Rectangular hollow sections

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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 joints of rectangular hollow sections.

Description

In this chapter, uniplanar welded rectangular, square, hollow sections T, X, and K-joints with gap predicted by CBFEM are verified. Square hollow sections (SHS) brace is welded directly onto an RHS chord without the use of reinforcing plates. The joints are loaded by an axial force. In CBFEM, the design resistance is limited by 5 % of strain or a force corresponding to 0,03b0 joint deformation and in FMM generally by plate out of plane deformation 0,03b0 where b0 is the depth of the RHS chord; see Lu et al. (1994).

Failure mode method

In the case of the axially loaded T, Y, X or K-joint with gap of the welded rectangular hollow sections, five failure modes can occur. These are chord face failure, chord plastification, chord side wall failure, chord web failure, chord shear failure, punching shear failure, and brace failure. In this study, chord face failure, brace failure, and punching shear failure are examined for T, Y and X-joint and chord face failure, chord shear failure, brace failure, and punching shear failure are examined for K-joint with gap; see Fig. 7.2.1. The welds designed according to EN 1993-1-8:2005 are not the weakest components in the joint.

Fig. 7.2.1 Examined failure modes: a) Chord face failure, b) Chord shear failure, c) Brace failure, and d) Punching shear failure

Chord face failure

The design resistance of an RHS chord face is determined by FMM model in section 9.5 of EN 1993‑1-8:2020. The method is also given in the ISO/FDIS 14346 and is described in detail in Wardenier et al. (2010). The design resistance of the axially loaded T, Y or X-joint of welded rectangular hollow sections is

\[ N_{i,Rd} = C_f \frac{f_{y0} t_0^2}{\sin{\theta_i}} \left ( \frac{2 \eta}{(1-\beta) \sin{\theta_i}} + \frac{4}{\sqrt{1-\beta}} \right ) Q_f / \gamma_{M5} \]

The design resistance of the axially loaded K-joint with gap of welded rectangular hollow sections is

\[ N_{i,Rd} = 8.9 C_f \beta \gamma^{0.5} \frac{f_{y,0} t_0^2}{\sin{\theta_i}} Q_f / \gamma_{M5} \]

where Cf is the material factor, fy0 is the yield stress of the chord, t0 is the wall thickness of the chord, η is the brace height to the chord width ratio, β is the brace width to the chord width ratio, qi is the included angle between the brace member i and the chord (i = 1, 2), Qf is the chord stress function, and γ is the chord slenderness ratio.

Brace failure

The design resistance of an RHS chord face can be determined using the method given by FMM model in section 9.5 of EN 1993-1-8:2020. The design resistance of the axially loaded T, Y or X-joint of welded rectangular hollow sections is

\[ N_{i,Rd} = C_f f_{yi} t_i (2 h_i - 4 t_i + 2 b_{eff} ) / \gamma_{M5} \]

The design resistance of the axially loaded K-joint with gap of welded rectangular hollow sections is

\[ N_{i,Rd} = C_f f_{yi} t_i (2 h_i - 4 t_i + b_i + b_{eff} ) / \gamma_{M5} \]

where Cf is the material factor, fyi is the yield stress of the brace member i (i = 1, 2), ti is the wall thickness of the brace member i, hi is the height of the brace member i, bi is the width of the brace member i, beff is the effective width of the brace member.

Punching shear

The design resistance of the axially loaded T, Y or X-joint of welded rectangular hollow sections is

\[ N_{i,Rd} = C_f \frac{f_{y0} t_0}{\sqrt{3}\sin{\theta_i}} \left( \frac{2h_i}{\sin{\theta_i}} + 2b_{e,p} \right ) / \gamma_{M5} \]

The design resistance of the axially loaded K-joint with gap of welded rectangular hollow sections is

\[ N_{i,Rd} = C_f \frac{f_{y0} t_0}{\sqrt{3}\sin{\theta_i}} \left( \frac{2h_i}{\sin{\theta_i}} + b_i+b_{e,p} \right ) / \gamma_{M5} \]

Where Cf is the material factor, fy0 is the yield stress of the chord, t0 is the wall thickness of the chord, qi is the included angle between the brace member i and the chord (i = 1, 2), hi is the height of the brace member i, bi is the width of the brace member i and be,p is the effective width for punching shear.

