# Shear Area Types and Their Meaning

## Technical Article on the Topic Structural Analysis Using Dlubal Software

### Technical Article

The cross -section properties in RFEM and RSTAB contain different types of shear surfaces. This technical article explains the calculation and meaning of the different values.

#### Shear area Ay and Az

The shear area is determined from the cross -section area using the shear correction factor κ. Depending on the selection of a thin -walled or thick -walled cross -section, this is calculated according to the corresponding theory. For thick sections, the calculation is performed according to the theory of Grasshof-ZURAVSKI (see also program description SHAPE-MASSIVE), for thin-walled cross-sections of the calculation of the thrust surfaces is in this technical paper explained.

The shear area of the cross -sections is used by default to determine the internal forces and deformations in RSTAB/RFEM. However, the influence of the shear deformation can also be neglected with the corresponding setting in the calculation parameters, in which case the shear areas of the cross -sections are not relevant. The influence of shear deformation on deformations and internal forces is described in this technical article using an example in timber construction.

#### Effective shear area according to EC3 Av, z and Av, y

For the design, custom shear areas are usually determined according to the corresponding standards, such as the effective shear area according to EC 3. The calculation is regulated there in Section 6.2.6 (Shear Force Resistance) depending on the cross -section shape.

This shear area is used in the RF-/STEEL EC3 add-on module to check the plastic shear force resistance. However, if an elastic stress analysis is performed with RF-/STEEL, the shear area is not required because the determination of the shear stresses is carried out independently of the stress points.

#### Plastic shear area Apl, z and Apl, y

The plastic shear area represents a simplified approach to the determination of the plastic shear force resistance. First, the cross -section is divided into rectangular elements. The plastic shear area results from the area of the elements running parallel to the force direction; existing fillets and elements transverse to the considered force direction are not considered. Inclined elements will be considered with regard to the angle.

The stand-alone program SHAPE-THIN performs the calculation of the plastic shear areas according to the same method.

#### Differentiation between thin -walled and thick -walled cross -sections

For some cross -sections, the question arises whether they are still considered thin -walled or have to be classified as thick -walled. If cross -sections cannot be clearly recognized as thick -walled, a look at the shear surfaces Az or Ay can help in the decision.

As an example, the parametric I-section IS 300/40/25/20/0 is entered as a thin-walled cross-section. According to the thin -walled theory, a shear area Ay = 95.4 cm 2 is determined. Thus, this is larger than the cross -section area A = 81 cm 2 and indicates that the cross -section should actually be calculated as a thick -walled cross -section. Therefore, before the calculation of a member with this cross -section in RSTAB/RFEM, a corresponding warning message appears due to the plausibility check.

If the shear stiffness has been deactivated in the design parameters, this warning can be ignored without consequences. If you want to consider the shear stiffness, you can either use a parametric, thick-walled I-section or adjust the shear area manually in the table of cross-sections. Since the subsequent design with RF-/STEEL EC3 requires the definition as a thin-walled cross-section and the shear area is not used there anyway, it is recommended to adjust the shear area of the thin-walled cross-section.

#### Dipl.-Ing. Oliver Metzkes

Product Engineering & Customer Support

Mr. Müller is responsible for the development of the add-on modules for steel structures and provides technical support for our customers.

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• Updated 05/05/2021

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