﻿Vibration 
  of'^Clamped-Directed^^ 
  Bars. 
  463 
  

  

  Similar 
  transformations 
  may 
  be 
  made 
  in 
  §§ 
  16 
  and 
  18, 
  and 
  

   important 
  results 
  obtained. 
  In 
  each 
  case 
  the 
  maximum 
  

   deflexion 
  is 
  at 
  the 
  directed 
  end. 
  

  

  When 
  the 
  bar 
  is 
  subjected 
  to 
  a 
  force 
  lo 
  per 
  unit 
  length 
  

   acting 
  normally 
  to 
  the 
  j.'-axis, 
  its 
  deflexion 
  curve 
  is 
  

  

  A\'e 
  notice 
  that, 
  for 
  a 
  force 
  concentrated 
  at 
  the 
  end, 
  the 
  

   maximum 
  deflexion 
  of 
  a 
  clamped-directed 
  bar 
  is 
  one-quarter 
  

   of 
  that 
  for 
  a 
  clamped-free 
  bar 
  ; 
  whilst 
  when 
  the 
  force 
  is 
  

   uniformly 
  distributed 
  the 
  ratio 
  is 
  one-third. 
  

  

  Section 
  VII. 
  — 
  Some 
  Experimental 
  Results. 
  

  

  § 
  20. 
  The 
  experiments 
  described 
  in 
  this 
  section 
  were 
  made 
  

   merely 
  to 
  compare, 
  in 
  a 
  few 
  cases, 
  the 
  frequency 
  calculated 
  

   by 
  the 
  methods 
  giyen 
  in 
  this 
  paper 
  with 
  that 
  obtained 
  by 
  

   direct 
  observation 
  . 
  Care 
  was 
  taken 
  that 
  the 
  accuracy 
  should 
  

   reach 
  certain 
  limits. 
  

  

  The 
  composite 
  beams 
  used 
  for 
  the 
  experiments 
  consisted 
  

   of 
  two 
  flat 
  wrought-iron 
  bars, 
  each 
  3*00 
  cms. 
  broad 
  by 
  

   0*315 
  cm. 
  thick, 
  the 
  latter 
  dimension 
  being 
  in 
  the 
  plane 
  of 
  

  

  Fig. 
  7. 
  

  

  m 
  rri 
  

  

  5 
  

  

  vibration. 
  The 
  bars 
  were 
  rigidly 
  connected 
  together 
  at 
  their 
  

   ends 
  by 
  being 
  securely 
  screwed 
  to 
  massive 
  cast-iron 
  blocks, 
  

   as 
  shown 
  in 
  fig. 
  7. 
  The 
  effective 
  length 
  was 
  measured 
  

   between 
  the 
  blocks, 
  and 
  this, 
  as 
  well 
  as 
  the 
  distance 
  between 
  

   the 
  bars, 
  was 
  varied. 
  

  

  A 
  striking 
  feature 
  of 
  the 
  apparatus 
  is 
  the 
  certainty 
  with 
  

   which 
  the 
  end 
  conditions 
  can 
  be 
  relied 
  upon. 
  When 
  this 
  is 
  

   the 
  case, 
  the 
  distance 
  between 
  the 
  bars 
  is 
  immaterial 
  ; 
  some 
  

   of 
  the 
  experiments 
  may, 
  in 
  this 
  respect, 
  be 
  taken 
  as 
  a 
  veri- 
  

   fication 
  of 
  the 
  absolute 
  rigidity 
  of 
  the 
  ends. 
  

  

  § 
  21. 
  The 
  flexural 
  rigidity 
  of 
  a 
  piece 
  of 
  one 
  of 
  the 
  bars 
  

   was 
  determined 
  by 
  supporting 
  it 
  on 
  knife-edges 
  at 
  each 
  end 
  

   of 
  a 
  span 
  of 
  58-1:2 
  cms. 
  (23 
  inches), 
  and 
  applying 
  loads 
  at 
  

   the 
  centre. 
  The 
  observed 
  deflexions 
  are 
  given 
  in 
  the 
  

   following 
  table. 
  

  

  