Reinforced Concrete Moment-Curvature – 4; Development of curvature over time

The previous post in this series looked at how specified shrinkage and creep strains affect the curvature of a reinforced consrete section subject to a constant load.  In this post I will present a User Defined Function (UDF) that analyses the curvature due to loading, prestress, creep and shrinkage over a series of time steps, allowing the interaction between these factors to be taken into account, and also allowing for variation in loading and the concrete stiffness over time.

The UDF has been added to RC design functions6.zip.  As usual, the spreadsheet includes full open sourec code.

The procedure used is:

• Read the section properties, creep and shrinkage parameters for each time step, and optionally load, prestress and concrete E value for each time step.
• For each time step:
• Adjust the applied loads, prestress, and concrete E value, if required.
• Adjust the concrete E value for the increase in creep from the  previous step.
• Calculate a virtual prestress force equivalent to the total shrinkage and creep strain up the the previous step, plus the shrinkage strain for the current step.
• Calculate the section strains and curvature for the current step.
• Update the virtual prestress to include the creep increment from the current step.
• Go to next time step.

The screenshot below shows typical input data and results from the TimeCurve function compared with a time-step analysis carried out in the finite element analysis program Strand7.

Click to view full size

This screenshot shows typical time-step data and results.  Note that the UDF must be entered as an array function (press ctrl-shift-enter) to view all the results.:

Click to view full size

The spreadsheet also includes the following new functions:

• TimeSteps – generates a series of timesteps with logarithmic spacing
• EC2Props – generates concrete properties for a given age and strength grade, as specified in Eurocode2.
This entry was posted in Concrete, Excel, Newton, UDFs, VBA and tagged , , , . Bookmark the permalink.

6 Responses to Reinforced Concrete Moment-Curvature – 4; Development of curvature over time

1. Mauro says:

Like

2. dougaj4 says:

Mauro – thanks for letting me know. The link has now been corrected.

Like

3. Mauro says:

Thank you for your answer. I looked at the excel file. I would ask you some questions:
– why in “Time_step” sheet you put beta factor equal 0.5 at 45.783 days? It should be 0.5 at “long term” (says 30 years)?
– in the same sheet you calculate the growing of Elastic Modulus with time, but also the “Concrete flexural tensile strength” should change with time (much more than elastic modulus). Since cracking is not reversible, I don’t know if increasing in tensile strenght will affect deflection. What do you think?
My poor English could seem a bit cold but I really appreciate your work!
Thank you
mauro

Like

• dougaj4 says:

In brief – the effect of shrinkage and creep strains results in tension stiffening reducing quite quickly, certainly much less than 30 years. As you suggest, increasing tensile strength becomes irrelevant if the concrete cracks at an early age. Also the effects of creep and shrinkage also tend to reduce the effective tensile strength. Differential temperature stresses can also have a significant effect.

These things make it very difficult to predict actual deflections (outside a laboratory), but applying conservative (low) tensile strength, and allowing for effects of shrinkage, creep, differential temperature, and loss of tensioning stiffening allows a reasonable upper bound prediction.

If interested you can find more detail in the link below, including references for early loss of tension stiffening:
http://www.interactiveds.com.au/Publications/Cracking%20and%20Deflections.doc

Like