Downstand Beams, Ribs, T-Beams: Modeling and Determination of Internal Forces

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Downstand beams or T-beams are often used in reinforced concrete structures. In contrast to the previous representation and calculation options where, for example, a downstand beam was considered as a fixed support and the determined support reaction was applied to a separate member structure using a T-beam section, the ultimate structural FEA software like RFEM allow you to consider the structure as a whole and thus achieve a more precise analysis.

Advantages of using the rib member type Rib in RFEM

The stiffness or flexibility of the downstand beam is taken into account. Thus, it is possible to model its influence on the distribution of internal forces and the deformation.

Parameters of the rib

Figure 01 - 1 - Parameters of Rib 3D

There are two main parameters for the rib in a 3D position. On the one hand, the integration width that defines the area for the integration of the internal forces. Please note that the integration area cannot extend over several surfaces per side. On the other hand, you have to specify where the rib should be arranged. The information regarding the position refers to the local axis system of the surface to which the rib is connected.

Cross-section of rib

The cross-section part that is available in addition to the surface must be defined as the cross-section of the rib. For the design, the entire cross-section of the T-beam is created internally.

Determination of internal forces for design

Before the design, the internal forces for the T-beam cross-section, usually a T-section or L-cross-section, are determined internally by integration and referring to the centroid of the T-beam cross-section. The internal force component from the plate and the component from the rib are integrated. The integration of the internal forces is performed perpendicular to the axis of the rib.

Figure 02 - 2 - Display of Internal Forces for Rib Only

For the plate component, the following internal forces result from the integration of the surface internal forces. It is assumed here that the local axis systems of the rib and the surface match. If they do not match, the internal forces must first be transformed to the local axis system of the rib.

Figure 03 - 3 - Eccentricity of Cross-Section Parts

The internal forces of the rib component correspond to those of the member with rib cross-section. In RFEM, they can be output by not including the components from the surface for the evaluation of the internal forces. The adjustments can be made in the Project Navigator - Display under "Results" -> "Ribs - Effective Action on Surface/Member".

Figure 04 - 4 - Display of Internal Forces for T-Beam 1

The internal forces of the plate beam resulting for the design are obtained by referring the internal forces of plate and rib component to the centroid of the plate beam cross-section.

Figure 05 - 5 - Cross-Section Parts - Rib 3D

The bending moment of the resulting T-beam would result, for example, for a T-section as follows:
M y = M y, plate + M y, rib - e plate ∙ N plate + e rib ∙ N rib
By default, the program always displays the resulting step sizes of the T-beam cross-section.

Figure 06 - 6 - Internal Force Component - Plate

Rib in 2D

Basically, slab beams are not a purely two-dimensional problem. The user should be aware that a consideration of ribs in 2D is necessarily accompanied by a simplification. Since the arrangement of eccentric elements is not possible in 2D, the centroidal axis of the plate beam cross-section runs in the plane of the surface. This approach requires additional considerations when considering the stiffness of the system.

Figure 08 - Rib 2D

In addition to the parameters of the rib in 3D, there are further parameters in 2D for considering the stiffness of the girder cross-section. The internal consideration of the rib in 2D results in a superimposed stiffness in the area of the integration widths b1 and b2. Therefore, from the default setting of the rib parameters, a reduction of the stiffness of the surface in the area of the integration width is active. However, it should be noted that due to this approach, the stiffness is concentrated along the axis of the rib, which does not occur in reality and also when the rib is displayed in 3D.

Figure 10 - 8 - Additional Parameters - Rib 2D

Since an eccentricity cannot be represented in 2D, the influence of the eccentricity via the stiffness, i.e. additional Steiner components, is taken into account. For the torsional stiffness, the proportion of the plate beam cross-section and the surface are superimposed. The user can reduce the effective torsional stiffness of the T-beam cross-section. Basically, however, it is not possible to specify a reduction factor or a percentage value for the effective torsional stiffness, as this depends on the cross-section geometry.

Insofar as a 3D version of RFEM is available, it is preferable in the context of the mapping of downstand beams to the 2D version.

Reference

[1]   Barth, C .; Rustler, W .: Finite Elements in Structural Engineering, 2nd Edition. Berlin: Beuth, 2013

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