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RAM Concept uses the ACI 209R-92 models for creep and shrinkage. In these models, only modifications that are a function of time are accounted for internally by the program. Other factors that affect creep and shrinkage rates are defined by the user in the Calc Options dialog (see Figure 1 below). The purpose of this tech note is to describe how these parameters are used in the load history calculations and discuss the default values.
More discussion on the theoretical basis for the load history deflection method used in RAM Concept can be found on the following web page:
Load History Article
Figure 1. Load History Parameters in Calc Options Dialog
The creep factor is defined as the ratio of total strain (elastic strain + creep strain) to elastic strain. According to ACI 209, an average value creep strain:elastic strain is 2.35. As a result, RAM Concept adopts a default creep factor of 1 + 2.35 = 3.35. The ACI 209 average value and the RAM Concept default are based on standard conditions. Other factors, like curing method, concrete composition, and cement content, can affect creep and should be incorporated into the creep factor that is defined.
The ACI 209 creep model assumes that the initial loading is applied at 7 days. Some codes, like AS 3600, assume adifferent time for initial load application. When using the load history calculations in RAM Concept, the creep factor should be converted for an initial loading time of 7 days.
ACI 209 defines a modification factor for initial load application times other than 7 days. This correction is automatically included in the load history calculations and should not be incorporated into the input creep value. The initial load application time defined in the Calc Options dialog is used to calculate this correction. This correction factor is automatically calculated and applied for each load history step and is based upon the time of application of loading in each step.
According to ACI 209, average shrinkage strains range from 0.000415 to 0.001070 for standard conditions. RAM Concept uses a default value of 0.0004.
Environmental factors, especially ambient relative humidity, can have a significant impact on the ultimate shrinkage strain and should be considered when inputting the value in the Calc Options dialog. If the relative humidity is low, the shrinkage value could be significantly higher than the default value.
ACI 209 defines a modification factor for shrinkage strain for conditions with a moist cure duration other than 7 days. RAM Concept uses the input Moist Cure Duration in the Calc options dialog to automatically account for this modification. Input shrinkage strains should not include this modification.
Elements like stiff columns and walls restrain shrinkage movements and cause a gradual buildup of tensile stress in the concrete, which leads to cracking. The shrinkage restraint percentage is a simple way to account for this cracking. The higher the percentage the earlier cracking will occur and the more the tension stiffening effect will be reduced.
RAM Concept uses the shrinkage restraint percentage as follows:
The ACI 209 time function for shrinkage and the input ultimate shrinkage strain are used to calculate the shrinkage strain at each given time step. This shrinkage strain is multiplied by the defined shrinkage restraint percentage. This tension strain is then summed with the modified concrete strain determined in the load history calculations (accounting for creep, etc.) for use with the concrete stress-strain curve to find the concrete stress.
Here is a simplified numerical example, illustrating the effect of the shrinkage restraint percentage:
User input shrinkage strain = 0.0004
User input shrinkage restraint = 10%
Elastic Modulus of Concrete = 3605 ksi
Assuming the concrete is linear elastic, the stress increase due to the shrinkage restraint would be (3605ksi)*(0.0004)*(0.1) = 0.144 ksi. This is roughly 1/3 of the cracking stress. In other words, the shrinkage restraint is reducing the cracking moment by about 1/3.
From a practical standpoint, setting the restraint percentage to 30% would reduce the cracking moment to zero (in theabsence of axial compression), cause all elements on the floor to crack, and significantly increase deflections. Increasing the value above 30% would have very little effect, since it would not affect cracking and would only reduce the tension stiffening effect slightly.
The following are some recommendations for the user input shrinkage restraint assuming an ultimate shrinkage strain of 0.0004 (use engineering judgment for interpolations between):
0% - unrestrained or very lightly restrained slabs (flexible columns only, single stiff element)
10% - normally restrained slabs (more than one stiff element, some flexibility)
20% - completely restrained slabs (basement walls around entire perimeter, etc. causing a high degree ofrestraint)
For other values of shrinkage strain, the percentages can be calculated based on an appropriate reduction to the cracking moment using the simple numerical example above. For example, for a given shrinkage strain and a desired reduction in cracking moment of 33%, the user input shrinkage restraint would be calculate from fr*0.33/(E*n)
fr = modulus of rupture
E = Elastic Modulus of Concrete
n = shrinkage strain
The ageing coefficient accounts for the rate of application loading for the calculation of creep effects. The RAM Concept Manual describes this parameter as follows:
“An ageing coefficient is used as a modifier of creep to account for the rate of application loading, its effect on the creep and the variation of concrete strength over the time period. While the rigorous calculation of the coefficient is rather involved, this value can normally be taken as 0.8 with little loss in accuracy.”
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