Concrete Shrinkage & Creep ACI 209R Simulator

Parameters

Curing method

Switches the time function constant f_t (moist=35 / steam=55)

Age at loading t₀

day

Elapsed time t

day

Sustained stress σ

MPa

Compressive sustained stress. Linear-creep limit ≈ 0.4·fc'

Ambient humidity RH

v/s ratio

Volume / surface ratio. Thin walls → smaller v/s, larger shrinkage

Slump

Shrinkage start age

day

Age when moist curing ends; formwork is stripped

Results

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Creep coeff. φ

—

Elastic strain (×10⁻⁶)

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Creep strain (×10⁻⁶)

—

Drying shrinkage (×10⁻⁶)

—

Ultimate creep φ_u

—

Long-term total strain (×10⁻⁶)

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Concrete beam — long-term deflection under sustained load

Under a sustained compressive load the beam creeps downward over time while drying shrinkage shortens the overall length. Colour shows the magnitude of total strain (green → orange → red).

Creep coefficient φ — time history

Shrinkage vs creep contribution

Theory & Key Formulas

$$\phi(t,t_0) = \frac{(t-t_0)^{0.6}}{10+(t-t_0)^{0.6}}\phi_u,\quad \varepsilon_{sh}(t) = \frac{t}{35+t}\varepsilon_{sh,u}$$

φ = creep coefficient, ε_sh = drying shrinkage, t_0 = age at loading. Correction factors γ apply humidity, size and slump effects. For steam curing the denominator 35 becomes 55.

$$\phi_u = 2.35\cdot\gamma_{la}\cdot\gamma_{RH}\cdot\gamma_{vs}\cdot\gamma_{slump}$$

Ultimate creep coefficient. γ_la = loading age, γ_RH = humidity (1.27-0.0067·RH), γ_vs = size and γ_slump = slump corrections.

$$\varepsilon_{c,total}(t) = \varepsilon_e(1+\phi(t,t_0)) + \varepsilon_{sh}(t)$$

Long-term total strain. Elastic strain ε_e = σ/E_c is scaled by (1+φ) to include creep, then drying shrinkage is added.

Concrete Shrinkage & Creep — ACI 209R Model

🙋

I have heard that concrete keeps shrinking for years after casting, and creeps slowly if you leave a load on it. Is that really true? You don't hear much about that for steel or aluminium.

🎓

Yes, that "long-term deformation" is very much a concrete thing. There are two main causes: drying shrinkage and creep. Drying shrinkage is when water inside the cement paste escapes to the air and the gel particles pull together, shrinking the volume — typically 300 to 1000 microstrain. Creep is a slow, time-dependent extra deformation under a sustained load: the gel structure keeps slipping, and after a year under 28-day-old loading you can easily reach 2× the original elastic strain.

🙋

So for bridges and high-rise buildings that stay loaded for decades, the structure just keeps sinking?

🎓

Good catch. In post-tensioned (PC) girders the mid-span typically drops several centimetres over 10-30 years from creep and shrinkage. Long-span PC bridges like Yokohama Bay Bridge or the Honshu-Shikoku bridges build in an upward camber during casting that is calculated to be cancelled out by the long-term creep deflection. Even worse is "prestress loss" — the tendons stretch less because the concrete around them shortens, losing 15-25% of the initial tension over decades. Engineers compensate by over-tensioning at installation.

🙋

I get why higher humidity reduces shrinkage, but what is the "v/s" ratio on the left? When I lower it the numbers shoot up.

🎓

v/s is the volume-to-surface ratio — an index of how hard it is for the cross-section to dry. A 100 mm thick wall has v/s ≈ 50 mm; a 1 m square column has v/s ≈ 250 mm. Small v/s means a big surface area relative to volume, so moisture leaves fast and both shrinkage and creep are large. That is why thin slabs and walls deform much more than thick columns. A 1 m thick reactor containment, on the other hand, has very large v/s and almost no shrinkage.

🙋

Are there models other than ACI 209R? Which should I use?

🎓

The three main ones are ACI 209R-92 (US), CEB-FIP MC2010 (Europe / Eurocode 2) and JSCE 2017 (Japan). ACI 209R has intuitive correction factors and is fine for everyday design. MC2010 models the gel-water physics in more detail and is preferred for research. JSCE 2017 tunes the constants to Japanese aggregates and climate. For a normal building ACI 209R is enough; for long-span bridges or nuclear vessels where long-term prediction must be accurate, use MC2010 plus an FEM (Abaqus, DIANA, MIDAS Civil) that superposes creep step by step.

