OF IRON BEAMS. 533 



RULE FOR THE STRENGTH OF BEAMS. 



65. Comparing the results of experiments 9, 

 11, 12, 19, 20 and 21, and allowing for 

 difference of iron, as indicated by the beams 

 of the common form cast with the others for 

 comparison; I find that the strength is nearly 

 in proportion to the size of the bottom rib or 

 flange : a bottom rib of double size giving nearly, 

 but not quite, double strength. And the 

 subsequent experiments show the strength to 

 be as the depth, every thing else being the 

 same. Therefore in different beams, whose 

 length is the same, the strength must be as 

 their depths multiplied by the areas of a middle 

 section of their , bottom ribs : and where the 

 lengths are different the strengths will be as 

 this product divided by the lengths. 



. -ixr __ cad 



where W = the breaking weight in the middle 

 of the beam, a = the area of a section of the 

 bottom rib in the middle of the beam, d = the 

 depth of the beam there, / = the length or 

 distance between the supports, and c = a quan- 

 tity, nearly constant in oiu- best forms of beams, 

 and which will be supplied by any of the 

 preceding experiments on them. But if used 

 for other forms, as in our earlier ones, it will 

 3 u 2 



