The fracture front in concrete, as well as rock, is blunted by a zone of microcracking, and in ductile metals by a zone of yielding. This blunting causes deviations from the structural size effect known from linear elastic fracture mechanics (LEFM). The size effect is studied first for concrete or rock structures, using dimensional analysis and illustrative examples. Fracture is considered to be caused by propagation of a crack band that has a fixed width at its front relative to the aggregate size. The analysis rests on the hypothesis that the energy release caused by fracture depends on both the length and the area of the crack band. The size effect is shown to consist in a smooth transition from the strength criterion for small sizes to LEFM for large sizes, and the nominal stress σN at failure is found to decline as (1+λ/λ0)-1/2 in which λ0=constant and λ=relative structure size. This function is verified by Walsh's test data. If reinforcement is present at the fracture front and behaves elastically, ...

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Size Effect in Blunt Fracture: Concrete, Rock, Metal

A precast segmental concrete bridge pier system is being investigated for use in seismic regions The proposed system uses unbonded posttensioning (UBPT) to join the precast segments and has the option of using a ductile fiber-reinforced cement-based composite (DRFCC) in the precast segments at potential plastic hinging regions The UBPT is expected to cause minimal residual displacements and a low amount of hysteretic energy dissipation The DFRCC material is expected to add hysteretic energy dissipation and damage tolerance to the system Small-scale experiments on cantilever columns using the proposed system were conducted The two main variables were the material used in the plastic hinging region segment and the depth at which that segment was embedded in the column foundation It was found that using DFRCC allowed the system to dissipate more hysteretic energy than traditional concrete up to drift levels of 36% Furthermore, DFRCC maintained its integrity better than reinforced concrete under high cyclic tensile-compressive loads The embedment depth of the bottom segment affected the extent of microcracking and hysteretic energy dissipation in the DFRCC This research suggests that the proposed system may be promising for damage-tolerant structures in seismic regions

Cyclic Response of Unbonded Posttensioned Precast Columns with Ductile Fiber-Reinforced Concrete

The segmental prestressed concrete box girder of Koror-Babeldaob (KB) Bridge in Palau, which had a record span of 241 m (791 ft), presents a striking paradigm of serviceability loss because of excessive multidecade deflections. The data required for analysis have recently been released and are here exploited to show how the analysis and design could be improved. Erected segmentally in 1977, this girder developed a midspan deflection of 1.61 m (5.3 ft) compared with the design camber after 18 years, and it collapsed in 1996 as a consequence of remedial prestressing, after a 3-month delay. Compared with three-dimensional analysis, the traditional beam-type analysis of box girder deflections is found to have errors up to 20%, although greater errors are likely for bridges with higher box-width-to-span ratios than the KB Bridge. However, even three-dimensional finite-element analysis with step-by-step time integration cannot explain the observed deflections when the current American Concrete Institute, Japan Society of Civil Engineers, Comite Euro-International du Beton (or Comite Euro- International du Beton—Federation internationale de la precontrainte), and Gardner and Lockman prediction models for creep and shrinkage are used. These models give 18-year deflection estimates that are 50-77% lower than measured and yield unrealistic shapes of the deflection history. They also predict the 18-year prestress loss to be 46-56% lower than the measured mean prestress loss, which was 50%. Model B3, which is the only theoretically based model, underestimates the 18-year deflection by 42% and gives a prestress loss of 40% when the default parameter values are used. However, in Model B3, several input parameters are adjustable and if they are adjusted according to the long-time laboratory tests of Brooks, a close fit of all the measurements is obtained. For early deflections and their extrapolation, it is important that Model B3 can capture realistically the differences in the rates of shrinkage and drying creep caused by the differences in the thickness of the walls of the cross section. The differences in temperature and possible cracking of the top slab also need to be taken into account. Other paradigms on which data have recently been released are four bridges in Japan and one in the Czech Republic. Their excessive deflections can also be explained. The detailed method of analysis and the lessons learned are presented in Part II. DOI: 10.1061/(ASCE)ST.1943-541X .0000487. © 2012 American Society of Civil Engineers. CE Database subject headings: Creep; Shrinkage; Box girders; Serviceability; Deflection; Span bridges. Author keywords: Prestressed box girder; Bridges; Segmental erection; Shear lag; Design standards; Concrete; Relaxation.

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Excessive Long-Time Deflections of Prestressed Box Girders. I: Record-Span Bridge in Palau and Other Paradigms

As a sequel to Part I, which clarified the causes of the unexpectedly large deflections of the Koror-Babeldaob Bridge in the Pacific island nation of Palau, Part II presents the numerical procedure and reviews the lessons learned. The box girder represents a thick shell that is discretized by eight-node, three-dimensional (3D) finite elements. Except for corrections due to cracking, concrete creep is assumed to follow aging linear viscoelasticity and is modeled by a rate-type law based on the Kelvin chain, the properties of which are adjusted for humidity conditions and temperature. In each time step and at each integration point, Widder’s formula is used to convert the aging compliance function to a continuous retardation spectrum for the current age of concrete, and discretization of the spectrum yields the current elastic moduli of the Kelvin units. The shrinkage strains depend on the environmental humidity and the thickness of each plate in the cross section. The computations proceed according to Bazant’s exponential algorithm, which is unconditionally stable and reduces the problem to a sequence of elasticity problems with an orthotropic effective stiffness of material and nonisotropic inelastic strains, different for each integration point in each time step. These problems are solved by commercial software ABAQUS. The segmental construction sequence is also modeled. The computer results reported in Part I explain the excessive deflections and compare the performance of various material models for creep and shrinkage. Part II formulates the lessons learned and makes recommendations for implementation.

Excessive Long-Time Deflections of Prestressed Box Girders. II: Numerical Analysis and Lessons Learned

Lateral load tests were performed on four full-scale precast concrete sandwich wall panels. The first panel was a typical precast, prestressed concrete sandwich panel that had shear transfer provided by regions of solid concrete in the insulation wythe, metal wythe connectors (M-ties), and bond between the concrete wythes and the insulation wythe. The degree of composite action developed by each shear transfer mechanism (regions of solid concrete, wythe connectors, and bond) was then evaluated by testing three additional panels that included only one mechanism each. The panels were tested in a horizontal position with simple supports under the action of a uniform lateral pressure. It was found that, for the panel geometries and materials treated in this study, the solid concrete regions provide most of the strength and stiffness that contribute to composite behavior. Steel M-tie connectors and bond between the insulation and concrete contribute relatively little to composite behavior. For design purposes, it is recommended that solid concrete regions be proportioned to provide all of the required composite action in a precast sandwich wall panel.

Experimental Evaluation of the Composite Behavior of Precast Concrete Sandwich Wall Panels

Basic Concepts Materials Flexural Analysis Flexural Design Shear and Torsion Partial Loss of Prestress Force Composite Beams Continuous Beams and Frames Deflections Slabs Axially Loaded Members Precast Construction Applications.

Arthur H. Nilson

Papers

Design of prestressed concrete