Frequently Asked Questions

ACI 209R-92 defines the creep coefficient as φ(t,t0) = ((t-t0)^0.6 / (10+(t-t0)^0.6)) · φ_u, where t is elapsed time (days), t0 is the age at loading (days), and φ_u is the ultimate creep coefficient. φ_u starts from a reference value of 2.35 and is multiplied by correction factors γ for age at loading, humidity, v/s ratio and slump. The expression captures the rapid early rise and the long-term saturation of creep.

For moist-cured concrete, drying shrinkage is εsh(t) = (t / (35+t)) · εsh_u. The ultimate shrinkage εsh_u starts from 780×10⁻⁶ and is scaled by humidity (γ_RH), v/s (γ_vs) and slump (γ_slump) corrections. For steam curing the denominator 35 becomes 55. γ_RH is about 1.0 at 40% RH and about 0.6 at 80% RH, so shrinkage is smaller in humid environments.

Long-term tendon losses from creep, drying shrinkage and steel relaxation typically total 15-25% in PC girders. Multiplying the long-term total strain (elastic + creep + shrinkage) returned by this tool by the tendon Young's modulus 195 GPa gives a first stress-loss estimate. Example: total strain 1200×10⁻⁶ → loss stress ≈ 234 MPa. Design codes such as JSCE 2017 and ACI 318 evaluate the three contributions separately.

v/s is the volume-to-surface ratio (mm) and is a measure of how slowly the cross-section can dry. Thin walls have small v/s and lose moisture quickly, so both shrinkage and creep are large. Thick columns and mat foundations have large v/s, keep moisture inside longer, and deform less. ACI 209R applies γ_vs = 1.2·exp(-0.00472·v/s) for shrinkage and γ_vs = 2/3·(1+1.13·exp(-0.0213·v/s)) for creep to capture this size effect.

Real-World Applications

Prestressed concrete (PC) bridges: Long-span PC girders such as Yokohama Bay Bridge (460 m main span) or the Honshu-Shikoku link drop several centimetres at mid-span over 10-30 years of creep. ACI 209R or JSCE 2017 predict the long-term deflection at design time, and an upward camber is cast in to compensate. Tendon stress losses are evaluated simultaneously, and the initial jacking force is set 15-25% higher to retain the design long-term force.

Prestressed concrete containment vessels (PCCV): Reactor containments with walls over 1 m thick have very large v/s, so internal drying proceeds over decades. Coupled with long-term internal pressure during operation, creep of the concrete and tendon stress history must be simulated for 40-60 years using time-stepped creep superposition in Abaqus or DIANA.

Vertical shortening of high-rise core columns: In RC or SRC towers above 50 stories, axial loads differ greatly between lower and upper columns, so creep shortening per floor differs by location. Ignoring this leads to tens of millimetres of step between core and perimeter columns after 10 years, damaging curtain walls. Creep shortening is forecast for each construction stage and jacks compensate floor by floor.

Mass concrete and dams: In massive sections over 1 m thick, hydration heat and subsequent cooling shrinkage are the main causes of cracks for the first month, then drying shrinkage continues over decades. ACI 207 combined with 209R is used to design crack-control reinforcement.

Common Misconceptions and Pitfalls

The first pitfall is assuming creep is always linear in stress. The ACI 209R formula assumes the linear-creep regime, where σ/fc' is below 0.4. Above 0.4 creep becomes non-linear and grows exponentially with stress; above 0.7-0.8 you enter "creep rupture" and the member can fail within days to months. Local stresses at prestress anchorages, or hot zones after a fire, are not on the safe side of this tool's linear prediction.

The second pitfall is assuming shrinkage is uniform through the section. Drying proceeds from the surface inward, so the surface shrinks first while the core lags. The resulting shrinkage gradient, if restrained, puts the surface in tension and produces classic drying-shrinkage cracks. The εsh returned here is the cross-section average; surface strain can be 1.5 to 2 times this value. Accurate surface prediction needs a separate humidity diffusion analysis.

The third pitfall is thinking that creep saturates and stops. The (t-t0)^0.6 term slows the growth but never freezes it; even 30 years out, creep continues at a rate of 0.5-1% per year. And whenever the stress history changes — added live load, retensioning — Boltzmann superposition of creep must be applied. Simple static calculations cannot capture that; long-life structures need step-wise numerical analysis.