5To prevent damage caused by corroding reinforcement, fiber reinforced polymer (FRP) 6 reinforcing bars have been used in place of steel in a relatively small but increasing number of 7 structures in the civil infrastructure. A concern with the use of traditional FRP bars, however, is 8 the resulting lack of ductility. This problem has been overcome with the development of a new 9 generation of composite reinforcement, ductile hybrid FRP (DHFRP) bars. However, standards 10 that address the design of DHFRP bars are unavailable, and appropriate resistance factors for the 11 use of DHFRP reinforcement are unknown. In this study, a reliability analysis is conducted on 12 tension-controlled concrete flexural members reinforced with DHFRP, with the intent to estimate 13 potential strength reduction factors. Flexural members considered include a selection of 14 representative bridge decks and building beams designed to meet AASHTO LRFD and ACI-318 15 strength requirements and target reliability levels. Nominal moment capacity is calculated from 16 standard analytical models and is taken as first DHFRP material failure. Statistical parameters 17 for load and resistance random variables in the reliability model are consistent with previous 18 code calibration efforts. The resulting resistance factors ranged from 0.61 to 0.64 for tension-19 controlled sections, which indicates a potential increase in allowed strength over flexural 20 members using non-ductile bars.

Behnam, B., and Eamon, C. (2013). "Reliability-based design optimization of concrete flexural members reinforced with ductile FRP bars." Construction and Building Materials, 47, 942-950, doi: 10.1016Materials, 47, 942-950, doi: 10. /j.conbuildmat.2013 ABSTRACTIn recent years, ductile hybrid FRP (DHFRP) bars have been developed for use as tensile reinforcement. However, initial material costs regain high, and it is difficult to simultaneously meet strength, stiffness, ductility, and reliability demands. In this study, a reliability-based design optimization (RBDO) is conducted to determine minimum cost DHFRP bar configurations while enforcing essential constraints. Applications for bridge decks and building beams are considered, with 2, 3, and 4-material bars. It was found that optimal bar configuration has little variation for the different applications, and that overall optimized bar cost decreased as the number of bar materials increased.

Steel-reinforced concrete structural components are often associated with significant maintenance costs as a result of reinforcement corrosion. To mitigate this problem, fiberreinforced polymer (FRP) bars have been used in place of traditional steel reinforcement for some applications. The non-ductile response of typical FRP bars is a concern, however. To overcome this problem, hybrid ductile FRP (HDFRP) bars have been developed for use in concrete flexural members with resulting ductility indices similar to sections reinforced with steel. In this study, five different HDFRP bar concepts are analyzed and compared in terms of ductility, stiffness, and relative cost. Of primary interest is the effect that the number of materials used in bar construction has on performance. Reinforced concrete beam and bridge deck applications are considered for analysis. It was found that all HDFRP-reinforced flexural members considered could meet code-specified strength and ductility requirements for steelreinforced sections, although service load deflections were approximately twice that of steelreinforced sections of the same depth. In general, ductility increased, and overall material cost decreased, as the bar material layers increased from 2 to 4. The 4-material continuous fiber bar approach was found to be most promising, with high ductility as well as relatively low cost.

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Many problems associated with the use of normal weight concrete have been solved with the development of structural ultra-lightweight engineered cementitious composite (SULWECC) that has the capability to exhibit strain-hardening behavior prior to failure. However, the feasibility and standards that address the design of such engineered cementitious composites (ECC) in flexural slab systems are not available. In this study, reliability analysis and calibration process are carried out on three different SULWECC slab systems with the intention of estimating the potential flexural resistance factors. Although the high volume of randomly dispersed synthetic short fiber is considered the main reinforcement, SULWECC slab systems internally reinforced with carbon FRP mesh are also considered. The reinforcement ratio is selected so that the section is under-reinforced. Relevant load and resistance random variables are used, and appropriate statistical parameters are selected. The target reliability indices are chosen to be consistent with those used to develop current design code specifications. The nominal moment capacity is calculated based on a new model that consists of: elastic linear stress distribution in the compression zone and elastic-perfectly-plastic uniform stress distribution in the tension zone. The determined flexural resistance factors ranged from 0.59 to 0.69, although higher values are justifiable in special circumstances. The average slab thickness needed to satisfy the strength requirements ranged from 1/37 to 1/22 times the slab length. Flexural toughness to measure ductility is evaluated using load-deflection curves of experimentally tested SULWECC specimens.