Creep and Shrinkage Estimator
Estimate concrete's creep coefficient and drying shrinkage strain at any age using the ACI 209 hyperbolic time-development model.
🧱 What is Concrete Creep and Shrinkage?
Creep is the gradual increase in concrete strain over time under a sustained applied stress, beyond the instantaneous elastic strain that occurs immediately upon loading. Shrinkage is the separate, load-independent reduction in concrete volume as moisture evaporates from the hardened paste. The widely used ACI 209 model describes both with a hyperbolic (saturating) time function, phi(t) = phi_u x dt^0.6 / (10 + dt^0.6) for creep, and eps_sh(t) = eps_shu x t / (35 + t) for shrinkage.
Structural engineers use these estimates to predict long-term prestress losses in prestressed concrete beams, long-term column shortening in tall concrete buildings (which can cause floor-to-floor differential movement issues), growing deflection in reinforced concrete slabs and beams over years of service, and time-dependent stress redistribution in composite construction.
A common point of confusion is treating creep and shrinkage as the same phenomenon. Creep requires a sustained applied stress and is measured from the age at loading (t0), shrinkage happens regardless of loading and is measured from the age drying begins. A concrete member can shrink even while carrying no load at all, but it cannot creep without one.
This calculator computes both the creep coefficient and drying shrinkage strain at any age, optionally combines them with an initial elastic strain into a total long-term strain estimate, and plots the creep coefficient's characteristic saturating curve over time.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — One-Year Estimate, Loaded at 28 Days
t = 365 days, t0 = 28 days, phi_u = 2.35, eps_shu = 780, eps_i = 200
Example 2 — Long-Term Estimate, No Total Strain
t = 1000 days, t0 = 14 days, phi_u = 2.35, eps_shu = 780, eps_i = 0
Example 3 — Early-Age Estimate With Different Mix Properties
t = 90 days, t0 = 7 days, phi_u = 2.0, eps_shu = 600, eps_i = 150
❓ Frequently Asked Questions
🔗 Related Calculators
What is concrete creep?
Concrete creep is the gradual increase in strain over time under a sustained (constant) applied stress, distinct from the instantaneous elastic strain that occurs immediately upon loading. It is commonly expressed through a dimensionless creep coefficient phi(t), where total creep strain equals the initial elastic strain times phi(t).
What is the ACI 209 creep coefficient formula?
phi(t) = phi_u x (t - t0)^0.6 / [10 + (t - t0)^0.6], where phi_u is the ultimate (long-term limiting) creep coefficient, t0 is the concrete's age at loading, and t is the age at which creep is being estimated, both in days.
What is concrete drying shrinkage?
Drying shrinkage is the reduction in concrete volume as moisture evaporates from the hardened paste over time, independent of any applied load. The ACI 209 model gives shrinkage strain as eps_sh(t) = eps_shu x t / (35 + t), where t is the time since drying began and eps_shu is the ultimate shrinkage strain.
Why do both curves use the same hyperbolic (t / (constant + t)) shape?
Both creep and shrinkage develop rapidly at early ages and then level off toward a limiting (ultimate) value as time passes, a hyperbolic function naturally captures this saturating behavior: it rises quickly at small t, then flattens as t grows large, approaching but never exactly reaching phi_u or eps_shu.
What are typical values for the ultimate creep coefficient and shrinkage strain?
ACI 209's standard-condition defaults are phi_u = 2.35 for the ultimate creep coefficient and eps_shu = 780 x 10^-6 for ultimate shrinkage strain, both calibrated to a reference set of humidity, curing, member size, and mix conditions, and adjusted with correction factors for other conditions.
Why does age at loading t0 matter for creep but not for shrinkage?
Creep only develops under sustained load, so it is measured from the moment loading begins (t0). Shrinkage is a load-independent volume change driven by moisture loss, so it depends only on the time since drying started, not on when (or whether) any load is ever applied.
How do I compute total long-term strain from creep and shrinkage?
Total long-term strain is commonly estimated as eps_total = eps_i(1 + phi(t)) + eps_sh(t), where eps_i is the initial instantaneous elastic strain under the sustained stress. This calculator computes this automatically when you provide a nonzero initial elastic strain.
What is this model commonly used for?
Concrete creep and shrinkage estimates are used to predict long-term prestress losses in prestressed concrete, long-term column shortening in tall buildings, deflection growth in reinforced concrete beams and slabs, and time-dependent stress redistribution in composite and continuous structures.
Are the ACI 209 default values universally accurate?
No, phi_u = 2.35 and eps_shu = 780 x 10^-6 are reference values for standard conditions (specific humidity, member size, slump, and curing period). ACI 209 provides correction factors to adjust these ultimate values for the actual conditions of a specific project, always apply them for a project-specific estimate.
What units does this calculator use?
Time (age at loading and age of concrete) is entered in days. The creep coefficient is dimensionless, shrinkage strain and the optional total strain are shown in microstrain (strain x 10^-6), the initial elastic strain input should also be entered in microstrain.