﻿and 
  Deflection 
  of 
  Braced 
  Girders. 
  51 
  

  

  =7>«pW 
  + 
  *{R 
  p 
  -R 
  p+1 
  + 
  . 
  . 
  . 
  +(-l)ff-pR 
  N 
  }. 
  

   Let 
  p 
  be 
  greater 
  than 
  m 
  ; 
  then 
  

  

  + 
  tB 
  , 
  vP- 
  m 
  {l- 
  v 
  + 
  v 
  2 
  — 
  . 
  . 
  . 
  4.(-l)N- 
  P 
  i 
  v 
  N-p| 
  

   =p 
  ap 
  W 
  + 
  1 
  — 
  { 
  A 
  V-* 
  + 
  BV-™- 
  1 
  + 
  ( 
  - 
  1) 
  x-p 
  (A'fu 
  n+l 
  + 
  Bty»») 
  } 
  

   =j% 
  W 
  + 
  f 
  — 
  (A'«p— 
  + 
  Bu 
  m 
  -o+ 
  l 
  ) 
  - 
  ( 
  - 
  iy-Pt 
  . 
  i 
  w 
  ^ 
  

  

  J. 
  "t~ 
  w 
  J^l 
  

  

  = 
  -(N-P 
  + 
  i)^W+ 
  T 
  ^(AV-»+B 
  , 
  tt 
  Bl 
  -p+ 
  1 
  ) 
  

   r 
  ' 
  JN 
  1 
  + 
  w 
  x 
  y 
  

  

  rn 
  t 
  

   = 
  — 
  (N~p-f 
  i) 
  ^*W 
  + 
  ^ 
  (Aw 
  wl 
  -p+ 
  l 
  H-BwP- 
  m 
  ) 
  

  

  v 
  r 
  7 
  JN 
  1 
  + 
  w 
  y 
  

  

  — 
  i*W 
  r 
  (t|»»— 
  P+l 
  — 
  MP— 
  »») 
  # 
  

  

  When 
  p<m 
  + 
  l 
  we 
  have 
  by 
  symmetry 
  

  

  77 
  f 
  

  

  Similarly 
  

  

  =p 
  cp 
  W-s(R 
  p 
  -R 
  p+1 
  + 
  . 
  . 
  .). 
  

   We 
  have 
  the 
  same 
  summation 
  as 
  before, 
  and 
  when 
  p>m, 
  

  

  T 
  cp 
  =p 
  ep 
  W- 
  =-£- 
  (AV-^B^-p^ 
  1 
  ) 
  + 
  (-1)*-* 
  . 
  iW~ 
  

  

  ItW 
  JN 
  

  

  - 
  |^ 
  5 
  w 
  - 
  j4^ 
  (A 
  V-» 
  + 
  B 
  V 
  l 
  -p 
  +1 
  ) 
  

  

  = 
  \^ 
  sW 
  - 
  -4-(A^-< 
  J 
  + 
  1 
  + 
  Bu»- 
  m 
  ) 
  + 
  isW 
  ~ 
  (*■*-»« 
  -«p-»). 
  

   2jN 
  1+w 
  1— 
  .m 
  v 
  -- 
  — 
  ' 
  

  

  We 
  at 
  once 
  deduce 
  from 
  this 
  the 
  value 
  of 
  T 
  . 
  for 
  the 
  case 
  of 
  

   p< 
  m 
  + 
  1 
  ; 
  and 
  all 
  the 
  other 
  tensions 
  can 
  be 
  written 
  down 
  

   with 
  the 
  help 
  of 
  equations 
  (5) 
  and 
  (6), 
  the 
  results 
  being 
  as 
  

   follows 
  in 
  terms 
  of 
  A 
  and 
  B 
  : 
  — 
  

   p 
  < 
  m 
  + 
  1 
  : 
  — 
  

  

  T 
  fl 
  ,= 
  - 
  (p- 
  h)^tW+ 
  JL(Ati—p+ 
  l 
  + 
  Bu<>- 
  m 
  

   JN 
  1 
  4- 
  it 
  

  

  E2 
  

  

  