Circular hollow sections

This is a selected chapter from book Component-based finite element design of steel connections by prof. Wald et al. The chapter is focused on verification of connections of circular hollow sections.

Failure mode method

In this chapter, component-based finite element method (CBFEM) for design of uniplanar welded Circular Hollow Sections (CHS) is verified to Failure Mode Method (FMM): T, X, and K-joints. In CBFEM, the design resistance is limited by reaching 5 % of strain or a force corresponding to 3% d0 joint deformation, where d0 is chord diameter. The resistance in FMM is generally determined by peak load or 3% d0 deformation limit, see (Lu et al. 1994). FMM is based on the principle of identifying modes that may cause joint failure. From the practical experience and experiments accomplished during the 70s and 80s, two modes of failure were identified for the CHS joints: chord plastification and chord punching shear. This calculation method is always limited to a probed geometry of joints. This means that different formulas always apply for each geometry. In the following studies, the welds are designed according to EN 1993‑1‑8:2006 not to be the weakest components in the joint.

Chord plastification

The design resistance of a CHS chord face can be determined using the method given by FMM model in Ch. 9 of prEN 1993-1-8:2020; see Fig. 7.1.1. The method is also given in ISO/FDIS 14346 and is described in more detail in (Wardenier et al. 2010). The design resistance of the axially loaded welded CHS joint is:

  • for T and Y joint

\[ N_{1,Rd} = C_f \frac{f_{y0} t_0^2}{\sin{\theta_1}} (2.6+17.7 \beta^2) \gamma^{0.2} Q_f / \gamma_{M5} \]

  • X joint

\[  N_{1,Rd} = C_f \frac{f_{y0} t_0^2}{\sin{\theta_1}} \left ( \frac{2.6+2.6 \beta}{1-0.7 \beta} \right ) \gamma^{0.15} Q_f / \gamma_{M5} \]

  • and for K gap joint

\[ N_{1,Rd} = C_f \frac{f_{y0} t_0^2}{\sin{\theta_1}} (1.65+13.2 \beta^{1.6}) \gamma^{0.3} \left [ 1+ \frac{1}{1.2+(g/t_0)^{0.8}} \right ] Q_f / \gamma_{M5} \]

where:           

  • di – an overall diameter of CHS member i (i = 0, 1, 2 or 3)
  • fyi – yield strength of member i (i = 0, 1, 2 or 3)
  • g – gap between braces of K joint
  • ti – thickness of the wall of CHS member i (i = 0, 1, 2 or 3)
  • \(\theta_i\) – included angle between brace member i and the chord (i =1, 2 or 3)
  • \(\beta\) – ratio of the mean diameter or width of brace members, to that of the chord
  • \(\gamma\) – ratio of a chord width or diameter to twice its wall thickness
  • Qf – chord stress factor
  • Cf – material factor
  • \(\gamma_{M5}\) – partial safety factor for resistance of joints in hollow section lattice girders
  • Ni,Rd – design resistance of a joint expressed in terms of the internal axial force in member i (i = 0, 1, 2 or 3)

Fig. 7.1.1 Examined failure mode – chord plastification

Chord punching shear

(for \(d_i \le d_0 - 2 t_0\))

The design resistance of the axially loaded T, Y, X, and K joint of welded circular hollow sections for chord punching shear (Fig. 7.1.2) is:

\[ N_{1,Rd} = C_f \frac{f_{y0}}{\sqrt{3}} t_0 \pi d_i \frac{1+\sin{\theta_1}}{2 \sin^2{\theta_1}} / \gamma_{M5} \]

where:

  • di – overall diameter of CHS member i (i = 0,1,2 or 3)
  • ti – thickness of the wall of CHS member i (i = 0,1,2 or 3)
  •  fy,i – yield strength of member i (i = 0,1,2 or 3)
  • \(\theta_i\) – included angle between brace member i and the chord (i = 1,2 or 3)
  • Cf – material factor
  • Ni,Rd – design resistance of a joint expressed in terms of the internal axial force in member i (i = 0, 1, 2 or 3)

Fig. 7.1.2 Examined failure mode – chord punching shear

Chord shear

(for X joints, only if \(\cos{\theta_1} > \beta\))

