# RF-CONCRETE Surfaces – Online Manual Version 5

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# 2.7.8 Material Stiffness Matrix D

### Material Stiffness Matrix D

Bending stiffness – plates and shells

The bending stiffnesses in the reinforcement directions φ are determined as follows:

The non-diagonal component of the material stiffness matrix is calculated identically for plates and shells:

For shells, the differences in the bending stiffnesses due to the moments of inertia are compensated via the eccentricity components in the material stiffness matrix.

Torsional stiffness – plates and shells

The stiffness matrix elements for torsion are calculated as follows for plates and shells:

Shear stiffness – plates and shells

The stiffness matrix elements for shear are not reduced for the deformation analysis. They are calculated from the shear modulus G of the ideal cross-section and the cross-section height h. The following applies for shells and plates:

Membrane stiffness – shells

The membrane stiffnesses in the reinforcement directions φ are determined as follows:

The non-diagonal component of the material stiffness matrix is calculated from:

The shear stiffness component is:

Eccentricity – shells

The stiffness matrix elements for the eccentricity of the centroid (ideal cross-section) in the reinforcement direction φ are calculated as follows:

The non-diagonal component of the material stiffness matrix is determined from:

The eccentricity components for torsion are calculated as follows: