﻿and 
  Deflection 
  of 
  Braced 
  Girders. 
  59 
  

  

  with 
  (4J 
  ) 
  the 
  value 
  of 
  /j, 
  must 
  be 
  considerably 
  reduced. 
  Let 
  

   us 
  suppose 
  the 
  diagonal 
  members 
  to 
  be 
  of 
  the 
  same 
  section 
  as 
  

   the 
  horizontals, 
  keeping 
  the 
  latter 
  of 
  the 
  same 
  section 
  as 
  

   before 
  ; 
  then 
  

  

  and 
  the 
  four 
  successive 
  values 
  of 
  (/-ts 
  2 
  — 
  |X^)^yJE 
  become 
  

   respectively 
  2*2, 
  3*8, 
  4-9, 
  5-4 
  ; 
  

  

  /3=-96, 
  u=— 
  39, 
  v=-2-57, 
  <£ 
  = 
  2'8, 
  i|r 
  = 
  -3-7, 
  <b=1-83, 
  

  

  and 
  the 
  four 
  successive 
  values 
  of 
  v(l 
  + 
  u)(l 
  — 
  u 
  x 
  ) 
  (1 
  — 
  w^ofE 
  

   are 
  1*5, 
  *9, 
  1*2, 
  and 
  1*1. 
  

  

  Here 
  the 
  expression 
  (41) 
  gives 
  a 
  comparatively 
  good 
  

   result. 
  

  

  It 
  is 
  clear 
  that 
  we 
  ought 
  not 
  to 
  correct 
  (41) 
  by 
  introducing 
  

   a 
  value 
  for 
  moment 
  of 
  inertia 
  of 
  web, 
  for 
  this 
  would 
  be 
  an 
  

   alteration 
  in 
  the 
  wrong 
  direction. 
  

  

  The 
  expression 
  co 
  may 
  be 
  written 
  

  

  2^ 
  1 
  J 
  + 
  qVl-tJ 
  (l-^) 
  2 
  . 
  

  

  so 
  it 
  is 
  easy 
  to 
  estimate 
  the 
  importance 
  of 
  the 
  term 
  involving 
  

   co 
  provided 
  that 
  u 
  is 
  not 
  nearly 
  equal 
  to 
  —1. 
  

  

  In 
  the 
  limiting 
  case 
  in 
  which 
  j>=co 
  we 
  get 
  the 
  frame 
  

  

  \/\/\/ 
  \/\/ 
  

  

  we 
  have 
  a=0, 
  £=0, 
  u=v= 
  — 
  I; 
  when 
  N 
  is 
  even 
  « 
  = 
  0, 
  

  

  , 
  „ 
  . 
  ,, 
  1 
  

  

  mmmm 
  i0 
  ^ 
  w 
  -2(N 
  + 
  l)' 
  -"""" 
  

  

  

  v(l 
  + 
  w)(l-^)(l- 
  

  

  -vy)a> 
  

  

  has 
  the 
  following 
  values 
  : 
  — 
  

  

  

  N 
  even 
  and 
  x 
  even 
  . 
  . 
  . 
  

  

  o, 
  

  

  N 
  even 
  and 
  x 
  odd 
  . 
  . 
  . 
  

  

  2(kt* 
  + 
  jJLS*), 
  

  

  N 
  odd 
  and 
  x 
  even 
  . 
  . 
  . 
  

  

  bSi^+^. 
  

  

  N 
  odd 
  and 
  x 
  odd 
  .... 
  

  

  j^Jl 
  (**+*•»■ 
  

  

  