Composite joints in frames for buildings
8.2. Analysis, including modelling and classification
Clause 8.2.1(1) Clause 8.2.1(1) refers to Section 5 of EN 1993-1-8, which covers the same subjects as clause
8.2. Table 5.1 in clause 5.1 of EN 1993-1-8 defines the links between the three types of global
analysis, elastic, rigid plastic, and elastic–plastic, and the types of models used for joints. This enables the designer to determine whether the stiffness of the joint, its resistance, or both properties, are relevant to the analysis.
Joints are classified in Section 5 by stiffness, as rigid, nominally pinned, or semi-rigid; and by strength as full-strength, nominally pinned, or partial-strength. This classification relates the property of the joint (stiffness or resistance) to that of the connected member, normally taken as the beam.
Clause 8.2.2(1) This applies also to composite joints. The only modification, in clause 8.2.2(1), concerns the rotational stiffness of a joint, Sj. This is bending moment per unit rotation, shown in Fig.
8.2(b). The symbol φ is used for rotation, as well as for bar diameter.
The initial elastic stiffness, Sj, ini, is reduced at high bending moments to allow for inelastic
behaviour. For global analysis, it is divided by η, values of which, between 3.0 and 3.5, are tabulated in clause 5.1.2 of EN 1993-1-8 for various types of steel joint. These apply where the joint is composite. Clause 8.2.2(1) provides a further value, for contact-plate joints, as shown on the right of Fig. 8.1 and in Fig. 8.4.
Clause 8.2.3(2)
The classification of a composite joint may depend on the direction of the bending moment (e.g. sagging or hogging). This is unlikely in a steelwork joint, and so is referred to in clause 8.2.3(2).
Clause 8.2.3(3) The reference in clause 8.2.3(3) to neglect of cracking and creep applies only to the classification of the joint according to stiffness. Its initial stiffness is to be compared with that of the connected beam, using Fig. 5.4 of EN 1993-1-8. The stiffer the beam the less likely it is that the joint can be classified as rigid.
A more precise calculation of beam stiffness is permitted by the use of ‘may’ in clause
8.2.3(3). For example, a representative value of modular ratio, to clause 5.4.2.2(11), may be
used. Account could also be taken of cracked and uncracked lengths within the beam
C B
A
Lb
Nominally pinned joint Semi-rigid joint
in accordance with clause 5.4.2.3, but the additional calculation would not normally be worthwhile.
Outline of modelling of joints for global analysis
In global analysis, nominally pinned joints are represented by pins, and semi-rigid joints by rotational springs, as shown in Fig. 8.1 for a two-span beam of uniform depth, supported by three columns in a braced frame. Joints to external columns are usually designed as nominally pinned, to reduce bending moments in the columns. The use of partial-strength semi-rigid joints at point B, rather than nominally pinned joints, has advantages in design: • possible reduction in the section sizes for beams
• reduction in the deflection of beams • reduction in crack widths near support B.
In comparison with full-strength rigid joints, the advantages are: • beams less susceptible to lateral–torsional buckling
• simpler construction and significant reduction in cost • lower bending moments in columns.
The stiffness of a rotational spring, Sj, is the slope of the moment–rotation relationship for
the joint (Fig. 8.2(a)). The stiffness class is determined by the ratio of the initial slope, Sj, ini, to
the stiffness EaIb/Lbof the beam adjacent to the joint, as shown.
The initial stiffness of a joint is assembled from the stiffnesses of its components, represented by elastic springs. Those for an end-plate joint with a single row of bolts in tension, between beams of equal depth are shown in Fig. 8.3, in which all elements except springs and pins are rigid. The notation for the spring stiffnesses kiis as in EN 1993-1-8 and in
Examples 8.1 and 10.1, as follows:
k1 shear in column web
k2 compression of column web
k3 extension of column web
k4 bending of column flange, caused by tension from a single row of bolts
k5 bending of end plate, caused by tension from a single row of bolts
k10 extension of bolts, for a single row of bolts.
Stiffnesses in EN 1994-1-1, but not in EN 1993-1-8, are:
ks, r extension of reinforcement (denoted k13by ECCS TC1139)
Ksc/Es slip of shear connection.
Each spring has a finite strength, governed by yield or buckling of the steel. The design method ensures that non-ductile modes, such as fracture of bolts, do not govern.
(1) Sj, ini ≥8EIb/Lb (3) Sj, ini £0.5EIb/Lb (2) Semi-rigid 0 tan–1 Sj, ini Mj 0 M j Mj, Ed Mj, Rd 2Mj, Rd/3 fCd (b) (a) (3) Nominal pin (1) Rigid tan–1 Sj (Sj = Sj, ini/m) (2) f f
For the tension region, the weakest of the springs numbered 3, 4, 5 and 10, and of the tension reinforcement, is found. This resistance is compared with the compressive resistance of spring 2. The product of the lower of these resistances and the effective lever arm gives the plastic bending resistance of the joint. The resistance can be increased by strengthening the weakest link; for example, by the addition of column-web stiffeners.
Where the beams are of unequal depth, or MEd, 1π MEd, 2(Fig. 8.3), rotation at the joint is
increased by shearing deformation of the column web. For beams of equal depth, this is the area ABCD in Fig. 8.3. Its deformation is resisted by the spring of stiffness k1. Depending
on the out-of-balance moment |MEd, 1– MEd, 2|, the column web panel may govern the
resistance of the joint.