practices.The...
4bstract-The purpose of this study is to develop a more exact horizontally curved beam finite ele... more 4bstract-The purpose of this study is to develop a more exact horizontally curved beam finite element n a cylindrical coordinate system. The variation method is used to formulate the stiffness matrix and the-esults of the solution are compared with another study using a closed form solution. The stiffness matrix 'or a curved beam element can be used in analyzing the behavior of horizontally curved bridges for either Jpen or closed sections.
A simple, easy-to-apply effective torsional constant for the rotational stiffness of a restrained... more A simple, easy-to-apply effective torsional constant for the rotational stiffness of a restrained open section was developed. This effective torsional constant takes both the pure torsion and the warping torsion into account. The final result is a simple formula for a modified torsional constant, which is in terms of unbraced length and can be easily calculated. The constant then can be used for any generic finite-element structural analysis program.
A methodology is developed to more accurately estimate the static response of bridges due to movi... more A methodology is developed to more accurately estimate the static response of bridges due to moving vehicles. The method can also be used to predict dynamic responses induced by moving vehicles using weigh-in-motion (WIM) techniques. Historically, WIM is a well-developed technology used in highway research, since it has the advantage of allowing for the stealthy automatic collection of weight data for heavy trucks. However, the lack of accuracy in determining the dynamic effect in bridges has limited the potential for its use in estimating the fatigue life of bridge structures and their components. The method developed herein amends the current WIM procedures by filtering the dynamic responses accurately using the Fast Fourier Transform (FFT). Example applications of the proposed method are shown by using computer-generated data. The method is fast and improves the predicted truck weight up to 5% of the actual weight, as compared to errors up to 10% using the current WIM methods.Key...
A cost optimized design method of steel bridge girders is studied by using the specifications of ... more A cost optimized design method of steel bridge girders is studied by using the specifications of the American Association of State Highway and Transportation (AASHTO) Working Stress Design (WSD) method and Load Factor Design (LFD) alternates. Here, cost trade+ffs for the steel plate (e.g., the base price plus extras for size, grade, testing and inspection, etc.), stiffeners and splicing are weighed throughout the entire span to minimize the objective function. The method is then applied to a set of over 30 steel bridge structures which collected from various state bridge inventories in order to obtain optimal cost configurations for both WSD and LFD methods. These results are analyzed by a linear regression model to define relationships between cast differences and bridge lengths. From these comparisons. conclusions are drawn to provide the guidelines. It is believed that effective application of these guidelines should lead to more economical designs, especially under the LFD method.
International Journal of Mechanical Sciences, 2008
ABSTRACT The exact stiffness matrix for the spatially coupled stability analysis of thin-walled c... more ABSTRACT The exact stiffness matrix for the spatially coupled stability analysis of thin-walled curved beam with non-symmetric cross-section subjected to uniform compression is newly presented. For this, the elastic strain energy including the axially/flexurally/torsionally coupled terms and the potential energy due to the initial stress resultant are introduced. Then, equilibrium equations and force–deformation relationship are derived from the energy principle and explicit expressions for displacement parameters are derived based on power series expansions of displacement components. Next, the exact element stiffness matrix is determined using force–deformation relationships. In order to verify the accuracy of this study, the numerical solutions are presented and compared with the finite element solutions using the Hermitian curved beam elements. In addition, the coupling of symmetric and anti-symmetric modes at the buckling load crossover with change in curvature of beam is investigated.
