LA RELEVANCIA DE FACTORES EXÓGENOS: ¿LA INDEPENDENCIA DEL PROCESO EVALUATIVO DETERMINA LA UTILIZACIÓN DE LAS RECOMENDACIONES?

The NCHRP Report findings most relevant to the shear design and behavior of PC beams of interest to this research were discussed earlier in this report (NCHRP 322; 368; and 549), when the literature review from technical journal papers was presented. However, a summary of additional report information is provided below.

The objective of NCHRP 368, Calibration of LRFD Bridge Design Code (Nowak 1999) was to develop the reliability-based calibration for the Load Resistance Factor Design bridge design code. Load and resistance factors were derived so that the reliability of bridges designed using the proposed provisions will be at the predefined target level. The report describes the calibration procedure and reviews proposed changes to load and resistance models. It was found that the AASHTO Standard Specifications resulted in PC beam designs in shear that generally had reliability indices lower than the target proposed for the AASHTO LRFD Specification, with least- reliable beams being in the longer span ranges.

The code calibration procedure in the NCHRP 368 project was formulated including the following steps:

1) Selection of representative bridges:

About 200 structures were selected from various geographical regions of the United States. The selection was based on structural type, material, and geographical location. Bridges

were grouped by material (steel, reinforced concrete, prestressed concrete and wood), span (simple and continuous) and structural type (slab, beam, box, truss, arch). Current and future trends were considered. The selected set also included representative existing bridges. For each selected bridge, load effects (moments, shears, tensions and compressions) are calculated for various components. Load carrying capacities were also evaluated .State DOT's were requested to provide the drawings and other relevant information.

2) Establishing the statistical data base for load and resistance parameters:

The available data on load components, including results of surveys and other measurements, was gathered. Truck survey and weigh-in-motion (WIM) data were used for modeling live load. There was little field data available for dynamic load therefore a numerical procedure was developed for simulation of the dynamic bridge behavior. Statistical data for resistance included material tests, component tests and field measurements. Numerical procedures were developed for simulation of behavior of large structural components and systems.

3) Development of load and resistance models:

Load and resistance parameters were treated as random variables. Their variation was described by cumulative distribution functions (CDF) and correlations. For loads, the CDFs were derived using the available statistical data base (Step 2). The live load model included the presence of multiple trucks in one lane and in adjacent lanes. Multilane reduction factors were calculated for wider bridges. Dynamic load was modeled for single trucks and two tucks side-by-side. Moreover, resistance models were developed for girder bridges. The variation of the ultimate strength was determined by simulations. In this study

the reliability analysis was performed using the Rackwitz and Fiessler procedure, Monte Carlo simulations and special sampling techniques.

4) Development of the reliability analysis procedure:

Structural performance was measured in terms of reliability. Limit states were defined as mathematical formulas describing the state (safe or failure). Reliability was measured in terms of the reliability index, 𝛽. Reliability index is calculated the Rackwitz and Fiessler procedure. The developed load and resistance models (step 3) were part of the reliability analysis procedure.

5) Selection of the target reliability index:

Reliability indices are calculated for a wide spectrum of bridges designed according to the 1989 AASHTO Standard Specifications. The target reliability index, 𝛽_𝑇, was selected to provide a consistent and uniform safety margin for all structures.

6) Calculation of load and resistance factors:

Load (ϒ) and resistance (Q) factors were calculated so that the structural reliability of all bridges is close to the target value, 𝛽_𝑇.

NCHRP 454, Calibration of Load Factors for LRFR Bridge Evaluation (Moses 2001) presented the derivation of live load factors and associated checking criteria incorporated in the proposed Manual for Condition Evaluation and Load and Resistance Factor Rating of Highway

Bridges prepared for NCHRP Project 12-46. A major goal in the study was to unify the reliability

analyses and corresponding database used in the load and resistance factor rating (LRFR) and the recommendations for the Evaluation Manual compatible with the AASHTO LRFD bridge design specifications. Although the report considers all types of bridges, it provides no particular insight for the shear design or behavior of prestressed concrete bridges.

