﻿Materials 
  subjected 
  to 
  Combined 
  Stresses. 
  723 
  

  

  Then 
  from 
  the 
  curve 
  

  

  SM- 
  1 
  w 
  

  

  Knowing 
  a 
  and 
  6 
  from 
  the 
  results 
  of 
  tests 
  of 
  the 
  material 
  in 
  

   simple 
  tension 
  and 
  torsion 
  and 
  either 
  p 
  or 
  p 
  g 
  , 
  the 
  other 
  may 
  

   be 
  determined. 
  

  

  The 
  equivalent 
  twisting-moment 
  for 
  a 
  shaft 
  subjected 
  to 
  

   combined 
  bending 
  and 
  twisting, 
  derived 
  from 
  (4), 
  is 
  given 
  

   by 
  the 
  relation 
  

  

  M^ 
  = 
  Mi 
  + 
  (^)M?, 
  (5) 
  

  

  where 
  M 
  e 
  is 
  the 
  equivalent 
  twisting-moment. 
  

  

  If 
  the 
  elastic 
  limit 
  in 
  shear 
  be 
  taken 
  as 
  one-half 
  of 
  the 
  

   elastic 
  limit 
  in 
  tension, 
  (5) 
  becomes 
  

  

  M* 
  = 
  Ml 
  + 
  M?, 
  

  

  (6) 
  

  

  which, 
  lacking 
  a 
  constant 
  factor, 
  is 
  the 
  formula 
  derived 
  

   by 
  considering 
  the 
  maximum 
  shear 
  theory 
  to 
  hold. 
  This 
  

   assumption 
  that 
  a 
  equals 
  one-half 
  of 
  b 
  is 
  hardly 
  borne 
  out 
  by 
  

   the 
  results 
  of 
  tests 
  that 
  have 
  been 
  made, 
  as 
  is 
  shown 
  by 
  the 
  

   following; 
  table 
  : 
  — 
  

  

  Material. 
  

  

  Steel 
  Tubing 
  21000 
  

  

  Nickel 
  Steel 
  76500 
  

  

  Mild 
  Carbon 
  Steel 
  47000 
  

  

  Steel 
  (Scoble) 
  64600 
  

  

  Carbon 
  Steel 
  35500 
  

  

  Rivet 
  Steel 
  38900 
  

  

  Nickel 
  Steel 
  56000 
  

  

  Steel 
  Tubing 
  17000 
  

  

  „ 
  28000 
  

  

  „ 
  20000 
  

  

  ~3 
  

  

  10500 
  

   38000 
  

   30400 
  

   29170 
  

   24400 
  

   23400 
  

   36000 
  

   11500 
  

   16000 
  

   12000 
  

  

  b/2. 
  

  

  10500 
  

   38200 
  

   23300 
  

   32300 
  

   17700 
  

   19400 
  

   28000 
  

   8500 
  

   14000 
  

   10000 
  

  

  a 
  <l- 
  

  

  

  

  Value 
  of 
  

   4a 
  2 
  

   b 
  2 
  ' 
  

  

  1-00 
  

   •98 
  

   1-66 
  

   •81 
  

   1-84 
  

   1-44 
  

   1-66 
  

   1-82 
  

   1-30 
  

   1-44 
  

  

  B2 
  

  

  