Fault Tree Analysis of Schoharie Creek Bridge Collapse

The United States has witnessed several bridge collapses that have resulted in human fatalities. One such failure was the Schoharie Creek Bridge (1987), which motivated the improvement of bridge management policies and procedures. This paper offers a detailed review of the events that resulted in this bridge failure through the use of fault tree analysis. A fault tree is a graphical depiction of the various failure paths that lead to an undesirable outcome. The tree presented considers a host of catastrophic events ranging from vessel collision to fire. Fault trees also provide quantitative assessment and comparison of different failure mechanisms. The results of this analysis present scour as the source of the collapse of this bridge, which was in reality the root cause. Knowledge of the vulnerabilities particular to a bridge aids in the management of similar bridge types, allowing focus upon critical aspects. Recognition of historical bridge failures offers awareness to current bridge engineers and managers that aids in the decision making that promotes public safety and structure preservation. Lessons learned will help avoid similar catastrophic failures in the future.     

Estimation of Collapse Load of Single-Cell Concrete Box-Girder Bridges

The simplified equations available at present to predict the collapse loads of single-cell concrete box-girder bridges with simply supported ends are based on either space truss analogy or collapse mechanisms. Experimental studies carried out by various researchers revealed that, of the two formulations available to predict the collapse load, the one based on collapse mechanisms is found to be more versatile and better suited to box sections. Under a pure bending collapse mechanism, the existing formulation is found to predict collapse load with high accuracy. However, in the presence of cross-sectional distortion, there are significant errors in the existing theoretical formulation. This paper attempts to resolve this problem, by proposing a modification to the existing theory, incorporating an empirical expression to assess the extent of corner plastic hinge formation, under distortion–bending collapse mechanism. The modified theoretical formulations are compared with the experimental results available in the literature. New sets of experiments are also conducted to validate the proposed modified theory to estimate the collapse load. In all cases, it is seen that the modified theory to predict the collapse load match very closely with the experimental results.     

Thermal Effects on Skewed Steel Highway Bridges and Bearing Orientation

An investigation is conducted to characterize and quantify external effects in composite steel highway bridges under thermal loading. Based on the results of a literature review, including thermal and thermoelastic analyses as well as current design code provisions, a simple but realistic thermal loading is developed for winter and summer conditions for AASHTO load and resistance factor design (LRFD) Zone 3. Three cases of bearing orientation, representative of current design practice, are examined. Parametric studies are then conducted. Hypothetical bridges are designed for a range of different span lengths, section depths, widths, and skews. Each bridge model is tested under all three constraint cases and both winter and summer thermal loading. Variations in structural response with each parameter are plotted, and the relative influence of each parameter is discussed. Design equations to predict the observed displacements and restraint forces at the bearings are then developed by a systematic regression procedure. The applicability of these proposed design equations is demonstrated by examples.     

Rotation Compatibility Approach to Moment Redistribution for Design and Rating of Steel I-Girder Bridges

Recent research has culminated in the development of moment redistribution design and rating procedures based on a “rotation compatibility” procedure. The key aspects of the rotation compatibility method are presented herein along with the resulting series of simple equations that may be used for both design and rating of straight continuous-span steel I-girders. This procedure has several advantages over the previous moment redistribution procedures. Most significantly, the rotation compatibility method provides a rational basis for removing the current restrictions on girder geometries permissible for use with moment redistribution provisions. Thus, sections that are more slender and/or have greater unbraced lengths, compared to previous inelastic procedures, may be considered. This is particularly beneficial for incorporating inelastic methods into rating specifications because many existing bridges have geometries such that they have previously been outside the scope of applicability of inelastic procedures. A second key advantage of the rotation compatibility procedure is that maximum allowable redistribution moments are specifically computed, which justifies the use of higher levels of moment redistribution and consequently greater design economy in some cases.     

