Abstract
Conservativeness (or conservatism), in general, is a measure of the lack of confidence in any activity that we do in the spheres of life. It is a reflection of our apprehension for the consequences of failure, and hence we instinctively tend to be conservative in order to be safe. Engineering design involves incorporation of various physical characteristics of the materials and systems through various mathematical models and design criteria. These models and criteria are developed based on empirically observed, experimentally measured, logically anticipated, analytically testified and/or hybrid behaviours and responses of materials and systems. All these processes invariably involve uncertainties arising from the deficiency in terms of knowledge, data and time-testimony. Uncertainties also arise from the lack of precision in expressing a phenomenon or mechanics, or from the inherent variability associated with them. All these factors lead to lack of confidence in the use of materials and systems, and compels our designs to be conservative. Comprehending uncertainties in engineering design, and refining their design treatment can pay big dividends.Design of fibre reinforced polymer (FRP) based structural strengthening systems involves an interesting interplay of uncertainties between those inherent in the existing structure being strengthened and those arising from the lack of complete knowledge and time-testimony of using FRP composites for structural strengthening. Most strengthening design guidelines tend to be more conservative than the conventional structural design norms in order to meet the safety targets. A popular approach for achieving this requirement is through prescribing a set of safety factors within the strengthening design, which are substantially higher compared to those used in structural design using conventional materials like concrete and steel. However, FRP composites in general, and their use as externally bonded reinforcement in particular, involve considerable peculiarities compared to the conventional structural materials. Also, the type and form of post-strengthening failure modes exhibit substantial qualitative distinctions compared to the pre-strengthening failure modes. Therefore, the design processes for strength (for new constructions) and additional strength (for strengthening existing structures) can have conflicting design requirements and objectives. A strategy of prescribing quantitatively higher safety factors, under this condition, could be ineffective in producing required conservativeness for some design scenarios, and can instigate undesirable side-effects.
This thesis aims at assessing performance of flexural and shear strengthening design processes under the identified contradictory and contrasting features of the safety format used in strengthening design. It also provides a deeper interpretation of conservativeness in strengthening design by identifying implications of the means employed for producing conservativeness on the course of strengthening design process and on the quality of the resultant strengthening design solutions.
An exhaustive review of literature, spanning over past three decades, on the design for structural strengthening using externally bonded FRP reinforcement has been carried out. This review has identified various sources of uncertainties, gap in knowledge and design conflicts associated with the mechanics of FRP-based structural strengthening systems. Detailed taxonomies of uncertainties and safety parameters concerning FRP-based structural strengthening systems have been proposed. The uncertainties are classified into constitutive and behavioural uncertainties. The former are attributed to the variability in constitutive material properties of FRP, while the latter are due deviations between the ideally expected or real behaviours of FRP composites and that predicted within the design process.
A comprehensive mapping of the identified uncertainties and safety parameters is developed, which presents a framework that enables analytical treatment of conservativeness within strengthening design. This mapping indicates four distinct levels at which safety parameters in various forms are incorporated within the design process with an intention to produce conservativeness while estimating the design value of post-strengthening resistance. The first two of these four levels within the strengthening design process include various safety parameters are prescribed on the mean and characteristic values of FRP material properties to arrive at their design values. This approach aims at setting ‘reserved strength’ while estimating the design post-strengthening resistance by under estimating the load carrying capacity of the FRP-based structural strengthening system. This reserved strength accounts for the constitutive uncertainties, and the conservativeness produced in design post-strengthening resistance due to safety parameters prescribed on FRP material properties is called the material conservativeness. The last two of the four levels within the strengthening design process include various safety parameters are prescribed on the nominal values of resistance contribution of FRP reinforcement and strengthened member to arrive at the design post-strengthening resistance. This approach aims at setting ‘over strength’ while estimating the design post-strengthening resistance by under estimating the load carrying capacity of the FRP-based structural strengthening system. This over strength accounts for the behavioural uncertainties, and the conservativeness produced in design post-strengthening resistance due to safety parameters prescribed on resistance is called the resistance conservativeness. The aggregative effect of the material and resistance conservativeness comprises the total conservativeness, which can be segregated from the design post strengthening resistance of a strengthening design solution. This process, when performed for a range of flexural and shear strengthening design solutions, enables assessing the effectiveness of various safety formats in producing conservativeness under different design scenarios. Conservativeness in estimation of the post-strengthening resistance, being a direct indicator of the global safety targets (e.g., probability of failure and reliability index), presents a very useful insight for a designer as well as for a calibrator of strengthening design guidelines.
