Stiffness and Strength of Metal Bridge Deck Forms

Light gauge metal sheeting is often utilized in the building and bridge industries for concrete formwork. Although the in-plane stiffness and strength of the metal forms are commonly relied upon for stability bracing in buildings, the forms are generally not considered for bracing in steel bridge construction. The primary difference between the forming systems in the two industries is the method of connection between the forms and girders. In bridge construction, an eccentric support angle is incorporated into the connection details to achieve a uniform slab thickness along the girder length. While the eccentric connection is a benefit for slab construction, the flexible connection limits the amount of bracing provided by the forms. This paper presents results from the first phase of a research study investigating the bracing behavior of metal bridge deck forms. Shear diaphragm tests were conducted to determine the shear stiffness and strength of bridge deck forms, and modified connection details were developed that substantially improve the bracing behavior of the forms. The measured stiffness and strength of diaphragms with the modified connection often met or exceeded the values of diaphragms with conventional noneccentric connections. The experimental results for the diaphragms with the modified connection details dramatically improve the potential for bracing of steel bridge girders by metal deck forms.     

Lateral-Torsional Buckling of Stepped Beams with Continuous Bracing

Continuous span multibeam steel bridges are common along the state and interstate highways. The top flange of the beams is typically braced against lateral movement by the deck slab, and in many bridges the cross section is stepped at discrete points along the span. Design equations for lateral–torsional buckling (LTB) resistance in the American Association of State Highway and Transportation Officials “Load and resistance factor design bridge design specifications” are for prismatic beams and ignore the lateral restraint provided by the bridge deck. A new design equation is proposed that can be applied to I-shaped stepped beams with continuous top flange lateral bracing. By including the effects of the change in cross section size and the continuous top flange bracing, the calculated LTB resistance is significantly increased. Critical bending moment values from the proposed equation are compared to values from finite element method buckling analyses. The new equation is sufficiently accurate for use in design and in the evaluation of existing bridges.     

Monitoring Steel Girder Stability for Safer Bridge Erection

The collapse of the State Route 69 Bridge over the Tennessee River near Clifton, Tennessee, is an example of how instability and lateral torsional buckling failure of a single steel bridge girder during erection might cause collapse of the whole steel superstructure. Close attention should be given to the stability of steel plate girders during erection when the lateral support provided to the compression flange might temporarily not be present. Rules of thumb in use today have been adopted by contractors/subcontractors to check the stability of cantilever or simply supported girders under erection using the L/b ratio, where L is the unbraced length and b is the compression flange width. For each girder section, a maximum L/b ratio exists beyond which lateral torsional buckling failure would occur under girder self-weight. Parametric studies were conducted following the latest AASHTO LRFD code in order to indentify the maximum L/b ratio for various girder sections and check the rules of thumb, as well as determine the dominating section parameters on girder stability under erection. Advanced nonlinear finite-element analyses were also conducted on a girder section for both the cantilever and the simply supported case in order to further understand the behavior of girder instability due to lateral torsional buckling under the self-weight, as well as to develop a trial-and-error methodology for identifying the maximum L/b ratio using computer analysis. At the same time, the effect of lateral bracing location on the cantilever free end has been investigated, and it turned out that bracing the top tension flange would be more effective to prevent lateral torsional buckling than bracing the bottom compression flange.     

Evaluation of Effective Width and Distribution Factors for GFRP Bridge Decks Supported on Steel Girders

Glass fiber-reinforced polymer (GFRP) bridge deck systems offer an attractive alternative to concrete decks, particularly for bridge rehabilitation projects. Current design practice treats GFRP deck systems in a manner similar to concrete decks, but the results of this study indicate that this approach may lead to nonconservative bridge girder designs. Results from a number of in situ load tests of three steel girder bridges having the same GFRP deck system are used to determine the degree of composite action that may be developed and the transverse distribution of wheel loads that may be assumed for such structures. Results from this work indicate that appropriately conservative design values may be found by assuming no composite action between a GFRP deck and steel girder and using the lever rule to determine transverse load distribution. Additionally, when used to replace an existing concrete deck, the lighter GFRP deck will likely result in lower total stresses in the supporting girders, although, due to the decreased effective width and increased distribution factors, the live-load-induced stress range is likely to be increased. Thus, existing fatigue-prone details may become a concern and require additional attention in design.     

