CHOIX DES ECHELLES DE MESURE

The strength of welded moment connections of RHS beams and columns without stiffen-ers is based on various failure modes, i.e.:

• column face yielding (plastification);

• cracking of the column face (chord punching shear);

• cracking in the beam (effective width);

• yielding or crippling of the column side walls;

• column shear.

stiffened

0 10 20 30 40 50 60 70 80 90 100

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

unstiffened

d t

reduction factor α

S 235 S 355 S 460 S 690 S 890

out-of-plane moments are also given for completeness and for three-dimensional frames.

However, it should be noted that the formulae for out-of-plane loading should only be used if distortion of the chord cross section is prevented, e.g. by stiffeners located close to the connection. These design recommendations have also been adopted for Eurocode 3, Annex K (CEN 1992).

The moment capacity of connections with low to moderate  values (0.85) can be deter-mined with a yield line model. The function f(n) is a function to allow for the reduction in moment capacity due to the presence of compression stresses in the column face. For values  > 0.85, depending on the geometry parameters, several failure modes may be critical. As shown in figure 6.5, the beam effective width criterion and the column side wall failure criterion have to be checked. For a better understanding these criteria are illustrat-ed in figure 6.6.

Punching shear was not observed in the tests and not given as a separate check in figure 6.5 but it is recommended to design the beams with a thickness t_b < 0.6t_c or avoid connections with b_b≈ bc- 2t_cwhere punching shear may occur. More detailed information is given in CIDECT Design Guide No. 3 (Packer et al., 1992).

From the expressions in figure 6.5 it can be seen that full width ( = 1.0) unstiffened RHS Vierendeel connections are capable of developing the full moment capacity of the beam, providing b_c/t_cis sufficiently low. For h_c= b_c= h_b= b_band b_c/t_c< 16 the chord side wall crippling is given by Wardenier (1982):

≈ . ...6.6

Thus, for beam to column connections of square sections with a  ≈ 1, a column width to thickness ratio b_c/t_c = 16 and a column to beam thickness ratio t_c/t_b= 2 the moment capacity will be equal to the beam plastic moment capacity. This agrees with findings from Korol et al. (1977).

The previous expressions for the moment capacity are based on moment loading only, however axial loads in the beams may also exist. The interaction between axial loads and bending moments depends on the failure criterion. A conservative approximation is to use a linear relationship:

+ + ≤ 1.0 ...6.7

Yu (1997), in a similar way to van der Vegte (1995) for CHS connections, investigated the geometrical and the loading effect in RHS multiplanar connections. In her study all kinds of loading situations were considered on the in-plane and out-of-plane members.

However, there are so many combinations of loading and the interactions are too compli-cated for routine design. Therefore, these interaction formulae have not been included in this design guide, but information can be obtained from the given reference. The work of Yu confirmed that the CIDECT formulae for moment loaded RHS to RHS connections in figure 6.5 give a lower bound for the FE results based on the load or moment capacity at a local deformation of 3% of the column width b .

M^*

Type of connection Factored connection resistance T and X connection under

in-plane bending moments b£0.85 basis: chord face yielding

T and X connection under

out-of-plane bending moments b£0.85 basis: chord face yielding

Figure 6.5 – Design recommendations for RHS-to-RHS connections loaded by primary bending moments

b_c

hc

tc

b_b h^b

a t^b Mb,ip

0.5b_e 0.5b_e hb

q = 90^o M_b,ip

Mb,ip

h_b

h_c tc

hb + 5 tc

f_k f_k

0.5hb + 2.5 tc

q = 90^o

hb + 5 tc

a. Yield line mechanism for chord face yielding under in-plane bending

b. Brace effective width criterion for T, Y and X joints

c. Chord side wall bearing or buckling failure model under in-plane bending

The design capacities for axial loading N_b* can be obtained from the CIDECT Design Guide No. 3 (Packer et al., 1992) and are not reproduced here again.

The connections between rectangular hollow sections with ratios  < 1.0 are not stiff enough to be used as moment connections. However, they can be stiffened by plates or haunches.

Figure 6.7 shows some knee connections for Vierendeel girders or for frame corners. These knee connections have been investigated at the University of Karlsruhe (Mang et al., 1991) and at the University of Sydney (Wilkinson and Hancock,1998). Based on the research evi-dence it is recommended in CIDECT Design Guide No. 3 to design these connections based on the following requirements for both members:

+ ≤ ...6.8

with V/V_pl≤ 0.5 and N/Npl≤ 0.2 ...6.9 Here N, M and V refer to the acting axial force, the acting bending moment and the acting shear force in a connecting member at the connection, whereas N_pl, M_pland V_plare the capacities of the connecting member with

V_pl= 2h t f_y/ 3 ...6.10

Similar to the approach for CHS-to-CHS knee connections the term is a stress reduction factor, which can be taken as 1.0 for mitre connections with stiffening plates. For the mitre connections without stiffening plates it is a function of the cross sectional dimen-sions and is shown in figures 6.8 and 6.9. If mitre knee connections are used with an angle

 > 90° between the members use conservatively the same design checks as for  = 90°.

5 10 15 20 25 30 35 40 45

Figure 6.8 – Stress reduction factor , for 90° unstiffened mitred RHS knee connections subjected to bending about the major axis

Figure 6.9 – Stress reduction factor , for 90° unstiffened mitred RHS knee connections subjected to bending about the minor axis

b/t

b/t

Since the rotation capacity of the unstiffened connections might be rather low, it is also recommended here to use a stiffened connection for those structural applications where a reasonable rotational capacity is required. For other structural applications it is recom-mended to use the unstiffened connections only if the sections satisfy at least the plastic design requirements.

The stiffening plate thickness should satisfy t_p ≥ 1.5t and not be taken smaller than 10 mm.

Additional requirements are that the welds should be at least equal to the connected wall thickness and that the factor used in design should be:

< 0.84 for fy= 235 N/mm² < 0.71 for fy= 355 N/mm²

The connections with a stiffening plate can be considered to be rigid whereas the stiffness behaviour of the unstiffened connections especially depends on the b/t and h/t ratio. Only for very low b/t ratios can the connection be assumed to be rigid. No formulae for the joint stiffness are available.

An alternative form of connection reinforcement is a haunch of the same width as the con-nected RHS members on the inside of the knee. However, insufficient test evidence is available to quantify the properties, especially the rotational capacity, of this connection type.