Diaphragm Stiffness Modifiers

Diaphragm stiffness properties can be modified to account for cracked properties of concrete decks for different directions and actions (in-plane and out-of-plane). Also, stiffness properties can be different for corrugated decks in which loads are transferred to supported members only along deck orientation, otherwise does not provide enough stiffness for other directions.

To modify stiffness properties of diaphragms in general, the program allows engineer to define 3 stiffness modifiers for in-plane action (i.e., f11, f22, and f12) and 3 stiffness modifiers for out-on-plane action (i.e., m11, m22, and m12). These modification factors can be defined in the RAM Modeler (the implementation supports all flooring systems such as composite, noncomposite and concrete systems).

Referring to the following figure, these 6 modifiers are further explained as follows:

f11, f22, and f12: These factors are intended to modify in-plane stiffness. The modification factors f11 and f22 are for flexural and axial behaviors and f12 is for shear behavior.
m11, m22, and m12: These factors are intended to modify out-of-plane (bending) stiffness. The factors m11, and m22 are out-of-plane bending along edges and m12 is for torsion (twisting moment).

In case of having f₁₁ = f₂₂ = f₁₂ = m₁₁ = m₁₂ = m₁₂ = 1.0 for a diaphragm, this means that no stiffness modification is applied.

In addition to stiffness modifiers, engineer is still allowed to define separate crack factors for a concrete deck: one for bending (out-of-plane) and one for diaphragm (in-plane) behavior. This feature is still available in the program. The following relationship holds between crack factors and diaphragm stiffness modifiers:

f₁₁ = f₂₂ = f₁₂= crack factor for diaphragm (in-plane)
m₁₁= m₁₂ = m₁₂ = crack factor for bending (out-of-plane)

Axial and bending (in-plane) behavior for a diaphragm can be controlled by f₁₁ and f₂₂. Note that axial and bending behavior cannot be decoupled (i.e., they are affected simultaneously whenever f₁₁ and f₂₂ are applied).

It is important to note that stiffness modifiers are direction-dependent. On the other hand, using the same values for f₁₁, f₂₂, and f₁₂ makes the direction choice irrelevant. This is also correct m₁₁, m₂₂, and m₁₂.

When analysis is started, the program orients diaphragm shell element local axes in such a way that it complies with direction of diaphragm stiffness modifiers. The following rules are applied in the program:

For one-way deck, diaphragm stiffness modifiers are always oriented along deck orientation (i.e., f₁₁ always coincides with deck orientation)
For two-way deck, diaphragm stiffness modifiers are defined along a user-defined angle measured from global X-axis (see the figure below for examples).

In the figure above, examples are shown for two decks on which different orientations are defined for stiffness modifiers. In both cases, modifiers are defined along a line making angle θ measured from global X-axis. Also, note that f₁₁ and f₂₂ are defined along axis 1 and 2 in the figure, respectively (similarly, m₁₁ and m₂₂ follow the same definition).

The Model Data report lists stiffness modifiers for each shell located in diaphragm (in order to include this section of the report, the command Reports > Include Results for All Nodes should be selected). In addition, Member Show Options dialog provide further options (under Slabs/Decks tab) so that Stiffness Modifiers\Crack Factors values can be displayed on model (similarly, shell local axes can be turned on but only available after analysis is run).