An approach to analyzing and designing horizontal structures subjected to shrinkage

Eurocode 2 is relatively precise in determining the evolution of concrete shrinkage over time. However, it remains much more succinct regarding how to incorporate this phenomenon into reinforced concrete design calculations.

Beyond deformations alone, the engineer is often faced with determining bending moments, axial forces, stresses in reinforcement, as well as crack widths, particularly in restrained shrinkage configurations.

The example presented below shows how the General Integral Method (GIM) makes it possible to capture physical phenomena that are often anticipated but difficult to access using conventional approaches. It progressively highlights:

• axial elongation under gravity loads,
• reduction of the cracking moment due to shrinkage,
• increase in curvatures and deflections,
• as well as the determination of tensile force in cases of restrained shrinkage.

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.

The behaviour of reinforced concrete flexural structures is intrinsically non-linear and depends on cracking and the progressive plastification of sections.

Compared with earlier generation codes (BAEL), Eurocode 2 now benefits from the theoretical contributions required to take these phenomena into account, notably enabling the calculation-based treatment of concrete adaptation, the formation of plastic hinges, moment redistribution, as well as deformation compatibility issues.

Depending on the required level of analysis, the code also allows simplified, regulated methods based on linear-elastic analyses, possibly combined with predefined moment redistributions.

These various approaches provide the calculation framework with a certain versatility and give the engineer a degree of flexibility suited to the diversity of situations encountered in practice.

While simplified analysis methods (§5.4 to §5.6) are widely used in practice, the present study proposes to utilize non-linear methods (§5.7) on simple cases in order to progressively highlight the mechanisms underlying structural analysis according to EC2, and to provide additional insight into linear-elastic analyses and redistribution practices.

Identify the vocabulary and the sequential logic “structural analysis → design of cross-sections” to better read and understand the code.

This article deciphers the precise semantics used in EC2 — analysis, design, actions, effects, mean and characteristic values — and shows how these definitions structure the entire code.

It clarifies the two-step process (structural analysis followed by cross‑section design) and describes the different regulatory material behaviour laws associated with each step.

This conceptual basis then makes it possible to understand the boundaries between the models involved, and in particular to address the issue of deformation compatibility.

This topic constitutes the first part of a series dedicated to the flexural behaviour of reinforced concrete beams (1/4).

In hyperstatic structures, deformation compatibility dictates the exact distribution of moments — a challenge that the simplified EC2 methods only partially address.

This article explains how a hyperstatic structure possesses, for each load case, a unique exact solution determined by the actual deformability of its sections and supports.

It shows that internal forces depend closely on varying stiffness, reinforcement layout, progressive cracking and plastification, making the EC2 sequential approach sometimes insufficient.
It also explores the conditions for nonlinear analysis, enabling the limitations of the “structural analysis → cross‑section design” framework to be overcome.

This topic constitutes the third part of a series dedicated to the flexural behaviour of reinforced concrete beams (3/4).

Elastic structural analysis, limited redistribution, and plastic analysis. Study on an example, verification of ductility, and the limits of these models

This article presents the four structural analysis methods proposed by Eurocode 2 for continuous beams, and shows how simplified approaches (elastic, limited redistribution, plastic) deliberately bypass the pursuit of the exact solution.

It explains the mechanisms of hinge formation, the conditions for valid redistribution, the verification of plastic rotation capacity, and the biases of linear models when cracking and stiffness loss become predominant.
Finally, it highlights possible discrepancies between simplified analysis and actual behaviour, especially regarding deflection, second‑order effects, and redistribution at SLS.

This topic is the final part of our series dedicated to the flexural behaviour of reinforced concrete beams (4/4).

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).