184 



ME. WILLIAM FAIEBAIRN ON 



exerted its full resistance to the tensile strain. In 

 estimating the dimensions for the application of the formula, 

 the excess therefore would have to be reduced to the due 

 proportion of 11:12; or, in other words, the additional 

 strength must be left out of the calculation in computing 

 the strength of the bridge* The same reasoning will appl j 

 when the excess of area happens to be in the cellular top, 



although in this case the formula (W,^^ . --^ / does apply, 



as the excess (in my opinion) goes for nothing in the cal- 

 culation of the strength of the girder. 



In every case, however, where these proportions are main-» 

 tained, we have, in the above formula, a nearly correct prin- 

 ciple on which to estimate the strength of similar wrought-iron 

 tubular girders, whatever may be their relative dimensions.* 



It must further be noticed, that in calculating the strength 

 of bridges of this description, it is always assumed, that 

 in addition to the proportions of the top and bottom of 

 the girder being maintained, the vertical sides are suffi- 

 ciently rigid to retain the girders in shape ; and it is further 

 assumed, that the whole of the plates, angle iron, &c., are 

 in the line of the forces, and that the workmanship as well 

 as the riveting is well executed. 



♦ Mr. Tate, an eminent mathematician, remarks upon the formula — 

 1st. With respect to (W_. 11, where A is the area of the section 



of the bottom, and C = 80, the constant deduced on this supposition will 

 apply to all depths of the tube within short limits of error where such 

 depths, or A, are large in proportion to the depths of the cells and the 

 thickness of the plates. 



2nd. With red|>ect to the formula (W=^^-^-, when A is the area of 



the whole section, and C = 267, then the tubes should be similar in all 

 respects j but a slight variation in depth from that of similar form will not 

 produce much error, especially where tlie depth is considerable. At the 

 same time, it must be observed that both formulae apply with great exact- 

 ness where the tubes are similar. 



