Proportion?

Cast-iron beam

I am currently doing a research about a huge cast-iron construction placed in New York City in 1853. I have found the formulas used in that era to calculate the "bearing capacity" of the given beam. Two British Engineers who extensively publish their work pop, Hodgkinson and Fairbairn. Fairbairn focused in the Worought-Iron beams whereas Hodgkinson digged more in the cast-iron beams. Through their experiments, which generally consisted in bending differente shapes of beams under a known load, they usually stablished a constant "c" for each type of shape. This constant is obtained according to this formula, which is valid both for cast-iron and wrought-iron beams:

W=c*a*d / l

where:

W= max. weight

c = constant

a = area of the bottom flange

d = depth of the beam

The relation between the area of the bottom flange and the depth of the beam is directly proportional.The constant "c" is given in Tons/in2, thus this is quite similar of the yielding point in wrought iron or the breaking point in cast iron (because of its brittle fracture).

Cast iron is a strong material that performs excellent in compression but fails in tension and not mention in fireproofing. According to this, the I-Beams were shaped in bizarre flanges. Hodgkinson established a general formula to shape the cast-iron beams. According to his experiments the cast iron is 6 times stronger in compression than in tension, so it is logical using the same proportion for the flanges. Usually we find cast-iron beams where the bottom flange is between 6-6.5 times the area of the top flange.

I do not why but I really like these beams, maybe it is because each beam was cast for one place, building or purpose; with such detail hard to find nowadays.

Typical fracture of a cast-iron beam due to bending