How Accurate Is AS 3600 For The Prediction Of Creep & Shrinkage Of Post-tensioned Beams
Section Properties Of The Beam Used:
Section height (mm) = 1200
Flange width (mm) = 600
Web thickness (mm) = 200
Modulus of elasticity of concrete (GPa) = 30
Modulus of elasticity of steel (GPa) = 200
Duct size (mm) = 100
Top bar cover (mm) = 50
Bottom bar cover (mm) = 50
Prestressing steel centre to edge dist. (mm) = 200
Creep coefficient = 2.5
Aging coefficient of AEMM = 0.65
Shrinkage strain = -600·10-6
Relaxation coefficient = 0.042 for 4% relaxation
External moment (kNm) = 725
Four variations of tensioning force and non-prestressing steel are used for the analyses. Below table shows the properties of the sections used:
| Name | Astop (mm2) |
Asbot (mm2) |
Aps (mm2) |
P (kN) |
P/fpb |
|---|---|---|---|---|---|
| SEC-I | 760 | 760 | 2465 | 3690 | 0.80 |
| SEC-II | 760 | 1900 | 2465 | 3690 | 0.80 |
| SEC-III | 760 | 760 | 2465 | 2768 | 0.60 |
| SEC-IV | 760 | 1900 | 2465 | 2768 | 0.60 |
For the analyses in-house coded software was used. The software started with a short-term analysis and at the end of the short-term analysis it performed time dependent analysis using AEMM. The output included time dependent losses as well as stress and strain values of the section.
The total time dependent loss Δσp is the sum of the losses because of creep, Δσp,cc, shrinkage, Δσp,cs, and relaxation Δσp,rel.
Comparison Of The Two Methods:
Time dependent losses were calculated by both methods and compared. AS 3600 predicted unconservative values for all the sections used. The error of AS 3600 was calculated as (AS3600 - AEMM) / AEMM x 100. The highest error of -17% was obtained for SEC-I.
The total time-depended losses predicted by the two methods and the error values of AS 3600 are given in the table below:
| Name | AS 3600 (MPa) |
AEMM (MPa) |
Error (%) |
|---|---|---|---|
| SEC-I | 307 | 369 | -17 |
| SEC-II | 294 | 345 | -15 |
| SEC-III | 242 | 284 | -15 |
| SEC-IV | 231 | 266 | -13 |
Conclusion:
The reason of the error is that AS 3600 cannot account for the restraining effect of non-prestressed reinforcement in the sections, properly especially when section is lightly reinforced at the bottom.
Although the results were presented for the tensioning forces only, it affects section strain and stress values. This means there may be cases bottom reinforcements can yield in serviceability conditions.
One can think of increasing tensioning forces by 20% when there is non-prestress reinforcement to be conservative. This will be conservative for the stresses at the bottom of the section at serviceability stage. However, increasing tensioning forces will be unconservative for the top of the section in transfer stage during transferring the pre-stress.
These results remind us of the importance of a well-known advice: A structural engineer should follow the rules in the structural standards not blindly but by understanding the underlying first principles.
References:
Australian Standard for Concrete Structures, AS3600-2018, 2018. Standards Association of Australia, New South Wales, Sydney.Guide for Modelling and Calculating Shrinkage and Creep in Hardened Concrete, 2008. ACI 209.2R08, Farmington Hills, MI.
Design of Concrete Structures, part 1.1 Eurocode 2, 2005. European Committee for Standardization, CEN, Brussels, Belgium.
Model Code 2010-Final Draft Vol.1, 2012. International Federation for Structural Concrete, Lausanne, Switzerland.
Bazant Z.P., 1972. Prediction of concrete creep effects using age-adjusted effective modulus method. ACI Journal 69, 212 - 217.
R. I. Gilbert, Design of Prestressed Concrete to AS3600-2009, Second Edition, CRC Press, London and New York, 2016.
J. Bezanson et all., 2017. High-Performance Dynamic Programming Language for Technical Computing, JULIA.