I'm trying to figure out what would cause the spandrel to pop out so far. I suspect that the spandrel was flexed horizontally and loaded like a spring. If you lightly hold a business card between your thumb and ringfinger and bend it in then release it, you can make it fly a good ways. A spandrel would be a rather stiff spring.
It's interesting that it can be bent either in or out and can be made to fly outward. If you bend it in (toward the deck)then release it from midspan, it will fly out. If you bend it outward then release it from the ends, it will also fly outward.
It was hot, so maybe the tees had expanded and were putting outward pressure on the spandrel. Then the end connections gave out and the spandrel flew away.
Or, shrinkage had caused it to pull the spandrel to flex inward until the deck to spandrel connection gave out and the spandrel flew away. I think this is less likely becuase it was hot and shrinkage takes place in the cold.
The photos show some tabs with bolt holes projecting from the columns that were probably meant to bolt the spandrel to the column. The tabs project straight out. It seems to me that if there were bolts in them the tabs would have bent as the spandrel flew away, but the tabs look pristine like there never was a bolt in them.
I can't get the basic physics to work out. I don't do these types of calculations very often (like once every 20 years), so I could be making some errors.
Assuming the panel width is 38" deep, 16" wide at the haunch and 8" thick it has an I of 5346 in.^4 about the vertical (weak) axis; and if the span is 30 ft., and the concrete is uncracked, I get a spring constant of about 22 kips/inch for a load applied at midspan. If it was bowed in 1", it would have a potential energy of .5Fx or 11 inch-kips, or 0.92 ft.kips.
How much energy would it take to horizontally project an 11.5 kip object 30 ft. while it dropped about 30 ft? It would take 1.86 sec to fall 30 ft., thus it would require a horizontal velocity of 16.1 ft/s to travel 30 ft. horizontally in that time. If I set the potential energy of the flexed spandrel 0.92 = 1/2 mv^2, the velocity of the panel would be 0.17 ft/s. I'm off by a factor of 100.