Water Tank Strain to Stress 1

[l______40mm______l]

Hi All,

I'm currently designing a self-standing concrete water tank to AS3735 (Concrete structures for retaining liquids). As per the code, you need to account for the forces (F_shrinkage and F_Swelling)from shrink/swell moisture variations. The code provides a table of mean shrinkage and swelling strains (creep adjusted) for various wall thicknesses. For example, a 200mm thick insitu wall equates to 70x10^-6 shrinkage strain and 135x10^-6 swelling strain.

My question is, how would you go about finding the F_shrinkage and F_swelling forces? Do you multiply the strains by the young's modulus of the concrete to get the stress? Not only does this lead to really large stresses, it also feels inaccurate as I'm assuming the concrete is elastic. It also incentivises low strength concrete.

Example calc for shrinkage stress in a 40MPa (E=32800MPa), 200mm thick wall (per m run) restrained at each end:
• (32800MPa)*(70*10^-6) = 2.3MPa
• As the wall is restrained by the adjacent walls, I'd get very high tension forces at the walls.

Appreciate any assistance.

 

[l______40mm______l]

I've decided to take the concrete as cracked and disregard the concrete in the strain / stress check. I'm now only checking the stress in the reinforcement.

As the code stipulates that the service stress in the bars must be limited to approx 150MPa (depending on the situation), then I'd simple be accounting for shrink and swell stresses within this limit.
i.e. E_steel * shrinkage strain = 200000MPa * 70x10^-6 = 14MPa. Therefore, the residual allowable stress for all other loads is 150MPa - 14MPa = 136MPa, for the restrained directions only.

Let me know if anyone agrees / disagrees.

 

[Retrograde]

I've decided to take the concrete as cracked and disregard the concrete in the strain / stress check.

I think if you take that approach you will no longer have a water retaining structure.

One approach would be to try and model the amount of restraint you expect in the structure. If the concrete is not restrained, then the shrinkage strains will not induce any stress.

 

[l______40mm______l]

I'm of the opinion that even though it's a tank, it's still going to crack. I think the aim is more to limit the stress in the bars to well below it's yeild stress so that you get a higher number of small cracks (<0.1mm) that reduce how much water can flow through. I suspect if you wanted to completely make it dry, you'd need a membrane on the inner surface in addition to the requirements of the code.

Also I don't think you can avoid the restraint, especially at the base of the walls where they meet the slab, so you're always going to get cracks there.

 

[BJI]

In my experience the intent is to avoid cracking of concrete tanks, and typically admixtures are required to achieve this. Even lining will fail if you don't suitably mitigate cracking.

 

[LittleInch]

Doesn't the slab on which the walls are connected not expand at the same rate?

Or am I being simplistic here?

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[Retrograde]

Doesn't the slab on which the walls are connected not expand at the same rate?

Not necessarily - it depends on the geometry/thickness of the slab compared to the wall.

 

[l______40mm______l]

Not necessarily - it depends on the geometry/thickness of the slab compared to the wall.

The slab will also be poured earlier in my case.

 

[WesternJeb]

ACI 224R has measures that control the crack width in concrete for America. Maybe it has the calculations you are looking for, or at least minimum provisions to mitigate such a thing.

 

[Retrograde]

Thinking about this some more and reviewing AS3735, I think your approach is probably correct. The strain (stress) caused by shrinkage (as well as temperature) get added to the stresses caused by structural loading and need to be below the values given in Table 3.2

As long as you have the minimum reinforcement as per Table 3.1, restraint is dealt with.

 

[l______40mm______l]

Agreed. Thanks Retrograde