The design resistance of the axially loaded X joint of welded circular hollow sections for chord shear, see Fig. 7.1.3, is:

\[ N_{1,Rd} = \frac{f_{y0}}{\sqrt{3}} \frac{(2/\pi A_0)}{\sin{\theta_1}} / \gamma_{M5} \]

where:

  • Ai – area of cross-section i (i = 0,1,2 or 3)
  • fy,i – yield strength of member i (i = 0,1,2 or 3)
  • \(\theta_i\) – included angle between brace member i and the chord (i = 1,2 or 3)
  • Ni,Rd – design resistance of a joint expressed in terms of the internal axial force in member i (i = 0, 1, 2 or 3)

Fig. 7.1.3 Examined failure mode - Chord shear

Range of validity

CBFEM was verified for typical joints of the welded circular hollow sections. Range of validity for these joints is defined in Table 7.1.8 of prEN 1993-1-8:2020; see Tab 7.1.2. The same range of validity is applied to CBFEM model. Outside the range of validity of FMM, an experiment should be prepared for validation or verification performed for verification according to a validated research model.

Tab. 7.1.2 Range of validity for method of failure modes

General\(0.2 \le \frac{d_i}{d_0} \le 1.0 \)\( \theta_i \ge 30^{\circ} \)\(-0.55 \le \frac{e}{d_0} \le 0.25 \)

\(g \ge t_1+t_2 \)\(f_{yi} \le f_{y0} \)\( t_i \le t_0 \)
ChordCompressionClass 1 or 2 and \(10 \le d_0 / t_0 \le 50 \) (but for X joints: \( d_0/t_0 \le 40 \))

 Tension\(10 \le d_0 / t_0 \le 50 \) (but for X joints: \( d_0/t_0 \le 40 \))
CHS bracesCompressionClass 1 or 2 and \(d_i / t_i \le 50\)

Tension\(d_i / t_i \le 50 \)

Uniplanar T and Y-CHS joint

Overview of the considered examples in the study is given in Tab. 7.1.3. Selected cases cover a wide range of joint geometric ratios. Geometry of the joints with dimensions is shown in Fig. 7.1.2. In the selected cases, the joints failed according to the FMM by the chord plastification or punching shear.

Fig. 7.1.4 Dimensions of T/Y joint

Tab. 7.1.3 Examples overview

ExampleChordBraceAngles
Material 
 SectionSection\(\theta\)fyfuE
   [°][MPa][MPa][GPa]
1CHS219.1/5.0CHS48.3/5.090355490210
2CHS219.1/5.0CHS114.3/6.390355490210
3CHS219.1/6.3CHS114.3/6.390355490210
4CHS219.1/10.0CHS60.3/5.090355490210
5CHS219.1/18,0CHS159/14,090355490210
6CHS219.1/8.0CHS48.3/5.090355490210
7CHS219.1/4.5CHS168.3/8.060355490210
8CHS219.1/5.0CHS60.3/5.060355490210
9CHS219.1/6.3CHS219.1/8.060355490210
10CHS219.1/8.0CHS88.9/5.060355490210
11CHS219.1/6.3CHS60.3/5.060355490210
12CHS219.1/6.3CHS76.1/5.060355490210
13CHS219.1/4.5CHS48.3/5.030355490210
14CHS219.1/4.5CHS193.7/10.030355490210
15CHS219.1/5,0CHS139.7/10.030355490210
16CHS219.1/8,0CHS114.3/6.330355490210
17CHS219.1/6.3CHS139.7/10.030355490210
18CHS219.1/6.3CHS88.9/5.030355490210

Verification of resistance

The results of the method based on FMM are compared with the results of CBFEM. The comparison is focused on the resistance and design failure mode. The results are presented in Tab. 7.1.4.

The study shows a good agreement for the applied load cases. The results are summarized in a diagram comparing CBFEM’s and FMM’s design resistances; see Fig. 7.1.5. The results show that the difference between the two calculation methods is in all cases less than 11%.