Chord shear failure

The design resistance of the axially loaded K-joint with gap of welded rectangular hollow sections is

\[ N_{i,Rd} = \frac{f_{y0}A_{V,0,gap}}{\sqrt{3}\sin{\theta_i}}/\gamma_{M5} \]

where fy0 is the yield stress of the chord, Av,0,gap is the effective area for chord shear failure, and qi is the included angle between the brace member i and the chord (i = 1, 2).

Range of validity

CBFEM was verified for typical T, Y X, and K-joints with gap of the welded rectangular hollow sections. Range of validity for these joints is defined in Table 9.2 of prEN 1993-1-8:2020; see Tab. 7.2.1. 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. 7.2.1 Range of validity for method of failure modes, Table 9.2 of EN 1993-1-8:2020

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

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

 Tension\(d_0 / t_0 \le 50 \) (but for X joints: \( d_0/t_0 \le 40 \))
CHS bracesCompressionClass 1 or 2 and \(b_i / t_i \le 35\) and \(\frac{h_i}{t_i} \le 35 \)

Tension\(b_i / t_i \le 35\) and \(\frac{h_i}{t_i} \le 35 \)


7.2.2 Uniplanar T and Y-SHS joint

An overview of the considered examples is given in Tab. 7.2.2. Selected cases cover a wide range of joint geometric ratios. Geometry of joints with dimensions is shown in Fig. 7.2.2. Selected joints failed according to the method based on FMM by the chord face failure or brace failure.

Tab. 7.2.2 Examples overview

ExampleChordBraceAngles
Material 
 SectionSectionθ1fyfuE
   [°][MPa][MPa][MPa]
1SHS200/6.3SHS70/8.090275430210
2SHS200/8.0SHS90/8.090275430210
3SHS200/12.5SHS120/12.590275430210
4SHS200/6.3SHS140/12.560275430210
5SHS200/8.0SHS80/8.060275430210
6SHS200/10.0SHS120/12.560275430210
7SHS200/12.5SHS90/8.060275430210
8SHS200/6.3SHS80/8.030275430210
9SHS200/8.0SHS150/16.030275430210
10SHS200/10.0SHS100/10.030275430210
11SHS200/12.5SHS100/10.030275430210

Fig. 7.2.2 Dimensions of T-joint

Verification of resistance

The results of 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. 7.2.3.

Tab. 7.2.3 Comparison of results of design resistances in tension/compression predicted by CBFEM and FMM

ExampleFMMMode of failureCBFEMMode of failureDiff.
 [kN] [kN] [%]
165.9Chord face failure66.0Chord face failure0.2
2123.7Chord face failure117Chord face failure5.7
3400.7Chord face failure435.5Chord face failure8
4160Chord face failure168Chord face failure4.8
5136.2Chord face failure129Chord face failure5.6
6310.8Chord face failure324Chord face failure4.1
7361.4Chord face failure332Chord face failure8.9
8170.9Chord face failure168Chord face failure1.7
9704Chord face failure738Chord face failure4.6
10531.1Chord face failure488Chord face failure8.8
11829.9Chord face failure758Chord face failure9.5

The study shows a good agreement for the applied load cases. The results are summarized in a diagram comparing design resistances of CBFEM and FMM; see Fig. 7.2.3. The results show that the difference between the two calculation methods is in all cases less than 10 %.

Fig. 7.2.3 Verification of resistance determined by CBFEM to FMM for the uniplanar SHS T and Y-joint

Benchmark example

Inputs

Chord

  • Steel S275
  • Section SHS 200×200×6.3

Brace

  • Steel S275
  • Section SHS 70×70×8.0
  • Angle between the brace member and the chord 90°

Weld

  • Butt weld

Mesh size

  • 16 elements on the biggest web of rectangular hollow member

Loaded

  • By force to brace in compression/tension

Outputs

  • The design resistance in compression/tension is NRd = 66.0 kN
  • The design failure mode is chord face failure

Vzorové projekty

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Uniplanar X-SHS joint

An overview of the considered examples is given in Tab. 7.2.4. Selected cases cover a wide range of joint geometric ratios. The selected joints failed according to the method based on FMM by the chord face failure or brace failure.

