Long Term Slab Deflection - Internal & External Restraint - Shrinkage

[Drapes]

When assessing long term slab deflections, the shrinkage-induced tensile stress due to restraint should be considered, as this reduces the flexural tensile strength (and cracking moment) of the concrete section and increases deflections. I understand the two primary sources of restraint are caused by internal restraint from bonded reinforcement, and external restraint from stiff walls and columns.

In calculating the cracking moment, the concrete code AS3600 explicitly accounts for internal restraint from bonded reinforcement by reducing the flexural tensile strength, but does not explicitly account for external restraint from stiff walls and columns, except that the effective moment of inertia Ieff is limited to a maximum value of 0.6Igross, which may be an attempt to capture this effect. Is this correct, what are other peoples thoughts on this?

I have also investigated how internal/external restraint is being captured in programs like SAFE, RAM Concept and RAPT when assessing long term deflections. My findings and comments are as follows, but please let me know if I have overlooked anything:

SAFE - does not allow for the effects of internal or external restraint, however it does allow the user to manually adjust or reduce the modulus of rupture (that is, the flexural tensile strength) to capture these effects if required, but this is a bit of a roundabout way of doing it, as most users will simply proceed based on the program default.
Interestingly, the program default for the modulus of rupture appears to be based on the uniaxial tensile strength of 0.36 sqrt fc' and not the flexural tensile strength of 0.6 sqrt fc', when AS3600 is specified as the code of choice. This appears to be an oversight, albeit conservative. I am following this up with the developers as we speak to clarify.

RAM Concept - does not allow for internal restraint, but allows for external restraint via the 'shrinkage restraint' parameter. The user can capture internal restraint effects by increasing the 'shrinkage restraint' parameter if they choose to, but unsure if this is ever done in practice. In any case, my only criticism of the 'shrinkage restraint' parameter is that it is a little too arbitrary, and the program appears to make a blanket reduction in the cracking moment at every single cross section, which in my view is a little over-conservative- in reality once the first crack forms, the restraint conditions are partially relieved and continue to be relieved for each subsequent crack. What are others peoples thoughts on this?
The program default modulus of rupture here appears to be correctly based on the flexural tensile strength of 0.6 sqrt fc' when AS3600 is specified.

RAPT - allows for internal restraint in accordance with the provisions of AS3600, and allows for external restraint by allowing the user to specify a max Ieff as a percentage of Igross at every cross section - typically recommended b/w 0.6 to 0.7Igross. I feel this is a more appropriate and balanced approach to capturing external restraint without explicitly calculating it, as opposed to making a blanket reduction to the flexural tensile strength at every cross section. What are other peoples thoughts on this?
The program default modulus of rupture here appears to be correctly based on the flexural tensile strength of 0.6 sqrt fc' when AS3600 is specified.

 

[Retrograde]

Interestingly the ratio between the uniaxial tensile strength and the flexural tensile strength used by SAFE is 0.6, which is the same as the maximum value of 0.6Igross is AS3600.

 

[Drapes]

Thanks Retrograde, didn't pick up on that although I wonder if that was the intent.

Do you have any thoughts/feedback in general on capturing internal and external restraint in deflection calculations?

Anyone else?

 

[Retrograde]

Personally I trust the results of RAPT over RAM Concept. Unfortunately, as you know, RAPT uses the strip method which can be very difficult to employ for a slab with irregular column grid. I wish RAPT included some definitive advice in the manual on how to employ the strip method in such situations.

Using something like Ieff = 0.7Igross is the only practical way to go I think. Even if you were to use a complicated finite element model to calculate the external restraint, I feel that the results would be too sensitive to other factors like curing that would be too difficult to quantify.