Design for Shear in Curved Composite Multiple Steel Box Girder Bridges

Modern highway bridges are often subject to tight geometric restrictions and, in many cases, must be built in curved alignment. These bridges may have a cross section in the form of a multiple steel box girder composite with a concrete deck slab. This type of cross section is one of the most suitable for resisting the torsional, distortional, and warping effects induced by the bridge’s curvature. Current design practice in North America does not specifically deal with shear distribution in horizontally curved composite multiple steel box girder bridges. In this paper an extensive parametric study, using an experimentally calibrated finite-element model, is presented, in which simply supported straight and curved prototype bridges are analyzed to determine their shear distribution characteristics under dead load and under AASHTO live loadings. The parameters considered in this study are span length, number of steel boxes, number of traffic lanes, bridge aspect ratio, degree of curvature, and number and stiffness of cross bracings and of top-chord systems. Results from tests on five box girder bridge models verify the finite-element model. Based on the results from the parametric study simple empirical formulas for maximum shears (reactions) are developed that are suitable for the design office. A comparison is made with AASHTO and CHBDC formulas for straight bridges. An illustrative example of the design is presented.     

Ultimate Capacity Destructive Testing and Finite-Element Analysis of Steel I-Girder Bridges

Current bridge design and rating techniques are based at the component level and thus cannot predict the ultimate capacity of bridges, which is a function of system-level interactions. While advances in computer technology have made it possible to conduct accurate system-level analyses, which can be used to design more efficient bridges and produce more accurate ratings of existing structures, the knowledge base surrounding system-level bridge behavior is still too small for these methods to be widely considered reliable. Thus, to advance system-level design and rating, a 1/5-scale slab-on-steel girder bridge was tested to ultimate capacity and then analytically modeled. The test demonstrated the significant reserve capacity of the steel girders, and the response of the specimen was governed by the degradation of the reinforced-concrete deck. To accurately capture the response of the specimen in an analytical model, the degradation of the deck and other key features of the specimen were modeled by using a dynamic analysis algorithm in a commercially available finite-element analysis program ABAQUS.     

Measurement and Analysis of Distortion-Induced Fatigue in Multigirder Steel Bridges

Fatigue damage to multigirder steel bridges on skew can result from distortion caused by differential deflection of adjacent girders that impose out-of-plane bending of girder web gaps. Existing design procedures give recommendations to mitigate the effects of distortional fatigue but do not directly address secondary, out-of-plane deformations, nor do they provide guidance in determining the magnitude of out-of-plane stresses in girder webs. An experimental study was conducted to (1) implement a field monitoring program for a typical multigirder steel bridge on skew supports; (2) assess the frequency and magnitude of distortional fatigue stresses at web-stiffener connections; and (3) evaluate the impact of these stresses on fatigue life. Measurements from twelve strain gauges were continuously monitored and recorded for a period exceeding three months on Minnesota Department of Transportation Bridge #27734. Web-gap stresses in negative-moment regions were found to be much larger than flange stresses. The results of a detailed finite-element study indicate that actual strains at the web gaps may be much larger than the values measured at the strain gauge locations. This study also revealed the mechanism of web-gap distortion, suggesting an approximate method for predicting web-gap stress based on known girder differential deflection.     

Lateral Load Distribution in Curved Steel I-Girder Bridges

The purpose of this paper is to develop new formulas for live load distribution in horizontally curved steel I-girder bridges. The formulas are developed by utilizing computer model results for a number of different horizontally curved steel I-girder bridges. The bridges used in this study are modeled as generalized grillage beam systems composed of horizontally curved beam elements for steel girders and substructure elements for lateral wind bracing and cross frames which consist of truss elements. Warping torsion is taken into consideration in the analysis. The effect of numerous parameters, including radius of curvature, girder spacing, overhang, etc., on the load distribution are studied. Key parameters affecting live load distribution are identified and simplified formulas are developed to predict positive moment, negative moment, and shear distribution for one-lane and multiple-lane loading. Comparisons of the formulas with finite element method and grillage analysis show that the proposed formulas have more accurate results than the various available American Association of State Highway and Transportation Officials specifications. The formulas developed in this study will assist bridge engineers and researchers in predicting the actual live load distribution in horizontally curved steel I-girder bridges.     

