Time-dependent effects

Analyse creep and shrinkage redistribution in concrete sections using the age-adjusted effective modulus method (AEMM).

Overview

Concrete undergoes time-dependent deformations — creep (sustained-load deformation) and shrinkage (moisture-loss contraction) — that redistribute internal stresses between concrete and reinforcement over the service life of the member. These effects are particularly significant for:

Prestressed members, where creep and shrinkage cause prestress losses
Composite sections, where differential shrinkage generates interface stresses
Long-span members, where long-term deflections may govern the design

ACS computes time-dependent stress redistribution using the Age-Adjusted Effective Modulus Method (AEMM), which accounts for the aging of concrete (increasing stiffness with time) when computing creep effects.

When to use time-dependent analysis

Run this analysis when you need to:

Estimate long-term concrete and steel stresses under sustained loads
Verify that long-term stress redistributions do not violate serviceability limits
Check long-term curvature increases for deflection estimates
Investigate the effect of different cement types or curing conditions on creep and shrinkage

Configuration

Open the Creep & Shrinkage section in the right panel to configure the analysis.

The TDE (Time-Dependent Effects) panel showing creep and shrinkage configuration inputs

Input parameters

Input	Description	Units	Default	Notes
Axial load	Sustained axial force $N$	kN	0	Positive = compression
Moment	Sustained bending moment $M$	kN.m	0	Use the quasi-permanent SLS combination
Age at loading	Concrete age when load is first applied ( $t_0$ )	days	28	Affects creep coefficient — earlier loading gives higher creep
Age at shrinkage start	Concrete age when shrinkage begins	days	3	Typically end of moist curing
Relative humidity	Ambient relative humidity (RH)	%	65	Lower RH increases both creep and shrinkage
Notional size	$h_0 = 2A_c/u$ (member perimeter ratio)	mm	Auto	Set to 0 for automatic calculation from the section geometry
Cement type	Hardening rate coefficient $s$	—	Normal (0.25)	Affects strength development and creep
Analysis ages	Ages at which to compute results	days	28, 90, 365, 1825, 18250	18250 days $\approx$ 50 years
Aging coefficient	Chi factor $\chi$ for AEMM	—	0.8	Typically 0.6—0.9; 0.8 is a common approximation

Cement type

The cement type coefficient $s$ affects the rate of concrete strength development, which in turn affects creep and shrinkage:

Type	Coefficient $s$	Example
Slow hardening	0.20	CEM II/B, CEM III — blast furnace slag cements
Normal	0.25	CEM I 42.5N — ordinary Portland cement
Rapid	0.38	CEM I 52.5R — high early strength

Override coefficients

If you have experimentally measured or externally computed creep or shrinkage values, you can override the code-calculated values:

Override	When to use
Creep coefficient override	Replace the calculated $\varphi(t, t_0)$ with a known value
Shrinkage strain override	Replace the calculated $\varepsilon_{cs}$ with a measured value

Set either override to 0 to use the code-calculated value (default).

Running the analysis

Click the Run Analysis button to compute results. Unlike the other ACS checks, the time-dependent analysis does not run automatically — it is triggered manually because it requires sustained-load inputs that may differ from the ULS/SLS combinations.

Results

Time-series snapshots

The analysis generates a snapshot at each specified age, reporting:

Output	Description	Units
Age	Concrete age	days
Creep coefficient $\varphi(t)$	Cumulative creep coefficient at time $t$	—
Shrinkage strain $\varepsilon_{cs}(t)$	Cumulative shrinkage strain at time $t$	—
Concrete stress (top)	Top fibre stress after redistribution	MPa
Concrete stress (bottom)	Bottom fibre stress after redistribution	MPa
Steel stress	Reinforcement stress after redistribution	MPa
Curvature	Section curvature at time $t$	1/mm
Effective EI	Effective flexural stiffness at time $t$	kN.m²

Charts

Two interactive charts visualise the time evolution:

Creep coefficient — plots $\varphi(t)$ over the analysis duration (logarithmic time axis)
Shrinkage strain — plots $\varepsilon_{cs}(t)$ over the analysis duration

These charts help you verify that the creep and shrinkage development follows a reasonable pattern and that the final values are consistent with your expectations for the concrete type and environment.

Interpreting results

Stress redistribution

Under sustained load, creep causes the concrete stress to reduce over time while the reinforcement stress increases to maintain equilibrium. This is a fundamental behaviour of reinforced concrete:

Concrete stress decreases by 20—40% of the initial elastic value over the first few years
Steel stress increases correspondingly (the reinforcement “picks up” the load shed by creeping concrete)
The rate of change is rapid initially and asymptotically approaches a final value

Practical significance

Deflection: The curvature at each snapshot can be used to estimate long-term deflections. The ratio of long-term to short-term curvature is approximately $(1 + \varphi)$ , reduced by the presence of compression reinforcement.
Crack width: Increased steel stress from creep redistribution may increase crack widths under sustained load. Cross-reference with the SLS crack width check using the long-term steel stress.
Prestress: For prestressed sections, creep and shrinkage contribute to long-term prestress losses. The loss values from this analysis should be consistent with those reported in the prestressing losses panel.

Tips and best practices

Use the quasi-permanent SLS load combination for the sustained loads (typically $G + \psi_2 Q$ where $\psi_2 = 0.3$ — $0.6$ )
The default analysis ages (28d, 90d, 1y, 5y, 50y) cover the key milestones for most members
If the creep coefficient exceeds 3.0, verify the inputs — this is at the upper end of the normal range and may indicate very early loading age, low humidity, or thin member geometry
For prestressed members, the creep and shrinkage results should be cross-checked with the prestress loss calculation to ensure consistency
The notional size $h_0 = 2A_c/u$ is computed automatically from the section geometry when set to 0. Override it only if the member has a non-standard exposure condition (e.g., only one face exposed to drying)

Prestressing — prestress losses include creep and shrinkage components
Section analysis — deflection parameters and SLS checks
Creep and shrinkage theory — mathematical background on AEMM
Design standards — code comparison for time-dependent effects