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Lecture 13.2: The Behaviour and Design

of Welded Connections between Circular

Hollow Sections under Predominantly

Static Loading

OBJECTIVE/SCOPE

To gain an understanding of the fundamental behaviour of connections between circular hollow sections.

PREREQUISITES

Lectures 2.3: Engineering Properties of Steels

Lectures 3.1: General Fabrication of Steel Structures

Lecture 11.1.2: Introduction to Connection Design

Lecture 13.1: Application of Hollow Sections in Steel Structures

RELATED LECTURES

Lectures 12.4: Fatigue Behaviour of Hollow Section Joints

Lecture 13.3: The Behaviour and Design of Welded Connections between Rectangular Hollow Sections (RHS) under Predominantly Static Loading

SUMMARY

Circular hollow sections (CHS) have been used in steel structures for many years. The most common form of connection in CHS construction is that in which the bracings are shaped to fit the circular profile of the chord and then welded to it.

The behaviour of welded, unstiffened CHS joints under static loading is discussed in this lecture, with emphasis on the connection behaviour and the governing connection parameters. Based on simplified theoretical models and test results, semi-empirical strength formulae for connections are given, which have been adopted in Eurocode 3 [1].

NOTATION

The notation in Eurocode 3, Annex K [2], has been adopted.

1. INTRODUCTION

The advantages of using circular hollow sections in steel structures are described in Lecture 13.1. Although bolting is used for connections in prefabricated substructures and in the assembly of proprietary types of space frames, it is much more common to use welded connections, particularly for lattice type constructions.

This lecture deals mainly with unstiffened welded connections between circular hollow sections. The behaviour of the connection is explained based on the assumption that the strength of the weld is adequate.

The design philosophy to execute hollow section joints is given in Lecture 13.1, whilst Lecture 13.3 deals with the design of welded, unstiffened joints between rectangular hollow sections.

For jointing circular chords with circular bracings in a lattice structure, the ends of circular bracings are usually cut as "saddles" (saddle profiling) by manual or automatic flame cutting. They are then welded together.

The complex load transfer and non-linear local stiffness distribution in CHS joints made it necessary to carry out extensive investigations into the joint behaviour. Theoretical model analysis and experimental results have led to design rules and semi-empirical design formulae for the basic types of CHS joints [3-6]. They are incorporated in Eurocode 3, Annex K [2].

2. CRITERIA AND MODES OF FAILURE

The load-bearing behaviour of hollow section joints is governed, on the one hand, by the joint geometry and, on the other hand, by the resulting locally effective loads longitudinal and transverse to the axis of the members. The behaviour of CHS joints has been examined in both the elastic and the post-elastic range up to their ultimate resistance. As the diagram of load against deformation (Figure 1) shows, the static strength of a hollow section joint can be characterized by the following criteria:

• Ultimate load-bearing resistance (5)
• Deformation criteria (2) or (3)
• Visually observed crack initiation (4)

When large compression forces are present in combination with thin-walled sections, instability failures can occur (low deformation capacity). In other circumstances, it is usual for the joint to show considerable post-elastic resistance. Failure occurs when sufficient area of the joint has reached the yield stress or stresses up to ultimate stress, such that further increases in load cannot be resisted.

Internationally, it has become common practice to base the design resistances for joints of circular hollow sections on the limit state criteria based on the failure modes given in Figure 2. They depend on specific geometrical parameters and loading conditions.

Based on theoretical investigations with analytical models, which are described later in this lecture, and the results of the strength tests on experimental joints, the following general equation to describe the ultimate joint strength N_u has been derived:

N_u = f_yo . t_o² f₁ (b) . f₂ (g) . f₃ (q) . f₄ (k_g) . f (k_p)

For the explanation of the symbols, see Eurocode 3, Annex K [2].

3. ANALYTICAL MODELS

Three models for the determination of the influencing parameters are currently used. The models are:

1. Ring model
2. Punching shear model
3. Chord shear model

3.1 Ring Model (Figure 3a)

The design of CHS joints was initially based on the strength obtained from a rigid plastic analysis of a two-dimensional ring, used to represent a CHS cross joint assuming point loads at the brace faces. The joint is schematized to a ring with an effective length B_e and the same geometrical and mechanical properties as the chord (Figure 3a).

Figure 3b shows the non-uniform stress distribution at the intersection of bracing and chord for T-, Y- and X-joints. Two line loads equal to half the bracing loads represent the loading system for a cross joint.

Neglecting the influence of axial and shear stresses, the plastic moment m_p can be calculated by the following equation:

(1)

where

N_1y is the load based on the yield strength of the ring.

q₁ is the angle between the chord and the brace.

Taking account of the effective length B_e of the ring, the plastic moment is given by:

(2)

Substituting Equation (2) in Equation (1) and assuming sin y » b and gives:

(3)

where

b is the ratio brace to chord diameter

The effective length B_e for different types of connections is determined experimentally. Furthermore, the term (1 - b) has to be corrected to avoid an infinitive strength for b = 1,0. Consequently, Equation (3) changes to:

(3a)

where

C_o and C₁ are constants.

For T-, Y- and X-joints reasonable agreement between test results and the semi-analytical ring model can be obtained. In more complicated joints, such as K- and N-types, other influencing parameters, i.e. gap between bracings and the presence of membrane forces have to be considered.

3.2 Punching Shear Model

This model is illustrated in Figure 4 for the case where a Y-joint is loaded in tension. It is assumed that the shear stress in the chord face around the perimeter of the bracing is uniform on the plan area of the connection, i.e. the effect on the bracing perimeter on the curvature of the chord is not taken into account.

For joints with q₂ = 90° , the theoretical uniformly distributed punching shear stress at its limiting value can be calculated as follows:

(4)

For joints with bracings with q₂ < 90° , the punching shear area is increased by a factor . Furthermore, punching shear is only caused by the load component perpendicular to the chord, i.e. N₂ . sin q₂, which leads to the following equation:

(5)

In general, this criterion is only applicable for joints with small b values, since, as the value of b increases, the applied load will be transferred by hoop stress to the chord.

The presentation of design rules in terms of punching shear is widely used in offshore recommendations.

3.3 Shear Model

As shown in Figure 5, in K- or N-type joints with a gap, the chord cross-section at the gap location can fail due to shear or a combination of shear, axial load and moment. When the chord section is compact, the following formulae for the plastic design can be applied:

N_i sin q_i £ 2 . (d_o - t_o) . t_o (6)

N_o gap £ p . (d_o - t_o) . t_o . f_yo (7)

M_o gap £ (d_o - t_o)² . t_o . f_yo (8)

Generally, the moments are small and only the interaction between axial load and shear load has to be considered:

(9)

In joints with small gaps, the cross-section of the chord is stiffened by the connected bracings which increases the shear load resistance considerably.

4. TEST EVIDENCE

Virtually all of the available test evidence on connections between circular hollow sections has been obtained from isolated joint specimens of the form shown in Figure 6. A few tests are known where the joints have been tested in complete frames. The majority of tests has been carried out in Japan, the U.S.A., the Netherlands, the United Kingdom and Germany.

The range of the chord diameters tested varied from 50 to 508 mm with different geometrical parameters (b, g, q, k_g, k_p, etc.) of the joint and mechanical properties.

5. STRENGTH FORMULAE FOR AXIALLY LOADED JOINTS

The experimental evidence generated by many investigators has been used in combination with the analytical models described in Section 3 to derive joint resistance equations for the mean joint strength. Characteristic joint strength formulae have been determined based on a statistical analysis taking account of the scatter in test results, the tolerances in dimensions and the variation in mechanical properties. The characteristic joint strength formulae divided by a partial factor g_m gives the design resistance formulae. The validity of the resulting semi-empirical design resistance formulae is restricted to the parametrical ranges of the experimental evidence.

The most recent design recommendations for uni-planar axially loaded T-, Y-, X- and K-joints of circular hollow sections have been derived from the research by IIW and CIDECT. The semi-empirical formulae for design resistance for uniplanar CHS joints have been adopted by Eurocode 3, Annex K [2], and are given in Tables 1a and 1b.

The design resistance formulae for T-, Y-, X- and K-joints have been based on the joint resistance under compression loading, but can also be used for tensile loading. The ultimate resistance under tensile loading is higher than that under compressive loading (see Figure 1). However, it is not always possible to take advantage of this joint resistance due to the reduced deformation capacity.

The design resistance is generally governed by two criteria, i.e. plastification of the chord cross-section and chord punching shear. Both criteria have to be checked using the formulae in Table 1.

For the factor K_p expressing the effect of prestress on the joint resistance, only the prestress of the chord has to be considered. Thus the horizontal bracings load components have to be extracted, see Figure 7.

6. OTHER TYPES OF JOINTS OR OTHER LOAD CONDITIONS

6.1 Special Types of Welded CHS Joints

Tubular joints can have various configurations and loading conditions, in addition to the basic types of joints described above. However, the design strength of these joints (see Table 2) can generally be related to that of the basic types.

6.2 Plate or I-Section Connected to CHS Chords

The joints can be divided into two basic groups, those with gusset plates symmetrically welded to the opposite sides of the chord (XP-joints) and those with gusset plates only welded to one side of the chord (TP-joints).

The XP-joints show a behaviour comparable to that of X-joints, whereas the TP-joints can be related to T-joints.