NCHRP 485, Bridge Software-Validation Guidelines and Examples (Baker et al. 2003) developed a process for bridge design and analysis software validation. The study has resulted in a test-bed of bridges with well-defined parametric inputs and outputs. This test-bed (or portions thereof) is readily usable by developers, end users, and others, and is available on CD-ROM. Using project 12-50 results, two or more software analysis packages and/or hand calculations with the same data set may be compared in tabular and/or graphical format. Project 12-50 permits drilling- down in the results to show how computations were performed and to clearly reveal differences between processes clearly. Various prestressed concrete sections were considered in the test-bed, and errors in some existing software for computing the shear in prestressed concrete girders were identified.

The objective of NCHRP 517, Extending Span Ranges of Precast Prestressed Concrete

Girders (Castrodale and White 2004) was to address the limitations caused by the infrequent use

of precast prestressed concrete girders for spans longer than 160 ft. The authors address this issue by extending the practical use of prestressed concrete girders to longer spans and to applications not normally associated with precast prestressed concrete girder construction. The major goal of the research was to provide a design procedure for long span precast, prestressed girders. Suggested design details and examples are presented. Particular attention was given to the effects of splicing long girders on shear and shear transfer through joints, with the interface shear at bent caps of interest.

NCHRP 549, Simplified Shear Design of Structural Concrete Members (Hawkins et al. 2005) developed simplified shear design provisions for the AASHTO LRFD Bridge Design Specifications that attempted would overcome perceived difficulties with using the previous shear

design provisions, which were the provisions of the Sectional Design Model. The detailed provisions recommended by this project were described earlier in this report.

NCHRP 579, Application of LRFD Bridge Design Specifications to High-Strength Structural

Concrete: Shear Provisions (Hawkins and Kuchma 2007), proposed guidelines to allow the use of

concrete strengths greater than 10 ksi, up to 18 ksi, for shear design. It addressed the compression angle θ; the proper concrete strength contribution to shear strength; minimum shear reinforcement; and maximum shear limits. It was found that the existing LRFD values for θ, β, and minimum shear reinforcement were safe to use for high strength concrete, but the maximum shear stress limit requires restriction.

In report NCHRP 654, Evaluation and Repair Procedures for Precast/Prestressed Concrete

Girders with Longitudinal Cracking in the Web (Tadros et al. 2010), a user’s manual was

established for the acceptance, repair, or rejection of precast/ prestressed concrete girders with longitudinal web cracking. The cracks of concern occur in the end zone as a result of prestress transfer, and may result in debonding and increased corrosion. Experimental tests determined that girder shear capacities were larger than estimated by code design procedures even with the longitudinal cracks present. The report proposes revisions to the AASHTO LRFD Bridge Design Specifications and provides recommendations to develop improved crack control reinforcement details for use in new girders. To achieve this objective, guidelines were established for various cracking categories such as: cracks that are not required to be repaired, cracks that are required to be repaired, including the methods and materials of repair, and cracks that cause structural capacity to be compromised and thus may cause the girders to be rejected.

Additional objectives were to propose revisions to the AASHTO LRFD Bridge Design Specifications as warranted, and to develop improved crack control reinforcement details for use in new girders.

NCHRP 678, Design of FRP Systems for Strengthening Concrete Girders in Shear (Belarbi et al. 2011) develops recommendations for a design method that can be used to strengthening concrete girders in shear using externally bonded FRP systems. It was found that beams with existing shear cracks displayed stirrup yield at a lower shear force than beams that did not have cracks, and limiting stirrup stress to the yield stress will avoid fatigue failures in the girder.

NCHRP 700, A Comparison of AASHTO Bridge Load Rating Methods (Mlynarski et al. 2011) compared the load factor rating to load and resistance factor ratings for various design vehicles. It provides proposals for changes to the AASHTO Manual for Bridge Evaluation through the extensive data analysis of 1,500 bridges of varying material types and structure configurations. The bridges were analyzed using the AASHTO Ware Virtis software (Thompson, 1999). It was found that a significant number of the girders analyzed achieved favorable LFR ratings but had LRFR ratings less than 1.0. This occurred because LRFR included evaluation criteria not covered by LFR that in fact governed the rating, though these criteria did not include prestressed concrete girder shear strength checks. However, for concrete structures, the suggested evaluation provisions include a check for shear capacity when the factored load effects from the permit load exceed the factored load effects from the design load, which was not previously included under LFR. Concrete bridges that show no visible signs of shear problems need not be checked for shear when rating for design or legal loads, however. Revisions to load factors for permit vehicles were suggested to increase the target reliability index to 3.5