The strength of a solid cylindrical beam varies directly as its diameter cubed, and inversely as its length.
The formula for finding the breaking weight (B.W.) of a solid cylindrical beam supported at each end and loaded at its centre is as follows:
B.W. = d3/l × c × 10/17
where d3 = least diameter in inches cubed;
l = length of beam between supports in feet;
c = the constant found by experiment on rectangular beams;
10/17 = the proportion that cylindrical beams bear to square beams,
Example.—Find the B.W. of a solid cylindrical beam of spruce fir 6 inches in diameter and 4 feet between supports.
The constant C for spruce fir is (Table I.) 403.
B.W. = (6 × 6 × 6 × 403 × 10)/(4 × 17)
= 12,8013⁄17 lbs.
= 5 tons 14 cwt. 1 qr. 53⁄17 lbs.
One-fifth of this must be taken as a safe load, say 1 ton 2 cwt. 3 qrs.
