30 The Tay Bridge. 



of train, and area of upper half of diagonals of leeward girder, 

 3800 square feet, which at 1 lb. per square foot wind pres- 

 sure gives 3800 lbs., or 1*696 tons. This will exist as a 

 horizontal shearing force on the upper story of the pier. 

 Lower down it becomes slightly larger, owing to the pres- 

 sure on the columns themselves and their bracing, but the 

 increase will be insignificant; by neglecting it we shall 

 simplify calculation, and the error will be very slight, and 

 favourable to the structure. 



The braces are so constructed as to act in tension 

 only; those, therefore, that slope downward away from 

 the wind will be altogether inoperative, and may be 

 omitted in our investigation. We will further suppose 

 that all the braces are carefully adjusted, so that each 

 does its fair share of work. It can then be shown that 

 under a given small lateral displacement of the structure 

 that the elongation of the braces in the diagonal faces of the 

 hexagon, the panels of which average 11 feet high and 8 feet 

 wide, will bear to that of those in the transverse faces, the 

 panels of which are 11 feet high and 10 feet wide, the ratio 

 of 12 to 19, and that, therefore, when the diagonals in the 

 transverse faces experience a tension of 19, those in the 

 diagonal faces endure only 12. Let, now, x equal the 

 tension on the diagonals in the transverse faces, then }|* 

 will be that of those in the diagonal ones. Thus we can 

 state the subjoined equation where x will be the tension for 

 1 lb. wind pressure on the structure and train. 



Taking resolved parts of all the tensions horizontally at 

 right angles to the bridge, we have — 



10 12 8 



2 x j^x x 4 X-nrX j3^-# = 3800 lbs. 



Or, 



x = 1347 lbs. 



Now let us examine the construction of the braces. They 

 consist of flat bars of wrought-iron, 4 J inches wide and half 

 an inch thick, secured at each end by a bolt 1J inches in 

 diameter, which appears to have fitted tightly into a hole 

 in the flat bar and loosely in a pair of lugs cast on the 

 column between which the end of the bar was placed. 

 Such a joint might break by shearing the bolt, and such 

 fracture would take place under a pull of 2 X (1 J) 2 X '7854 

 X 50,000 = 99,400 lbs. = 44 tons, nearly; or it may give way 

 by tearing the metal on each side of the bolt hole ; the 



