﻿•464 
  Deflexion 
  and 
  Vibration 
  of 
  Clamped-Directed^^ 
  Bars. 
  

  

  Load 
  in 
  lbs. 
  

  

  Deflexion. 
  

   Inches. 
  

  

  Difference. 
  

   Inches. 
  

  

  

  

  •627 
  

   •580 
  

   •532 
  

   •483 
  

   •433 
  

   •483 
  

   •531 
  

   •580 
  

   •629 
  

  

  •047 
  

   •048 
  

   •049 
  

   •050 
  

   •050 
  

   •048 
  

   •049 
  

   •049 
  

  

  1 
  

  

  2 
  

  

  3 
  

  

  4 
  

  

  3 
  

  

  2 
  

  

  1 
  

  

  

  

  

  Average 
  difference 
  per 
  pound 
  -0488 
  

  

  The 
  average 
  deflexion 
  at 
  the 
  centre 
  was 
  thus 
  found 
  to 
  be 
  

   0'0488 
  inch 
  per 
  pound, 
  correspondino- 
  to 
  a 
  flexural 
  rigidity 
  

   of 
  15*20 
  X 
  10^ 
  grammes 
  weight-cms.^ 
  The 
  value 
  of 
  E 
  here 
  

   involved 
  is 
  the 
  static 
  modulus, 
  but 
  the 
  difl'erence 
  between 
  it 
  

   and 
  the 
  kinetic 
  modulus 
  would 
  be 
  too 
  small 
  to 
  affect 
  the 
  

   calculations. 
  

  

  § 
  22. 
  The 
  results 
  of 
  the 
  experiments 
  on 
  the 
  compound 
  

   bars 
  are 
  given 
  in 
  the 
  following 
  table. 
  In 
  each 
  case 
  vibrations 
  

   took 
  place 
  in 
  a 
  horizontal 
  plane, 
  that 
  is, 
  in 
  the 
  plane 
  of 
  fig. 
  7. 
  

  

  The 
  clamped 
  end 
  was 
  very 
  securely 
  bolted 
  to 
  a 
  large 
  

   lathe-bed 
  in 
  such 
  a 
  manner 
  as 
  to 
  leave 
  no 
  room 
  for 
  doubt 
  as 
  

   to 
  the 
  applicability 
  of 
  the 
  terminal 
  conditions 
  at 
  that 
  end. 
  

  

  1 
  

  

  No. 
  of 
  

   Experiment. 
  

  

  Effective 
  

  

  Length. 
  

  

  cms. 
  

  

  ^ 
  Weight 
  at 
  

  

  Directed 
  end, 
  

  

  gms. 
  

  

  Distance 
  

  

  apart 
  

  

  of 
  bars. 
  

  

  cms. 
  

  

  Observed 
  

   Frequency. 
  

  

  Calculated 
  

   Frequency. 
  

  

  1 
  

  

  114-3 
  

   114-3 
  

   91-5 
  

   91-5 
  

   114-3 
  

   114-3 
  

  

  1604 
  

  

  780 
  

   1604 
  

  

  780 
  

   1604 
  

  

  802 
  

  

  16-5 
  

   16-5 
  

   16-5 
  

   16-5 
  

   6-0 
  

   0-0 
  

  

  1-27 
  

   1-66 
  

  

  1-78 
  

   2^40 
  

   1-26 
  

   1-65 
  

  

  1-26 
  

   1-67 
  

  

  1-78 
  

   2-40 
  

   1-26 
  

   1-65 
  

  

  2 
  

  

  3 
  

  

  4 
  

  

  5 
  

  

  6 
  

  

  

  The 
  last 
  column 
  is 
  calculated 
  from 
  equation 
  (20) 
  ; 
  the 
  

   values 
  are, 
  however, 
  practically 
  identical 
  with 
  those 
  given 
  

  

  