Reliability-based design of corrugated web steel girders in shear as per AASHTO LRFD

Highlights

• The resistance factor for welded plate girders designed for shear as per AASHTO LRFD was evaluated.

• For AASHTO LRFD, ϕ = 0.95 for welded plate girders in shear is more appropriate.

• For corrugated web steel girders (CWSGs), the resistance factor for shear limit state was calibrated for AASHTO LRFD.

• A resistance factor of 0.95 is found to be suitable for AASHTO LRFD.

• The contribution of each design parameter to the overall girder reliability was quantified through sensitivity analysis.

Abstract

Despite their successful use in many bridges across several countries around the world, corrugated web steel girders (CWSGs) haven't been yet recognized formally by mainstream design codes and standards. CWSGs can be an economical alternative to conventional welded plate girders; they can achieve higher shear strengths with lesser material usage. Corrugated webs have been demonstrated to carry about half of their ultimate shear strength after buckling, which is an important reserve strength to overcome sudden collapses of bridge structures. The current design practice combines the latest research in the field with engineering judgment with no regard for reliability-based design. In light of the new developments in the field of bridge design and reliability analysis techniques, this paper revisits first the reliability of welded plate girders in shear and verifies their target reliability index and the corresponding resistance factor as per AASHTO LRFD. Then, and in an attempt to prepare the inclusion of CWSGs shear design in AASHTO LRFD, a probabilistic-based calibration procedure is applied to calibrate the resistance factor for bridges having a range of span lengths and girder spacings, with consideration of different average daily truck traffic. A series of sensitivity analyses were carried out in order to quantify the relative contribution of each design parameter to the overall reliability of CWSGs in shear. The findings of this study suggest that, for CWSGs in shear, a resistance factor of 0.95 is appropriate to ensure a reliability level that is consistently close to the target. The sensitivity analysis showed that the web thickness, web depth, and the yield strength of the web's steel material are the most influential parameters on the reliability index of CWSGs.

Introduction

AASHTO adopted the concept of Load and Resistance Factor Design for bridges and published its first Bridge Design Specifications in 1994 [1]. In the framework of LRFD, designs are generally economical and meet a pre-set safety level, which is represented by a target reliability index. In the development of resistance factors for AASHTO LRFD, the specifications considered typical construction materials, including timber, reinforced concrete, prestressed concrete, and structural steel. For structural steel, the specification addressed girders, trusses, arches, cable-stayed, and suspension.

Around the world, the most common type of steel bridges is composed of a cast-in-place concrete slab that is supported on multiple steel girders oriented along the bridge centerline. Such a structural form is widely used for short and medium spans because it can accommodate different alignments and geometric constraints, including curvature and skewness. The concrete slab and steel girders can act together as a composite system through shear connectors to support the entire load on the bridge. The steel girders, which can have I- or box cross-section, carry the imposed load by the internal actions of shear and bending moment (with the help of the slab, if composite action is present). The system is economical and long lasting for the vast majority of bridges, although stability concerns limit the stresses, especially during construction.

Structural design codes and specifications include rules and guidelines that specify minimum acceptable level of safety for constructed facilities. They aim at protecting public health, safety and the general welfare in relation to construction. Bridge specifications become law of a particular jurisdiction when formally enacted by the appropriate authority, such as the department of public work. Nowadays, the majority of the bridges around the world are designed following the Load and Resistance Factor Design (LRFD) philosophy. Such an approach considers the variability of loads and material properties in structural design in order to ensure uniform safety. Reliability calibration procedures for the AASHTO LRFD Bridge Design Specifications are well documented in the available literature [2,3]. New research on the statistical parameters of loads and material properties often results in proposed modifications to existing load and resistance factors [4,5]. Development of new material that is not adequately covered in the current specifications, such as fiber reinforced polymer concrete, requires the development of resistance factors to meet the target reliability [6]. Also, the move from working stress design to LRFD-based approach in the field of geotechnical engineering has prompted research in the area [[7], [8], [9], [10]]. Adapting the AASHTO Bridge Design Specification into a country that have different traffic characteristics and construction practice than the US may require revisiting the load and resistance factors [11].

With the development of LRFD, reliability-based design is now considered the standard in designing new bridge structures. In this context, load and resistance data are treated as uncertain quantities characterized by appropriate probabilistic models. In the framework of LRFD, load effects on structural members are scaled-up by a load factor, and resistance is scaled down by a resistance factor. In this way, it is expected that the structural member would achieve the reliability index that is consistent with the design standard.

To determine the appropriate load and resistance factors, a calibration process is needed to achieve the target reliability. This process is based on a series of reliability analyses assuming a large database of structural members and statistical data on both load and resistance models. For bridges in the US, Nowak [2,3] presented a calibration procedure to develop load and resistance factors for LRFD bridge code. In this work, the load and resistance were treated as random variables and described through their bias factors, coefficients of variation, and probability distributions. The calibration process assumed a target reliability index of 3.5, which was selected based on the performance of existing bridges that were designed based the AASHTO standard specifications to ensure consistent and uniform safety margin for all structures. More recently, Nowak and Iatsko [4] revised the load and resistance factors for the AASHTO LRFD bridge design specifications due to the fact that the existing specifications used statistical parameters dating back to the 1970s and 1980s.

From the above review, it becomes clear that probabilistic-based approaches are becoming the de-facto tool to design structural members and there is always a necessity to update design codes and standards by re-calibrating load and resistance factors in light of the availability of new statistical data, development of new materials, and advancement of reliability methods. Additionally, there is a growing interest in using new structural forms, such as corrugated web steel girders (CWSGs) for the construction of bridges [12]. For example, Abbas [13] investigated the behavior of girders with corrugated web made of high-performance steel. The popularity of CWSGs as a viable alternative to welded plate I-girders has led to its adoption in many bridge projects; examples can be found in [14,15]. One notable example is the demonstration bridge built by the Pennsylvania Department of Transportation [16]. This bridge is made of four equally spaced girders with corrugated web formed using high-performance steel plates (HPS-485 W). Large-scale tests on the demonstration bridge enabled the development of new shear and flexural strength criteria, but no reliability-based studies were conducted.

The present paper aims at addressing a deficient research area concerning CWSGs; namely, the development of reliability-based resistance factors for shear design. To do so, first there is a need to evaluate the current shear resistance factor of welded plate girders as per the AASHTO LRFD Bridge Design Specifications [17], and then calibrate the resistance factor for CWSGs in shear as per the current edition of the specifications. Moreover, sensitivity analyses are carried out to investigate the most influential design parameters on the reliability index of CWSGs.