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 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]

Eurocode 2 provides practical design and calculation methods applicable on the one hand to continuous and simply‑bent members such as beams and slabs, and on the other hand to axially‑compressed members supported at two ends, such as columns and walls. The points of attention differ and are specific to each case.

The case of an infrastructure slab acting as a strut lies at the intersection of these two canonical types of structural members: it is both slender and axially compressed with a significant first‑order moment, and at the same time continuous, sensitive to crack width and to deformation.

The Integral General Method can provide an appropriate framework for addressing these intermediate configurations and verifying all applicable Eurocode 2 criteria. This article presents the design of such a 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.

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).