Tension stress on rebars provided on the Reinf. Foundation caused by Shrinkage and Temperature 2

[Gnoowij]

Dear,

To calculate Tension stress on rebars provided on the Reinf. Foundation caused by Shrinkage and Temperature,

Considering the affect by Shirnkage and Temperature on the Reinf. Foundation, Minimum Reinforcement Rebar Ratio should be used.

To calculate specific stress on the one rebar due to con'c drying shrinkage and temperature, I approach as the following,

[calculation]
Con'c strength : 30MPa
Act, con'c tension zone/area : 150mm x 1000mm = 150000mm2
Effective depth, heff : 150mm
Provided rebar : 20mm (Dia)
Rebar spacing : 200mm
Unit width : 1000mm

Shrinkage strain, εsh : 0.0002
Thermal Strain, εt : 0.0002 (=0.000001 x ΔT, ΔT=20)
εtot = εsh + εt = 0.0004
Ec ((=Ec / (1+φ), φ=2) = 10000 MPa

Con'c tensile stress due to Shrinkage and Temperature (εtot x Ec) : 4Mpa
(*) 4MPa > fctm (2.9MPa) ---- so crack occurs

Con'c tensile force (4Mpa x 150000mm2) = 600kN

Consideirng that only rebar resist against the tensile force due to shrinkage and temperature (because crack occurs)

5ea rebar is considered in unit meture (1000mm / 200mm spacing)

Tension force on one rebar : 600kN / 5ea = 120kN

If my approach is correcet, 12ton is loaded only one rebar. However, I don't believe that that sort of huge tension force on one rebar only due to shrinkage and temperature.

As long as my calculation is correct, I should provid rebars way more than the result by calculating from Min. Reinf. ratio.

Please check whether my understanding is correct or not.

 

[BridgeSmith]

I have no idea what you did there, but Shrinkage and Temperature reinforcement is added to minimize crack widths when the concrete cracks. When a crack happens in the concrete, the stress in the concrete is relieved, and therefore the stress in the steel goes to zero. So, the only stress in the steel is the little bit that develops between the cracks in the concrete, which isn't going to be much.

Calculating the stress in S&T reinforcement is not only pointless, but also nigh impossible to do with any degree of accuracy.

 

[bugbus]

There's a few problems. Main one, which BridgeSmith alluded to, is that you've predicted cracking will occur but have not considered how that would relieve the tension in the slab. Instead you have kept the original tension force calculated on the basis that it is uncracked and applied that just to the reinforcement, which is inconsistent. Secondly, you have assumed that the slab is restrained at its edges (such that all shrinkage and thermal strain has to be accommodated by elastic strain), which is probably not realistic for a slab on grade.

 

[Gnoowij]

Thank you,

I agree on the idea that calculating stress in S&T reinforcement is nearly impossible.

In accordance with 7.3.2, EN 1992-1-1, Eurocode gives the minimum reinforcement ratio to control crack.

As,min x σs = Kc x K x fct,eff x Act (7.1)

Could it be possible to calculate the tension stress caused by Shrinkage & Temperature as the following?
(I'm not sure that the cl 7.3.2 is right to be applied on Block foundation)

Condition
Foundation size : 6m x 4m x H 1.5m (Block foundation)
Provided rebar : 20mm Dia
Spacing of the rebar : 200mm
fct,eff = fctm = 2.9MPa (C30)
Unit width : 1m
No. of rebar, provided in unit width : 5ea
As,provided : 1571mm2 (in unit width)
Crack width_limit : 0.3mm
Effective depth, hc,ef : 150mm
Act, tension zone of concrete (by shrinkage and Temperature) : 1000mm (unit widht) x 150 mm

σs is limited as 230MPa when 0.3mm crack width is allowed. (assumed according to Table 7.2N, EN 1992-1-1)
-> 230MPa is forced to the rebars which arranged in Act. Unless none of tension force exsists, the stress, 230MPa can be assumed as a stress from drying shrinkage and Temperature.

Kc x K x fct,eff x Act = 1 x 0.65 x 2.9MPa x 150000mm2 = 282.75kN (in unit width)
where, Kc=1.0 K= 0.65 (h>800)
-> As,provided x σs shouldn't be larger than the result from the right-hand side of eq. to limit 0.3 crack width.

If the 20mm rebars with 200mm spacing are provided, so Provided As is 1571mm2, the the Force per rebar by Shrinkage and Temperature would be 56.6kN (=282.75kN / 5ea)

Result : The shrinkage and temperature rebars should be provided more than now

In terms of the crack control, shrinkage and temperature rebar can be assumed I think. Am I correct?

Regards,

 

[HTURKAK]

No! .. your approach implies you are in confusion.

Just for to remind for your case ( 6m x 4m x H 1.5m ,Block foundation)

- Shrinkage ; changes in moisture content of the concrete and drying leads to shrinkage.During hydration of cement, heat is generated and as the concrete cools, it contracts. If the concrete restrained , they lead to tensile stresses in concrete and
possibility of cracks. You may minimize the shrinkage stresses with sequencing of construction, using pe film under the mat ..

- Temperature ; In your case , temperature change btw top and bottom of the block will cause curvature and tension at the top . The thermal and shrinkage strains are not additive.

My suggestion would be ;

Provide minimum steel reinforcement as given in Eurocode 2, clause 7.3.2, equation (7.1)
As,min σs = kc* k *fct, eff* Act




Use it up, wear it out;
Make it do, or do without.

NEW ENGLAND MAXIM

 

[BridgeSmith]

S&T reinforcement is provided to minimize crack width, period. It makes it so that the concrete develops many small cracks instead of a few big ones; that's it. The numerous researchers that have studied concrete over many decades, and the code writers who used that information to formulate the code provisions, have a very good grasp of what's needed to make concrete slabs function adequately. There's no need to second guess the code provisions.