Design of Concrete Members Subjected to Uniaxial Bending and Compression Using Reinforcement Sizing Diagrams

ACI Structural Journal, Jan/Feb 2005 by Hernández-Montes, Enrique, Gil-Martín, Luisa María, Aschheim, Mark

Traditional approaches to the design of reinforced concrete members for flexural moment and axial load have emphasized analysis to determine the location of the neutral axis for a given configuration of longitudinal reinforcement and axial load. An alternate approach is described in this paper, wherein the reinforcement required to resist the specified design moment and axial load is determined as a function of the neutral axis depth. A range of neutral axis depths is considered, resulting in a number of potential design solutions consisting of different combinations of top and bottom reinforcement. These potential design solutions are portrayed graphically using a new diagram termed a reinforcement sizing diagram (RSD). The comprehensive set of solutions displayed by the RSD provides a basis for the design engineer to select a specific combination of top and bottom reinforcement to be used in a particular design. Reinforcement may be selected to minimize total reinforcement area or to accommodate nominal amounts of compression reinforcement as may be required for convenience in construction. Several examples are presented, illustrating the technique according to the assumptions adopted in the provisions of ACI 318 and Eurocode 2. The effects of optimal reinforcement on the axial load-moment interaction diagram are illustrated for one example.

Keywords: beams; columns; prestressed concrete; reinforced concrete.

(ProQuest Information and Learning: ... denotes formulae omitted.)

INTRODUCTION

The development of numerical analysis techniques in conjunction with dramatic improvements in computational power has contributed a great deal to the solution of analysis problems in structural engineering. Many of the assumptions and hypotheses required for analysis are now explicitly stated in provisions governing the design of structures, whereas earlier codes and provisions gave the engineer greater latitude in the choice of acceptable assumptions and simplifications. As the assumptions have become codified and as computer software now makes solutions to complex problems accessible, the design aids used in routine practice can make solutions to problems of greater complexity readily available to the engineer. The availability of these solutions allows the engineer to concentrate on the physical aspects of the design problem. For example, Chakrabarty1 describes the optimal design of singly-reinforced concrete beams.

Diagrams representing the interaction of axial load and moment on ultimate strength, known as P-M interaction diagrams, were presented originally by Whitney and Cohen2 in 1956 and continue to be widely used today. These diagrams provide solutions for the reinforcement required to resist a specified combination of axial load and moment under the constraint that the reinforcement is arranged in a predetermined pattern. A symmetric distribution of longitudinal reinforcement is typically assumed. However, a predetermined distribution of longitudinal reinforcement may not always be the most convenient or efficient form, and with today's computational abilities, a different basis may be more useful for establishing the required reinforcement.

Reinforcement sizing diagrams (RSDs) display a comprehensive set of acceptable combinations of top and bottom reinforcement, thereby allowing the engineer to rapidly select the reinforcement to be used in reinforced and prestressed concrete sections subjected to combined flexure and axial load. The diagrams allow the design engineer to choose a particular combination of top and bottom reinforcement that achieves whatever may be dictated by the design objectives, such as minimizing cost, facilitating construction, or providing a structure that has a very simple pattern of reinforcement. The focus of this paper is the potential savings in reinforcement where non-symmetric patterns of reinforcement are selected and the consequences of optimal (minimum) reinforcement on the P-M interaction diagram.

RESEARCH SIGNIFICANCE

This paper describes a new approach to the sizing of reinforcement in members subjected to combined flexure and axial load. Rather than using analysis to determine a neutral axis depth for a given configuration of reinforcement, the reinforcement required to provide adequate strength is determined as a function of the neutral axis depth. Acceptable combinations of top and bottom reinforcement are plotted as a function of the neutral axis depth on a new diagram, termed a reinforcement sizing diagram (RSD). This design aid provides the engineer with a new tool for selecting reinforcement to achieve design objectives. These objectives may include minimizing total reinforcement or accounting for compression reinforcement that may be used to facilitate construction. Significant savings in reinforcement may be achieved in some cases.

EQUILIBRIUM SOLUTIONS FOR CROSS SECTION STRENGTH

The design problem for combined flexure and axial load involves the simultaneous consideration of equilibrium, compatibility, and the constitutive relations of the steel and concrete materials at the section level.