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Publication Number: FHWA-HRT-06-115
Date: August 2006

Index, Structural Behavior of Ultra-High Performance Concrete Prestressed I-Girders

CHAPTER 7. DESIGN PHILOSOPHY FOR UHPC BRIDGE GIRDERS

7.1 Introduction

The experimental research and associated analyses undertaken in this research program provide significant insight into the potential structural behavior of UHPC bridge girders. The design of prestressed concrete I-girders normally focuses on flexural and shear behaviors. The results of this research program indicate that the flexural and shear behaviors of prestressed I-girders that are composed of UHPC can be modeled through straightforward analytical procedures. Therefore, rational design of UHPC I-girders based on these same analytical principles is possible. This chapter presents a rational design philosophy for prestressed UHPC I-girders.

7.2 Flexure

The flexural behavior of an AASHTO Type II UHPC girder has been extensively discussed in this report. The behavior of this girder from initial elastic loading through failure was analyzed to determine the contribution of the UHPC to the overall flexural behaviors of the girder. Figure 70 provides the analytically determined uniaxial stress-strain response of UHPC within the girder during the test. With this knowledge, the flexural design for other prestressed I-girders is possible.

The design of a prestressed UHPC I-girder for flexure requires only two factors. First, a conservative approximation of the UHPC’s uniaxial stress-strain response must be applied to the cross section. Second, the occurrence of the expected flexural behaviors must be ensured. A primary factor must be taken into consideration in an I-girder to ensure the expected UHPC behavior: Sufficient prestressing strands or mild steel reinforcement must exist in the primary flexural tensile regions so that cracks in the UHPC remain tightly closed and closely spaced. Without sufficient gross reinforcement restraining the tensile flexural regions, individual cracks will begin to widen as the fibers pull out, and the tightly spaced cracking, shown in figure 16, probably will not occur.

Determining a sufficiently conservative approximation of UHPC uniaxial stress-strain behavior depends on the structure and on the prescribed design limits. In a situation where cracking of the girder is not allowed at service loads, the girder can easily be designed using normal design procedures with the known modulus of elasticity and tensile cracking strength of UHPC. In a situation where a minimal amount of cracking will be allowed at service loads, a postcracking uniform tensile stress capacity will need to be assumed. Finally, for the ultimate load state, a full compressive and tensile stress-strain response will be required. This response will include an effective tensile strain that causes fiber pullout, a limiting tensile capacity relevant at any strain below the fiber pullout strain, and a limiting compressive strength.

A conservative uniaxial stress-strain response for UHPC could be described by the following three conditions. First, the UHPC could be assumed to behave in a linear elastic manner in compression up to 0.85 times the compressive strength. Second, in tension, the UHPC could be assumed to behave in a rigid-plastic fashion at a conservative percentage of the postcracking tensile capacity at strains below the tensile pullout strain. Third, based on the results presented in this report, sample values could include 165 MPa (24 ksi) for the compressive strength, 10.3 MPa (1.5 ksi) for the tensile capacity, and 0.007 for the limiting tensile strain. Figure 77 graphically presents this sample stress-strain behavior.

Figure 77. Graph. Sample uniaxial stress-strain behavior for I-girder flexural design. This figure graphically represents the assumed U H P C stress-strain response that would coincide with the proposed flexural design philosophy. The compressive behavior is linear elastic according tot the modulus of elasticity up to 0.85 times the compressive strength. In tension, the graph shows a rigid plastic behavior wherein the U H P C displays a constant tensile capacity of 1.5 megapascals (3.1 times 10 to the fourth pounds per square inch) from 0 to 7,000 microstrain tension.

1 MPa = 145 psi

Figure 77. Graph. Sample uniaxial stress-strain behavior for I-girder flexural design.

Determining the flexural capacity of a UHPC I-girder using a stress-strain response such as the one shown in figure 77 can be completed using basic mechanics of materials concepts. A number of iterations on the neutral axis depth and on the limiting strain condition will likely be needed before a final solution is reached.

7.3 Shear

The shear behavior of prestressed UHPC I-girders also was extensively discussed in this report. Three AASHTO Type II prestressed girders that did not contain any mild steel shear reinforcement or any draped prestressing strands were tested to determine their shear capacities. The shear capacities exhibited by these girders were very large in comparison to normal AASHTO Type II girders. The behaviors also were very consistent with the mechanics of materials concepts of the flow of tensile and compressive forces in the shear region of a bridge girder.

A basic design philosophy, based on these results, is proposed to aid in the shear design of UHPC girders. The results presented in section 6.5 indicate that a reasonable estimate of the shear capacity can be determined by assuming that all shear forces are carried by diagonal tension and compression in the web of the girder. Given the high compressive strength of UHPC, the limiting value will be the postcracking tensile stress capacity. The shear capacity of a UHPC girder can be conservatively estimated with the area of the web as a variable and an approximated angle of the diagonal tensile failure plane in the girder. A conservative estimate of the average tensile stress capacity of UHPC must be known before the fiber pullout.

The analyses discussed in section 6.5 indicate that the average tensile strengths in the unreinforced webs of two AASHTO I-girders were 12.4 MPa (1.8 ksi) and 15.9 MPa (2.3 ksi). In both cases, conservatively large shear areas were assumed so that the average tensile strength determined was minimized. Regardless, a conservative estimate of the available average tensile strength of UHPC could be set at a reasonable percentage of the observed strengths. From this value, the shear failure plane area required can be determined, which leads directly to the necessary dimensions of the girder web.

To ensure that the expected shear behaviors occur, the girder must be detailed to allow for tight crack spacing and small crack widths in the highly stressed shear region. Therefore, to ensure this cracking behavior, the shear region must be restrained by the top and bottom flanges of the girder. Additionally, draped prestressing strands that pass through highly stressed shear regions will likely help to retard crack growth. However, even with these details, the crack-restraining actions in the web will not be as efficient as the ones that occur in the bottom flange of a prestressed girder. Thus, the tensile stress and strain capacities, discussed in section 7.2, are not expected to be applicable in this situation.

Finally, determining the state of stress in the girder web under prestressing and dead loads is important when designing a prestressed girder for shear. The significant compressive forces in the web could possibly delay the onset of tensile cracking and the eventual tensile fiber pullout behaviors.

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