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001656

Dipl.-Ing. (FH) René Flori

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.

1 Spatial Truss Girder

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.

Roof Structure Truss Girder Curved from CHS

2 Curved Spatial Truss Girders of Welded CHS

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

3 Truss Dimensions

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.

4 Distribution of Internal Forces for Axial Force

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 ≤ d_i / d_o ≤ 1.0, it is impossible to perform the design. The diameter ratio d_i / d_o 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.

5 Displaying Window 1.3 Geometry in RF-/HSS

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 = \frac{d_{0}}{2 \cdot t_{0}}

γ	Verhältnis der Breite oder des Durchmessers des Gurtstabes zum zweifachen seiner Wanddicke
d₀	Gesamtdurchmesser Gurtstab
t₀	Wanddicke des Gurtstabquerschnitts

Determination of Diameter-Wall Thickness Ratio γ

γ = 8.57

Determination of Factor k_g

k_{g} = γ^{0.2} \cdot (1 + \frac{0.024 \cdot γ^{1.2}}{1 + e^{(0.5 \cdot g / t_{0} - 1.33)}})

k_g	Beiwert bei Knotenanschlüssen mit Spalt g
γ	Verhältnis der Breite oder des Durchmessers des Gurtstabes zum zweifachen seiner Wanddicke
e	Eulersche Zahl
g	Spaltweite zwischen den Streben eines K- oder N-Anschlusses
t₀	Wanddicke des Gurtstabquerschnitts

Factor k_g According to EN 1993-1-8, Table 7.2

k_g = 1.72

Determination of Chord Tension Coefficient k_p

k_{p} = 1 + 0.3 \cdot n_{p} \cdot (1 - n_{p})

n_{p} = \frac{f_{p}}{f_{y}}

f_{p} = \frac{N_{p}}{A_{0}} - \frac{|M_{0}|}{W_{0}}

k_p	Gurtvorspannungsbeiwert
n_p	Verhältniswert
f_p	Wert der einwirkenden Druckspannung im Gurtstab ohne die Spannungen infolge der Komponenten der Strebenkräfte am Anschluss parallel zum Gurt
f_y	Streckgrenze
N_p	Anlaufende Normaldruckkraft im Gurt
A₀	Querschnittsfläche Gurtstab
M₀	Sekundäres Moment aus Exzentrizität
W₀	Elastisches Widerstandsmoment des Gurtquerschnitts

Chord Prestress Coefficient k_p EN 1993-1-8

f_p is the chord tension from the axial force N_p and the additional moment from eccentricity. Since there is compression and tension in the chors, it is assumed that N_p = 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 k_p.
k_p = 1.0

Determination of Allowable Limit Internal Force N_Rd

N_{1, Rd} = \frac{k_{g} \cdot k_{p} \cdot f_{y 0} \cdot {t_{0}}^{2}}{\sin (θ_{1})} \cdot (1.8 + 10.2 \cdot \frac{d_{1}}{d_{0}}) / γ_{M 5}

N_{2, Rd} = \frac{\sin (θ_{1})}{\sin (θ_{2})} \cdot N_{1, Rd}

N_1,Rd	Bemessungswert der Normalkrafttragfähigkeit des Anschlusses für Strebe 1
k_g	Beiwert bei Knotenanschlüssen mit Spalt g
k_p	Gurtvorspannungsbeiwert
f_y0	Streckgrenze des Werkstoffs eines Gurtstabes
t₀	Wanddicke des Gurtstabquerschnitts
θ₁	Eingeschlossener Winkel zwischen Strebe 1 und Gurtstab
d₁	Gesamtdurchmesser Strebe 1
d₀	Gesamtdurchmesser Gurtstab
y_M5	Teilsicherheitsbeiwert
N_2,Rd	Bemessungswert der Normalkrafttragfähigkeit des Anschlusses für Strebe 2
θ₂	Eingeschlossener Winkel zwischen Strebe 2 und Gurtstab

Flange Failure According to EN 1993-1-8, Table 7.2, Row 3.2

N_1,Rd = N_2,Rd = 257.36 kN
N_1,Ed / N_1,Rd = 197.56 / 257.36 = 0.77 < 1.0
N_2,Ed / N_2,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 N_Rd

N_{i, Rd} = \frac{f_{y 0}}{\sqrt{3}} \cdot t_{0} \cdot π \cdot d_{i} \cdot \frac{1 + \sin (θ_{i})}{2 \cdot \sin^{2} (θ_{i})} / γ_{M 5}

N_i,Rd	Bemessungswert der Normalkrafttragfähigkeit des Anschlusses für das Bauteil i
f_y0	Streckgrenze des Werkstoffs eines Gurtstabes
t₀	Wanddicke des Gurtstabquerschnitts
π	Kreiszahl
d_i	Gesamtdurchmesser bei KHP-Bauteilen i
θ_i	Eingeschlossener Winkel zwischen Strebe i und Gurtstab
γ_M5	Teilsicherheitsbeiwert

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

N_1,Rd = N_2,Rd = 417.58 kN
N_1,Ed / N_1,Rd = 197.56 / 417.58 = 0.47 < 1.0
N_2,Ed / N_2,Rd = 186.89 / 417.58 = 0.45 < 1.0

Flange Failure of Chord Member due to Moment M_op 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 M_op,Rd