To study the effect of stress-activated positive hole (p-hole) charge carriers on the infrared (I... more To study the effect of stress-activated positive hole (p-hole) charge carriers on the infrared (IR) emission from rocks, we subjected a portion (∼10 vol.%) of a large (30×60×7.5 cm 3) block of anorthosite, a nearly monomineralic (Ca-rich feldspar) igneous rock, to uniaxial deviatory stress up to failure. We measured the IR emission from a flat surface ≈40 cm from the stressed rock volume over the 800-1300 cm −1 (7.7-12.5 µm) range. Instantly, upon loading, the emission spectrum and intensity change. At first narrow bands appear at 930 cm −1 (10.75 µm), 880 cm −1 (11.36 µm), 820 cm −1 (12.4 µm) plus additional narrow bands in the 1000-1300 cm −1 (7.7-10.0 µm) range. The 10.75-12.4 µm bands are thought to arise from vibrationally excited O-O stretching modes, which form when p-hole charge carriers, which spread from the stressed rock volume into the unstressed rock, recombine at the surface. They radiatively decay, giving rise to "hot" bands due to transitions between excited states. Before failure the broad emission bands at 1170 cm −1 and 1030 cm −1 (8.7 and 9.7 µm) also increase slightly in intensity, suggesting a small increase in temperature due to thermalization of the energy deposited into the surface through p-hole recombination. Stimulated IR emission due to hole-hole recombination and its followon effects may help understand the enhanced IR emission seen in night-time satellite images of the land surface before major earthquakes known as "thermal anomalies".
Based on the power series method, the static and dynamic stiffness matrices for the flexural-tors... more Based on the power series method, the static and dynamic stiffness matrices for the flexural-torsional buckling and free vibration analysis of thin-walled beam with non-symmetric cross-section subjected to linearly variable axial force are newly presented. Additionally, the static stiffness matrix for the lateral buckling analysis of non-symmetric beam is presented for the first time. For this, the elastic strain energy, the potential energy considering the second-order terms of finite rotations, and the kinetic energy for thin-walled beam with non-symmetric cross-section are introduced. Then equations of motion and force-deformation relations are derived from the energy principle. Explicit expressions for displacement parameters are derived based on power series expansions of displacement components. Finally, the static and dynamic element stiffness matrices are determined using force-deformation relationships. In order to verify the accuracy of this study, the numerical solutions are presented and compared with the finite element solutions using the Hermitian beam elements and ABAQUS's shell elements.
This article notes that the truss bridge contains the potential for achieving a high degree of re... more This article notes that the truss bridge contains the potential for achieving a high degree of redundancy if properly designed and if trusses, floorbeams, and the longitudinal stringer elements are properly interconnected. The effectiveness of such design relies on the adequacy of the analysis method used to quantify the level of redundancy. Although such an assessment is generally very difficult, it is relatively straightformward in the case of the highway truss bridge where the primary and alternate load paths are generally well defined. It is pointed out that the acceptability of the highway truss bridge is highly dependent upon the analysis method which quantifies structural redundancy levels in the design and evluation of the highway bridge system.
A discussion of a paper with the aforementioned title by Hsu, Fu, and Schelling, published in thi... more A discussion of a paper with the aforementioned title by Hsu, Fu, and Schelling, published in this journal (Volume 121, Number 3, March 1995), is presented. Discussers Cortinez and Piovan report that the EBEF method for the distortional analysis of box girder bridges proposed by the authors is more versatile than the traditional beam on elastic foundation (BEF) analysis because it can be applied with great simplicity to more complex problems, such as varied sections and multispan beams. Cortinez and Piovan present an alternative finite-element (FE) formulation, based on exact solution, that is more convenient, for some situations, than the authors' approach. Discussion is followed by closure from the authors.
The effect of steel bridge diaphragms, with partial warping restraint, on the torsional behavior ... more The effect of steel bridge diaphragms, with partial warping restraint, on the torsional behavior of the grid model is presented. The element stiffness matrix is developed from thin-walled beam theory and can be easily implemented into a computer program, which will make the analytical process more practical and efficient. A numerical example that shows the effect of partial warping is also presented. The results of the example clearly exhibits that the warping boundary condition provided by the diaphragm elements can increase the torsional constants of the main girder.