Transverse Cracking of Concrete Bridge Decks: Effects of Design Factors

Early transverse cracking is one of the dominant forms of bridge deck defects experienced by a large number of transportation agencies. These cracks often initiate soon after the bridge deck is constructed, and they are caused by restrained shrinkage of concrete. Transverse cracks increase the maintenance cost of a bridge structure and reduce its life span. Most of the past efforts addressing transverse bridge deck cracking have focused on changes over the years in concrete material properties and construction practices. However, recent studies have shown the importance of design factors on transverse bridge deck cracking. This paper presents results of a comprehensive finite-element (FE) study of deck and girder bridge systems to understand and evaluate crack patterns, stress histories, as well as the relative effect of different design factors such as structural stiffness on transverse deck cracking. The results of this study demonstrate the development of transverse deck cracking and emphasize the importance of these design factors. They also recommend preventive measures that can be adopted during the design stage in order to minimize the probability of transverse deck cracking.     

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.     

Simply Supported Curved Cellular Bridges: Simplified Design Method

The use of curved composite bridges in interchanges of modern highway systems has become increasingly popular for economic and aesthetic considerations. Bridges with a concrete deck composite with a steel multicell section can adequately resist torsional and warping effects induced by high curvature. Although current design practices in North America recommend few analytical methods for the design of curved multicell box girder bridges, economical requirements in the design process point to a need for a simplified design method. This paper summarizes the results from an extensive parametric study, using the finite-element method, in which simply supported curved composite multicell bridge prototypes are analyzed to evaluate the moment and deflection distributions between girders, as well as the axial forces expected in the bracing system, due to truck loading as well as dead load. Results from tests on four, 1∕12 linear-scale, simply supported curved composite concrete deck-steel multicell bridge models are used to substantiate and verify the analytical modeling. The parameters considered in the study are cross-bracing system, aspect ratio, number of lanes, number of cells, and degree of curvature. Based on the data generated from the parametric study, expressions for moment and deflection distribution factors are deduced. Expressions for the maximum axial force in bracing members are also derived. An illustrative design example is presented.     

Field Testing and Analysis of CRC Deck Girder Bridges

This paper presents findings of field tests and analysis of two conventionally reinforced concrete (CRC) deck girder bridges designed in the 1950s. The bridges are in-service and exhibit diagonal cracks. Stirrup strains in the bridge girders at high shear regions were used to estimate distribution factors for shear. Impact factors based on the field tests are reported. Comparison of field measured responses with AASHTO factors was performed. Three-dimensional elastic finite-element analysis was employed to model the tested bridges and determine distribution factors specifically for shear. Eight-node shell elements were used to model the decks, diaphragms, bent caps, and girders. Beam elements were used to model columns under the bent caps. The analytically predicted distribution factors were compared with the field test data. Finally, the bridge finite-element models were employed to compare load distribution factors for shear computed using procedures in the AASHTO LRFD and Standard Specifications.     

Number of Cable Effects on Buckling Analysis of Cable-Stayed Bridges

Cables instead of interval piers support cable-stayed bridges, and the bridge deck is subjected to strong axial forces due to the horizontal components of cable reactions. The structural behavior of a bridge deck becomes nonlinear because of the axial forces, large deflection, and nonlinear behavior of the cables and the large deformation of the pylons as well as their interactions. The locations and amplitude of axial forces acting on the bridge deck may depend on the number of cables. Agrawal indicated that the maximum cable tension decreases rapidly with the increase in the number of cables. This paper investigates the stability analysis of cable-stayed bridges and considers cable-stayed bridges with geometry similar to those proposed in Agrawal's paper. A digital computer and numerical analysis are used to examine 2D finite element models of these bridges. The eigen buckling analysis has been applied to find the minimum critical loads of the cable-stayed bridges. The numerical results indicate that the total cumulative axial forces acting on the bridge girder increase as the number of cables increases, yet because the bridge deck is subjected to strong axial forces, the critical load of the bridges decreases. Increasing the number of cables may not increase the critical load on buckling analysis of this type of bridge. The fundamental critical loads increase if the ratio of Ip∕Ib increases until the ratio reaches the optimum ratio. If the ratio of Ip∕Ib is greater than the optimum ratio, depending on the geometry of an individual bridge, the fundamental critical load decreases for all the types of bridges considered in this paper. In order to make the results useful, they have been normalized and represented in graphical form.     

