| Applies To | ||

| Product(s): | RAM Concept | |

| Version(s): | V8.2.0 and later | |

| Area: | Analysis |

The following creep/shrinkage models are implemented in RAM Concept Version 8 Update 2 and later:

- ACI 209.2R-08/GL 2000
- AS 3600-2018
- Eurocode 2-2004
- ACI 209R-92 (ECR Values)

RAM Concept calculates creep and shrinkage strains over time using one of these creep/shrinkage models and the load history parameters that are defined in the Calc Options dialog (see image below). The parameters boxed in blue are general parameters that apply to any of the implemented creep/shrinkage models. The parameters boxed in green are code-specific parameters that may be active or disabled depending on which creep/shrinkage model is selected. This article discusses how RAM Concept uses these parameters in the load history deflection calculations.

The Initial Load Application represents the time when loads are first applied to the structure and becomes the start time of the first load history step specified. The input initial loading time should be based on the construction and shoring schedule of your specific project. For example, it is common in the United States for formwork to be removed anywhere between 3-7 days, which represents the time of initial loading.

RAM Concept uses the input Initial Load Application to calculate adjustment factors for creep. This adjustment is calculated internally for all creep/shrinkage models implemented in the program, including ACI 209R-92 which uses the ultimate creep factor defined in the ECR box of the Calc Options dialog. See Table 1 below for more details about this adjustment for each creep/shrinkage model.

*Table 1. Initial Load Application Adjustments for Implemented Creep/Shrinkage Models*

The Cure Duration represents the time when the moist cure period ends and when shrinkage period begins. For creep/shrinkage models that distinguish between autogenous and drying shrinkage (AS 3600-2018 and Eurocode 2-2004), the cure duration marks the time at which the drying shrinkage period begins. The input Cure Duration is also used to calculate an adjustment factor for shrinkage strain for the ACI 209.2R-92 (ECR values) creep/shrinkage model (see Clause 2.5.3).

Actual creep behavior is affected by the rate of load application and the variation of concrete strength over time. To account for these effects, RAM Concept adjusts the creep strains using an ageing coefficient and uses the resulting modified creep strain in the cross-section strain compatibility calculations (age-adjusted effective modulus method). See Section 5.2 in ACI 209R-92 for more discussion. While the rigorous calculation of the coefficient is rather involved, this value can normally be taken as 0.8 with little loss in accuracy. More about the ageing coefficient can be found in this article.

External restraint to shrinkage is a simple way to account for cracking due to the gradual buildup of tensile stress that can occur when stiff supports restrain shrinkage movements. In general, as the input percentage increases, the tensioning stiffening effect will be reduced, cracking will occur at earlier times and lower loading levels, and load history deflections will increase. This effect should be distinguished from internal restraint to shrinkage due to reinforcement, which is rigorously calculated separately from external restraint to shrinkage and always included in RAM Concept’s load history calculations. More about external and internal restraint to shrinkage can be found in this article.

Internal and external shrinkage restraint effects are often approximated in long-term deflection calculations using one of the following methods:

- Reduced modulus of rupture. ACI 435R-95 recommends using a reduced effective modulus of rupture of 4*sqrt(f’c) psi or 0.33*sqrt(f’c) Mpa (approximately half of the ACI design value) for slab systems subject to significant restraint.
- Reduced cracking moment. In ACI 318-19, Bischoff’s tension stiffening equation reduces Mcr by 1/3 (Mcr’ = 2/3Mcr). In Eurocode 2-2004, the use of b = 0.5 (Clause 7.4.3) effectively reduces the cracking moment by 30%
^{1}.

RAM Concept does not use these approximate methods to account for shrinkage because:

- RAM Concept rigorously calculates the internal shrinkage restraint effect for each section, but the methods listed above include that effect (together with external restraint) in the reduction. Using a reduced modulus of rupture or cracking moment, then, would double count an effect that is always accounted for in the RAM Concept calculations.
- For severely restrained slabs, use of the reductions noted above may underestimate the external shrinkage restraint effect. Bischoff states this as follows: “using a reduced cracking moment less than the assumed value of 2/3
*M**cr*may be merited in cases with increased restraint at the supports^{2}.”

In the Load History Calc Options dialog, the user has the option of entering a specific percentage for external shrinkage restraint or selecting one of the pre-set options. The pre-set options are mapped to assumed percentages as tabulated below.

*Table 2. Pre-Set External Shrinkage Restraint Options*

Prior to Version 8 Update 2, a default value of 20% was used in new RAM Concept models. In Version 8 Update 2 and after, the default selection is None, which results in a shrinkage restraint of 0%. This setting may be appropriate for a typical, intermediate floor in a multi-story structure. However, a larger percentage may be more appropriate for other conditions (podium slab, transfer plate, basement slab, etc.). Click here to download a technical note with more information.

__References__

^{1} Gilbert, R.I and Ranzi, G., “Time-Dependent Behavior of Concrete Structures”, CRC Press, 2019.

^{2} Bischoff, P., “Comparison of Existing Approaches for Computing Deflection of Reinforced Concrete”, ACI Structural Journal, 117 (1), 2020, pp. 231-240.

