Creep Coefficient Calculator

The Creep Coefficient Calculator calculates the concrete creep coefficient from humidity, strength class, member size and age at loading.

What Is a Creep Coefficient Calculator?

A creep coefficient calculator is a tool that computes φ(t, t0), the time‑dependent creep coefficient at time t for a load applied at age t0. It converts material data, environment, and member dimensions into a single dimensionless number that scales initial elastic deflection or strain. With φ, you can estimate long‑term deflection, stress redistribution, and prestress losses.

The calculator implements accepted models from structural codes and research. It guides you through input fields for compressive strength, modulus of elasticity, relative humidity, loading age, and size effects. The result helps you compare options, refine an estimate, and document your assumptions.

How the Creep Coefficient Method Works

The creep coefficient method separates immediate (elastic) response from time‑dependent (creep) response. You compute the elastic strain or deflection at loading, then multiply by 1 + φ to represent the added creep component over time.

• Immediate elastic response: Calculate strain εe = σ/Ec or deflection from standard formulas at the loading age.
• Creep growth: Evaluate φ(t, t0) using a model that accounts for humidity, strength, and notional size.
• Total long‑term response: Multiply the elastic result by 1 + φ to include creep effects.
• Time dependence: φ evolves from 0 at t = t0 and approaches an asymptote as t increases.
• Separation from shrinkage: Shrinkage strain is independent of stress; creep requires sustained stress.

This method is common in codes and textbooks because it is clear and practical. It works best when stress levels remain moderate and geometry stays within typical ranges for building elements.

Formulas for Creep Coefficient

The creep coefficient is defined relative to compliance or direct strain ratios. Several widely used formulations exist. The calculator supports a simplified path consistent with popular models while keeping the inputs practical.

• Definition: φ(t, t0) = εcreep(t, t0) / εelastic(t0). It is dimensionless and applies to concrete under sustained stress.
• Compliance relation: J(t, t0) is the creep compliance. Then φ = Ec(t0) × J(t, t0) − 1, where Ec(t0) is modulus at loading.
• Development function: φ(t, t0) = φ0 × βc(t − t0), where φ0 is a basic creep coefficient and βc is a growth function from 0 to 1.
• Basic coefficient factors: φ0 often splits into multipliers for humidity, strength, notional size, and loading age: φ0 = kRH × kf × ksize × kt0.
• Simple time growth (example): βc(Δt) = Δt / (Δt + τ), where Δt = t − t0 and τ is a time constant dependent on humidity and size.
• Total strain: εtotal(t) = εelastic(t0) × [1 + φ(t, t0)] + εsh(t), where εsh(t) is shrinkage strain evaluated separately.

Codes differ in exact functions and coefficients, but the structure is similar. If you choose a specific model in the Calculator, its coefficients and growth law are applied consistently, and the final φ is reported alongside intermediate factors.

Inputs, Assumptions & Parameters

The calculator needs material, time, environment, and size data to assess creep. The parameters below summarize the essential inputs and how they influence the result.

• Concrete compressive strength f′c: Cylinder strength at 28 days or at testing. Higher strength usually reduces creep.
• Modulus of elasticity Ec: Either measured or estimated from f′c. It sets the elastic strain reference.
• Age at loading t0: The concrete age in days when sustained load begins. Later loading age reduces creep.
• Final time t: The duration to evaluate. Typical values include 1 year, 5 years, or service life.
• Relative humidity RH: Ambient humidity near the member. Dry environments increase drying creep.
• Notional size or thickness: A measure of cross‑section dimensions that controls moisture diffusion and creep development.

Reasonable ranges help the estimate. Typical f′c is 20–60 MPa, RH is 30–90%, t0 is 3–56 days, and notional sizes span 50–500 mm. Extreme temperatures, very low water‑cement ratio, or unusual aggregates can push results outside standard models. Use measured Ec and actual curing conditions when available.

Step-by-Step: Use the Creep Coefficient Calculator

Here’s a concise overview before we dive into the key points:

1. Select the preferred model in the Calculator (for example, code‑based or research‑based).
2. Choose your units system and keep it consistent for all inputs.
3. Enter compressive strength f′c and modulus Ec, or choose “estimate Ec from f′c.”
4. Specify loading age t0 and the target evaluation time t.
5. Enter relative humidity, member dimensions for notional size, and curing conditions if known.
6. Review the intermediate factors (humidity, size, age) and adjust assumptions if they differ from site conditions.

These points provide quick orientation—use them alongside the full explanations in this page.

Case Studies

A 200 mm one‑way slab in an office building has f′c = 35 MPa and Ec estimated at 30 GPa. The sustained load starts at t0 = 7 days. The engineer needs φ at t = 365 days with RH = 50%. Using a typical model, factors give φ0 ≈ 1.55 and βc(358 days) ≈ 0.85, so φ ≈ 1.55 × 0.85 ≈ 1.32. If the immediate midspan deflection is 12 mm, the creep component adds 12 × 1.32 = 15.8 mm, so the long‑term deflection is about 27.8 mm.

