Non-linear design of reinforced concrete
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The Secret Life of a Simple Beam
Non-linear analysis is a powerful method for reinforced concrete design, generating design data not available from the traditional Rectangular Stress Block (RSB) method (AS3600 Clause 8.1.3). An experienced engineer, using non-linear analysis, is able to better optimise design, for strength and serviceability, safety performance, and weight and cost.
Concrete under compression behaves in a highly non-linear manner. Definitions of concrete’s non-linear load response were first developed over 120 years ago, and take the general form of a fractional parabolic equation. Solution of such equations is not trivial, and their use in the design of reinforced concrete was not possible 120 years ago. To overcome this problem, a simplified method for estimating the moment strength of a given concrete section, based on the characteristics of the fractional parabolic curve, was introduced in the early 1900’s. This method was known as the Rectangular Stress Block (RSB) method. It provides a simple-to-calculate desk-top procedure to estimate the bending strength of a concrete beam. The RSB method is still used around the world today, 120 years after its initial introduction, and with little real change from its initial form.
Although RSB has a strong empirical basis, it is actually inconsistent in its applied theory. A number of assumptions are required to ensure the validity of the RSB method, and these assumptions are enforced in Clause 8.1 of AS3600 through the various factors and coefficients there defined. RSB is based on Euler-Bernoulli’s linear strain beam theory, which generally defines strain at the level of the bottom tension steel as being greater than ϵsy. Yet, one of the key assumptions of RSB is that bottom steel stress does not exceed fsy, which is inconsistent with the basic linear strain model. Under the RSB method, the location of the neutral axis (the k’ value) is fixed, yet k’ actually varies as the applied load increases, due to the non-linear behaviour of concrete. The RSB method gives no information on intermediate steel or concrete forces under varying applied loads. Importantly, the RSB method provides no indication of the overload behaviour of a beam, whether brittle or ductile. Non-linear analysis answers all of these issues, and in doing so, shines a spotlight on the previously secret life of a simple beam.
The non-linear design methodology presented here has been developed to become a desk-top application for structural engineers. It is simply the result of combining a number of existing well known and widely used engineering theories and practices, publicly available mean data rather than characteristic data on steel and concrete, and the non-linear design requirements of AS3600, along with application of an advanced mathematical package to solve the fractional parabolic concrete response equations. There is nothing new with this method, other than the way its components have been combined and presented.
This new non-linear analysis methodology provides valuable insights and improvements in concrete design. It opens new design concepts and hopefully will initiate a new approach to reinforced concrete design standards.