Joints with a plate in the longitudinal direction show very high deformations at the maximal load resistance. The load deformation diagrams of these joints show a more pronounced yield load resistance than tubular joints. Although the deformations at this "yield load resistance" can still be considerable, the yield load resistance is used in the analysis.

Table 3 gives the design resistances of various joints under axial load, in-plane bending moment and out-of-plane bending moment.

6.3 CHS Joints Loaded by Bending Moments

The design resistance formulae for CHS joints loaded by bending moments are derived in a similar way to those for axially loaded joints (see Table 4). When the members are not critical and the welds are strong enough, two main modes of failure exist in principle: (a) plastic failure of the chord face or chord cross-section, and (b) cracking leading to rupture of the bracing from the chord.

6.4 Multiplanar CHS Joints (KK- and TT-Connections)

Finite element calculations have shown that multi-planar members and multiplanar loading show substantial differences in the resistance and stiffness compared to a uniplanar X-joint. Various tests on K-joints in triangular girders led to an interaction equation, which can easily be replaced by a constant of 0,9, to be applied to the resistance of uniplanar joints.

For T-joints, tests carried out on double T-joints (V-joints) with a 90° included angle between bracings and both bracings loaded in compression, showed that the resistance of the multi-planar joint did not vary substantially from the uniplanar joint resistance. Table 5 gives simplified design recommendations for CHS multi-planar joints using the strength formulae for uniplanar joints with correction factors.

7. DESIGN CHARTS

To judge whether the joint resistance is sufficient for the selected members, a designer often requires a checking 'tool'. This tool is provided by the design charts given in Figures 8-12, where the design resistances are presented graphically in terms of bracing efficiency C_e, i.e the design resistance N_1Rd of the joint divided by the yield load A_1× f_y1 of the connected bracing [7].

The following formula is obtained for the efficiency:

(10)

The efficiency parameter C_e (C_T for T- and Y-joints, C_X for X-joints and C_K for K- and N-joints) gives the efficiency for a joint with K_p = 1,0, a bracing inclination q₁ = 90°, and an identical wall thickness and design yield stress for the chord and bracing members.

The design charts also show the factor K_p depending on n_p = s_op/f_yo

For lattice girders simply supported at the ends of a span, the prestressing is small at the girder ends, where bracing loads are highest. The prestressing is high where the bracing loads are low (in the centre). For continuous lattice girders, K_p needs special attention at the supports.

8. DESIGN PROCEDURE FOR JOINTS IN LATTICE GIRDERS

The design procedure for the design of lattice girders is given in Lecture 13.1.

9. CONCLUDING SUMMARY

• The resistance of joints made between circular hollow sections is governed by various failure mechanisms.
• The local stiffness around the connection perimeter determines the elastic stress distribution in both the chord and bracing at the intersection.
• The chord diameter to wall thickness ratio d_o /t_o and the wall thickness ratio between chord and bracing t_o /t₁ largely influence the efficiency of the joint.
• It is possible to avoid stiffeners if the designer selects the members and the joint configuration in such a manner that the joint resistance is sufficient.
• The effects of secondary bending moments can be neglected, provided the joint satisfies the ranges of validity given in Eurocode 3 (sufficient rotation capacity).
• The connecting welds have to be stronger than the bracings.
• The ring model is not applicable to complicated joints, i.e. K and N types.
• The shear model may only be applicable for K and N joints with low d_o/t_o ratios.
• Longitudinal plates induce large deformations.

10. REFERENCES

[1] Eurocode 3: "Design of Steel Structures": ENV 993-1-1: Part 1.1: General Rules and Rules for Buildings, CEN, 1992.

[2] Eurocode 3: ENV 993-1-1: Annex K: Hollow Section Lattice Girder Connections, CEN, 1992.

[3] Wardenier, J.: Hollow section joints, ISBN 90-6275-084-2, Delft University Press, Delft 1982.

[4] Wardenier, J., Giddings, T.W.: The strength and behaviour of statically loaded welded connections in structural hollow sections, CIDECT Monograph No.6, 1986.

[5] Wardenier, J., Stark, J.W.B.: The static strength of welded lattice girder joints in structural, hollow sections, ECSC Report EUR 6428C MF 1980.

[6] Packer, J. A. and Henderson, J. E.: Design guide for hollow structural section connections, Canadian Institute of Steel Construction, 1992.

[7] Wardenier, J., Kurobane, Y., Packer, J.A., Dutta, D., Yeomans, N.: Design guide for circular hollow section (CHS) joints under predominantly static loading, CIDECT publication, Verlag TÜV Rheinland, 1991, ISBN 3-88585-975-0.

[8] Design recommendation for hollow section joints - predominantly statically loaded. 2nd Ed., IIW Doc. XV-701-89, September 1989, International Institute of Welding.