What this means

A 300 mm deep interior beam in a dry region has f′c = 40 MPa and Ec = 33 GPa. Loading begins at t0 = 28 days, RH = 30%, and the engineer evaluates t = 10 years. The dry climate and moderate size lead to φ0 ≈ 1.80, with βc(≈ 9.97 years) ≈ 0.95. The result is φ ≈ 1.71. If the elastic midspan deflection is 8 mm, the creep portion adds 8 × 1.71 = 13.7 mm, bringing long‑term deflection to about 21.7 mm.

What this means

Assumptions, Caveats & Edge Cases

Creep models are calibrated to common concretes and standard climates. They are robust for building elements within typical stress ranges. Edge cases require caution and often testing or project‑specific calibration.

• High stress levels: If sustained stress exceeds about 40–50% of strength, nonlinearity can increase creep beyond model predictions.
• Lightweight or high‑performance concrete: Properties can deviate from ordinary mix behavior; confirm Ec and moisture diffusion data.
• Massive sections: Very large dimensions delay drying; time growth βc can be much slower than usual.
• Severe environments: High temperature or sustained wetting/drying cycles require model adjustments.
• Composite action and restraint: Tension stiffening, composite slabs, or restrained members change effective creep response.

Use the calculator to explore sensitivity. Small changes in RH, t0, or notional size can shift φ significantly. When results drive major decisions, validate with measurements or recognized project‑specific guidance.

Units & Conversions

Consistent units are essential because φ depends on elastic strain and modulus. Enter strength, modulus, and dimensions in a single system. The table below lists common conversions for stress, modulus, length, strain, and time used in creep calculations.

Choose one column as your base and convert all inputs before calculating. For example, if Ec is in GPa and stresses are in MPa, keep all other quantities in SI to avoid hidden scaling errors.

Tips If Results Look Off

Unexpected φ values usually trace back to a unit mismatch, an unrealistic loading age, or humidity settings. Check the items below before changing the model.

• Confirm Ec is consistent with f′c and the same units system.
• Verify t0 and t are reasonable; t must be greater than t0.
• Match RH to interior or exterior conditions near the member.
• Re‑enter dimensions used for notional size; thickness errors cause large changes.
• Reduce sustained stress if it exceeds typical service levels.

If φ remains unusually high or low, try a different model option and compare. Use measured modulus or project test data when available.

FAQ about Creep Coefficient Calculator

Is the creep coefficient dimensionless?

Yes. It is a ratio of strains, so it has no units. It scales the elastic response to include time‑dependent creep.

Do I include shrinkage in the creep coefficient?

No. Shrinkage is added separately as a free strain εsh(t). The total strain is elastic × (1 + φ) plus shrinkage.

How accurate are model‑based estimates?

They are usually within engineering accuracy for normal concretes and climates. Accuracy improves when you use measured Ec and realistic RH and loading age.

Which model should I choose?

Choose the model aligned with your design code or specification. If none is mandated, select a well‑documented model and keep your assumptions transparent.

Key Terms in Creep Coefficient

Creep

Time‑dependent, stress‑induced strain that develops under sustained load. It accumulates after the initial elastic response.

Creep Coefficient φ(t, t0)

The ratio of creep strain to initial elastic strain at a time t for a load applied at age t0. It is dimensionless.

Elastic Modulus Ec

The slope of the stress‑strain curve in the linear range. It converts stress to elastic strain and anchors the creep ratio.

Compliance J(t, t0)

The time‑dependent strain per unit stress. It includes both elastic and creep components and connects to φ through Ec.

Relative Humidity RH

The moisture content of surrounding air expressed as a percentage. Lower RH increases drying and typically increases creep.

Notional Size

A characteristic dimension related to thickness and surface‑to‑volume ratio. It controls drying rate and the development of creep over time.

Age at Loading t0

The concrete age when sustained load begins. Later loading reduces creep because hydration and stiffness are more developed.

Shrinkage Strain εsh

Stress‑free volumetric contraction of concrete from moisture loss and hydration. It is separate from creep and must be added to total strain.

References

Here’s a concise overview before we dive into the key points:

• fib Model Code 2010: Creep and Shrinkage Provisions
• ACI 209R: Prediction of Creep, Shrinkage, and Temperature Effects in Concrete
• EN 1992-1-1 Eurocode 2: Design of Concrete Structures, Annex for Creep and Shrinkage
• Bažant and Baweja (2000): Creep and Shrinkage Model B3
• Bažant et al. (2015): B4 Model for Creep and Shrinkage of Concrete
• Portland Cement Association: Creep and Shrinkage Overview

These points provide quick orientation—use them alongside the full explanations in this page.