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

The American Society for Testing and Materials (ASTM) is an independent organization devoted to the development of standards.

American Society for Testing and Materials

The “Building Code Requirements for Structural Concrete” (“Code”) covers the materials, design, and construction of structural concrete used in buildings and where applicable in nonbuilding structures. The Code also covers the strength evaluation of existing concrete structures. Among the subjects covered are: contract documents; inspection; materials; durability requirements; concrete quality, mixing, and placing; formwork; embedded pipes; construction joints; reinforcement details; analysis and design; strength and serviceability; flexural and axial loads; shear and torsion; development and splices of reinforcement; slab systems; walls; footings; precast concrete; composite flexural members; prestressed concrete; shells and folded plate members; strength evaluation of existing structures; provisions for seismic design; structural plain concrete; strut-and-tie modeling in Appendix A; alternative design provisions in Appendix B; alternative load and strength reduction factors in Appendix C; and anchoring to concrete in Appendix D. The quality and testing of materials used in construction are covered by reference to the appropriate ASTM standard specifications. Welding of reinforcement is covered by reference to the appropriate American Welding Society (AWS) standard. Uses of the Code include adoption by reference in general building codes, and earlier editions have been widely used in this manner. The Code is written in a format that allows such reference without change to its language. Therefore, background details or suggestions for carrying out the requirements or intent of the Code portion cannot be included. The Commentary is provided for this purpose. Some of the considerations of the committee in developing the Code portion are discussed within the Commentary, with emphasis given to the explanation of new or revised provisions. Much of the research data referenced in preparing the Code is cited for the user desiring to study individual questions in greater detail. Other documents that provide suggestions for carrying out the requirements of the Code are also cited.

"building code requirements for structural concrete (aci 318-11) and commentary"

A model for evaluating structural damage in reinforced concrete structures under earthquake ground motions is proposed. Damage is expressed as a linear function of the maximum deformation and the effect of repeated cyclic loading. Available static (monotonic) and dynamic (cyclic) test data were analyzed to evaluate the statistics of the appropriate parameters of the proposed damage model. The uncertainty in the ultimate structural capacity was also examined.

Mechanistic Seismic Damage Model for Reinforced Concrete

In the usual local finite element analysis, strain softening causes spurious mesh sensitivity and incorrect convergence when the element is refined to vanishing size. In a previous continuum formulation, these incorrect features were overcome by the imbricate nonlocal continuum, which, however, introduced some unnecessary computational complications due to the fact that all response was treated as nonlocal. The key idea of the present nonlocal damage theory is to subject to nonlocal treatment only those variables that control strain softening, and to treat the elastic part of the strain as local. The continuum damage mechanics formulation, convenient for separating the nonlocal treatment of damage from the local treatment of elastic behavior, is adopted in the present work. The only required modification is to replace the usual local damage energy release rate with its spatial average over the representative volume of the material whose size is a characteristic of the material. Avoidance of spurious mesh ...

Nonlocal damage theory

An experimental study of the strength and behavior of plain concrete subjected to repetitions of compressive stress of relatively high magnitude is described and evaluated. The characteristics of the loading and unloading stress-strain relationships of 46 short rectangular columns are studied. Expressions for these relationships are derived and used to estimate the response of plain concrete subjected to varying load histories. The expressions developed are functions of the ultimate stress and strain values of standard 6 × 12-in. control cylinders and the loading history. The results indicate that the response at a given point in the load history is dependent on the preceeding loading and that the number of cycles to failure can be reasonably estimated.

Behavior of concrete under compressive loadings

An equation has been developed for calculating lengths of lap splices of deformed bars from a nonlinear regression analysis of test results of beams with lap splices. It reflects the effect of length, cover, spacing, bar diameter, concrete strength, transvers reinforcement, and moment gradient on the strength of lap splices. The equation is also applicable in determining basic development lengths. Based on the equation developed, design recommendations are proposed for development lengths and lap splices and compared with AASHTO Interim Specifications for Bridges, 1974. The comparison shows that for the most unfavorable splice conditions (a clear cover of 1-1/2 in. on sides or bottom, splices with no transverse reinforcement, all bars spliced in a region of maximum moment, and bar spacing less than 6 in. on centers) AASHTO provisions overestimate lap lengths by 11 percent for #6, 16 percent for #8, and 25 percent for #11 bars. If cover is increased to 3 in. or transverse reinforcement is added, the splice length of large bars may be reduced by as much as 60 percent over that required by present AASHTO provisions. Furthermore, the equations governing development length are essentially the same as those for splice length. /FHWA/

The strength of anchor bars: a reevaluation of test data on development length and splices

Reevaluation of test data on development length and splices

Recommendations for design of beam-column joints in monolithic reinforced concrete structures.

The use of steel bracing systems for retrofitting seismically inadequate reinforced concrete frames is examined. Diagonal bracing provides an excellent approach for strengthening and stiffening existing buildings for lateral forces. A variety of retrofitting objectives, ranging from drift control to collapse prevention, can be achieved. The designer can determine the force path in the retrofitted structure and adjust the strength and stiffness as needed. An analytical study is performed to gain understanding into the behavior of a braced frame under cyclic lateral loading, particularly frames with weak short columns. Inelastic buckling of the braces influences detrimentally the inelastic cyclic behavior of a braced frame. Instability can be prevented by using braces that yield in compression or buckle elastically at low axial loads. The advantages of altering beams of a braced frame with weak short columns are described. The beam strength can be reduced to produce a more favorable (ductile) frame failure mechanism. Combining bracing with beam alterations can significantly improve inelastic behavior of the braced frame.

James O. Jirsa

Papers

Behavior of concrete under compressive loadings

The strength of anchor bars: a reevaluation of test data on development length and splices

Reevaluation of test data on development length and splices

Recommendations for design of beam-column joints in monolithic reinforced concrete structures.

Steel Bracing of RC Frames for Seismic Retrofitting