Steel Frame Considering Connection Stiffness

Technical Article on the Topic Structural Analysis Using Dlubal Software

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Technical Article

This technical article analyzes the effects of the connection stiffness on the determination of internal forces, as well as the design of connections using the example of a two-story, double-spanned steel frame.

The model of this technical article is based on Example 5.5.3 in the technical literature [1]. It explains the effects of the connection stiffness on the determination of internal forces, as well as the design of connections using the example of a two-story, double-spanned steel frame.

Loading

Loads resulting from a feed width of four meters are applied according to [1]. Only the displacement of the member hinges by 0.1 m from the axis of the columns is omitted. The global initial inclinations are calculated according to Equation 5.5 in [2]:

Formula 1

Φ = Φ0 · αh · αm


where

Formula 2

αh = 2h = 29,50 = 0.649 < 0.667


Formula 3

αm = 0.5 · 1  13 = 0.816


to

Formula 4

Φ = 1200 · 0.667 · 0.816 = 1367

Image 01 - Design Loads and Imperfections for Structural Analysis

Geometry of Connections and Moment-Rotation Characteristics

The connections of the beams in the intermediate ceiling as well as in the roof are formed with extended end plates without stiffeners in the columns. This design leads to economical advantages in the current case.

Image 02 - Connection Geometry

According to [1], the effect of the moment-rotation characteristics of the connections on the distribution of internal forces in a structure for deformable connections usually has to be taken into account. With the component method specified in EN 1993-1-8, it is possible to calculate the initial elastic stiffness Sj,ini for the connections. The RF-/JOINTS Steel Rigid add-on module is utilized here.

Image 03 - Calculation of the Elastic Initial Stiffness S, j, ini for the Connection of the IPE 240

Image 04 - Calculation of the Elastic Initial Stiffness S, j, ini for the Connection of the IPE 300

The application of the torsional spring stiffness in the model is simplified according to EN 1993-1-8 Section 5.1.2 (4) and is defined for quick adjustment in the system in the case of changes by means of the parametrization.

IPE 240: Sj,Model = Sj,ini / η = 16,304 / 2 = 8,152 kNm/rad

IPE 300: Sj,Model = Sj,ini / η = 26,372 / 2 = 13,186 kNm/rad

Image 05 - Definition of the Parameters for the Member end Hinges

Image 06 - Assignment of the Parameter "S_j_ini_IPE240" to Member end Hinge 1

Internal Forces and Connection Design

The determination of the first mode shape in the frame plane with the RSBUCK or RF-STABILITY add-on modules results in a critical load factor acr of 12.6. Thus, it is possible to calculate the internal forces according to Equation 5.1 in [2] according to the linear static analysis.

The calculation of the load case with rigidly modeled member hinges results in the following internal forces.

Image 07 - Distribution of Internal Forces M, y with Yielding Connections

Based on these internal forces, the connection is designed according to EN 1993-1-8 in the RF-/JOINTS Steel Rigid add-on module.

Image 08 - Design of Connections in the System with Flexible Connections

The calculation of the load case with rigid member hinges results in the following internal forces.

Image 09 - Distribution of Internal Forces M, y with Rigid Connections

With these higher internal forces at the connections between the beam and the column, it is no longer possible to design the connections.

Image 10 - Connection Design in the System with Rigid Connections

Summary

Considering the connection stiffness in the structural analysis allows for the unreinforced design of the connections as well as a more homogeneous utilization of the beams in the present two-story, double-spanned steel frame in steel skeleton construction.

Author

Dipl.-Ing. (FH) Frank Sonntag, M.Sc.

Dipl.-Ing. (FH) Frank Sonntag, M.Sc.

Sales & Customer Support

Mr. Sonntag coordinates the Dlubal Software office in Leipzig and is responsible for sales and customer support.

Keywords

Connection stiffness Structural analysis Torsional stiffness Flexibility

Reference

[1]   Kindmann, R.; Kraus, M.: Finite-Elemente-Methoden im Stahlbau. Berlin: Ernst & Sohn, 2007
[2]   Eurocode 3: Design of steel structures - Part 1‑1: General rules and rules for buildings; EN 1993‑1‑1:2010‑12

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  • Updated 26 August 2021

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