Fig. 7.1.5 Verification of CBFEM to FMM for the uniplanar CHS T and Y-joint

Tab. 7.1.4 Comparison of design resistances for loading in tension/compression: prediction by CBFEM and FMM

 ExampleFMM Mode of failureCBFEMMode of failurediff.
 [kN] [kN] [%]
156,9Chord plastification57,9Chord plastification2
2122,0Chord plastification116,1Chord plastification5
3185,0Chord plastification166,6Chord plastification10
4225,8Chord plastification200,6Chord plastification11
51842,8Chord punching shear1672,0Chord punching shear9
6132,7Chord plastification124,7Chord plastification6
7205,0Chord plastification201,9Chord plastification2
874,9Chord plastification75,7Chord plastification1
9584,7Chord plastification538,6Chord plastification8
10244,1Chord plastification221,5Chord plastification9
11113,5Chord plastification109,6Chord plastification3
12136,4Chord plastification131,2Chord plastification4
1394,2Chord plastification97,7Chord plastification4
14447,4Chord plastification399,1Chord plastification11
15322,4Chord plastification314,1Chord plastification3
16568,8Chord plastification504,6Chord plastification11
17488,7Chord plastification439,7Chord plastification10
18275,1Chord plastification284,8Chord plastification4

Benchmark example

Inputs

Chord

  • Steel S355
  • Section CHS219.1/5.0

Brace

  • Steel S355
  • Sections CHS48.3/5.0
  • Angle between the brace member and the chord 90°

Weld

  • Butt weld around the brace

Loaded

  • By force to brace in compression

Mesh size

  • 64 elements along surface of the circular hollow member

Outputs

  • The design resistance in compression is NRd = 57,9 kN
  • The design failure mode is chord plastification

Uniplanar X-CHS joint

Overview of the considered examples in the study is given in the Tab. 7.1.5. Selected cases cover a wide range of joint geometric ratios. Geometry of the joints with dimensions is shown in Fig. 7.1.6. In the selected cases, the joints failed according to the FMM by the chord plastification or punching shear.

Fig. 7.1.6 Dimensions of X joint

Tab. 7.1.5 Examples overview

ExampleChordBraceAngles
 Material 
 SectionSection\(\theta\)fyfuE
   [°][MPa][MPa][GPa]
1CHS219.1/6.3CHS60.3/5.090355490210
2CHS219.1/8.0CHS76.1/5.090355490210
3CHS219.1/10.0CHS139.7/10.090355490210
4CHS219.1/12.5CHS114.3/6.390355490210
5CHS219.1/10.0CHS76.1/5.090355490210
6CHS219.1/8.0CHS114.3/6.390355490210
7CHS219.1/6.3CHS48.3/5.060355490210
8CHS219.1/6.3CHS114.3/6.360355490210
9CHS219.1/8.0CHS60.3/5.060355490210
10CHS219.1/10.0CHS114.3/6.360355490210
11CHS219.1/12.5CHS139.7/10.060355490210
12CHS219.1/8.0CHS139.7/10.060355490210
13CHS219.1/6.3CHS48.3/5.030355490210
14CHS219.1/6.3CHS193.7/16.030355490210
15CHS219.1/6.3CHS219.1/20.030355490210
16CHS219.1/8.0CHS76.1/5.030355490210
17CHS219.1/8.0CHS168.3/12.530355490210
18CHS219.1/12.5CHS168.3/12.530355490210

Verification of resistance

The results of CBFEM are compared with the results of FMM. The comparison is focused on the resistance and design failure mode. The results are presented in Tab. 7.1.6.

Tab. 7.1.6 Comparison of results of prediction of design resistances for loading in tension/compression by CBFEM and FMM

ExampleFMM Mode of failureCBFEMMode of failurediff.
 [kN] [kN] [%]
188,8Chord plastification91,5Chord plastification3
2155,7Chord plastification155,8Chord plastification0
3390,9Chord plastification366,4Chord plastification6
4478,7Chord plastification427,0Chord plastification11
5235.3Chord plastification215.6Chord plastification8
6209.7Chord plastification214.5Chord plastification2
793,7Chord plastification89,8Chord plastification4
8155,6Chord plastification167,3Chord plastification8
9159,5Chord plastification153,4Chord plastification4
10365,8Chord plastification348,1Chord plastification5
11682,1Chord plastification591,5Chord plastification13
12298.7Chord plastification291.9Chord plastification2
13162,3Chord plastification162,0Chord plastification0
14555,8Chord plastification566,1Chord plastification2
15749,7Chord plastification697,8Chord plastification7
16311,4Chord plastification289,5Chord plastification7
17669,1Chord plastification699,7Chord plastification5
181527.7Chord plastification1393.3Chord plastification9

The study shows a good agreement for most of the applied load cases. The results are summarized in a diagram comparing CBFEM’s and FMM’s design resistances; see Fig. 7.1.7. The results show that the difference between the two calculation methods is in most cases less than 11%. In one case, the CBFEM proves to be slightly conservative with the difference of 13%.