Journal of Performance of Constructed Facilities, 2004
ABSTRACT This paper reports the bridge damage in the Chi Chi earthquake. Damage to bridge structu... more ABSTRACT This paper reports the bridge damage in the Chi Chi earthquake. Damage to bridge structures may occur in the superstructure, the substructure, or the approaches. Typical types of damage are discussed and illustrated in this paper. A review of the design specifications in Taiwan is also presented to give the background on the seismic design of highway bridges in Taiwan.
In this paper, a method for designing a statistically valid sample of bridges is proposed. The ne... more In this paper, a method for designing a statistically valid sample of bridges is proposed. The need for such a sampling procedure arises from the impracticality of a detailed analysis of the structural effects of new candidate truck configurations on the whole bridge inventory. In this study, a set of bridges from the national inventory was determined for the purpose of selecting a bridge sample. This set of bridges is referred to as the population. The selection of bridges for inclusion in the population was based on the status of the bridge, type of service, structural material, structural system type and functional class. The stratified sampling method was used in the determination of the required sample sizes. According to this method, the population was first divided into sub‐populations, or strata. These sub‐populations were non‐overlapping. In turn, each strata was divided into sub‐strata. The characteristics of each sub‐stratum were estimated and combined to determine the ch...
Contained herein are the results of research which quantifies the effects that various existing a... more Contained herein are the results of research which quantifies the effects that various existing and projected truck configurations have as live loadings upon bridges which currently exist on the National Bridge Inventory (NBI). The truck configurations were determined from those actual or proposed vehicles which exhibit the highest GVW and which either are causing or are perceived to cause the highest levels of overstress on bridge superstructure elements.In order to simulate most accurately the actual field conditions, a criterion was defined which contained three major requirements: 1) The bridges utilized within the study shall be defined as being a statistically significant sample and be actual bridges taken from the NBI; 2) The analysis method shall be consistent with those actually used by engineers in designing and rating bridges, and; 3) The criteria utilized in evaluating the various bridge structures under the defined loadings shall be consistent with current practices.The...
4bstract-The purpose of this study is to develop a more exact horizontally curved beam finite ele... more 4bstract-The purpose of this study is to develop a more exact horizontally curved beam finite element n a cylindrical coordinate system. The variation method is used to formulate the stiffness matrix and the-esults of the solution are compared with another study using a closed form solution. The stiffness matrix 'or a curved beam element can be used in analyzing the behavior of horizontally curved bridges for either Jpen or closed sections.
A simple, easy-to-apply effective torsional constant for the rotational stiffness of a restrained... more A simple, easy-to-apply effective torsional constant for the rotational stiffness of a restrained open section was developed. This effective torsional constant takes both the pure torsion and the warping torsion into account. The final result is a simple formula for a modified torsional constant, which is in terms of unbraced length and can be easily calculated. The constant then can be used for any generic finite-element structural analysis program.
A methodology is developed to more accurately estimate the static response of bridges due to movi... more A methodology is developed to more accurately estimate the static response of bridges due to moving vehicles. The method can also be used to predict dynamic responses induced by moving vehicles using weigh-in-motion (WIM) techniques. Historically, WIM is a well-developed technology used in highway research, since it has the advantage of allowing for the stealthy automatic collection of weight data for heavy trucks. However, the lack of accuracy in determining the dynamic effect in bridges has limited the potential for its use in estimating the fatigue life of bridge structures and their components. The method developed herein amends the current WIM procedures by filtering the dynamic responses accurately using the Fast Fourier Transform (FFT). Example applications of the proposed method are shown by using computer-generated data. The method is fast and improves the predicted truck weight up to 5% of the actual weight, as compared to errors up to 10% using the current WIM methods.Key...
