﻿and 
  Defection 
  of 
  Braced 
  Girders. 
  49 
  

  

  Combining 
  this 
  with 
  (12) 
  we 
  got 
  

  

  A 
  , 
  =B 
  i±»w. 
  

  

  1— 
  u 
  2 
  ! 
  

  

  B<=A-I±^ 
  f 
  * 
  " 
  ' 
  • 
  (19) 
  

   1— 
  u 
  2J 
  

  

  from 
  (17) 
  and 
  (18) 
  Ej(2-f 
  /3) 
  + 
  R 
  2 
  + 
  T 
  a=0, 
  

  

  .-. 
  T 
  a=Au 
  m 
  + 
  Bv 
  m 
  (20) 
  

  

  Substituting 
  this 
  value 
  of 
  T 
  in 
  (17) 
  we 
  get 
  

  

  1 
  1 
  n 
  

  

  - 
  (1-t-u)— 
  u 
  = 
  (f> 
  . 
  and 
  - 
  (1 
  + 
  v) 
  — 
  v=yfr, 
  

  

  so 
  that 
  

  

  <£ 
  — 
  uyjr=l 
  — 
  u 
  ; 
  

  

  then 
  this 
  equation 
  may 
  be 
  written 
  

  

  A^u 
  m 
  + 
  1 
  + 
  B^v 
  m 
  =-iW^(l+u). 
  . 
  . 
  (21) 
  

  

  To 
  get 
  another 
  equation 
  for 
  A 
  and 
  B 
  we 
  must 
  sum 
  the 
  

   series 
  in 
  equation 
  (16) 
  ; 
  the 
  result 
  is 
  

  

  i 
  1 
  ( 
  f,\m 
  

  

  - 
  {Au™ 
  + 
  Bv 
  m 
  )=p 
  W-(-l) 
  m 
  A 
  

  

  a 
  

  

  1 
  + 
  u 
  

  

  _(- 
  irB 
  ^ipL% 
  ( 
  _ 
  irA 
  > 
  M 
  i-;-»)''- 
  1 
  

  

  V 
  X 
  1+17 
  V 
  1 
  + 
  U 
  

  

  + 
  ( 
  - 
  l) 
  m 
  B'v 
  1 
  ~(-^) 
  n 
  ~ 
  1 
  _ 
  / 
  _ 
  Y) 
  n 
  - 
  (Mu 
  n 
  + 
  B 
  V), 
  

  

  l 
  + 
  -y 
  a 
  

  

  (22) 
  

  

  which 
  reduces 
  to 
  

  

  A 
  / 
  n 
  W 
  D 
  C<b—TlrU 
  2n 
  + 
  1 
  m+(-l) 
  N 
  W) 
  

  

  Ai?"+ 
  (— 
  l) 
  N 
  Br™ 
  = 
  <! 
  r 
  /_ 
  v 
  n 
  V 
  N 
  ; 
  I 
  

  

  1 
  + 
  u 
  W 
  

  

  X 
  ^+(-l)^ 
  N 
  +i 
  2* 
  ' 
  ' 
  

   and 
  solving 
  equations 
  (21) 
  and 
  (22) 
  we 
  get 
  

  

  f 
  0(l-tt»)(0 
  + 
  ^K 
  +1 
  ) 
  n 
  -) 
  l 
  + 
  ii 
  W 
  

  

  A 
  -| 
  (l- 
  W 
  )(<^ 
  + 
  A/ru 
  N 
  + 
  1 
  ) 
  ^N^ 
  J^-^+i 
  2 
  ;l 
  ° 
  ; 
  

  

  ^_ 
  f 
  ^(l-M«)(0 
  + 
  ^rtt» 
  +1 
  )u 
  w+ 
  1 
  n 
  \ 
  (l+u)u 
  m 
  W 
  

   ■ 
  b 
  "" 
  \ 
  (l-u)(4> 
  + 
  fu^+ 
  l 
  ) 
  + 
  N 
  J 
  ^-f^N+i 
  2 
  ' 
  ^ 
  4 
  ) 
  

   Pfo'Z. 
  1%. 
  S. 
  D. 
  Vol 
  4.5. 
  No. 
  272. 
  Jan. 
  1898. 
  E 
  

  

  