## Friday, November 30, 2012

### The Collapse of the Silver Bridge (A Not-So-Happy Physics Tale)

On December 15, 1967 around 5 pm, The Silver Bridge (which connected Ohio and West
Virginia) collapsed. The bridge was suspended by eyebar chains (an eyebar is a long
steal plate with a large circular end with a hole through which a pin is used to connect to
other eyebars and make a chain). The collapse was due to a fracture in an eyebar induced
at least partially from the cold. What I want to figure out is what was the change in
temperature and the change in volume the steel bridged experienced, causing it to crack
(assuming the crack was purely temperature induced and not from corrosion/stress from
car weight).
The Silver Bridge eyebars were around 13.7- 16.8 m long; 300mm wide, varied in
thickness (but average thickness of typical eyebar was around 25-50 mm, so we’ll
approximate around 35 mm). Assuming the eyebar is a perfect rectangle, its volume is
approximately 14.5mm*300mm*35mm= 0.0145m*0.300m*0.035m= 1.52 x 10-4 m3

(=Vo).

βsteel= 33.0
αsteel= 11.0
Ysteel= 200 x 109 Pa
Ultimate strength of steel (max)= 550,000,000 Pa

YαΔT= F/A
550,000,000 = (200 x 109) (11.0) ΔT
ΔT= 2.5 X 10-4 K

ΔV= βVoΔT
ΔV = (33.0) (1.52 x 10-4) (2.5 X 10-4) =1.3 x 10-6 m3.