Analysis, classification and modelling
Global analysis
General
(1) The effects of the behaviour of the joints on the distribution of internal forces and moments within a structure, and on the overall deformations of the structure, should generally be taken into account, but where these effects are sufficiently small they may be neglected.
(2) To identify whether the effects of joint behaviour on the analysis need be taken into account, a distinction may be made between three simplified joint models as follows:
– simple, in which the joint may be assumed not to transmit bending moments;
– continuous, in which the behaviour of the joint may be assumed to have no effect on the analysis;
– semi-continuous, in which the behaviour of the joint needs to be taken into account in the analysis.
(3) The appropriate type of joint model should be determined from Table 5.1, depending on the
classification of the joint and on the chosen method of analysis.
(4) The design moment-rotation characteristic of a joint used in the analysis may be simplified by adopting any appropriate curve, including a linearized approximation (e.g. bi-linear or tri-linear), provided that the approximate curve lies wholly below the design moment-rotation characteristic.
Elastic global analysis
(1) The joints should be classified according to their rotational stiffness, see 5.2.2.
(2) The joints should have sufficient strength to transmit the forces and moments acting at the joints resulting from the analysis.
(3) In the case of a semi-rigid joint, the rotational stiffness $S_{j}$ corresponding to the bending moment $M_{j,Ed}$ should generally be used in the analysis. If $M_{j,Ed}$ does not exceed 2/3 $M_{j,Rd}$ the initial rotational stiffness $S_{j,ini}$ may be taken in the global analysis, see Figure 5.1(a).
(4) As a simplification to 5.1.2(3), the rotational stiffness may be taken as $S_{j,ini}/\eta$ in the analysis, for all values of the moment $M_{j,Ed}$ , as shown in Figure 5.1(b), where $\eta$ is the stiffness modification coefficient from Table 5.2.
(5) For joints connecting H or I sections $S_{j}$ is given in 6.3.1.
Rigid-plastic global analysis
(1) The joints should be classified according to their strength, see 5.2.3.
(2) For joints connecting H or I sections, $M_{j,Rd}$ is given in 6.2.
(3) For joints connecting hollow sections the method given in section 7 may be used.
(4) The rotation capacity of a joint should be sufficient to accommodate the rotations resulting from the analysis.
(5) For joints connecting H or I sections the rotation capacity should be checked according to 6.4.
Elastic- plastic global analysis
(1) The joints should be classified according to both stiffness (see 5.2.2) and strength (see 5.2.3).
(2) For joints connecting H or I sections $M_{j,Rd}$ is given in 6.2, $S_{j}$ is given in 6.3.1 and $\phi _{Cd}$ is given in 6.4.
(3) For joints connecting hollow sections the method given in section 7 may be used.
(4) The moment rotation characteristic of the joints should be used to determine the distribution of internal forces and moments.
(5) As a simplification, the bi-linear design moment-rotation characteristic shown in Figure 5.2 may be adopted. The stiffness modification coefficient $\eta$ should be obtained from Table 5.2.
Classification of joints
General
(1) The details of all joints should fulfil the assumptions made in the relevant design method, without adversely affecting any other part of the structure.
(2) Joints may be classified by their stiffness (see 5.2.2) and by their strength (see 5.2.3).
NOTE: The National Annex may give additional information on the classification of joints by their stiffness and strength to that given in 5.2.2.1(2).
Classification by stiffness
General
(1) A joint may be classified as rigid, nominally pinned or semi-rigid according to its rotational stiffness, by comparing its initial rotational stiffness $S_{j,ini}$ with the classification boundaries given in 5.2.2.5.
NOTE: Rules for the determination of $S_{j,ini}$ for joints connecting H or I sections are given in 6.3.1. Rules for the determination of $S_{j,ini}$ for joints connecting hollow sections are not given in this Standard.
(2) A joint may be classified on the basis of experimental evidence, experience of previous satisfactory performance in similar cases or by calculations based on test evidence.
Nominally pinned joints
(1) A nominally pinned joint should be capable of transmitting the internal forces, without developing significant moments which might adversely affect the members or the structure as a whole.
(2) A nominally pinned joint should be capable of accepting the resulting rotations under the design loads.
Rigid joints
(1) Joints classified as rigid may be assumed to have sufficient rotational stiffness to justify analysis based on full continuity.
Semi-rigid joints
(1) A joint which does not meet the criteria for a rigid joint or a nominally pinned joint should be classified as a semi-rigid joint.
NOTE: Semi-rigid joints provide a predictable degree of interaction between members, based on the design moment-rotation characteristics of the joints.
(2) Semi-rigid joints should be capable of transmitting the internal forces and moments.
Classification boundaries
(1) Classification boundaries for joints other than column bases are given in 5.2.2.1(1) and Figure 5.4.