Extreme Thermal Loading on Steel Bridges in Tropical Region

In the design of highway bridges, it is important to consider the thermal stresses induced by the nonlinear temperature distribution in the bridge deck irrespective of their spans. To cope with this, design temperature profiles are provided by many bridge design codes, which are normally based on extensive research on the thermal behavior of bridges. This paper presents the results of a comprehensive investigation on the thermal behavior of steel bridges carried out in Hong Kong. A method for predicting bridge temperatures from given meteorological conditions is briefly discussed. The theoretical results have been validated by temperature measurements on experimental models mounted on the roof of a building as well as on an existing steel bridge. Both the theoretical and field results confirm the validity of the one-dimensional heat transfer model on which most design codes are based. Values of design thermal loading for a 50-year return period are determined from the statistics of extremes over 40 years of meteorological information in Hong Kong. The design temperature profiles for various types of steel bridge deck with different thickness of bituminous surfacing are developed.     

Investigation of East Chicago Ramp Collapse

A summary is presented of the investigation performed by the National Bureau of Standards (NBS), at the request of the Occupational Safety and Health Administration, to determine the most likely cause of the collapse of a portion of a highway ramp in East Chicago, Indiana. The investigative effort included an extensive field study to ascertain the conditions prior to and after the accident. In addition, the NBS performed physical tests on key components of the temporary support system used to build the ramp. A structural analysis was performed to compute the magnitude of the forces acting in various components of the support system prior to the failure. The calculated forces were compared with the expected strengths of the structural components. It was concluded that the most likely triggering mechanism of the collapse was the cracking of concrete pads supporting a shoring tower. It was further concluded that there were four deficiencies that contributed directly to the collapse. Had any of these deficiencies not existed, it is unlikely that the collapse would have occurred.     

Rapid Ranking Procedures for Gusset Plate Connections in Existing Steel Truss Bridges

Evaluation and rating of steel truss bridge connections has become imperative for many transportation agencies after the recent collapse of the I-35W Bridge in Minneapolis. Detailed engineering capacity calculations of gusset plate connections are time consuming and thus expensive. Large numbers of connections are in the national inventory and must be evaluated. A screening process and a simplified rapid screening process are proposed for ranking gusset plate connections in steel truss bridges to help bridge engineers identify possible vulnerable connections and aid field inspections. The procedures consider member demands relative to the connection geometric proportions for four different parameters: fasteners, plate tension, plate compression, and overall horizontal shear. The methods are demonstrated for two bridges, including the collapsed I35W Bridge, and clearly identify connections U10 and L11 as vulnerable for three of the four parameter types (fasteners were not identified as vulnerable for these connections). The ranking approach is not proposed as a substitute for thorough, detailed, and expert assessment of the connections, but rather allows rating engineers to more quickly prioritize detailed evaluations in an ordered systematic way from the most likely vulnerable connections to the least likely vulnerable connections. This technique may be considered analogous to performing screening tests on a new patient to indicate the likely medical condition prior to conducting more sophisticated and costly investigations.     

Recommended Procedures for Simplified Inelastic Design of Steel I-Girder Bridges

This paper presents summary recommendations pertaining to new AASHTO procedures for simplified inelastic design of steel I-girder bridges. First, key developments are summarized that lead to the proposed inelastic design approach. The paper then outlines a set of equations that provide an improved characterization of the inelastic moment-rotation response for a wide range of I-beams and plate girders. Effective plastic moment predictions based on these equations are combined with the recently proposed design method, resulting in greater accuracy and simplicity of the proposed approach. The ease of use of the resulting procedure is illustrated by a design example.     

