﻿Collapse 
  of 
  Tubes 
  by 
  External 
  Pressure. 
  509 
  

  

  maxima, 
  only 
  obtainable 
  under 
  ideally 
  perfect 
  conditions 
  *. 
  

   It 
  is 
  remarkable 
  that 
  the 
  actual 
  values 
  obtained 
  from 
  tests 
  

   on 
  new 
  tube 
  (in 
  cold 
  water) 
  are 
  so 
  largely 
  in 
  excess 
  of 
  these, 
  

   in 
  spite 
  of 
  the 
  effects 
  of 
  imperfect 
  circularity 
  and 
  uniformity 
  

   of 
  thickness, 
  which 
  Professor 
  Slocum 
  f 
  has 
  shown 
  to 
  be 
  

   important. 
  

  

  Fig. 
  3. 
  — 
  Collapsing- 
  Pressures 
  of 
  Seamless 
  Steel 
  Tubes. 
  

  

  Diameter 
  10 
  

   Fractional 
  

  

  I, 
  II 
  — 
  Compressive 
  Stress-Strain 
  Dia- 
  

   grams 
  for 
  Hard 
  and 
  Annealed 
  Steel. 
  

   HE, 
  IV— 
  Theoretical 
  Curves 
  of 
  Fibre 
  

   Stress 
  for 
  Hard 
  and 
  Annealed 
  Steel. 
  

   V 
  — 
  Fibre 
  Stress 
  by 
  Carman's 
  formula 
  

  

  $,, 
  = 
  50,200,000 
  (j)'- 
  

  

  20 
  Ticbe 
  30du/ideal 
  40 
  by 
  soThicJwessQQ 
  

   O-l 
  Compressive- 
  0-2 
  Strain,. 
  0-3 
  

  

  Exactly 
  similar 
  considerations 
  apply 
  to 
  steel 
  tubes, 
  and 
  

   are 
  illustrated 
  in 
  fig. 
  3. 
  Curve 
  V 
  is 
  drawn 
  to 
  represent 
  the 
  

   equation 
  

  

  t 
  2 
  

  

  /? 
  = 
  25,100,000 
  

  

  (7) 
  

  

  the 
  numerical 
  coefficient 
  being 
  an 
  estimate 
  drawn 
  by 
  Carman 
  

   from 
  his 
  experimental 
  results. 
  In 
  constructing 
  the 
  theoretical 
  

   Curves 
  III 
  and 
  IV 
  a 
  more 
  representative 
  value 
  for 
  E 
  has 
  

   been 
  taken. 
  We 
  are 
  confronted 
  by 
  the 
  difficulty 
  that 
  no 
  

   stress-strain 
  diagrams 
  were 
  published 
  by 
  Carman 
  for 
  the 
  

   materials 
  of 
  his 
  tests. 
  The 
  want 
  is 
  more 
  seriously 
  felt 
  in 
  

   connexion 
  with 
  this 
  figure, 
  owing 
  to 
  the 
  greater 
  diversity 
  in 
  

   quality 
  of 
  steels 
  as 
  compared 
  with 
  brasses, 
  and 
  more 
  especially 
  

  

  * 
  Flue-tubes 
  may 
  be 
  overheated 
  if 
  the 
  water-level 
  is 
  allowed 
  to 
  fall 
  

   imduly 
  ; 
  and 
  although, 
  they 
  may 
  be 
  saved 
  from 
  immediate 
  collapse 
  if 
  

   the 
  pressure 
  is 
  relieved, 
  the 
  annealing 
  thus 
  induced 
  may, 
  according 
  to 
  

   the 
  above 
  theory, 
  reduce 
  their 
  fitness 
  for 
  future 
  service, 
  in 
  a 
  way 
  which 
  

   has 
  been 
  overlooked. 
  

  

  t 
  " 
  The 
  Collapse 
  of 
  Tubes 
  by 
  External 
  Pressure," 
  Engineering, 
  Jan. 
  8, 
  

   1009. 
  

  

  Phil 
  Mag. 
  S. 
  6. 
  Vol. 
  26. 
  No. 
  153. 
  Sept. 
  1913. 
  2 
  M 
  

  

  