Modelled
2.5 Connection Fracture
The Northridge earthquake uncovered the fact that steel moment resisting frames may not always be as ductile as engineers expected. Several steel-framed buildings had numerous fractures at beam-to-column moment connections. Most of these cracks stemmed from the welds between the beam and column, and cracking spread into the beam or column flanges and beyond (SAC 1994).
Instead of trying to capture every type of observed damage, the formulation models fracture of individual fibers that are deemed susceptible. Potential fracture areas include those shown in figure 2.10. For example, a beam is likely to fail at its connections to columns, so if the beam has eight segments, segments 1 and 8 can be identified as potential fracture zones. Similarly, the base of the lowest level column (segment 1) can be modeled to predict base plate failure. Since most
Beam to Column Column Baseplate Column Splice
Figure 2.10 Welds that may pose a problem.
column splices occur several feet above floor level (to avoid maximum moment and to make on-site welding easier), the fourth segment out of eight can be modified to model splice connection fracture. Other fracture areas could be modeled, including brace to gusset plate welds. Fibers not representing weld fracture will all follow their individual hysteretic stress-strain relations with rupture as the only failure mechanism.
The actual level of cracking for a group of connections can be chosen in sev- eral ways. There have been several large-scale tests of beam-column connections performed in recent years. Static studies have been performed at the Earthquake Engineering Research Center, University of California, San Diego, University of Cal- ifornia Berkeley, and University of Texas at Austin (SAC 1997a). Dynamic testing has been performed at Lehigh University (Xue, Kaufmann, Lu, and Fisher 1997).
Unfortunately, there have not been enough tests on various member sizes to ade- quately predict a probabilistic distribution of tensile strains or plastic rotations at failure. The formulation used in this work assigns a fracture strain E 1 to a fiber using a randomized process (Hall 1998). Sets of fracture strains are established with associated probabilities of occurrence in units of 10%. An example of a set is:
Ef
=
0.7Ey at 20%; Ef=
l.OEy at 50%; Ef=
2.0Ey at 30%, where Ey is the yield strain.The ten strain values in a set can be chosen to approximate a normal distribution, or all ten values can be the same making it deterministic, or some other distribution
can be chosen. A continuous model instead of this discretization is not warranted due to the lack of data available.
Fibers to be assigned fracture strains are placed into groups of which there are four types that model the potential fracture areas mentioned above. These types are column splice, column base plate, top beam flange, and bottom beam flange. A group of column-splice fibers consists of all eight fibers of segment 4 in a column containing a slice. A group of column-base-plate fibers consists of all eight fibers of segment 1 in a column attached to a base plate. A group of top beam-flange fibers consists of fibers 1 to 4 in segment 1 or 8 where a moment connection exists, and similarly for a bottom beam flange group except that the fibers are 5 to 8. Each group type is associated with one of the sets of fracture strains. Once the sets of fracture strains and the groups of fibers are established, the fracture strains are assigned randomly to the groups within each type using the specified occurrence probabilities of the associated set. All fibers in a group receive the same fracture strain, but the fracture strain would vary from group to group within each type throughout the building (Hall 1998).
As an example, assume the same probability distribution is desired for the frac- ture strains at the top and bottom of both ends of all the beams in a building. The top left beam-flange fibers (segment 1, fibers 1 to 4) are one group. The bottom-left beam-flange fibers (segment 1, fibers 1 to 4) are a second group. The right beam- flange fibers form two more groups, (segment 8, fibers 1 to 4) and (segment 8, fibers 5 to 8). Even though each group uses the same fracture set, the fracture strains are assigned randomly so that one beam could have four different fracture strains (top left, bottom left, top right and bottom right). The strain will be the same for all fibers in a group, but the same group of fibers in another beam could have a different fracture strain.
When an identified fiber reaches its specified tensile fracture strain value, it releases its tensile stress and loses its ability to carry tension in the future, but it can carry compression if contact is regained. If all fibers of a column splice fracture, the column is assumed not to carry any load thereafter (tension or compression).
The assumption here is that the lateral offset of the story would be sufficient to bring the column-section plates out of alignment, and so the load carrying capacity woula be reduced dramatically. For a base plate, tensile capacity will be lost, but compression can be achieved if contact is regained. If all beam fibers of a beam- to-column connection fracture, the shear transfer capacity is assumed to remain intact.