﻿722 
  

  

  Prof. 
  E. 
  L. 
  Hancock 
  : 
  Results 
  of 
  Tests 
  of 
  

  

  It 
  is 
  seen 
  that 
  the 
  curve 
  is 
  an 
  ellipse 
  with 
  the 
  unit 
  tensile 
  

   (or 
  compressive) 
  stress 
  as 
  one 
  semi-axis 
  and 
  the 
  unit 
  shear 
  

   as 
  the 
  other 
  semi-axis. 
  If 
  the 
  shearing 
  strength 
  equals 
  the 
  

  

  Fig. 
  1. 
  — 
  Results 
  of 
  Tests 
  of 
  Materials 
  subjected 
  to 
  Combined 
  Stresses. 
  

  

  1-0- 
  

  

  tensile 
  strength, 
  the 
  curve 
  becomes 
  a 
  circle 
  ; 
  this, 
  however, 
  

   is 
  not 
  generally 
  the 
  case. 
  The 
  equation 
  of 
  the 
  ellipse 
  may 
  

   he 
  derived 
  as 
  follows 
  : 
  — 
  

  

  Letp 
  be 
  the 
  fibre 
  stress 
  in 
  tension 
  or 
  compression. 
  

   „ 
  p 
  s 
  „ 
  „ 
  „ 
  shear. 
  

  

  „ 
  b 
  „ 
  „ 
  „ 
  at 
  the 
  elastic 
  limit 
  in 
  tension. 
  

   55 
  a 
  55 
  i5 
  55 
  j? 
  >> 
  ?j 
  snear. 
  

  

  „ 
  Mj 
  be 
  the 
  bending-moment 
  in 
  flexure. 
  

  

  M, 
  

  

  twisting-moment. 
  

  

  