## Design of beams and columns

In beams of classes 1 and 2, the value of bit of walls of sections are such that local buckling only takes place after substantial plastic rotations, large enough to fulfil the plastic rotation demand from the earthquake.

The prevention of lateral torsional buckling is another serious concern in beam elements, in particular those made of H or I sections, due to coupling between the local and lateral buckling instability phenomena: inward buckling on one side of the flange is accompanied by outward buckling on the other side, which makes the profile unsymmetrical and generates lateral movement. Substantial lateral restraint of the flanges is thus absolutely needed to develop the full plastic capacity of beams. Connection to a floor slab provides excellent lateral support; however, both the upper and lower flanges should be restrained, because of the reversal of plastic moments at beam ends (Fig. 6.7).

The rule for calculation of the design shear force,

reflects a capacity design requirement: the seismic component VEd M of the design shear VEd in a beam is related to the ULS situation, in which the plastic moments Mpl Rd develop at both beam ends (and not only the bending moments computed as seismic action effects in the elastic analysis), following a rationale explained in Section 6.5 above,

where A and B denote the beam end sections.

The rule for calculation of the design axial force in columns, equation (D6.1) in Section 6.5, and similar rules for calculation of the design shear force and bending moment of the column, VEd and MEd respectively, also reflect capacity design requirements. In this case, the

element considered (a column) is not the same as the element in which the plastic zone develops (a beam). Attention has to be paid to the fact that the yield stress of the beam may be higher than the design yield stress, so that the value of the axial force NFd in the column corresponding to the formation of the plastic hinge in the beam is higher than the value /VEd E computed from the elastic analysis. The factor l.l70V takes care of this material overstrength problem, while Q takes into account the section overstrength resulting from the fact that the value M , Rd, of most sections is higher than the value of MEd, computed from the analysis.

Formation of plastic hinges in columns at the base of the frame is an expected feature of moment-resisting frames, as it is required for compatibility of deformations in the global plastic mechanism. Stability checks of base columns at the ULS have to consider a bending moment diagram which corresponds to this situation.

Clauses 6.6.3(6), The design of the panel zone of the column has to fulfil

Due to the existence of plastic bending moments of opposite signs at the beam ends adjacent to a column as indicated in Fig. 6.8, the design shear Kwp Ed applied to the panel zone is high (Fig. 6.9). If the plastic hinges are formed in the beam sections adjacent to the column on its left- and right-hand sides, the horizontal design shear Kwp Ed in the panel zone is equal to

Kvp, Ed , Rd, left /(4ft " 2h left) + -^pl, Rd, right/(^right 2/,.^,) (D6.7)

The value of V >Ed computed from equation (D6.7) has to be compared according to equation (D6.6) with the design resistance of the panel zone of the column, V Rd, computed considering the geometric dimensions of the column section, in particular the column depth dc (see Fig. 6.9) and the column depth of the web hw. If the plastic hinges are formed at a distance D from the column face, the moments to consider in equation (D6.7) are

^Sd, left ~ ^pl, Rd, left + ^Ed, M, lefr^ -^Sd, right = -^pl, Rd, right + ^Ed, M, right^ (D6.8)

Equation (D6.6) refers to the case of column web panels of small slenderness, which are able to develop their full plastic strength. Buckling limits the capacity of more slender webs, in which case the shear buckling resistance of the web panel should be used on the right-hand side of equation (D6.6).

The design shear Fwp Ed generally surpasses the shear resistance Fwp Rd of the panel zone in columns made of standard rolled sections, requiring that reinforcing plates are installed, either in the form of a 'doubler' plate welded onto the column web or by means of two plates welded to the flanges and transverse stiffeners (Fig. 6.10). Welds should be sized to the additional plate thickness.

Column panel zone

Fig. 6.9. Moments of opposite signs generate high shear in the column panel zone

Fig. 6.9. Moments of opposite signs generate high shear in the column panel zone

Section A-A

'Doubler' plate

Fig. 6.10. Additional plates to increase resistance of the panel zone

Equation (D6.6) reflects a decision on the acceptability of the plastic deformation in shear of column web panels. This plastic mechanism is known to be very ductile and stable. However, two reasons justify why it should not be the basic local energy dissipative mechanism in moment-resisting frames:

• The global mechanism selected as a design objective for moment-resisting frames corresponds to 'weak beams-strong columns', the intention being that beam yielding spreads throughout the whole structure, a local 'soft-storey'-type mechanism being avoided. In this concept, columns remain fully elastic. Accepting dissipative mechanisms in column web panels would violate the concept. 8 The plastic deformation in shear of column web panels results in local bending of the column flanges at the location where web stiffeners and column flanges intersect. If the beam is welded to the column flanges, the aforementioned local bending of column flanges may cause high plastic strains in the connection zone and generate early failure.

The decision behind equation (D6.6) means that the plastic shear deformation of column web panels is accepted in a limited manner, by allowing plastic hinge deformation in the beam and a plastic shear deformation in the web panel to take place simultaneously. This decision is also supported by experiments that have shown that the most ductile connection behaviour is observed when the two phenomena take place simultaneously. In the case of experimental evidence, the contribution of the web panel to the plastic rotation capability is limited to 30% of the total.

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