The basic creep coefficient and basic shrinkage strains represent the base code values under standard conditions without the adjustment for time and other environmental factors. In general, these values can be determined automatically by RAM Concept (select “Code” in entry field) or input directly by the user (enter value in entry field). Using the default “Code” selection for these parameters will work well in most cases and is the recommended approach.

The remaining code-specific parameters are used to calculate adjustment factors that are applied to the base code values. The selections used for these parameters can vary significantly from project to project and region to region. The defaults used for these parameters in RAM Concept should be viewed as selections that may be appropriate for a variety of projects/regions, but not as endorsed selections to be used for all models.

Code-specific parameters that do not apply to a given creep/shrinkage model are automatically disabled when that model is selected for use. The modulus of rupture for the selected Design Code is used for the concrete flexural tension strength in the tension stiffening equation. RAM Concept calculates this rupture strength using the 28-day design concrete strength that is input in the Materials window (Criteria – Materials). Since the compressive strength increases over time, the program applies a correction factor to covert the modulus for rupture from 28-days to the actual time of loading in order to account for the reduced strength at early age loading (before 28 days). The adjustment factors used for each model are referenced in Table 3 below. When calculating the adjustment, RAM Concept uses the modulus of rupture calculated with f’ci in the Materials window as the lower bound for the early age modulus of rupture.

*Table 3. Adjusted Modulus of Rupture Equations (used at 0 days < t < 28 days)*

The ACI 209.2R-08/GL 2000 creep/shrinkage model is the default creep model for new models that are created when any of the following design codes are selected for use: ACI 318, CAN/CSA A23.3, IS 456. The GL2000 model was developed by Gardner and Lockman and is outlined in ACI 209.2-08.

The active Calc Options parameters for the ACI 209.2R-08/GL 2000 model and the default settings are summarized in the image and table below. The table also defines what value or equation is used when “Code” is selected for the active parameter.

The ACI 209.2R-08/GL 200 model calculates creep strain based upon the 28-day mean concrete elastic modulus. Since RAM Concept assumes that the Ec value is a 28-day mean modulus as a result, no adjustment for the elastic modulus is required at early ages.

The AS 3600-2018 creep/shrinkage model is the default creep model for new models that are created when any of the AS 3600 design codes are selected for use.

The active Calc Options parameters for the AS 3600-2018 model and the default settings are summarized in the image and table below. The table also defines what value or equation is used when “Code” is selected for the active parameter.

The AS 3600-2018 model calculates creep strain based upon the mean modulus of elasticity at 28 days (Ec), which is a function of the mean in situ compressive strength (fcmi). When calculating the mean elastic modulus, RAM Concept internally adjusts from the input characteristic cylinder strength to the mean in-situ.

The Eurocode 2-2004 creep/shrinkage model is the default creep model for new models that are created when any of the Eurocode 2 or BS 8100 design codes are selected for use.

The active Calc Options parameters for the Eurocode 2-2004 model and the default settings are summarized in the image and table below. The table also defines what value or equation is used when “Code” is selected for the active parameter.

The Eurocode 2-2004 model calculates the creep coefficient based upon the tangent modulus, Ec. Since RAM Concept assumes that the calculated or input Ec value is the secant modulus, Ecm, an adjustment is needed to convert creep strains to the code model values. This is adjustment factor is taken as 1.05 based on Clause 3.1.4(2).

The ACI 209R-92 (ECR values) model was the only creep and shrinkage model implemented in RAM Concept prior to Version 8 Update 2. This creep/shrinkage model will automatically be selected in models that were created in one of those prior versions and opened in a version later than Version 8 Update 2.

Unlike the other creep/shrinkage models, the ACI 209R-92 (ECR Values) model uses the creep factor and shrinkage strain that are input in the ECR box in the Calc Options box instead of the basic creep and shrinkage strain parameters. The creep factor is defined as the ratio of total strain (elastic strain + creep strain) to elastic strain. According to ACI 209R-92, an average value of creep strain:elastic strain is 2.35. As a result, RAM Concept adopts a default creep factor of 1 + 2.35 = 3.35. The creep factor that is input in RAM Concept should represent the final ultimate creep value including all adjustment factors except the adjustment for initial load application (γ* _{la}* ), which is calculated automatically by the program. Similarly, the input shrinkage strain should represent the ultimate shrinkage strain including all adjustment factors except the adjustment for moist cure duration (γ

The ACI 209R-92 model calculates creep strain based upon the modulus of the mean concrete strength at time of loading. Since RAM Conce*pt* calculates curvatures based upon the concrete modulus value at 28 days, an adjustment is needed to convert creep strains to the code model values. A similar adjustment is needed for the modulus of rupture, which is calculated using the 28-day design concrete strength and then used for the concrete flexural tension strength in the tension stiffening equation. These adjustments are automatically calculated by the program for the ACI 209R-92 model in RAM Concept Version 8 Update 2 and later.

The applicable Calc Options parameters for the ACI 209R-92 (ECR Values) model and the default settings are summarized in the image and table below.

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