﻿and 
  Deflection 
  of 
  Braced 
  Girders. 
  53 
  

  

  Let 
  us 
  now 
  calculate 
  the 
  deflection 
  of 
  the 
  girder 
  at 
  a 
  point 
  

   distant 
  k 
  bays 
  from 
  A 
  and 
  I 
  bays 
  from 
  B. 
  The 
  deflection 
  is 
  

   by 
  Maxwell's 
  formula 
  

  

  Wtepq 
  + 
  'Rjtegri 
  + 
  B 
  3 
  2^r 
  2 
  + 
  (28) 
  

  

  and 
  to 
  find 
  the 
  q's 
  we 
  have 
  only 
  to 
  substitute 
  k 
  and 
  I 
  respec- 
  

   tively 
  for 
  m 
  and 
  n 
  in 
  the 
  expression 
  for 
  the 
  p's. 
  Let 
  us 
  first 
  

   deal 
  with 
  the 
  case 
  in 
  which 
  k 
  < 
  m 
  4- 
  1 
  ; 
  when 
  we 
  have 
  found 
  

   the 
  deflection 
  for 
  this 
  portion 
  of 
  the 
  girder 
  the 
  deflection 
  for 
  

   the 
  remainder 
  can 
  be 
  obtained 
  by 
  symmetry, 
  

  

  %=^o^* 
  2 
  {3^^+ 
  i, 
  )(4 
  +i 
  ' 
  / 
  ) 
  

  

  k 
  

  

  H 
  

  

  + 
  ,X(^- 
  1 
  ') 
  (N 
  " 
  p) 
  s 
  + 
  (N 
  - 
  m)3 
  S 
  

  

  (Yi 
  \ 
  Jc 
  'Win 
  I 
  

  

  where 
  single 
  dashes 
  indicate 
  that 
  the 
  term 
  in 
  question 
  is 
  to 
  be 
  

   omitted 
  if 
  n 
  is 
  even, 
  and 
  double 
  dashes 
  that 
  it 
  is 
  to 
  be 
  omitted 
  

   if 
  I 
  is 
  even. 
  Performing 
  the 
  summations 
  indicated 
  we 
  find 
  

   that 
  

  

  + 
  {\t 
  2 
  + 
  fjLS 
  2 
  )^ 
  (2W"-n'-n"j; 
  

   and 
  the 
  last 
  term 
  may 
  be 
  written 
  

  

  Now 
  when 
  p<k 
  + 
  l 
  

  

  Zeqr 
  p 
  = 
  (-1)p+V'+ 
  (-l) 
  K 
  ' 
  p 
  /> 
  {I 
  -(-!)*} 
  (W 
  + 
  *"■), 
  

   and 
  when 
  p>k 
  

  

  