10325x
001656
2020-09-11

Design of K-Type Joint Using CHS Sections According to EN 1993-1-8

Closed circular cross-sections are ideal for welded truss structures. The architecture of such constructions is popular when designing transparent roofs. This article shows the special features of the connection design using hollow sections.

General

Slender truss structures made of closed cross-sections are popular in architecture. Due to computer-aided production of cuts and connection geometries, it is possible also to have complex spatial nodes. This technical article deals with the design of a K‑node. The node definition and the design, in particular, are described in detail.

Details of Model

  • Material: S355
  • Chord cross-section: RO 108x6.3 | DIN 2448, DIN 2458
  • Strut cross-section: RO 60.3x4 | DIN 2448, DIN 2458
  • Dimensions: see the graphic

Assigning Node to Joint Type

The connection type for a hollow section node is not only defined by the geometry, but also by the orientation of the axial forces in the struts. In our example, there is a tensile force in Member 35 (Strut 1) and a compression force in Member 36 (Strut 2) on Node 28 to be designed. Given this distribution of internal forces and moments, the joint type is a K‑node. If there was compression or tension in both struts, the connection type would be a Y‑node.

Checking Validity Limits

Compliance with the validity limits is crucial for any design. The ratio of the diameters of struts and chords is important. If it is not in the range of 0.2 ≤ di / do ≤ 1.0, it is impossible to perform the design. The diameter ratio di / do is also referred to as β. The European standard EN 1993-1-8 [1] specifies in Table 7.1 the validity limits for struts and chord members, as well as a limitation of the struts' overlap. If you want to have a gap between the struts, a minimum dimension of g ≥ t1 + t2 must be observed, too. t is the respective wall thickness of the struts. Structural components subjected to compression also need to be classified into cross-section classes 1 or 2. A corresponding check is carried out according to EN 1993-1-1 [2], Chapter 5.5.

Design

In our example, the connection meets the validity limits according to Table 7.1. Therefore, it is sufficient according to EN 1993-1-8, Section 7.4.1 (2), to analyze the chord member for flange failure and punching shear.

Flange Failure of Chord Member due to Axial Force According to EN 1993-1-8, Table 7.2, Row 3.2

Determination of Diameter-Wall Ratio γ


γ = 8.57

Determination of Factor kg


kg = 1.72

Determination of Chord Tension Coefficient kp

fp is the chord tension from the axial force Np and the additional moment from eccentricity. Since there is compression and tension in the chors, it is assumed that Np = 0. Furthermore, the eccentricity of the joint is so small that an additional moment from any eccentric connection of the struts does not have to be considered. The auxiliary coefficient is thus zero. The sign convention for compression and tension forces in RFEM and RSTAB differs from those of the European standard EN 1993-1-8. Therefore, the formula is adjusted to kp.
kp = 1.0

Determination of Allowable Limit Internal Force NRd


N1,Rd = N2,Rd = 257.36 kN
N1,Ed / N1,Rd = 197.56 / 257.36 = 0.77 < 1.0
N2,Ed / N2,Rd = 186.89 / 257.36 = 0.73 < 1.0

Punching of Chord Member due to Axial Force According to EN 1993-1-8, Table 7.2, Row 4

Determination of Allowable Limit Internal Force NRd


N1,Rd = N2,Rd = 417.58 kN
N1,Ed / N1,Rd = 197.56 / 417.58 = 0.47 < 1.0
N2,Ed / N2,Rd = 186.89 / 417.58 = 0.45 < 1.0

Flange Failure of Chord Member due to Moment Mop According to EN 1993-1-8, Table 7.5, Row 2

This design is only relevant for 3D structures where moments may also occur from the truss plane.

Determination of Allowable Limit Internal Force Mop,Rd


Mop,1,Rd = Mop,2,Rd = 5.92 kNm
Mop,1,Ed / Mop,1,Rd = 0.08 / 5.92 = 0.01 < 1.0
Mop,2,Ed / Mop,2,Rd = 0.01 / 5.92 = 0.00 < 1.0

Flange Failure of Chord Member due to Moment Mip According to EN 1993-1-8, Table 7.5, Row 1

Determination of Allowable Limit Internal Force Mip,Rd


Mip,1,Rd = Mip,2,Rd = 9.53 kNm
Mip,1,Ed / Mip,1,Rd = 0.37 / 9.53 = 0.04 < 1.0
Mip,2,Ed / Mip,2,Rd = 0.14 / 9.53 = 0.01 < 1.0

Punching of Chord Member due to Moment Mop According to EN 1993-1-8, Table 7.5, Row 3.2

This design is only relevant for 3D structures where moments may also occur from the truss plane.

Determination of Allowable Limit Internal Force Mop,Rd


Mop,1,Rd = Mop,2,Rd = 8.70 kNm
Mop,1,Ed / Mop,1,Rd = 0.08 / 8.70 = 0.01 < 1.0
Mop,2,Ed / Mop,2,Rd = 0.01 / 8.70 = 0.00 < 1.0

Punching of Chord Member due to Moment Mip According to EN 1993-1-8, Table 7.5, Row 3.1

Determination of Allowable Limit Internal Force Mip,Rd


Mip,1,Rd = Mip,2,Rd = 7.33 kNm
Mip,1,Ed / Mip,1,Rd = 0.37 / 7.33 = 0.05 < 1.0
Mip,2,Ed / Mip,2,Rd = 0.14 / 7.33 = 0.02 < 1.0

Interaction Conditions According to EN 1993-1-8, Chapter 7.4.2, Equation 7.3

In this design step, the struts are designed for the shared loading from axial force and bending. Currently, only bending perpendicular to the truss plane is considered here.

Conclusion

The technical article shows that the design for a K-node is not trivial. With the RF-/HSS add-on module, Dlubal offers a tool for designing all nodal types defined in the European standard, for CHS as well as SHS and RHS sections.


Author

Mr. Flori is the customer support team leader and provides technical support for customers of Dlubal Software.

Links
References
  1. European Committee for Standardization. (2009). Eurocode 3: Design of Steel Structures – Part 1-8: Design of Joints; EN 1993‑1‑8:2005 + AC:2009. Berlin: Beuth Verlag GmbH.
  2. European Committee for Standardization (CEN). (2010). Eurocode 3: Design of Steel Structures – Part 1‑1: General Rules and Rules for Buildings, EN 1993‑1‑1:2010‑12. Berlin: Beuth Verlag GmbH.
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