Behavior of Curved I-Girder Webs Subjected to Combined Bending and Shear

Two previous papers by the writers described the buckling and finite-displacement behavior of curved I-girder web panels subjected to pure bending, presented a theoretically pure analytical model, and presented equations that describe the reduction in strength due to curvature. This paper describes the buckling and finite-displacement behavior of curved web panels under combined bending and shear. Unlike straight girder web panels, the addition of shear in curved panels is shown to increase the transverse “bulging” displacement of the web prior to buckling. The accompanying decrease in moment carrying capacity is analyzed in a manner similar to that used for the combined bending and shear nominal strength interaction for straight girder design. Preliminary recommendations are made toward forming design criteria for curved webs.     

Stability Bracing Requirements for Steel Bridge Girders with Skewed Supports

Cross frames and diaphragms are critical elements for the stability of I-shaped steel bridge girders during construction. The AASHTO specifications are relatively vague with regards to the stability design requirements of the braces. Spacing limits that have been used in past AASHTO specifications have been removed from the Load and Resistance Factor Design Specification, which instead requires the bracing to be designed by a rational analysis. Whereas the AASHTO specification does not define what constitutes a rational analysis, stability bracing systems must possess adequate stiffness and strength. The commercially available software packages that are typically used in bridge design generally do not have the capabilities to determine the adequacy of the bracing from a stability perspective. This paper outlines the stability bracing requirements for bridges with normal and skewed supports. The effects of support skew on the stiffness and strength requirements for stability bracing are addressed. Solutions that are available for systems with normal supports were modified to account for the effects of the support skew angle. Two orientations of the intermediate bracing were considered: parallel to the skew angles and perpendicular to the longitudinal girder axis. The solutions are presented and compared with finite-element results. The design solutions have good agreement with the finite-element solutions.     

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.     

Impact Factors for Horizontally Curved Composite Box Girder Bridges

This paper presents a method for determining the dynamic impact factors for horizontally curved composite single- or multicell box girder bridges under AASHTO truck loading. The bridges are modeled as three-dimensional structures using commercially available software. The vehicle is idealized as a pair of concentrated forces, with no mass, traveling in two circumferential paths parallel to the curved centerline of bridges. An extensive parametric study is conducted, in which over 215 curved composite box girder bridge prototypes are analyzed. The key parameters considered in this study are: Number of cells, number of lanes, degree of curvature, arc span length, slope of the outer steel webs, number and area of bracing and top chord systems, and truck(s) speed and truck(s) positioning. Based on the data generated from the parametric study, expressions for dynamic impact factors for longitudinal moment, reaction, and deflection are proposed as function of the ratio of the arc span length to the radius of curvature. The results from this study would enable bridge engineers to design horizontally curved composite box girder bridges more reliably and economically. Furthermore, the results can be used to potentially increase the live-load capacity of existing bridges to prevent posting or closing of the bridge.     

Stability Analysis of Box-Girder Cable-Stayed Bridges

The objective of this study is to investigate the stability characteristics of box-girder cable-stayed bridges by three-dimensional finite-element methods. Cable-stayed bridges have many design parameters, because they have a lot of redundancies, especially for long-span bridges. Cable-stayed bridges exhibit several nonlinear behaviors concurrently under normal design loads because of large displacements; the interaction among the pylons, the stayed cables, and the bridge deck; the strong axial and lateral forces acting on the bridge deck and pylons; and cable nonlinearity. A typical two-lane, three-span, steel box-girder cable-stayed bridge superstructure was selected for this paper. The numerical results indicate that, if the ratio of the main span length with respect to the total span length, L1∕L, is small, the structure usually has a higher critical load. If the ratio Ip∕Ib increases, the critical load of the bridge decreases, in which Ip is the moment of inertia of the pylon and Ib is the moment of inertia of the bridge deck. When the ratio Ip∕Ib is greater than 10.0, the decrement becomes insignificant. For cable arrangements, bridges supported by a harp-type cable arrangement are the better design than bridges supported by a fan-type cable arrangement on buckling analysis. The numerical results also indicate that use of either A-type or H-type pylons does not significantly affect the critical load of this type of structure. In order to make the numerical results useful, the buckling loads have been nondimensionalized and presented in both tabular and graphical forms.     

