# Downstand Beams, Ribs, T-Beams: Deformation and Deflection in Cracked State

### Technical Article

25 September 2017

001480

RFEM and the RF-CONCRETE add-on modules provide various options for the deformation analysis of a T-beam in cracked state (state II). This technical article describes the calculation methods (C) and modelling options (M). Both the calculation methods and the modelling options are not limited to T-beams, but will only be explained using an example of this system.

#### Calculation Methods of Deformation/Deflection Anal

C1: Analytical Calculation - Member
The calculation method according to EN 1992‑1‑1, Section 7.4.3 [1], allows for a simplified approximation of the deformation in cracked state. Using this method, the deformation is determined on an extracted member structure. The connected structural elements such as surfaces, for example, are not considered in the calculation.

C2: Analytical Calculation - Surface
The RF-CONCRETE Deflect add-on module determines the deformations in the cracked state by using a method based on the analytical calculation method according to EN 1992‑1‑1, Section 7.4.3. In this case, linear-elastic material properties are applied to the reinforcing steel and concrete until the tension strength is reached. If the tension strength of the concrete is exceeded, damage development occurs. The analysed structure must consist entirely of surfaces. This calculation method is suitable for surfaces subjected to bending.

C3: Nonlinear Calculation - Member
This is a physically nonlinear method, which considers the crack formation and the accompanying redistribution of internal forces in the deformation analysis. The analysed structure must be a pure member structure.

C4: Nonlinear Calculation - Surface
This is a physically nonlinear method, which considers the crack formation and the accompanying redistribution of internal forces in the deformation analysis. The analysed structure must consist entirely of surfaces. In this method, a two-dimensional surface model is internally expanded via the height. For this, the steel cross-section is divided into a defined number of steel and concrete layers, so-called layers. For further information, see the manual RF-CONCRETE Surfaces, Chapter 2.8.2 [1].

C5: Nonlinear Calculation - Combined Structure
In theory, structures consisting of both surfaces and mambers can be analysed using the stiffness export. RF-CONCRETE Members and RF-CONCRETE Surfaces provide the option to export the stiffness determined in the cracked state to RFEM in a load case or a load combination. The calculation is started in one of the two modules, the stiffness is exported to RFEM and the other module performs the nonlinear calculation once again to consider the exported stiffness. It should be noted that the interaction between the surface and the member element might not be considered in a single export of the stiffness.

#### Modelling Options

The available calculation methods can be combined with various modelling approaches in the modeling or they can be linked to them. This will be explained below, using an example of a simply supported beam with a T-section.

M1: Beam Structure
The structure is modelled as a pure member structure. A possible modelling option is to detach the individual components from the entire structure and analyse them separately, or to create the structure from members only.

M2: Combined Structure of Member and Surface Elements
T-beam chords are modelled as a surface element element and the web as a member element. This is a typical model when using members of the Rib type. The member type of a rib can only be used for the analytical calculation (C1). For the nonlinear calculation method (C3), the rib must be converted into an eccentric beam member because since it has no actual stiffness in the model.

M3: Folded Plate Structure with Vertically Arranged Web
The structure is modelled as a pure folded plate structure without any member elements. In the case of modelling the structure as a surface model, you can attribute the cross-section of the T-beam to a structural line, which defines the position and the orientation of the surfaces. Thus, the web would be modelled as a vertical surface, which is orthogonal to the surfaces of the chord.

M4: Folded Plate Structure with Horizontally Arranged Web
As in the case of M3, the model consists entirely of surfaces. Both the chords and the web are modelled as a surface with eccentricity arranged horizontally to the centroidal axis. The surface forming the web has a thickness corresponding to the overall height of the structure.

Basically, the calculation of the deformation in cracked state requires a definition of an existing reinforcement in the structure, which is as close as possible to the actually designed reinforcement or case coincides with it, at best. In RF-CONCRETE Members, it is possible to adjust the existing reinforcement and save it as a template (see RF-CONCRETE Members, Chapter 3.6 [3]). In RF-CONCRETE Surfaces, you can define the amount of the existing reinforcement manually or for each element, surface by surface (see RF-CONCRETE Surfaces, Chapter 3.4.3 [2]).

#### Combination of Methods for Determining Deformation and Modelling

Depending on the modelling, only certain methods are suitable for the deformation analysis. The following table shows the possible combinations.

*1) If using a Rib member type in M2, it is possible to perform the analytical calculation C1. In the case of eccentric members, a part of the surface would be neglected when using C1.

*2) It should be noted that the C2 method is designed for structural components predominantly subjected to bending.

#### Literature

 [1] Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings; EN 1992-1-1:2004 + AC:2010 [2] Manual RF-CONCRETE Surfaces. Tiefenbach: Dlubal Software, May 2017. Download [3] Manual RF-CONCRETE Members. Tiefenbach: Dlubal Software, July 2017. Download