﻿724 
  lests 
  of 
  Materials 
  subjected 
  to 
  Combined 
  Stresses. 
  

  

  An 
  attempt 
  has 
  been 
  made 
  in 
  fig. 
  2 
  to 
  show 
  the 
  difference 
  

   in 
  the 
  shearing 
  strength 
  given 
  by 
  the 
  formulae 
  representing 
  

   theories 
  (1), 
  (2), 
  and 
  (3), 
  and 
  expressed 
  in 
  equations 
  (1) 
  ? 
  

   (2), 
  and 
  (5). 
  The 
  material 
  under 
  consideration 
  had 
  an 
  

   elastic 
  limit 
  in 
  tension 
  of 
  7G500 
  lbs. 
  per 
  sq. 
  inch 
  and 
  an 
  

   elastic 
  limit 
  in 
  torsion 
  of 
  38000 
  lbs. 
  per 
  sq. 
  inch. 
  Equa- 
  

   tion 
  (5), 
  the 
  equation 
  of 
  the 
  curve 
  in 
  fig. 
  1, 
  gives 
  the 
  proper 
  

   elastic 
  limit 
  in 
  shear 
  (the 
  elastic 
  limit 
  in 
  tension 
  was 
  assigned 
  

   in 
  all 
  cases), 
  while 
  (1) 
  and 
  (2) 
  give 
  an 
  elastic 
  limit 
  much 
  too 
  

   large. 
  Nearly 
  all 
  values 
  in 
  shear 
  given 
  by 
  (1) 
  and 
  (2) 
  are 
  

   larger 
  than 
  those 
  obtained 
  from 
  tests. 
  This 
  means 
  that 
  the 
  

   corresponding 
  bending- 
  or 
  twisting-moment 
  will 
  be 
  too 
  small 
  

   and 
  if 
  used 
  in 
  design 
  may 
  lead 
  to 
  disaster. 
  

  

  Fig. 
  2. 
  — 
  Curves 
  showing 
  Shear 
  as 
  given 
  by 
  the 
  Formulae. 
  

   8 
  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  *. 
  

  

  

  

  

  \m) 
  

  

  

  

  

  2 
  

  

  

  

  \ 
  

  

  \(2) 
  

  

  

  

  

  

  

  

  \(3) 
  

  

  

  k 
  

  

  

  

  to 
  

  

  <5 
  

  

  

  

  

  

  \ 
  

  

  

  

  1? 
  

  

  

  

  1 
  

  

  

  \ 
  

  

  

  \ 
  

  

  <* 
  

  

  

  

  

  

  \ 
  

  

  

  \ 
  

  

  I 
  2 
  3 
  4 
  5 
  6 
  

  

  f% 
  /N 
  TEN-THOUSfi/VD 
  LBS. 
  P£/f 
  SQ./A? 
  

  

  (1) 
  Maximum 
  Stress 
  Theory 
  :—q= 
  1/2 
  (p± 
  <s/p 
  2 
  +4p 
  2 
  ). 
  

  

  (2) 
  Maximum 
  Strain 
  Theory 
  :—q=3/8p± 
  5/8 
  */p*+ift. 
  

  

  (3) 
  Maximum 
  Shear 
  Theory:— 
  q= 
  V 
  p 
  2 
  + 
  — 
  p 
  2 
  

  

  a 
  2 
  L 
  "' 
  

  

  The 
  last 
  agrees 
  with 
  the 
  results 
  of 
  tests. 
  

  

  In 
  conclusion, 
  it 
  may 
  be 
  said 
  that 
  both 
  the 
  maximum 
  

   stress 
  theory 
  and 
  the 
  maximum 
  strain 
  theory 
  give 
  an 
  equi- 
  

   valent 
  moment 
  that 
  is 
  too 
  small. 
  They 
  should 
  not, 
  therefore, 
  

  

  