This article describes how to scale for notional size when inputting user-defined curves for creep and shrinkage under time-dependent material properties.

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Notional size

Notional size scaling is used to specify how the user-defined curve will be modified by the notional size of a member. Each section property (frame and shell) has a notional size that is calculated automatically or can be specified by the user. Notional size, h, is essentially the twice the ratio of volume to the surface area for the cross section of a frame or shell section property. This works out, for example, to be equal to the thickness of a shell if you ignore the edges. For a circular frame section, the notional size is the radius.

For a larger notional size, moisture takes longer to migrate from the interior of the member to the surface where it can evaporate, and this slows the rate of creep and shrinkage.

Accounting for notional size in CEB and ACI codes

Each code has its own way of relating notional size to creep and shrinkage. While the CEB codes are more complicated, the ACI code is relatively simple and uses the following formulas:

• Creep:  C = C₀ * 2⁄3 [1+1.13 exp(-0.54 h⁄2)] for notional size h in inches, where C is the creep coefficient considering notional size, and C₀ is the specified creep coefficient taking into account all other factors.
• Shrinkage:  S = S₀ * 1.2 exp(-0.12 h⁄2) for notional size h in inches, where S is the shrinkage strain considering notional size, and S₀ is the specified shrinkage strain taking into account all other factors.

Note that the ACI formulas actually specify v/s = volume/surface = h/2,

CSI products provide the following formula for scaling user-defined creep and shrinkage curves for notional size:

f = a + b exp(-h/h₀)

where f is the scale factor multiplying the ordinate of the curve, h is the notional size, a and b are dimensionless constants, and h₀ is a reference notional size.

So for user-defined curves that are going to use the ACI formula for notional-size effect, specify

• Creep:  a = 0.67,  b = 0.75, and h₀ = 3.70 in = 94 mm.
• Shrinkage:  a = 0,  b = 1.2, and h₀ = 16.7 in = 423 mm.

You can choose other vales of these parameters to best match the data available for each material.