Minimum Depth of Soil Cover above Soil–Steel Bridges

Soil–steel bridges are built of flexible corrugated steel panels buried in well-compacted granular soil. Their design is based on the composite interaction between the soil pressures and the displacements of the conduit wall. The structure failure could be initiated by shear or tension failure in the soil cover above the steel conduit. The provisions for design given in different codes, such as the Canadian Highway Bridge Design Code, managed to avoid some of the problems associated with the failure of soil above soil–steel bridges by requiring a minimum depth of soil cover over the crown of the conduit taking into consideration the geometric shape of the conduit. However, the present code requirements for a minimum depth of cover were developed for a maximum span of 7.62 m and using nonstiffened panels of 51 mm depth of corrugation. The effect of having larger spans or using more rigid corrugated panels has not been examined before and is the subject of this paper. The present study uses the finite-element analysis to re-examine the possible soil failures due to centric live loads (i.e., loads acting symmetrically about the mid span of conduit) or eccentric live loads. The study deals with spans up to 15.24 m of circular conduits and 21.3 m of arches with deep corrugations. It has been found that, in addition to the conduit geometry, the actual dimension of the span should be considered to determine the required depth of soil cover.     

Vulnerability Assessment of Cable-Stayed Bridges in Probabilistic Domain

Vulnerability of a structure under terrorist attack can be regarded as the study of its behavior against blast-induced loads. A structure is vulnerable if a small damage can trigger a disproportionately large consequence and lead to a cascade of failure events or even collapse. The performance of structural vulnerability depends upon factors such as external loading condition and structural properties. As many of these factors are random in nature, it is necessary to develop a vulnerability assessment technique in the probabilistic domain. In this study, one such assessment framework is proposed for cable-stayed bridges. The framework consists of two stages of analysis: determining the probability of direct damage due to blast loads and assessing the subsequent probability of collapse due to component damage. In the first stage assessment, damage of the bridge component is defined as the exceedance of a predefined limit state such as displacement or yielding. The damage probability is obtained through a stochastic finite-element analysis and the first-order second-moment reliability method. The second stage assessment further calculates the probability of collapse due to direct damage of some component via an event tree approach. The proposed assessment methods are illustrated on a hypothetical single-tower cable-stayed bridge. It is seen that the proposed methods provide a quantitative tool for analyzing the vulnerability performance of cable-stayed bridges under terrorist attack.     

Truck Models for Improved Fatigue Life Predictions of Steel Bridges

A new fatigue load model has been developed based on weigh-in-motion (WIM) data collected from three different sites in Indiana. The recorded truck traffic was simulated over analytical bridge models to investigate moment range responses of bridge structures under truck traffic loadings. The bridge models included simple and two?equally continuous spans. Based on Miner’s hypothesis, fatigue damage accumulations were computed for details at various locations on the bridge models and compared with the damage predicted for the 240-kN (54-kip) American Association of State Highway and Transportation Officials (AASHTO) fatigue truck, a modified AASHTO fatigue truck with an equivalent effective gross weight, and other fatigue truck models. The results indicate that fatigue damage can be notably overestimated in short-span girders. Accordingly, two new fatigue trucks are developed in the present study. A new three-axle fatigue truck can be used to represent truck traffic on typical highways, while a four-axle fatigue truck can better represent truck traffic on heavy duty highways with a significant percentage of the fatigue damage dominated by eight- to 11-axle trucks.     

Seismic Response of Multiple Span Steel Bridges in Central and Southeastern United States. II: Retrofitted

Part I of this two-part paper evaluated the seismic response of typical multispan simply supported (MSSS) and multispan continuous steel girder bridges in the central and southeastern United States. The results showed that the bridges were vulnerable to damage resulting from impact between decks, and large ductility demands on nonductile columns. Furthermore, fixed and expansion bearings were likely to fail during strong ground motion. In this paper, several retrofit measures to improve the seismic performance of typical multispan simply supported and multispan continuous steel girder bridges are evaluated, including the use of elastomeric bearings, lead-rubber bearings, and restrainer cables. It is determined that lead-rubber bearings are the most effective retrofit measure for reducing the seismic vulnerability of typical bridges. While isolation provided by elastomeric bearings limits the forces into the columns, the added flexibility results in pounding between decks in the MSSS steel girder bridges. Restrainer cables, which are becoming a common retrofit measure, are effective in reducing the hinge opening in MSSS bridges with steel bearings. However, when used with elastomeric bearings, the restrainer cables negate the isolation effect of the bearings.     