M_{op, i, Rd} = \frac{f_{y 0} \cdot {t_{0}}^{2} \cdot d_{i}}{\sin (θ_{i})} \cdot \frac{2.7}{1 - 0.81 \cdot β} \cdot k_{p} / γ_{M 5}

M_op,i,Rd	Bemessungswert der Momententragfähigkeit des Anschlusses bei Biegung aus der Tragwerksebene für das Bauteil i
f_y0	Streckgrenze des Werkstoffs eines Gurtstabes
t₀	Wanddicke des Gurtstabquerschnitts
d_i	Gesamtdurchmesser bei KHP-Bauteilen i
θ_i	Eingeschlossener Winkel zwischen Strebe i und Gurtstab
β	Verhältnis der mittleren Durchmesser oder mittleren Breiten von Strebe und Gurtstab
k_p	Gurtvorspannungsbeiwert
y_M5	Teilsicherheitsbeiwert

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

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

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

Determination of Allowable Limit Internal Force M_ip,Rd

M_{ip, i, Rd} = 4.85 \cdot \frac{f_{y 0} \cdot {t_{0}}^{2} \cdot d_{i}}{\sin (θ_{i})} \cdot \sqrt{γ} \cdot β \cdot k_{p} / γ_{M 5}

M_ip,i,Rd	Bemessungswert der Momententragfähigkeit des Anschlusses bei Biegung in der Tragwerksebene für das Bauteil i
f_y0	Streckgrenze des Werkstoffs eines Gurtstabes
t₀	Wanddicke des Gurtstabquerschnitts
d_i	Gesamtdurchmesser bei KHP-Bauteilen i
θ_i	Eingeschlossener Winkel zwischen Strebe i und Gurtstab
γ	Verhältnis der Breite oder des Durchmessers des Gurtstabes zum zweifachen seiner Wanddicke
β	Verhältnis der mittleren Durchmesser oder mittleren Breiten von Strebe und Gurtstab
k_p	Gurtvorspannungsbeiwert
γ_M5	Teilsicherheitsbeiwert

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

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

Punching of Chord Member due to Moment M_op 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 M_op,Rd

M_{op, i, Rd} = \frac{f_{y 0} \cdot t_{0} \cdot {d_{i}}^{2}}{\sqrt{3}} \cdot \frac{3 + \sin (θ_{i})}{4 \cdot \sin^{2} (θ_{i})} / γ_{M 5}

M_op,i,Rd	Bemessungswert der Momententragfähigkeit des Anschlusses bei Biegung aus der Tragwerksebene für das Bauteil i
f_y0	Streckgrenze des Werkstoffs eines Gurtstabes
t₀	Wanddicke des Gurtstabquerschnitts
d_i	Gesamtdurchmesser bei KHP-Bauteilen i
θ_i	Eingeschlossener Winkel zwischen Strebe i und Gurtstab
y_M5	Teilsicherheitsbeiwert

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

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

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

Determination of Allowable Limit Internal Force M_ip,Rd

M_{ip, i, Rd} = \frac{f_{y 0} \cdot t_{0} \cdot {d_{i}}^{2}}{\sqrt{3}} \cdot \frac{1 + 3 \cdot \sin (θ_{i})}{4 \cdot \sin^{2} (θ_{i})} / γ_{M 5}

M_ip,i,Rd	Bemessungswert der Momententragfähigkeit des Anschlusses bei Biegung in der Tragwerksebene für das Bauteil i
f_y0	Streckgrenze des Werkstoffs eines Gurtstabes
t₀	Wanddicke des Gurtstabquerschnitts
d_i	Gesamtdurchmesser bei KHP-Bauteilen i
θ_i	Eingeschlossener Winkel zwischen Strebe i und Gurtstab
y_M5	Teilsicherheitsbeiwert

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

M_ip,1,Rd = M_ip,2,Rd = 7.33 kNm
M_ip,1,Ed / M_ip,1,Rd = 0.37 / 7.33 = 0.05 < 1.0
M_ip,2,Ed / M_ip,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.

\frac{N_{i, Ed}}{N_{i, Rd}} + \frac{|M_{op, i, Ed}|}{M_{op, i, Rd}} \leq 1.0

\frac{197.56}{257.36} + \frac{|- 0.08|}{5.92} = 0.78 < 1.0 (S 1)

\frac{- 186.89}{257.36} + \frac{|- 0.01|}{5.92} = 0.72 < 1.0 (S 2)

N_i,Ed	Bemessungswert der einwirkenden Normalkraft für das Bauteil i
N_i,Rd	Bemessungswert der Normalkrafttragfähigkeit des Anschlusses für das Bauteil i
M_op,i,Ed	Bemessungswert des einwirkenden Momentes aus der Tragwerksebene für das Bauteil i
M_op,i,Rd	Bemessungswert der Momententragfähigkeit des Anschlusses bei Biegung aus der Tragwerksebene für das Bauteil i
S1	Strebe 1
S2	Strebe 2

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

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.

Knowledge Base

KB 001656 | Design of K-Type Joint Using CHS-Sections According to EN 1993-1-8

Author

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

Links

References

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.
DIN. (1993). Eurocode 3: Design of Steel Structures – Part 1‑1: General Rules and Rules for Buildings, EN 1993-1-1:2005. Berlin: Beuth Verlag GmbH.

Downloads

Model of Technical Article | RFEM 5 File

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Display Product Family

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

General

Details of Model

Assigning Node to Joint Type

Checking Validity Limits

Design

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

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

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

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

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

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

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

Conclusion

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

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

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

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