﻿Materials 
  subjected 
  to 
  Combined 
  Stresses. 
  72.1 
  

  

  amount. 
  It 
  holds 
  that 
  Poisson's 
  ratio 
  (the 
  ratio 
  of 
  

   lateral 
  contraction 
  to 
  longitudinal 
  deformation) 
  is 
  025. 
  

   Using 
  this 
  ratio 
  the 
  following 
  formula 
  results: 
  

  

  ?=3/8p±5/8yy 
  + 
  4pJ, 
  .... 
  (2) 
  

  

  where 
  the 
  symbols 
  have 
  the 
  same 
  meaning 
  as 
  before. 
  

   The 
  values 
  of 
  Poisson's 
  ratio 
  for 
  various 
  materials 
  as 
  

   determined 
  from 
  tests 
  are 
  : 
  

  

  Steel, 
  hard 
  0-295 
  

  

  „ 
  soft 
  0-299 
  

  

  Iron 
  0*277 
  

  

  Brass 
  0'357 
  

  

  Lead 
  0-375 
  

  

  It 
  will 
  be 
  seen 
  that 
  these 
  values 
  differ 
  considerably 
  

   from 
  the 
  value 
  0*25, 
  so 
  that 
  the 
  formula 
  can 
  hardly 
  

   be 
  expected 
  to 
  furnish 
  correct 
  results. 
  This 
  formula 
  

   is 
  in 
  use 
  to 
  a 
  considerable 
  extent 
  in 
  continental 
  

   Europe. 
  

  

  (3) 
  Maximum 
  Shear 
  Theory. 
  — 
  The 
  third 
  theory, 
  and 
  one 
  

   but 
  little 
  used, 
  is 
  that 
  the 
  material 
  yields 
  when 
  the 
  

   shear 
  on 
  any 
  element 
  reaches 
  a 
  maximum. 
  This 
  leads 
  

   to 
  the 
  relation 
  : 
  

  

  q=ll2Vf 
  + 
  Itf, 
  (3) 
  

  

  where 
  q 
  8 
  is 
  the 
  greatest 
  shear 
  on 
  any 
  element. 
  It 
  

   will 
  be 
  seen 
  from 
  fig. 
  1 
  and 
  fig. 
  2 
  that 
  this 
  formula 
  

   fits 
  the 
  results 
  of 
  all 
  the 
  tests 
  much 
  more 
  exactly 
  than 
  

   either 
  of 
  the 
  others. 
  

  

  Tests 
  made 
  by 
  the 
  writer, 
  by 
  Mr. 
  J. 
  J. 
  Guest, 
  and 
  by 
  

   Mr. 
  W. 
  A. 
  Scoble 
  (see 
  note 
  *) 
  have 
  been 
  used 
  in 
  making- 
  

   fig. 
  1. 
  The 
  tests 
  made 
  by 
  Mr. 
  Guest 
  and 
  Mr. 
  Scoble 
  were 
  

   made 
  by 
  taking 
  the 
  yield-point 
  as 
  a 
  basis, 
  while 
  those 
  made 
  

   by 
  the 
  writer 
  were 
  made 
  by 
  taking 
  the 
  elastic 
  limit 
  as 
  a 
  

   basis. 
  Examination 
  of 
  fig. 
  1 
  shows 
  very 
  little 
  difference 
  as 
  

   to 
  which 
  is 
  taken 
  as 
  a 
  basis. 
  The 
  convenience 
  of 
  locating 
  

   the 
  yield-point 
  suggests 
  an 
  advantage 
  in 
  its 
  favour. 
  

  

  * 
  u 
  

  

  Effect 
  of 
  Combined 
  Stresses 
  on 
  the 
  Elastic 
  Properties 
  of 
  Steel.*' 
  

   E. 
  L. 
  Hancock, 
  Am. 
  Soc. 
  Test. 
  Mat. 
  vol. 
  v. 
  1905 
  ; 
  vol. 
  vi. 
  1906 
  ; 
  vol. 
  vii. 
  

   1907. 
  Also 
  Phil. 
  Mag-. 
  Feb. 
  & 
  Oct. 
  1906 
  and 
  Feb. 
  1908. 
  J. 
  J. 
  Guest, 
  

   Phil. 
  Mag. 
  July 
  1900, 
  Proc. 
  Physical 
  Soc. 
  of 
  London, 
  Sept. 
  1900. 
  W. 
  A. 
  

   Scoble, 
  Phil. 
  Mag-. 
  Dec. 
  1907. 
  

  

  Phil. 
  Mag. 
  S. 
  6. 
  Vol. 
  16. 
  No. 
  95. 
  Nov. 
  1908. 
  3 
  B 
  

  

  