In addition to enabling the analytical treatment of conservativeness, the mapping of uncertainties and safety parameters also reveals some interesting facts, which by-and-large remain hidden within the different formats of prescribing design criteria. Firstly, it reveals existence of ‘failure mode switchers’ within the strengthening design process. The strategic locations of these switchers set bifurcations within the strengthening design process by manipulating the design predictions for the modes of failure for an externally bonded FRP reinforcement (e.g., rupture and debonding). It is shown in this thesis that different modes of failure of FRP are differently sensitive to the safety parameters prescribed on FRP material properties. It is also shown that certain formats of the failure mode switcher (e.g., switcher for flexural strengthening according to ACI440) can quantitatively inflate the prescribed material safety parameters, without projecting any increase in the safety factors on FRP material properties. Thus, understanding of the working mechanism of failure mode switchers in manipulating modes of failure of FRP can be a means of controlling conservativeness. Switchers in flexural and shear strengthening design processes are identified, and the mathematical criteria depicting design predictions for modes of failure of FRP are presented.
Secondly, the contention raised by the fact that the material and resistance safety parameters account for the constitutive and behavioural uncertainties respectively sets a ground to contest the strategy, adopted by many strengthening design guidelines, of not prescribing safety factors on post-strengthening structural resistance merely on the basis of the differences arising from the limit state design (LSD) and load and resistance factor design (LRFD) philosophies. In light of the confirmed differential sensitivity of various failure modes to the material safety parameters, it is demonstrated that such a strategy not only suggests ignorance towards accounting behavioural uncertainties in strengthening design, but also results into substantial reduction in conservativeness in estimated design post-strengthening resistance for strengthening design solutions governed by certain types of failure modes.
Assessment methodologies for flexural and shear strengthening are developed, which provide a common platform for comprehending flexural and shear strengthening design processes irrespective of all the philosophical and operational distinctions associated with various strengthening design guidelines. Both methodologies are in non-dimensional format, which can be calibrated against any existing strengthening design guidelines. For illustration, these methodologies are calibrated against ACI440 and TR55 design specifications. The assessment methodology for flexural strengthening design is based on ductility-based definitions of the post-strengthening failure modes. These definitions takes the strain in tension steel reinforcement as a prime parameter that intuitively classifies the possible post-strengthening failure modes into concrete- and FRP-controlled failure modes covering all the possible variants based on sectional ductility and possibility of debonding or rupture of FRP. The assessment methodology for shear strengthening design presents the shear resistance contribution of FRP reinforcement comprising of an effective failure strain in FRP with modifications accounting for variations in orientation of principal fibres and wrapping configurations. These design solutions are primarily clustered into productive and unproductive design solutions. The former and the latter involve a positive and a non-positive value of shear resistance contribution of FRP under given conditions respectively. These methodologies present a complete picture of the internal architecture of flexural and shear strengthening design processes, and enable tracking propagation of conservativeness within them.
Both methodologies can produce a wide range of possible strengthening design solutions under given conditions, which can be clustered according to their qualitative characteristics and governing failure modes. The influence of differences in qualitative and quantitative prescriptions for various safety parameters, and different formats of FRP debonding limits, FRP bond length models, failure mode switchers and different approaches for accounting bond reduction (for FRP shear reinforcements only) on strengthening design processes are captured through a set of parametric and sensitivity analyses.
Based on this study it is concluded that the quantitative prescription of the material safety parameters can influence the design predictions for the modes of failure of FRP and the governing post-strengthening failure mode for the strengthening design solutions. This in turn, influences the course of strengthening design process and quality of strengthening design solutions considerably. Mathematical expressions depicting various post-strengthening failure modes and their design predictions within flexural strengthening design are provided. Mathematical criteria for avoiding undesirable failure modes and promoting optimal design solutions are also provided. For the strengthening design guidelines not prescribing resistance safety parameters (e.g. TR55), suitable strength reduction factors to compensate for the reduced in conservativeness for the design solutions governed by concrete-controlled and FRP controlled involving debonding of FRP are recommended. It is also recommended to include design criteria for mechanically anchored FRP reinforcement allowing an increase in the permissible strain in FRP at debonding towards better utilising the higher rupture strain capacity FRP materials. It is concluded that a certain format of debonding strain limit (e.g., according to ACI440) can produce significantly higher permissible value of strain in FRP at debonding, especially for low modulus high rupture strain capacity FRP materials. An upper limit, in form of a pre-set numerical constant strain value, is suggested for such circumstances. An apparent oversight in the numerical values for bond reduction coefficients for FRP shear reinforcement prescribed by ACI440 is identified. It is demonstrated that this values of bond reduction coefficients are thrice as high as compared to those prescribed by TR55, and results into a substantial increase in the extent of unproductive shear strengthening design solutions. A modification of these values is recommended.
It is suggested that the utility of this study can further be increased by developing an expert system based on the directions and knowledge-based presented within this study. The applicability of this study can be expanded by converting it into probability-based reliability format that can inform us on the fragility and risk profiling. It is also shown that the concept of conservativeness can also be extended to cover issues related to structural robustness and resiliency.
| Date of Award | 1 Jan 2014 |
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| Original language | English |
| Awarding Institution |
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| Supervisor | Tim Ibell (Supervisor), Antony Darby (Supervisor) & Mark Evernden (Supervisor) |
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