﻿Collapse 
  of 
  Tabes 
  by 
  External 
  Pressure. 
  

  

  507 
  

  

  not 
  depend 
  upon 
  the 
  elastic 
  properties 
  of 
  the 
  material. 
  

   On 
  the 
  other 
  hand, 
  since 
  it 
  involves 
  m, 
  the 
  latter 
  factor 
  

   will 
  be 
  changed 
  when 
  the 
  limit 
  of 
  elasticity 
  has 
  been 
  ex- 
  

   ceeded 
  : 
  it 
  represents 
  the 
  additional 
  strength 
  of 
  a 
  long 
  tube 
  

   due 
  to 
  the 
  prevention 
  in 
  it 
  of 
  what 
  is 
  known 
  as 
  " 
  anticlastic 
  

   curvature/'' 
  and 
  its 
  value 
  after 
  elastic 
  breakdown 
  cannot 
  be 
  

   easily 
  predicted 
  ; 
  but 
  it 
  is 
  certainly 
  greater 
  than, 
  and 
  differs 
  

   only 
  by 
  a 
  small 
  amount 
  from 
  unity, 
  and 
  may 
  therefore 
  be 
  

   neglected 
  with 
  safety. 
  

  

  From 
  these 
  considerations 
  we 
  are 
  led 
  to 
  the 
  following 
  

   general 
  formula 
  for 
  the 
  collapsing 
  pressure 
  : 
  — 
  

  

  (8) 
  

  

  13,= 
  

  

  ('VD' 
  

  

  d* 
  

  

  where 
  E' 
  is 
  given 
  by 
  the 
  slope 
  of 
  the 
  compressive 
  stress- 
  

   strain 
  diagram 
  at 
  a 
  stress 
  equal 
  to 
  9 
  /$ 
  c 
  . 
  If 
  the 
  latter 
  

  

  diagram 
  is 
  known 
  for 
  the 
  material 
  under 
  consideration, 
  we 
  

   can 
  by 
  this 
  equation 
  readily 
  construct 
  a 
  curve 
  which 
  will 
  

   give 
  estimates 
  of 
  the 
  strength 
  of 
  tubes. 
  

  

  -Fig. 
  2. 
  — 
  Collapsing 
  Pressures 
  of 
  Seamless 
  Brass 
  Tubes. 
  

  

  S 
  

  

  

  

  \ 
  

  

  

  I, 
  II 
  — 
  Compressive 
  Stress-Strain 
  Dia- 
  

   grams 
  for 
  Hard 
  and 
  Annealed 
  Brass. 
  

  

  y 
  

  

  V 
  

  

  

  Ill, 
  IV 
  — 
  Theoretical 
  Curves 
  of 
  Fibre 
  

   Stress 
  for 
  Hard 
  and 
  Annealed 
  Brass. 
  

  

  ( 
  \ 
  

  

  

  

  V 
  — 
  Fibre 
  Stress 
  by 
  Carman 
  s 
  formula 
  

   39 
  —25 
  150 
  000 
  I^X 
  

  

  1 
  ^ 
  

  

  

  

  jpc 
  -U,±U\J 
  } 
  \J\J\J 
  1 
  1 
  . 
  

  

  

  ^/ 
  

  

  

  "v 
  

  

  

  

  

  

  

  

  <r 
  N 
  

  

  V 
  

  

  

  

  

  

  

  

  *^ 
  

  

  

  s**^ 
  

  

  

  

  

  

  

  

  H* 
  

  

  *"*■**■ 
  

  

  

  

  

  

  

  

  

  Diameter 
  io 
  

   FractzonaL 
  

  

  of 
  20 
  Tubs 
  zocuvuzed. 
  40 
  by 
  5o77iickness.60 
  

   0-1 
  Compressive 
  0-2 
  Strain. 
  0-3 
  

  

  The 
  application 
  of 
  these 
  methods 
  to 
  the 
  present 
  problem 
  

   is 
  illustrated 
  in 
  figs. 
  2 
  and 
  3, 
  in 
  which 
  the 
  results 
  of 
  Carman's 
  

   experiments 
  on 
  seamless 
  brass 
  and 
  steel 
  tubes 
  * 
  are 
  compared 
  

  

  * 
  Lor. 
  cit., 
  Tables 
  V. 
  and 
  III. 
  It 
  was 
  thought 
  that 
  Stewart's 
  results, 
  

   which 
  were 
  derived 
  from 
  tests 
  of 
  lap-welded 
  tubes, 
  were 
  less 
  suited 
  to 
  

   the 
  purpose 
  of 
  the 
  present 
  paper. 
  

  

  