A cost optimized design method of steel bridge girders is studied by using the specifications of ... more A cost optimized design method of steel bridge girders is studied by using the specifications of the American Association of State Highway and Transportation (AASHTO) Working Stress Design (WSD) method and Load Factor Design (LFD) alternates. Here, cost trade+ffs for the steel plate (e.g., the base price plus extras for size, grade, testing and inspection, etc.), stiffeners and splicing are weighed throughout the entire span to minimize the objective function. The method is then applied to a set of over 30 steel bridge structures which collected from various state bridge inventories in order to obtain optimal cost configurations for both WSD and LFD methods. These results are analyzed by a linear regression model to define relationships between cast differences and bridge lengths. From these comparisons. conclusions are drawn to provide the guidelines. It is believed that effective application of these guidelines should lead to more economical designs, especially under the LFD method.
International Journal of Mechanical Sciences, 2008
ABSTRACT The exact stiffness matrix for the spatially coupled stability analysis of thin-walled c... more ABSTRACT The exact stiffness matrix for the spatially coupled stability analysis of thin-walled curved beam with non-symmetric cross-section subjected to uniform compression is newly presented. For this, the elastic strain energy including the axially/flexurally/torsionally coupled terms and the potential energy due to the initial stress resultant are introduced. Then, equilibrium equations and force–deformation relationship are derived from the energy principle and explicit expressions for displacement parameters are derived based on power series expansions of displacement components. Next, the exact element stiffness matrix is determined using force–deformation relationships. In order to verify the accuracy of this study, the numerical solutions are presented and compared with the finite element solutions using the Hermitian curved beam elements. In addition, the coupling of symmetric and anti-symmetric modes at the buckling load crossover with change in curvature of beam is investigated.
To study the effect of stress-activated positive hole (p-hole) charge carriers on the infrared (I... more To study the effect of stress-activated positive hole (p-hole) charge carriers on the infrared (IR) emission from rocks, we subjected a portion (∼10 vol.%) of a large (30×60×7.5 cm 3) block of anorthosite, a nearly monomineralic (Ca-rich feldspar) igneous rock, to uniaxial deviatory stress up to failure. We measured the IR emission from a flat surface ≈40 cm from the stressed rock volume over the 800-1300 cm −1 (7.7-12.5 µm) range. Instantly, upon loading, the emission spectrum and intensity change. At first narrow bands appear at 930 cm −1 (10.75 µm), 880 cm −1 (11.36 µm), 820 cm −1 (12.4 µm) plus additional narrow bands in the 1000-1300 cm −1 (7.7-10.0 µm) range. The 10.75-12.4 µm bands are thought to arise from vibrationally excited O-O stretching modes, which form when p-hole charge carriers, which spread from the stressed rock volume into the unstressed rock, recombine at the surface. They radiatively decay, giving rise to "hot" bands due to transitions between excited states. Before failure the broad emission bands at 1170 cm −1 and 1030 cm −1 (8.7 and 9.7 µm) also increase slightly in intensity, suggesting a small increase in temperature due to thermalization of the energy deposited into the surface through p-hole recombination. Stimulated IR emission due to hole-hole recombination and its followon effects may help understand the enhanced IR emission seen in night-time satellite images of the land surface before major earthquakes known as "thermal anomalies".
Based on the power series method, the static and dynamic stiffness matrices for the flexural-tors... more Based on the power series method, the static and dynamic stiffness matrices for the flexural-torsional buckling and free vibration analysis of thin-walled beam with non-symmetric cross-section subjected to linearly variable axial force are newly presented. Additionally, the static stiffness matrix for the lateral buckling analysis of non-symmetric beam is presented for the first time. For this, the elastic strain energy, the potential energy considering the second-order terms of finite rotations, and the kinetic energy for thin-walled beam with non-symmetric cross-section are introduced. Then equations of motion and force-deformation relations are derived from the energy principle. Explicit expressions for displacement parameters are derived based on power series expansions of displacement components. Finally, the static and dynamic element stiffness matrices are determined using force-deformation relationships. In order to verify the accuracy of this study, the numerical solutions are presented and compared with the finite element solutions using the Hermitian beam elements and ABAQUS's shell elements.
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Papers by C.-c. Fu