Reinforced Concrete Moment-Curvature – 2; Shrinkage and Creep

The previous post in this series provided an Excel User Defined Function (UDF) to find  the short term curvature of a reinforced concrete section subject to combined bending and axial load.  In this post UDFs will be presented to determine the strain in a concrete section due to creep and shrinkage, and in the final post these will be incorporated with the curvature UDF to find the curvature of the section under load for any given period.

Time related strains in concrete are divided into three categories:

  • Endogenous (or chemical) shrinkage; the shrinkage of the concrete due to the hydration of the cement.
  • Drying shrinkage; the shrinkage due to loss of water.
  • Creep; long term strain in the concrete due to applied loads.

In all three cases internal or external restraint of the strain will result in a change in the state of stress of the section.  The methods examined in this post assume no restraint of the strain.  The effect of restraint will be examined in the following posts.

The UDFs Shrink() and Creep() have been added to the RC Design Functions6 spreadsheet.  These functions provide estimated shrinkage strain and creep coefficients to either the Australian Standard Concrete Structures Code (AS 3600) or the Eurocode Concrete Code (EC2).  A third UDF, AdjustedAge() calculates the adjusted age of a concrete section according to EC 2, based on the time/temperature history.  This age can be used as input to the Creep function.  As usual, the spreadsheet includes open source code for the UDFs.

The next version of the AS 3600 code contains significantly different provisions for the calculation of shrinkage and creep, and the UDFs follow these recommendations, as published in the last public draft version of the code.  The UDFs will be updated if required when the final version of the code is issued (which is expected any day now!)

Input for all three UDFs and typical output is shown in the screenshots below:

Input to Shrink() and Creep()

Adjusted Age input and output

Shrink() Output

Creep() Output

This entry was posted in Concrete, Excel, Newton, UDFs, VBA and tagged , , , , , , , . Bookmark the permalink.

4 Responses to Reinforced Concrete Moment-Curvature – 2; Shrinkage and Creep

  1. metroxx says:

    It’s not take into account temperature?
    Only humidity … (I talk about EC2 calculation mainly).
    With regards.


    • dougaj4 says:

      metroxx – the creep and shrinkage coefficients are related to humidity in EC2, and to four general environment catagories in the Australian code (arid, interior, temperate and tropical), so they are not related directly to temperature. AS 3600 does however note that creep may be greater if the temperature is above 25C for long periods, and practical experience shows that extreme differential shrinkage effects can occur in hot dry conditions. It’s probably an area where more research work needs to be done.

      The temperature input in the spreadsheet relates to the maturity of the concrete at the age of first loading, and this comes straight from EC2.


  2. dougaj4 says:

    metroxx – reply sent.


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