How moment redistribution leads to more efficient designs

In this tutorial, we’ll discuss moment redistribution in reinforced concrete. We’ll see how we can use the plastic behaviour of reinforced concrete at the ultimate limit state to develop more efficient designs. We’ll do this by first explaining the moment redistribution behaviour in a statically indeterminate structure and then exploring what it means for the design of reinforced concrete sections.

I’ll assume that you have some familiarity with reinforced concrete section analysis. If not, read my previous article on reinforced concrete fundamentals first.

If you want to take a deeper dive into reinforced concrete design and see how we can use Python to automate some of the routine design calculations, you might find my Fundamentals of Reinforced Concrete Design to Eurocode 2 course helpful.

1.0 Introduction – What is moment redistribution?

When designing any structural element, our first pass usually involves an elastic design – i.e. we assume that the materials involved all remain within their elastic range – baked into this assumption is a further underlying assumption that the materials are linearly-elastic. This is an inherently conservative approach and makes sense for our first analysis and design iteration. If the element we’re designing happens to form part of a statically determinate structure that has no structural redundancy, this is the only approach we can take since plastic hinge formation would lead to collapse!

However, if we’re dealing with a statically indeterminate structure that, by definition, has at least one degree of statical indeterminacy (redundancy), then allowing a hinge to form may be beneficial from an efficiency point of view. Assuming the materials have an acceptable degree of ductility to allow hinge rotation to occur, hinge formation allows internal bending moments within the structure to be redistributed as further load is applied after the hinge has formed – this is moment redistribution.

Put another way, moment redistribution refers to the process by which internal bending moments are redistributed within a continuous reinforced concrete member, typically beams, to improve structural efficiency. This phenomenon arises due to the ductile nature of steel reinforcement and the nonlinear stress-strain behaviour of a reinforced concrete section.

Again, it can’t be stressed enough that plastic hinge formation and the resulting redistribution of moments is only acceptable in a statically indeterminate structure where hinge formation will not lead to the formation of a mechanism and collapse.

When we first discussed reinforced concrete section analysis, we derived a limit on neutral axis depth, $x$, based on the simultaneous failure of the reinforcing steel in tension and the concrete compression block. We referred to this as a ’balanced section’. This limit was $x_{lim} = 0.617d$. We went on to conclude that this limit should actually be reduced to $x_{lim} = 0.45d$. At the time, we somewhat cryptically said that this was to allow plastic hinge formation, such that rotation of the section could take place prior to the concrete compression block crushing. Well, let’s now dig into this statement and see exactly what we meant by this.