where Tg is the glass transition temperature (or the heat distortion temperature) of the FRP composite material. The material manufacturer is required to provide proof that the material is fully cured before the designer can use the fully cured partial safety coefficients.

Additionally, the design resistance is multiplied by an analytical uncertainty factor that ranges from 0.5 to 1.0 depending on the sophistication of the analytical method used in the design procedure. The material partial safety factors and the analytical uncertainly factors provided are based on standard industry practice and were not determined by probabilistic methods. They do not provide a measurable reliability index. Load and Resistance Factor Design

A probability-based LRFD guide for FRP composite structures does not exist at present. Conceptually, the use of the LRFD approach for the design of FRP pultruded structures is quite possible and a prestandard outline has been prepared by ASCE (Chambers 1997). Fundamental issues associated with developing an LRFD procedure for pultruded FRP structural sections, with measurable reliability indices, have been discussed by Ellingwood (2003).

The difficulties associated with an LRFD reliability approach are primarily associated with the determination of the statistical material design properties for common pultruded sections. Since a standard material specification does not exist at this time, the statistical properties of pultruded materials are not well defined. A material specification for FRP composite materials for civil engineering applications has been proposed (Bank et al. 2002).

An LRFD procedure for the design of doubly symmetric and singly symmetric pultruded columns that accounts for global flexural buckling, global torsional buckling, flexural-torsional buckling, and material compression has been presented by Zureick and Scott (1997) and Zureick and Steffen (2000). According to these studies, load factors provided by ASCE 7-02 (2002) are used in conjunction with resistance factors that have been determined based on detailed tests of pultruded materials and pultruded column buckling experiments. Equations are presented for determining the capacity of the column with appropriate resistance factors as follows:

Doubly symmetric sections

Flexural buckling f = 0.85

Axial shortening f = 0.80 Singly symmetric angles

Flexural buckling f = 0.65

Flexural-torsional buckling f = 0.85

Compressive failure f = 0.50

For the singly symmetric angles Zureick and Steffen (2000) have targeted reliability indices, b, of 3, 3, and 4 for the flexural buckling, flexural-torsional buckling, and material compressive failure limit states. Design values for the material properties were based on the 95% lower confidence limit on the fifth percentile of the population, obtained from tests conducted on the materials. For doubly symmetric sections (Zureick and Scott 1997) a rigorous statistical analysis was not performed and the resistance factors were obtained from lower bounds of comparisons between experimental data and theoretical predictions. Reliability indices were therefore not provided for these resistance factors.

Based on a recent analysis, Ellingwood (2003) has concluded that as more data become available from experiments on FRP composites for structural applications, LRFD design procedures for FRP pultruded structural members "might be expected to fall in the following ranges'' (Ellingwood 2003): Performance-Based Design

A design can be based on a performance specification. In this approach the entire structure or a portion of the structure is required to meet certain performance requirements. The performance requirements are typically applied to both local and global deformations and capacities. Full-scale testing of the structure or a portion of the structure is usually required to meet the performance specification. Both proof testing of the actual structure and failure testing of a full-size mock-up of the structure (or parts thereof) are used.

In many cases for FRP composite structures a prescriptive set of material specifications is provided along with the structural performance requirements. The material specification can stipulate the manufacturing method, the limiting mechanical and physical properties of the materials produced, and the requirements for quality assurance testing.

The factor of safety for a PBD is defined in the design basis documents. ASTM and other standard test methods are usually used to conduct the performance testing. Special performance testing is defined in the design basis documents that are incorporated into the construction specifications.

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