Allowable Tensile Stress for Webs of Prestressed Segmental Concrete Bridges

Structural, economical, and aesthetic advantages have helped prestressed (PS) concrete segmental box girder bridges gain popularity. The long-term endurance of PS segmental bridges depends on being free of cracking. Designers limit structural cracking by ensuring that service stresses do not exceed the tensile strength of concrete. An allowable tensile stress, which is more stringent than tensile strength, is often used to account for the uncertainties in both capacity and demand. Design codes clearly provide the allowable tensile stress for top and bottom fibers. This paper investigates establishing an allowable tensile stress limit for consideration in webs, where research is currently lacking. The proposed limit is obtained through a reliability study where three expressions were calibrated to conform to HL-93 loading. The effect of the accompanying principal compressive stress is accounted for in two of the expressions. Six PS concrete bridge designs were used to demonstrate the importance of accounting for the biaxial state of stress. A parametric study shows that one of the proposed expressions provides a more uniform range of reliability index β than the other two, including the one currently used by designers.

Keywords: bridges; prestressed; reliability; tensile strength.

(ProQuest-CSA LLC: ... denotes formulae omitted.)

INTRODUCTION

Segmental construction is an appealing choice to many bridge designers and owners. It makes achieving longer span lengths possible while still handling and transporting manageable size segments (Fig. 1). The prestressed (PS) concrete box girder is one of the segmental alternatives that has been gaining popularity in the past 30 years as it becomes more competitive to other alternatives. Box sections provide favorable structural properties such as high flexural stiffness and superior torsional rigidity. They can also be used to construct variable depth spans that are aesthetically appealing. Cracking of PS concrete segmental box girder bridges negatively impacts their durability; therefore, they are designed to be free of cracks under service conditions. Designers are often faced with the challenge of estimating an allowable tensile stress that can achieve this goal. Allowable tensile stresses for consideration at the top and bottom fibers of the girder are well established in design codes.1-3 They vary based on several factors such as the type of joint (Type A or B). These stresses are usually provided as a function of the compressive strength f^sub c^' and normally range from 6[and the square root of]f^sub c^' to zero tension. In some cases, such as the case for Type B joints with external tendons, AASHTO-Segmental2 calls for a minimum compressive stress of 100 psi.

By complying with the aforementioned allowable tensile stresses, the possibility of flexural cracking at the top and bottom fibers should be eliminated. These allowable stresses are only good for the extreme fibers and are not applicable to webs. In webs, cracks may form due to a biaxial state of stress resulting from a combination of shear and normal stresses. The normal stresses are usually in the longitudinal direction σ^sub x^ (refer to Fig. 1 for coordinate system). They are caused by straining actions due to gravity loads, long-term effects, and post-tensioning (PT) forces. In regions with high shear demands, another normal stress σ^sub y^ may exist if vertical PT bars are used in the webs. Shear stresses ν are caused by direct shear forces as well as torsional effects. This state of stress (Fig. 2) is somewhat different than the state of stress at the top and bottom fibers in that the critical stress that may cause cracking is the principal stress σ^sub 1^, as can be demonstrated by Mohr's circle (Fig. 3). Controlling shear cracking requires that the principal stress σ^sub 1^ be limited to an allowable tensile stress f^sub t,all^. AASHTO-Segmental2 does not offer guidance to designers with regard to f^sub t,all^ in webs, which consequently shifts the burden of choosing f^sub t,all^ to the designer (or the client). Alleviating this burden from the designer is important as it will make the design process clearer and more uniform. Visiting allowable stresses is an ongoing process. Noppakunwijai et al.4 recently recommended some changes to the provisions controlling compression limits in prestressed girders. The Florida Department of Transportation (FDOT) has embarked on an effort to address some of the issues that PS bridge designers face. The document5 produced by this effort has recommendations for the allowable tensile stresses to be used for web principal tension checks. The limits are provided for design of new bridges as well as for load rating of existing bridges. Both the current practice and FDOT's recommendations express the allowable tensile stress as a function of f^sub c^' using the known form: constant ×[the square root of]f^sub c^'. Although values between 0.25 and 0.33 in MPa (3.0 and 4.0 in psi) have been used for the constant, the author is not aware of any calibration studies based on structural reliability to determine its value. Furthermore, this expression implies that the focus is on the tensile principal stress σ^sub 1^ and ignores the accompanying compressive principal stress σ^sub 2^. It is well established in the literature6-10 that σ^sub 2^ has a significant effect on the tensile strength of concrete, especially if it is a compressive stress.