## Reinforced Concrete Moment Curvature – Development over time

I recently noticed that in the RC Design Functions spreadsheet the TimeCurve function had stopped working.  The function calculates the development of reinforced concrete section curvature over time, and was previously presented in Reinforced Concrete Moment-Curvature – 3; Restrained Shrinkage and Creep and Reinforced Concrete Moment-Curvature – 4; Development of curvature over time.

In the course of fixing the problem I took the opportunity to add some further refinements:

• The function previously did not allow for changes in the cracking stress over time, or for the effect of creep on the cracking strain.  It now either calculates a cracking strain, which may include a proportion of the creep strain, or a cracking strain can be specified for each time step.
• The tension-stiffening factor calculation has been revised to take account of the effect of creep and shrinkage on the cracking moment.
• The output table has been rearranged and extended to include:
• The virtual prestress stress, as well as strain.
• The adjusted concrete elastic modulus.
• The cracking moment.
• The depth of the Neutral Axis
• The concrete stress at the top and bottom face
• The concrete strain including creep at the top and bottom face, and the cracking strain.

Examples of the function results, compared with experimental data, will be included in the next post on this subject.  The screen-shots below show input and results for a typical beam loaded to just below the cracking moment, with cracking occurring as a result of the combined action of shrinkage and creep.  Click any image for a full-size version:

Function input documentation:

Typical section properties input and output graph:

Time related data input:

Note that the function may be used anywhere in the spreadsheet.  To display all the results it must be entered as an array function, using Ctrl-Shift-Enter. See Using Array Functions and UDFs for details.
Output results columns 1 to 9:

Output results columns 10 to 17:

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