Ductility

The two basic requirements of a ductile moment frame are: firstly, a ductile configuration and, secondly, ductile members. Application of the Capacity Design approach ensures both are satisfied as explained below.

Observation of seismic damage to frames shows time and again how poor frame configuration leads to concentration of damage in too few members such as ground floor columns that are incapable of absorbing the earthquake energy. Where damage occurs in columns they may be unable to continue to carry their gravity forces in which case collapse is inevitable.

Studies show that moment frames exhibit two failure mechanisms under seismic force overload. Firstly, plastic hinges or structural fuses can form at the top and bottom of the columns of just one storey, usually at ground floor level. In this case the earthquake energy is

(b) Strong column-weak beam Structural fuses or plastic hinges form in beams at each floor level

▲ 5.44 Two potential overload mechanisms of moment frames. Only the strong column-weak beam configuration is ductile.

▲ 5.45 A collapsed building with weak columns and strong beams. Ironically the architect enlarged the columns with non-structural masonry. Mexico City, 1985 Mexico earthquake.

(Reproduced with permission from R.B. Shephard).

▲ 5.45 A collapsed building with weak columns and strong beams. Ironically the architect enlarged the columns with non-structural masonry. Mexico City, 1985 Mexico earthquake.

(Reproduced with permission from R.B. Shephard).

absorbed in just several locations and the most important load-bearing members of all, the columns, are badly damaged (Fig. 5.44(a)). The second, and ideal situation, is shown in Fig. 5.44(b). Plastic hinges form at the ends of many beams. This means less energy absorbed and less damage per hinge. Earthquake energy is now dissipated far more uniformly throughout the entire structure rather than concentrated in one floor. When a beam end forms a plastic hinge the beam can still support its gravity forces even though it is damaged. This is a far better situation than column hinging because beams, without significant compression forces within, are inherently more ductile than columns, and their damage does not jeopardize the safety of the entire building. The only hinges permitted in columns are structurally unavoidable and they form just above the foundations. Those hinge regions are specially detailed in the case of reinforced concrete construction with very closely-spaced ties to confine the concrete.

The scenario of Fig. 5.44(b) is an example of the application of Capacity Design. Beams are chosen as sacrificial members to dissipate the earthquake energy long before the columns are damaged. All other elements are designed to be stronger than the beam hinges. Columns are designed stronger than the beams and foundations stronger than the columns since foundation damage is difficult to detect and repair. Fig. 5.45 shows a collapsed building with columns smaller and weaker than the beams. As explained previously, damage that concentrates in the columns of a ground floor or any other single storey of a weak column-strong beam structure must be strenuously avoided.

As noted previously, a serious implication for architects adopting a ductile moment frame configuration is that the depth of columns must be approximately equal to or greater than the depth of beams. Reinforced concrete columns can be slightly smaller than beams provided that the columns contain more and/or stronger reinforcing steel.

Structural redundancy, a desirable configuration characteristic also increases ductility. More beam and column hinges mean less damage to each. Also, if one member fails prematurely, perhaps due to a construction defect, then the forces it was designed to resist can be shared by other intact members.

The terms 'plastic hinge' or 'structural fuse' describe the ductile energy-absorbing damage incurred where longitudinal reinforcing steel or a steel section in a moment frame yields plastically. Some good and poor examples of these hinges after strong quakes and full-scale laboratory tests are illustrated. Fig. 3.15 shows a damaged reinforced concrete column. Due to the large horizontal deflections it has undergone its cover concrete in the fuse region has spalled off but closely-spaced spiral ties successfully confine the core concrete and prevent shear failure. The column has performed in a ductile mode displaying the type of damage expected during a design-level earthquake.

Fig. 5.46 illustrates poor performance of a beam plastic hinge. The beam longitudinal steel has yielded in tension due to gravity and seismic bending moments, but because the beam ties are spaced too far apart large pieces of concrete have dropped from the core of the beam. The beam bars then buckled during reversed load cycles further weakening the beam and leaving the building in considerable danger should it be struck by a large after-shock.

A full-scale interior beam-column assemblage tested in a laboratory has been subject to cyclic loading to simulate the actions of a strong earthquake. Severe beam damage is localized in the plastic hinge region where the beams join the column (Fig. 5.47). Because the column and beam-column joint are stronger than the beam, damage is intentionally localized at the end of the beam. The beam longitudinal steel has been stretched plastically in tension and compression during the load cycles but closely-spaced ties have confined it well and prevented it from buckling. Similar damage is expected in beam plastic hinges of real buildings after a severe earthquake. This is what ductile behaviour looks like. Although structural damage has occurred the beam is almost as strong as it was before the quake.

How do designers achieve ductile steel moment frames? If not designed and detailed according to Capacity Design principles even steel frames

▲ 5.46 Poor example of a beam plastic hinge. The column is to the left. Mexico City, 1985 Mexico earthquake.

(Reproduced with permission from R.B. Shephard).

▲ 5.46 Poor example of a beam plastic hinge. The column is to the left. Mexico City, 1985 Mexico earthquake.

(Reproduced with permission from R.B. Shephard).

▲ 5.47 Full-scale laboratory test of a beam-column assemblage. A plastic hinge has developed after loading equivalent to a severe quake. Canterbury University.
▲ 5.48 Intentional weakening of a moment frame beam to form a structural fuse. The fuse region is weaker than any other structural member or connection. The wood flooring is unusual, but appropriate for this hotel built above an existing concrete parking building. Wellington.

are brittle. Columns must be stronger than beams. Hundreds of steel moment frames developed serious cracks where beams connected to columns during the 1994 Loma Prieta, California earthquake. Now more ductile details have been developed, including one where a potential plastic hinge is intentionally formed by locally weakening beam flanges (Fig. 5.48). Having created a fuse region, all other connections including welds are designed to be stronger so as not to suffer damage.

A final cautionary note: although designers may intend that moment frames be ductile, in practice ductility is difficult to achieve. Very high structural design and construction standards are necessary. Moment frame performance is sensitive to small design and detailing errors that can have grave consequences. If there is doubt about quality assurance standards consider using shear walls instead of frames to resist seismic forces.

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