456 



Royal Society : — 



As an example of the application of the foregoing method to the 

 purposes of calculation, let the case of the Britannia Bridge be taken, 

 and let the large span be supposed to be divided into five, and the 

 small span into three equal parts, and let the moments of inertia of 

 the sections and loads per unit of length be supposed constant within 

 each part and equal to their mean values. 

 1 2 



A b' 



a' A 



a 



b 



d A 



We have then the following data : — 

 In spans (1 2) and (1 0), 







a = 92, 



b = 2a, 



c= 3a, 



d=4a, 



l=5a, 





a' = 76'7, 



b=2a, 



l' = 3a; 





1 



1 

 62 1520E' 



1 



1 

 64 1664E' 



1 



Cl 1132E' 



Ca 1746E' 



Cfl 1857E' 





1 



1 



1 

 63 720E' 







Cl 1100E' 



Ca 960E ' 





^ = 2-89, ju 2 = 3-31, 

 i"/ = 2-84, 

 T + T' = 0, 



^3 = 3-57, 

 A*,' = 2-67, 



^=3-49, 

 M 3 ' = 2'32; 

 E= 1440000 



yu 6 =3*65, 



1. 



In span (2 



1), 









0=92, 



b = 2a, 



c=3a, 



d= 4a, 



l=5a ; 



1 

 e, = 



1 



1 

 63 1746E' 



€ - l 



64 1520E' 



1 



1 1857E 



° 2 1664E' 



e& 1132E ; 



^ = 3-65, 



iu 2 =3-49, 



^=3-57, 



iu 4 =3-31, 



A' 5 = 2-89; 



and, from sym 



metry of loading, T = - 1 = ■ 



-0-002035. 





Applying equations (30) and (32) to spans (1.0) and (lj.2) respec- 

 tively and eliminating T and T' by adding them, we obtain 



0-1888^ + 0-04827^- 10481 =0 ; 

 and applying equation 32 to span (2 1), 



0-04827^ + 0-08765^- 5420=0, 

 whence ^=46206, 2 = 36387. 



Taking these values of <f> and <£ 2 , and applying equation (33) to 

 the calculation of the deflection at the middle of the large span, 



Y=0-375ft.=4-5 inches. 



If, now, the values of <p v 2 , and Y be calculated from equations 

 (26) and (19), on the supposition that the moments of inertia of 

 the section and the loads are constant throughout each span and 

 equal to their mean values, they are 



^=47030, 2 =3561O, Y=4'62, 



which are almost identical with the values ascertained by Mr. Pole. 