Tab. 7.2.4 Examples overview

ExampleChordBraceAngles
Material 
 SectionSectionθfyfuE
   [°][MPa][MPa][MPa]
1SHS200/6.3SHS140/12.590275430210
2SHS200/8.0SHS70/8.090275430210
3SHS200/10.0SHS120/12.590275430210
4SHS200/12.5SHS90/8.090275430210
5SHS200/6.3SHS70/8.060275430210
6SHS200/8.0SHS80/8.060275430210
7SHS200/10.0SHS150/6.060275430210
8SHS200/12.5SHS140/12.560275430210
9SHS200/16.0SHS120/12.560275430210
10SHS200/6.3SHS80/8.030275430210
11SHS200/8.0SHS150/16.030275430210
12SHS200/10.0SHS100/10.030275430210
13SHS200/16.0SHS90/8.030275430210

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; see Tab. 7.2.5.

Tab. 7.2.5 Comparison of results of prediction of resistance by CBFEM and FMM

ExampleFMMode of failureCBFEMMode of failureDiff.
 [kN] [kN] [%]
1130.6Chord face failure137.6Chord face failure5.4
2106.3Chord face failure94Chord face failure13.1
3256.4Chord face failure258Chord face failure0.6
4302.1Chord face failure273Chord face failure10.7
578.2Chord face failure71.1Chord face failure10
6136.2Chord face failure121Chord face failure12.6
7474Chord face failure465Chord face failure1.9
8629.7Chord face failure648Chord face failure2.8
9795.7Chord face failure762Chord face failure4.4
10170.9Chord face failure164Chord face failure4.2
11704Chord face failure719Chord face failure2.1
12531.1Chord face failure477Chord face failure11.3
13721.6Brace failure652Brace failure10.7

The study shows a good agreement for the applied load cases. The results are summarized in a diagram comparing design resistances of CBFEM and FMM; see Fig. 7.2.4. The results show that the difference between the two calculation methods is in all cases less than 13 %.

Fig. 7.2.4 Verification of resistance determined by CBFEM to FMM for the uniplanar SHS X-joint

Benchmark example

Inputs

Chord

  • Steel S275
  • Section SHS 200×200×6,3

Braces

  • Steel S275
  • Sections SHS 140×140×12,5
  • Angle between the brace members and the chord 90°

Welds

  • Butt welds

Mesh size

  • 16 elements on the biggest web of rectangular hollow member

Loaded

  • By force to brace in compression/tension

Outputs

  • The design resistance in compression/tension is NRd = 137,6 kN
  • The design failure mode is chord face failure

Vzorové projekty

Otevřít v aplikaci Viewer Stáhnout

7.2.4 Uniplanar K-SHS joint

An overview of the considered examples is given in Tab. 7.2.6. Selected cases cover a wide range of joint geometric ratios. The selected joints failed according to the method based on FMM by the chord face failure or brace failure.

Tab. 7.2.6 Examples overview

ExampleChordBracesAngles
Material 
 SectionSectionsθfyfuE
   [°][MPa][MPa][MPa]
1SHS200/8.0SHS160/16.045275430210
2SHS200/10.0SHS150/16.045275430210
3SHS200/10.0SHS160/16.045275430210
4SHS200/12.5SHS140/12.545275430210
5SHS200/12.5SHS150/16.045275430210
6SHS200/12.5SHS160/16.045275430210

Verification

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. 7.2.7.

Tab. 7.2.7 Comparison of results of prediction of resistances by CBFEM and FMM

ExampleFMMode of failureCBFEMMode of failurediff
 [kN] [kN] [%]
1.0626.6Chord face failure645.0Chord face failure2.9
2.0800.1Chord face failure809.0Chord face failure1.1
3.0875.6Chord face failure906.0Chord face failure3.4
4.01070.8Chord face failure984.0Chord face failure8.8
5.01147.3Chord face failure1126.0Chord face failure1.9
6.01223.8Chord face failure1352.0Chord face failure9.5

The study shows a good agreement for the applied load cases. The results are summarized in a diagram comparing design resistances of CBFEM and FMM; see Fig. 7.2.5. The results show that the difference between the two calculation methods is in all cases less than 10%.

Fig. 7.2.5 Verification of resistance determined by CBFEM to FMM for the uniplanar SHS K-joint

Benchmark example

Inputs

Chord

  • Steel S275
  • Section SHS 200×200×8,0

Braces

  • Steel S275
  • Sections SHS 160×160×16,0
  • Angle between the brace members and the chord 45°

Welds

  • Butt welds

Mesh size

  • 16 elements on the biggest web of rectangular hollow member

Loaded

  • By force to brace in compression/tension

Outputs

  • The design resistance in compression/tension is NRd = 645 kN
  • The design failure mode is chord face failure

Vzorové projekty

Otevřít v aplikaci Viewer Stáhnout

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