A stress‐strain model is developed for concrete subjected to uniaxial compressive loading and confined by transverse reinforcement. The concrete section may contain any general type of confining steel: either spiral or circular hoops; or rectangular hoops with or without supplementary cross ties. These cross ties can have either equal or unequal confining stresses along each of the transverse axes. A single equation is used for the stress‐strain equation. The model allows for cyclic loading and includes the effect of strain rate. The influence of various types of confinement is taken into account by defining an effective lateral confining stress, which is dependent on the configuration of the transverse and longitudinal reinforcement. An energy balance approach is used to predict the longitudinal compressive strain in the concrete corresponding to first fracture of the transverse reinforcement by equating the strain energy capacity of the transverse reinforcement to the strain energy stored in the concret...

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Theoretical stress strain model for confined concrete

*Co-chairs of the subcommittee that prepared this document. Note: The committee acknowledges the contribution of associate member Paul Kelley. ACI encourages the development and appropriate use of new and emerging technologies through the publication of the Emerging Technology Series. This series presents information and recommendations based on available test data, technical reports, limited experience with field applications, and the opinions of committee members. The presented information and recommendations, and their basis, may be less fully developed and tested than those for more mature technologies. This report identifies areas in which information is believed to be less fully developed, and describes research needs. The professional using this document should understand the limitations of this document and exercise judgment as to the appropriate application of this emerging technology.

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Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures

A concise state-of-the-art survey of fiber-reinforced polymer (also known as fiber-reinforced plastic) composites for construction applications in civil engineering is presented. The paper is organized into separate sections on structural shapes, bridge decks, internal reinforcements, externally bonded reinforcements, and standards and codes. Each section includes a historical review, the current state of the art, and future challenges.

Fiber-Reinforced Polymer Composites for Construction—State-of-the-Art Review

The concept of designing structures to achieve a specified performance limit state defined by strain or drift limits was first introduced, in New Zealand, in 1993. Over the following years, and in particular the past five years, an intense coordinated research effort has been underway in Europe and the USA to develop the concept to the stage where it is a viable and logical alternative to current force-based code approaches. Different structural systems including frames, cantilever and coupled walls, dual systems, bridges, wharves, timber structures and seismically isolated structures have been considered in a series of coordinated research programs. Aspects relating to characterization of seismic input for displacement-based design, and to structural representation for design verification using time-history analysis have also received special attention. This paper summarizes the general design approach, the background research, and some of the more controversial issues identified in a book, currently in press, summarizing the design procedure. perceived in terms of simple mass-proportional lateral forces, resisted by elastic structural action. In the 1940's and 50's the influence of structural period in modifying the intensity of the inertia forces started to be incorporated into structural design, but structural analysis was still based on elastic structural response. Ductility considerations were introduced in the 1960's and 70's as a consequence of the experimental and empirical evidence that well- detailed structures could survive levels of ground shaking capable of inducing inertia forces many times larger than those predicted by elastic analysis. Predicted performance came to be assessed by ultimate strength considerations, using force levels reduced from the elastic values by somewhat arbitrary force-reduction factors, that differed markedly between the design codes of different seismically-active countries. Gradually this lead to a further realization, in the 1980's and 90's that strength was important, but only in that it helped to reduce displacements or strains, which can be directly related to damage potential, and that the proper definition of structural vulnerability should hence be related to deformations, not strength. This realization has lead to the development of a large number of alternative seismic design philosophies based more on deformation capacity than strength. These are generally termed " performance-based" design philosophies. The scope of these can vary from comparatively narrow structural design approaches, intended to produce safe structures with uniform risk of damage under specified seismicity levels, to more ambitious approaches that seek to also combine financial data associated with loss-of-usage, repair, and a client-based approach (rather than a code-specified approach) to acceptable risk. This paper does not attempt to provide such ambitious guidance as implied by the latter approach. In fact, it is our view that such a broad-based probability approach is more appropriate to assessment of designed structures than to the design of new structures. The

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Displacement-based seismic design of structures

This book should be of interest to practicing bridge designers and researchers investigating the seismic design of bridges It is appropriate for graduate courses or upper level undergraduate courses in seismic design of bridges The approach relies heavily on the principles of capacity design, where a strength hierarchy is established in a bridge to ensure that damage is controllable and occurs only where the designer intends This approach, which is well established for seismic design of buildings, has been extended and modified to reflect the special demands and characteristics of bridges Particular emphasis is placed on designing adequate displacement and ductility capacity into new bridges, with less significance placed on strength The book is developed around two alternative design strategies: the traditional force-based approach where force levels are related to acceleration spectra, with checks to ensure adequate displacement capacity exists, and the newer displacement-based design approach, where displacements are the starting point in the design Introductory chapters discuss design philosophy and its impact on the performance of bridges in recent earthquakes, seismicity and soils effects, including liquefaction, in a form facilitating understanding by structural engineers, and the importance of rational consideration, from a seismic design viewpoint, of the various structural configuration possibilities in the conceptual design phase Extensive discussion of analysis is provided in Chapter 4, with emphasis on the importance of realistic modeling assumptions and appropriate choice of analytical tools Chapters 5 to 8 provide detailed information on the design of new bridges and the assessment and retrofit of existing bridges A separate chapter is devoted to design and retrofit using seismic isolation and dissipation devices Many design and analysis examples, some quite extensive in scope, are included Design aids in the form of charts and tables are also provided An index is provided

Seismic Design and Retrofit of Bridges

Thirty‐one nearly full‐size reinforced concrete columns, of circular, square, or rectangular wall cross section, and containing various arrangements of reinforcement, were loaded concentrically with axial compressive strain rates of up to 0.0167/s. The circular sections contained longitudinal and spiral reinforcement, the square sections contained longitudinal reinforcement and square and octagonal transverse hoops, and the rectangular wall sections contained longitudinal reinforcement and rectangular hoops with or without supplementary cross ties. The longitudinal stress‐strain behavior of the confined concrete was measured and compared with that predicted by a previously derived stress‐strain model with allows for the effects of various configurations of transverse confining reinforcement, cyclic loading, and strain rate. The measured longitudinal concrete compressive strain when the transverse steel first fractured was also compared with that predicted by equating the strain energy capacity of the tran...

Observed Stress‐Strain Behavior of Confined Concrete

Strength and ductility of concrete bridge columns under seismic loading

One of the major developments in seismic design over the past 10 years has been increased emphasis on limit states design, now generally termed Performance Based Engineering. Three techniques - the capacity spectrum approach, the N2 method and direct displacement-based design have now matured to the stage where seismic assessment of existing structures, or design of new structures can he carried out to ensure that particular deformation-based criteria are met The paper will outline and compare the three methods, and discuss them in the context of traditional force-based seismic design and earlier design approaches which contained some elements of performance based design. Factors defining different performance states will be discussed, including the need, not yet achieved, to include residual displacement as a key performance limit. Some emphasis will be placed on soil-related problems, and the incorporation of soil/structure interaction into performance-based design. It will be shown that this is relatively straightforward and results in consistent design solutions not readily available with force-based designs using force-reduction factors.

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M. J. N. Priestley

Papers

Theoretical stress strain model for confined concrete

Seismic Design and Retrofit of Bridges

Observed Stress‐Strain Behavior of Confined Concrete

Strength and ductility of concrete bridge columns under seismic loading

Performance based seismic design