Assumingthe load is 10 tons distributed overa span of 18 ft.,the calculations will be as follows. (1) Flitch beam: W= d2/L(Cb + 30 t); where W= breaking weight in cwt. in centre; d = depth in inches; L = span in feet; C = constant = 3 for Memel; b = total breadth of timber in inches t - thickness of flitch plate in inches. Factor of safety, 10. One or two trial designs may be necessary before fin ding a suitable one, when Fig. 1 may be decided upon. Ten tons distributed = .3 tons in centre multiplied by 1J for breaking weight = .10 tons = 1,000 cwt. Breaking weight = (14x14)/18 (3 x 14 + 30 x 1 3/4) = 93/9(42+52 1/2) = (98x94 1/2)/9 = 1,029, or a trifle in excess of the strength required. (2) Cast-iron girder: Depth, say, one-twelfth of the span = 18 in. Stress in bottom flange Wl/8d =(10x18)/(8x1.5) = 15 tons. Allow l 1/2 tons per square inch in 8 x F5 tension; 15/1.5 =10sq.in. Make top flange same size to allow width for building upon and possible tension in top flange from ends being built in, so that the section will be as Fig. 2. (3) Wrought-iron plate girder: For the same depth the stress in bottom flange will be as found above = 15 tons. Allow 4 tons per square inch on the gross sectional area = 3 3/4sq. in. Say, one 1/2-in. plate 8in. wide for each flange, with 2 1/2-in. by 2 1/2-in. by ,5/16-in. angle irons, and 1/4-in. web, and stiffeners every 4ft., as in Fig. 3. Rolled steel joist: By reference to Dorman Long & Co.'s section book, a 12 in. by 5 in. by 321b. rolled steel joist will carry 10 tons distributed over a span of 18ft.; but 5 in. is narrow to build upon, and a 3/8-in. top plate would be a desirable addition, as in Fig. 4.

Fig. 1. Fig. 2. Fig. 3. Fig. 4. Comparative Designs of Girders.