Creep and shrinkage

What this page computes

The page determines the two long-term deformations of concrete, to EN 1992-1-1 §3.1.4 and Annex B:

• the creep coefficient \(\varphi(t,t_0)\), which says by how much the deformation grows under a sustained load;
• the shrinkage \(\varepsilon_{cs}\), which occurs independently of loading.

They are different phenomena with different causes, and the code treats them separately. They share a page because they share the same inputs — concrete class, humidity, and the notional size of the section.

The notional size h₀ is the geometric parameter that matters

Both phenomena depend on how quickly water can leave the concrete, and that is expressed through the notional size:

\(h_0 = \frac{2 A_c}{u}\)

where \(u\) is the perimeter in contact with the atmosphere, not the total perimeter. For a slab drying on both faces, \(h_0\) comes out equal to its thickness — a useful coincidence for hand checking. For a member with one sealed face, or cast against soil, \(u\) drops and \(h_0\) grows, so the processes slow down.

A massive member does not dry less, it dries more slowly. In the long run it ends up in roughly the same place, but at one year the difference is large: a 100 mm slab has realised 90% of its drying shrinkage, a 600 mm member only 38%.

Creep: φ(∞,t₀) is the number you want

The coefficient splits into two parts:

\(\varphi(t,t_0) = \varphi_0 \cdot \beta_c(t,t_0)\)

The factor \(\beta_c\) describes the development in time and tends to 1. So \(\varphi_0\) is not an intermediate quantity but the final value \(\varphi(\infty,t_0)\) — the one entering serviceability checks and slender column design, through the effective coefficient:

\(\varphi_{ef} = \varphi(\infty,t_0) \cdot \frac{M_{0Eqp}}{M_{0Ed}}\)

The notional coefficient is a product of three independent factors:

\(\varphi_0 = \varphi_{RH} \cdot \beta(f_{cm}) \cdot \beta(t_0)\)

Each corresponds to a trend you can check intuitively: a humid environment reduces creep (the water has nowhere to go), stronger concrete reduces it, and later loading reduces it. Of the three, the age at loading has the most brutal effect: a member loaded at 7 days creeps appreciably more than one loaded at 90.

The 35 MPa threshold applies to f_cm, not to f_ck

Expressions B.3 and B.8 have two branches, and the boundary is at 35 MPa on the mean strength, not the characteristic one. Since \(f_{cm} = f_{ck} + 8\), a C30/37 has \(f_{cm} = 38\) and already takes the branch with the \(\alpha_1\) and \(\alpha_2\) corrections — even though \(f_{ck} = 30\) suggests otherwise.

It is easy to miss, because the two branches give close results exactly around the threshold, so the mistake does not stand out.

The cement class shifts the age at loading

Expression B.9 does not change the coefficient directly; it corrects \(t_0\). A rapid-hardening cement makes the concrete more mature at the same calendar age, so the equivalent is a larger \(t_0\) and less creep. For normal cement the factor is exactly 1, so \(t_0\) is unchanged.

Shrinkage: two components that behave differently

\(\varepsilon_{cs} = \varepsilon_{cd} + \varepsilon_{ca}\)

Drying shrinkage \(\varepsilon_{cd}\) comes from water loss to the environment. It depends on humidity and thickness, and it is slow. At 100% humidity it is zero — concrete in saturated air does not dry, which is visible directly in the last column of Table 3.2, zero throughout.

Autogenous shrinkage \(\varepsilon_{ca}\) comes from cement hydration: the water is chemically consumed, not lost. It therefore does not depend on humidity and is consumed quickly — about 75% within the first 50 days.

The split matters more than it seems. For ordinary concrete the autogenous part is small and could be neglected. For high-strength concrete it becomes dominant, because it grows linearly with the class while drying decreases. At C90/105 in a humid environment the autogenous part exceeds the drying part — omitting it seriously underestimates the deformation.

An erratum in the Romanian edition

Expression (3.10), which gives the development of drying shrinkage in time, is printed in SR EN 1992-1-1:2004 with a minus in the denominator:

\(\beta_{ds} = \frac{t - t_s}{(t - t_s) - 0.04\sqrt{h_0^3}} \qquad \text{(as printed)}\)

The correct form, from the original EN 1992-1-1, has a plus. The error can be detected without comparing to the original: \(\beta_{ds}\) is the fraction of shrinkage already realised, so it must increase monotonically from 0 to 1. With a minus, the denominator vanishes at \(t - t_s = 0.04\sqrt{h_0^3}\) — for \(h_0 = 200\) mm that falls at 113 days, right in the range of interest — and the function turns negative before that point.

The page uses the correct form.

What the calculation does not cover

• The restraining effect of reinforcement. The values are for plain concrete. Reinforcement opposes shrinkage, which reduces the free deformation but introduces tensile stress in the concrete — the origin of restrained-shrinkage cracking.
• Lightweight aggregate concrete, which follows a different regime (EN 1992-1-1 section 11).
• The temperature correction of expression B.10, for casting outside the usual temperature range.
• Relaxation and prestress losses, which use these quantities but have rules of their own.

The values in Table 3.2 of the code — 30 points for the reference drying shrinkage — are reproduced exactly by the implementation, so the shrinkage side is verified against the very code it applies.