(2) Column bases may be classified as rigid provided the following conditions are satisfied:
– in frames where the bracing system reduces the horizontal displacement by at least 80 % and where the effects of deformation may be neglected:
if $\overline{\lambda _{0}}\le 0.5$
if $0.5 < \overline{\lambda _{0}}< 3.93$ and $S_{j,ini} \ge 7(2\overline{\lambda _{0}}-1)EI_{c}/L_{c}$
if $\overline{\lambda _{0}} \ge 3.93$ and $S_{j,ini} \ge 48EI_{c}/L_{c}$
otherwise if $S_{j,ini} \ge 30EI_{c}/L_{c}$
where:
$\overline{\lambda _{0}}$ is the slenderness of a column in which both ends are assumed to be pinned;
$I{c}$, $L_{c}$ are as given in Figure 5.4.
Classification by strength
General
(1) A joint may be classified as full-strength, nominally pinned or partial strength by comparing its design moment resistance $M_{j,Rd}$ with the design moment resistances of the members that it connects. When classifying joints, the design resistance of a member should be taken as that member adjacent to the joint.
Nominally pinned joints
(1) A nominally pinned joint should be capable of transmitting the internal forces, without developing significant moments which might adversely affect the members or the structure as a whole.
(2) A nominally pinned joint should be capable of accepting the resulting rotations under the design loads.
(3) A joint may be classified as nominally pinned if its design moment resistance $M_{j,Rd}$ is not greater than 0.25 times the design moment resistance required for a full-strength joint, provided that it also has sufficient rotation capacity.
Full-strength joints
(1) The design resistance of a full strength joint should be not less than that of the connected members.
(2) A joint may be classified as full-strength if it meets the criteria given in Figure 5.5.
Partial-strength joints
(1) A joint which does not meet the criteria for a full-strength joint or a nominally pinned joint should be classified as a partial-strength joint.
Modelling of beam-to-column joints
(1) To model the deformational behaviour of a joint, account should be taken of the shear deformation of the web panel and the rotational deformation of the connections.
(2) Joint configurations should be designed to resist the internal bending moments $M_{b1,Ed}$ and $M_{b2,Ed}$ , normal forces $N_{b1,Ed}$ and $N_{b2,Ed}$ and shear forces $V_{b1,Ed}$ and $V_{b2,Ed}$ applied to the joints by the connected members, see Figure 5.6.
(3) The resulting shear force $V_{wp,Ed}$ in the web panel should be obtained using:
$$ V_{wp,Ed}=(M_{b1,Ed}-M_{b2,Ed})/z-(V_{c1,Ed}-V_{c2,Ed})/2$$ where:
$z$ is the lever arm, see 6.2.7.
(4) To model a joint in a way that closely reproduces the expected behaviour, the web panel in shear and each of the connections should be modelled separately, taking account of the internal moments and forces in the members, acting at the periphery of the web panel, see Figure 5.6(a) and Figure 5.7.
(5) As a simplified alternative to 5.3(4), a single-sided joint configuration may be modelled as a single joint, and a double-sided joint configuration may be modelled as two separate but inter-acting joints, one on each side. As a consequence, a double-sided beam-to-column joint configuration has two moment-rotation characteristics, one for the right-hand joint and another for the left-hand joint.
(6) In a double-sided, beam-to-column joint, each joint should be modelled as a separate rotational spring, as shown in Figure 5.8, in which each spring has a moment-rotation characteristic that takes into account the behaviour of the web panel in shear as well as the influence of the relevant connections.
(7) When determining the design moment resistance and rotational stiffness for each of the joints, the possible influence of the web panel in shear should be taken into account by means of the transformation parameters $\beta _{1}$ and $\beta _{2}$ , where:
$\beta _{1}$ is the value of the transformation parameter $\beta$ for the right-hand side joint;
$\beta _{2}$ is the value of the transformation parameter $\beta$ for the left-hand side joint.
NOTE: The transformation parameters $\beta _{1}$ and $\beta _{2}$ are used directly in 6.2.7.2(7) and 6.3.2(1). They are also used in 6.2.6.2(1) and 6.2.6.3(4) in connection with Table 6.3 to obtain the reduction factor w for shear.
(8) Approximate values for $\beta _{1}$ and $\beta _{2}$ based on the values of the beam moments $M_{b1,Ed}$ and $M_{b2,Ed}$ at the periphery of the web panel, see Figure 5.6(a), may be obtained from Table 5.4.
(9) As an alternative to 5.3(8), more accurate values of $\beta _{1}$ and $\beta _{2}$ based on the values of the beam moments $M_{j,b1,Ed}$ and $M_{j,b2,Ed}$ at the intersection of the member centrelines, may be determined from the simplified model shown in Figure 5.6(b) as follows:
$$\beta _{1}=|1-M_{j,b2,Ed}/M_{j,b1,Ed}| \le 2$$ $$\beta _{2}=|1-M_{j,b1,Ed}/M_{j,b2,Ed}| \le 2$$ where:
$M_{j,b1,Ed}$ is the moment at the intersection from the right hand beam;
$M_{j,b2,Ed}$ is the moment at the intersection from the left hand beam.
(10) In the case of an unstiffened double-sided beam-to-column joint configuration in which the depths of the two beams are not equal, the actual distribution of shear stresses in the column web panel should be taken into account when determining the design moment resistance.