When designing a beam or a two‑way slab, reinforcement is usually determined at the ULS after optionally applying a redistribution of bending moments between supports and spans, based on an assumed elastic model.

However, once the structure has been fully defined in terms of formwork and reinforcement, the actual distribution of bending moments is no longer a matter of choice: it is governed by deformation compatibility within the structure.

This “typical” exercise on a continuous slab supported on three spans aims to evaluate the actual redistribution of bending moments at both ULS and SLS, as well as crack width and deflection at SLS, depending on the different redistribution strategies initially considered.

[Article to be published soon]

This article addresses a common situation in infrastructure slabs that are sensitive to shrinkage and thermal strain effects.

The proposed calculation method incorporates shrinkage directly into the concrete constitutive laws and evaluates the resulting shortening, lengthening and bending effects, depending on the slab’s continuity conditions, restraints, self‑stress mechanisms and cracking behaviour.

A sensitivity study is also performed, showing how the structural response varies depending on the orientation of the beams with respect to the long dimension of the slab, and highlighting several good‑practice considerations that may be of interest for design.

[Article to be published soon]

The Eurocode 2 General Method reduced to the analysis of a critical section (MG1) relies on a strong assumption regarding the shape of the deformed configuration, which is often taken as sinusoidal. This sinusoidal form derives from the case of an elastic column subjected to a negligible first‑order effect, just sufficient to bring the column out of its unstable equilibrium state (y(x)=0) and generate an instability that leads to an increasing deformation until a stable equilibrium is reached.

In a case such as a pinned‑pinned column subjected to progressive axial loading and bending moments at different locations along its height, the sinusoidal model becomes very unrealistic. Using the General Method allows an exact global‑stability verification at ULS without any assumption on the shape of the deformation, and an SLS calculation of total and serviceability‑critical deformation, while satisfying all Eurocode 2 requirements.

This article also proposes an extrapolation of Eurocode 3 to define acceptable horizontal‑displacement criteria for this type of slender structure.

[Article to be published soon]

This article presents the benefits of a nonlinear approach for the analysis of reinforced concrete line elements, intended to determine the unique solution of the mechanical problem — when it exists — by enforcing flexural and axial deformation compatibility at every point along the member.

Inspired by the General Method and fully covered by Eurocode 2, this approach, referred to as the “Integral General Method” or IGM, opens up possibilities for analysing and optimising many common situations, from slender columns to continuous members in combined bending and compression.

Analysis of a little‑known axial phenomenon: the elongation of simply‑bent RC beams under gravity loads, a direct consequence of reinforced‑concrete behaviour.

This article introduces the first axial effect observable in flexural reinforced‑concrete elements: the elongation of simply‑bent beams under gravity loads.
This phenomenon—often overlooked despite being non‑negligible—results directly from the fundamental behaviour of reinforced concrete, especially once cracking develops. Understanding it is essential before rigorously addressing the effects of thermal expansion and shrinkage.
It forms the first part of the series “Axial behaviour of flexural reinforced‑concrete elements” (1/4). 

Thermo‑mechanical analysis of RC sections: constitutive laws, effects of thermal expansion and thermal gradients, and cases where EC2 requires their consideration.

This article examines the thermo‑mechanical behaviour of reinforced‑concrete members subjected to thermal expansion or thermal gradients, based on the assumptions of Eurocode 2.
It first analyses how the constitutive laws of concrete and steel are modified and how the mechanical diagrams of RC sections (strains, stresses, internal forces) evolve under thermal actions.
The article then reviews the regulatory situations in which thermal effects must be considered, illustrates the physical behaviour that can be observed, and presents the gravity/thermal concomitances that may become governing.
This is the second part of the series “Axial behaviour of flexural reinforced‑concrete elements” (2/4). 

Analysis of concrete shrinkage, the induced self‑stresses, the differences with thermal effects, and the conditions for applying EC2 formula (7.21).

This article examines the mechanical behaviour of reinforced concrete subjected to shrinkage, highlighting the fundamental differences between shrinkage and thermal effects, and introducing the notion of self‑stresses that develop within the section.
It then analyses how the constitutive laws of concrete and steel are modified and how the mechanical diagrams of a reinforced‑concrete section (geometry, strains, stresses, internal forces) evolve under shrinkage.
Finally, the article clarifies the conditions under which Eurocode 2 formula (7.21)—used to estimate the curvature of a flexural member due to shrinkage—can be validly applied.
This contribution forms the third part of the series “Axial behaviour of flexural reinforced‑concrete elements” (3/4). 

Synthesis of simultaneous axial effects: shrinkage, thermal actions, gravity‑induced elongation, cracking, and the limitations of elastic analyses.

This final part broadens the analysis of axial effects by considering the concomitance between shrinkage, thermal expansion and gravity‑induced elongation, as well as the impact of cracking.
The article highlights several points of vigilance regarding the elastic structural analysis of axial effects, and proposes that shrinkage studies should systematically include the effect of gravity‑induced elongation, and that thermal analyses at the characteristic SLS should jointly include shrinkage + gravity effects.
It constitutes the fourth part of the series “Axial behaviour of flexural reinforced‑concrete elements” (4/4).