No, the slides do not show the girder buckled. It is deflected. The beams keep it from rotating and for lateral torsional buckling and vertical load capacity to be lost the beam or girder needs to rotate. NIST used a rule of rotation equal to half the flange width for saying the beam or girder lost its load carrying capacity. That did not occur in the FEA I sent you the results of.
Additionally, the girder gets locked up against the flange of column 79 due to thermal expansion and is unable to traverse westward. So I don't see how you got the notion that the bottom flange moved more than 6.5 inches. On top of that the beams can't expand more than about 4.75 inches no matter what the temperature was due to sagging induced shortening becoming greater than expansion at a little over 600 degrees C. Then there are the flange stiffeners which would require about 9 inches of westward travel before the girder would come off the seat.
There is no chance that girder came off its seat under any fire heating scenario.
Other engineers show this is wrong.
TS’ FEA color gradient displacement slides show:
[1] The girder expanded along its length and was restrained by cols. 79 and 44. = buckled
[2] (Measurements rounded to one decimal point.) The girder is shown with a west displacement of 0.1 to 2.6 inches for a distance of ~ 1 foot from the trapped girder end at C79 and by the flange at C44. The rest of the girder is shown having moved west by 3.8 to 6.3 inches. = buckled. (due to 0.1 to 6.3 inches horizontal differential)
[3] The 3D graphics show the girder rotated about its vertical axis and deformed about its horizontal axis. = buckled.
“Restrained beams, when exposed to fire, develop significant restraint forces and these forces
can alter the response of the beam. The development of fire induced forces, and gradual
softening of steel resulting from high temperature, produce large deflections in the beam.
Strength failure occurs in the beam either when the capacity of the connections is exceeded due to large rotations, or when a plastic mechanism develops in the beam after undergoing large deflections.
There have been limited studies on the behavior of restrained beams under fire conditions.
Fire resistance tests on axially restrained steel beams revealed the development of significant axial force and large deflections due to restraint [1-3].” Pp.106
(Thanks to Sunstealer’s link of
Structures in Fire - Proceedings of the Sixth International Conference. 123 papers selected for publication,2010)
http://www.egr.msu.edu/sif10/flyer of conf/SiF10 Conference Proceedings.pdf
“….. As steel temperature continues to increase with fire exposure time, softening of steel causes larger deflections and rotations until the first plastic hinge develop in the beam. The plastic hinge, which forms at the location of maximum bending moment in the beam, causes sudden increase in deflection (see Fig.1(c)), which leads to reduction and then reversal of the axial force in the beam from compressive to tensile force.
The beam enters a catenary phase in Stage III when the fire-induced compressive axial force vanishes as shown in Fig. 1(b). In the catenary phase, tensile force develops in the beam and the load bearing mechanism gradually shifts form flexural to cable (tensile) until failure occurs by rupture of the beam (or in the connections). When the beam undergoes the above three stages, it is assumed that the connections continue to perform elastically. Therefore, fire-induced forces and rotations in the beam must not exceed the connections capacity.”
P. 107. – ibid.
TS’ slides show the girder buckled. The slides show the horizontal displacement but not the large vertical deflections of the girder. The girder was pushed and twisted past the seat by the expanding and sagging beams or the girder fractured and failed.
The weight of the buckled beams, with a 20” deflection (NIST), and whose horizontal axes were above the girder’s horizontal axis, torqued the girder towards the beams. The girder’s bottom flange rotated past the already 6.3” bottom flange lateral displacement.
There is no chance that girder came off its seat under any fire heating scenario.
Heated beams pushed the girder west 6.3”, the girder expanded, restrained, buckled, greatly deflected. The 20” sagged beams twisted the top of the girder towards them and the bottom flange away additionally >0.2”, =>6.5” , >half the 12” seat, girder fell off. Or the girder ruptured (above) since it was not restrained by the failed bolts.
Fire caused the failure of Girder 44-79, not CD.
