Creep of Concrete

Figure 2.5 indicates that the stress-strain relationship of concrete is a function of time. Concrete under stress undergoes a gradual increase of strain with time because of creep deformations of deformation of the concrete. The final creep strain may be several times as large as the initial elastic strain. Generally creep has little effect on the strength of a structure, but it will cause a redistribution of stress in reinforced concrete members at the service loads, and.lead to an increase in the service load deflections. Creep deflections are beneficial in some cases. For example, concrete stresses due to differential settlement of structures are reduced by creep. Creep in tension also delay shinkage cracking in concrete. The method of calculation of stresses and deformations due to creep is examined in Chapter 10.

the creep deformation of concrete under constant axial compressive stress is illustrated in Fig. 2.20. As the figure reveals, the creep proceeds at a decreasing rate with time. If the load is removed, the elastic strain is immediately recovered. However, this recovered elastic strain is less than the initial elastic strain because the elastic modulus increases with age. The elastic recovery is followed by a creep recovery, which is a small proportion of the total creep strain.

Experimental evidence indicates that the creep strain occurring over a given period is proportional to the applied stress, provided the stress level is not high. Research evidence is conflicting· with respMlfto the stress level at which the linearity between creep and applied stress ceases. Some research indicates loss of linearity at compressive stresses as low as 0.2fc’ other data suggest a value as high as 0.5fc’ . However, the assumption of a linear relationship between creep strain and applied stress for the usual range of service load stresses used in structural design results in acceptable accuracy.

According to ACI Commite 209, for normal weight, sand linghtweight, and all light weight concrete (using both moist and steam curing and types I and III cement), the creep coefficient C, (defined as the ratio of creep strain to initial elastic strain) at any time may be written as

Ct = Cu Kt Ka Kh Kth Ks Kf Ke

Dimana

Cu (ultimate creep coefficient)

The value of Cu can vary widely. In the ACI Commite 209 review, Cu was found to be in the range 1.30 to 4.15, with an average value of 2.35. This average value should be assumed only in the absence of more exact data for the concrete to be used.

Kt (time of under load coefficient)

Kt …

Dimana t = time in days after application of load (Kt = 0.44, 0.60, 0.69, 0.78, and 0.90 for t = 1 month, 3 months, 6 months, l year, and 5 years, respectively)

Ka (Age when loaded coefficient)

Ka … forr moist-cured concret, orKa… , for steam-cured concret

where t; = age of concrete in days when load is first applied (K0 = 1.00, 0.95, 0.83, and 0.74 for moist-cured concrete loaded at 7, 10, 30, and 90 days, respectively; Ka= 1.00, 0.90, 0.82, and 0.74 for steam-cured concrete loaded at 1 to 3, 10, 30, and 90 days; respectively

Kh (relative humidity coefficient)Kh ….

where H = relative humidity in percent (Kh = 1.00, 0.87, 0.73, and 0.60, for ~ 40, 60, 80, and 100% relative humidity)

kth (minimum thikness of member coefficient)

kth = 1.00 for 6 in or less, and 0.82 for 12 in (1 in = 25.4 mm)

Ks (slump of concrete coefficient)

Ks = 0.95 for 2 in, LOO for 2. 7 in, 1.02 for 3 in, l.09 for 4 in, and 1.16for 5 in slump (fIn = 25.4 mm)

kf (fines coefficient)

Kf = 0.95 for 30 %, 1.00 for 50 %, and 1.05 for 70 % fines by weight

Ke (air content coefficient)

Ke = 1.00 up to 6 %, 1.09 for 7 %, and 1.17 for 8 % air

the cement content need not be taken into account for concrete with cement contents between 470 and 750 lb/yd3 (l lb/yd3 = 0.593 kg/m3).

Shrinkage of concrete

when concrete loses moisture by evaporation, it shrinks. Shrinkage strains are independent of thestress conditions in the concrete. If restrained, shrinkage strains can cause cracking of concrete and will generally cause the deflection of structural members to increase with time. A curve showing the increase in shrinkage strain with time appears in fig. 2.21. the shrinkage occus at decreasing rate with time. the final shrinkage strains vary greatly, being grenerally in the range 0.0002 to 0.0006 but sometimes as much as 0.0010.

According to ACI Commite 209 for normal weight, sand lightweight, and all lightweight concrete (using both moist and steam curing and types I and III cement), the unrestrained shrinkage strain at any time t is given

………

Where :

1 ultimate shrinkage strain,

the value of 1 can vary widely. In the ACI Committee 209 review, 1 was found to be in the range 0.000415 to 0.00107, with mean values of 0.00080 for moist-cured concrete or 0.00073 for steamcured concrete. These average values should be assumed only in the absence of more exact data for the concrete to be used.

2 Time of shrinkage coefficient,

At any time after age 7 days, for moist-cured concrete

……..

where t = time in days from age 7 days (S, = 0.46, 0.72, 0.84, 0.91, and 0.98 for t = 1 month, 3 months,6 months, 1 year, and 5 years, respectively) or, at any time after age 1 to 3 days for steam-cured concrete.

……….

where t = time in days from age 1 to 3 days (S, = 0.35, 0.62, 0.77, 0.87, and 0.97 for t = 1 month, 3 months, 6 months, 1 year, and 5 years, respectively}

For shrinkage considered-from greater ages than given above, the difference may be determined using Eq. 2.17a or 2.17b for any period after that time. That is, shrinkage for moist-cured concrete between, say, 1 month and 1 year would be equal to the 7-day to 1-year shrinkage minus the 7-day to 1-month shrinkage. The foregoing procedure assumes that the moist-cured concrete has been cured for 3 to 7 days. For the shrinkage of moist-cured concrete from 1 day, the shrinkage needs to be multiplied by 1.2; a linear interpolation between 1.2 at 1 day and 1.0 at 7 days may be used.

3 -Rela.tfoe humidity coefficient,

………..Or……….

where H = relative humidity in percent (Sh = 1.00, 0.80, 0.60, 0, for s; .4o. 60, 80, and 100% relative humidity)

4 Minimum thickness of member coefficient,S1h = 1.00 for 6 in or less and 0.84 for 9 in (1 in = 25.4 mm)

5 Slump of concrete coefficient,

S, = 0.97 for 2 in, 1.00 for 2.7 in, 1.01 for 3 in, 1.05 for 4 in, and l.09 for 5 in (1 in = 25.4 mm)

6 Fines coefficient, S

Sf = 0.86 for 40 %. 1.00 for 50 %, and 1.04 for 70 % fines by weigh

7 A ir content coefficient,

Se = 0.98 for 4 %, 1.00 for 6 %, and 1.03 for 10 % air

8 Cement content factor, S

Sc = 0.87 for 376 lb/yd3, 0.95 for 564 lb/yd3, LOO for 705 lb/yd ', arid 1.09 for 940 lb/yd3 (1 lb/yd3 = 0.593 kg/m3)