Service Load Effective Compression Flange Width in Fiber Reinforced Polymer Deck Systems Acting Compositely with Steel Stringers

This paper reports on the field study of a steel stringer-fiber reinforced polymer (FRP) deck composite bridge in Pennsylvania. The objective of the study is to assess the effective compression flange width in the FRP deck and floor systems when they act compositely with underlying steel girders at service conditions. The research results reported herein support the notion of employing a design approach, for both interior and exterior girders of a composite floor system, that is philosophically consistent with current practice related to steel girders acting compositely with concrete decking. It appears from the results presented herein that FRP decks and floors acting compositely with underlying steel girders exhibit an effective width that is close to the actual girder spacing for interior beams, and approximately one-half this value for exterior beams.     

Inner ear perfusion: indications and applications

This paper presents experimental investigations on Bailey bridges. Seven one-sixth scale models of the Bailey bridge trussed-steel frame were constructed in the laboratory and tested. All members of the scale models of steel frames are solid rectangular sections. Both ends of the members are fully welded. Some members of three selected specimens were removed to study their effects on degradation of limit loads. The cross-section areas of some members in two of the specimens were reduced to simulate the phenomenon of member corrosion. Two numerical methods, second-order elastic and inelastic analyses are used to predict the behavior of the steel frames. The responses determined by numerical methods are compared with test results. The scale model without lateral bracing members collapsed in the global lateral buckling mode at a very small limit load. The lateral bracing system of a planar frame is very important for preventing an early collapse and allows the ultimate strength to be reached.     

Shear Strength of a Lightweight Self-Consolidating Concrete Bridge Girder

Lightweight self-consolidating concrete (LWSCC) is advantageous in the bridge industry because members made with this material have a significantly lower self-weight, and in its fresh state, LWSCC has a low viscosity which eliminates the need for vibration during fabrication. A composite section was fabricated with a single precast bulb-tee LWSCC beam and a lightweight concrete cast-in-place deck. A simply supported test configuration was constructed with two point loads to quantify the web-shear strength of the girder. The experimental shear strength is compared to four analytical models from different AASHTO specifications. Based on the results of this limited study, the theoretical predictions for the web-shear strength of this girder were all conservative when compared to the experimentally measured failure strength. With these results in mind, further research is recommended on the use of LWSCC girders in the bridge industry to better understand the material properties, structural properties, and cost advantages.     

Control of Seismically Excited Cable-Stayed Bridge Using Resetting Semiactive Stiffness Dampers

Cable-stayed bridges are prone to exhibit large amplitude oscillations because of their large flexibility, small mass, and small inherent damping. Hence, the reduction of seismic or wind-induced vibration of cable-stayed bridges is vital for their safety and serviceability. In this paper, a resetting semiactive stiffness damper (RSASD) is used to control the peak dynamic response of a recently developed benchmark problem on a cable-stayed bridge subject to earthquakes. The model of the benchmark cable-stayed bridge is based on the actual cable-stayed bridge that is under construction on Cape Girardeau, Mo. The prime aim of this study is to investigate the application of protective devices, such as semiactive and passive dampers, in reducing the displacement of the deck as well as base shear and moments at the base of the towers. In this research, the applications of the RSASD as well as passive viscous and fluid dampers to the benchmark bridge problem have been investigated. Numerical simulations are conducted by installing RSASD devices as well as passive viscous and friction dampers between the pier and the deck of the bridge. Numerical results clearly indicate that the displacement of the deck, and shear and moments at the base of the towers, are reduced substantially by installing these protective devices. In particular, energy dissipating capabilities and performance of the RSASD are quite remarkable. It is shown that the RSASD is quite effective in reducing peak response quantities of the bridge to a level similar to that of the sample active controller. A further reduction in response quantities can be achieved by using the RSASD in a combination of passive viscous dampers.