TUBULAE GIRDER BKEDGES. 



isa 



On the contrary, if additions be made to the one (assum- 

 ing the ratio to be correct) without a proportional addition 

 to the other, if the girder does not become absohitely 

 weaker, it is evidently not increased in strength ; inasmuch 

 as increased dead-weight is given to the girder by the 

 introduction of a quantity of material which is totally 

 inoperative.* This being the case, it is of import- 

 ance to preserve as nearly as possible the correct pro- 

 portion of the parts, in order to ensure the maximum of 

 strength in the two resisting forces of tension and compres- 

 sion, an arrangement essentially important in those struc- 

 tures r and atlso in the application of the formula to determine 

 the utmost strength of the girder.f If, for example, an 

 excess of material were given to the bottom of the girder 



shown in the plate, the formula (W= — f would not 



apply, inasmuch as the top and bottom areas would be- 

 disproportionate to each other, and the girder would fail 

 from the yielding of the top before the stronger bottomii 



* It may be said that an increase of material to either top or bottom 

 will increase its stiffness, and— a fortiori — its strength. I do not, how- 

 ever, admit this dootrine, as there is no telling to what extent these dis- 

 crepancies may be carried, and the consequence of a disproportion of the 

 parts, if once allowed, might lead to dangerous error. Besides, these 

 proportions must either be correct or incorrect — if the former, any devia- 

 tion from them i& inadmissible. 



f It is important to bear in mind, that in devising the formula for 

 calculating the utmost strength of a tubular girder — which formula i?, 

 that the breaking weight is equal to the sectional area of the bottom 

 multiplied by the depth, and by a constant derived from experiment for' 

 the particular form of girder rmder consideration, and tl^ whole divided 

 by the length — I have invariably assumed that the proportions which I 

 have announced, and which were arrived at by frequent and direct ex- 

 periment, are maintained ; and further, that the constant which I have 

 given is for a tubular girder constructed after these proportions, and with 

 a cellular top. Other constructions would require other constants to bo 

 derived from experiment 