Optimal Inspection Scheduling of Steel Bridges Using Nondestructive Testing Techniques

A probabilistic approach is proposed to help select the most suitable nondestructive inspection (NDI) technique and associated optimal schedule for fracture-critical member/detail fatigue inspections on a specific steel bridge. The probability of detection (POD) function for the NDI technique, which is a measure of the detection accuracy, is employed. By combining probability calculations based on use of the POD function together with numerical Monte Carlo simulations of the crack propagation of the fracture-critical detail, a cost function is formulated that includes the expected cost of inspections and failure resulting from the chosen NDI technique and alternative inspection schedules. In summary, the selection of an NDI technique with an associated inspection schedule for fracture-critical inspections is formulated as an optimization problem that can guarantee minimum total cost. The inspection frequency is determined as part of the optimization that utilizes appropriate constraints on inspection intervals and a minimum acceptable (target) structural safety level. A case study for a box girder bridge is presented to demonstrate the application of the proposed probabilistic method.     

Influence of Secondary Elements and Deck Cracking on the Lateral Load Distribution of Steel Girder Bridges

The AASHTO LRFD load distribution factor equation was developed based on elastic finite element analysis considering only primary members, i.e., the effects of secondary elements such as lateral bracing and parapets were not considered. Meanwhile, many bridges have been identified as having significant cracking in the concrete deck. Even though deck cracking is a well-known phenomenon, the significance of pre-existing cracks on the live load distribution has not yet been assessed. The purpose of this research is to investigate the effect of secondary elements and deck cracking on the lateral load distribution of girder bridges. First, secondary elements such as diaphragms and parapets were modeled using the finite element method, and the calculated load distribution factors were compared with the code-specified values. Second, the effects of typical deck cracking and crack types that have a major effect on load distribution were identified through a number of nonlinear finite element analyses. It was established that the presence of secondary elements may produce load distribution factors up to 40% lower than the AASHTO LRFD values. Longitudinal cracking was found to increase the load distribution factor by up to 17% when compared to the LRFD value while the transverse cracking was found to not significantly influence the transverse distribution of moment.     

Failure of Cold-Formed Steel Beams during Concrete Placement

During a concrete placement on the second story of a building under construction, the supporting cold-formed steel beams collapsed. Four workers were injured. The collapse occurred while concrete was being placed onto steel decking on the second floor of the structure. Cold-formed steel beams, without shoring, supported the steel decking. Analysis of the steel beams under the weight of concrete and workers using the applicable American Concrete Institute and American Iron and Steel Institute documents indicated that the beams were overstressed for construction loads. After the collapse, part of the structure was rebuilt using thicker beams. For the reconstruction, the slab was shored. Designing with cold-formed steel requires knowledge of failure modes that can often be safely ignored with hot-rolled steel, such as local buckling. Engineers designing with this material should take care to obtain the proper codes and design documents.     

Feasibility of a 1,400 m Span Steel Cable-Stayed Bridge

This paper describes the feasibility of 1,400 m steel cable-stayed bridges from both structural and economic viewpoints. Because the weight of a steel girder strongly affects the total cost of the bridge, the writers present a procedure to obtain a minimum weight for a girder that ensures safety against static and dynamic instabilities. For static instability, elastoplastic, finite-displacement analysis under in-plane load and elastic, finite-displacement analysis under displacement-dependent wind load are conducted; for dynamic instability, multimodal flutter analysis is carried out. It is shown that static critical wind velocity of lateral torsional buckling governs the dimension of the girder. Finally, the writers briefly compare a cable-stayed bridge with suspension bridge alternatives.