Fig. 7.1.7 Verification of CBFEM to FMM for the uniplanar CHS T and Y-joint

Benchmark example

Inputs

Chord

  • Steel S355
  • Section CHS219.1/6,3

Brace

  • Steel S355
  • Sections CHS60,3/5,0
  • Angle between the brace member and the chord 90°

Weld

  • Butt weld around the brace

Loaded

  • By force to brace in compression

Mesh size

  • 64 elements along surface of the circular hollow member

Outputs

  • The design resistance in compression is NRd = 91,5 kN
  • The design failure mode is chord plastification

Uniplanar K-CHS joint

Overview of the considered examples in the study is given in the Tab. 7.1.7. Selected cases cover a wide range of joint geometric ratios. Geometry of the joints with dimensions is shown in Fig. 7.1.8. In the selected cases, the joints failed according to the method based on the failure modes (FMM) by the chord plastification or punching shear.

Tab. 7.1.7 Examples overview

ExampleChordBraceGapAngles
Material 
 SectionSectiong\(\theta\)fyfuE
   [mm][°][MPa][MPa][GPa]
1CHS219.1/4,5CHS139.7/10,020,160355490210
2CHS219.1/4,5CHS219.1/20,039,960355490210
3CHS219.1/5,0CHS88.9/5,09,960355490210
4CHS219.1/5,0CHS219.1/20,039,960355490210
5CHS219.1/6,3CHS48.3/5,09,960355490210
6CHS219.1/6,3CHS60.3/5,09,960355490210
7CHS219.1/8,0CHS114.3/6,312,560355490210
8CHS219.1/8,0CHS139.7/10,020,160355490210
9CHS219.1/6.3CHS114.3/6.312.560355490210
10CHS219.1/6.3CHS139.7/10,0a20.160355490210

Fig. 7.1.8 Dimensions of K joint

Verification of resistance

The results of the method based on failure modes (FMM) are compared with the results of CBFEM. The comparison is focused on the resistance and design failure mode. The results are presented in Tab. 7.1.8 and in Fig. 7.1.9.

Tab. 7.1.8 Comparison of results of design resistances by CBFEM and FMM

ExampleFMM Mode of failureCBFEMMode of failurediff.
 [kN] [kN] [%]
1213,3Chord plastification235,6Chord plastification10
2367,5Chord plastification377,5Chord plastification3
3165,4Chord plastification185,7Chord plastification12
4443,6Chord plastification443,5Chord plastification0
5149,2Chord plastification153,4Chord plastification3
6175,7Chord plastification181,9Chord plastification4
7501,1Chord plastification460,1Chord plastification8
8605,6Chord plastification540,5Chord plastification11
9324.4Chord plastification330.5Chord plastification2
10392.4Chord plastification384.7Chord plastification2

The study shows a good agreement for the applied load cases. The results are summarized in a diagram comparing CBFEM’s and FMM’s design resistances; see Fig. 7.1.6. The results show that the difference between the two calculation methods is in all cases less than 12 %.

Fig. 7.1.9 Verification of CBFEM to FMM for the uniplanar CHS K-joint

Benchmark example

Inputs

Chord

  • Steel S275
  • Section CHS 219.1/4,5

Brace

  • Steel S275
  • Sections CHS 139,7/10
  • Angle between the brace member and the chord 60°

Weld

  • Butt weld around the brace

Loaded

  • By force to brace in compression

Mesh size

  • 64 elements along surface of the circular hollow member

Outputs

  • The design resistance in compression is NRd = 235,6 kN
  • The design failure mode is chord plastification

Sample files

Open in Viewer Download

Give us feedback. Was this article useful?

Yes No

Related articles

Become a certified connection design professional

Ready to master analysis, design, and code-check skills of various steel connections for everyday engineering practice? Our online course can help you

Try idea statica for free

Download a free trial version of IDEA StatiCa