of  Loaded  and  Unloaded  Bars. 
369 
ctly  in  tenths,  further  interpolation  is  required  for  accuracy. 
s    may    easily    be    obtained   graphically  by  plotting   the 
exactly 
This   may   easily 
values  of  ft  given  by  the  curves  for  the  required  position  of 
the  load. 
In  the  tables  I  is  the  effective  length  of  the  bar,  and  a  the 
distance  of  the  centre  of  gravity  of  the  load  from  either  end. 
The  numbers  on  the  curves  represent  the  ratio  of  mass  of 
load  to  that  of  effective  length  of  bar. 
Table  I. 
Values  of  /3  for  Bars  Supported  at  Each  End, 
Ratio. 
Mass  of  Load. 
Val 
ues  of  j3  for  different  positions  of  Load. 
Mass  of  Bar. 
a/l=-l. 
all=-2. 
a/l=w3. 
a/l=-4. 
a/l='5. 
01 
95-56 
90-98 
85-91 
82-03 
79-80 
02 
93-74 
85-20 
76-71 
70-85 
67-73 
0-3 
91-95 
80-02 
69-22 
62-35 
58-99 
0-4 
90-21 
75-36 
6301 
55-68 
5231 
0-5 
88-69 
71-17 
57-81 
50-30 
4703 
0-6 
86-86 
67-39 
5391 
45-86 
42-74 
0-7 
85-24 
6396 
49-56 
4215 
39-18 
0-8 
8367 
60-84 
46-25 
38-99 
36-17 
0-9 
82-15 
57-99 
43-35 
36-27 
33-60 
10 
80-66 
55-39 
40-78 
33-91 
31-38 
§  23.  Bar  Clamped  at  Both  Ends. — The  values  of  /3  are 
here  found  from  the  last  equation  of  §  19.  They  are  given 
in  Table  II.  and  fig.  2. 
Table  II. 
Values  of  ft  for  Clamped-Clamped  Bar. 
Ratio. 
Mass  of  Load 
Mass  of  13a 
o-i 
0-2 
03 
0-4 
0-5 
0-6 
0-7 
0-8 
0-9 
10 
Values  of  j3  for  different  positions  of  Load. 
a/ 1: 
499-9 
497-9 
495-9 
4939 
491-8 
489-6 
487-3 
484-9 
482-6 
480-1 
ajl- 
480-9 
460-8 
441-3 
422-6 
404-7 
387'8 
371-9 
357-0 
342-9 
329-8 
a/l='S. 
all-. 
a/l='o. 
443-9 
411-2 
396-7 
347-9 
357-4 
301-1 
324-6 
265-2 
2969 
2367 
273-3 
213-8 
2530 
194-8 
235-4 
178-9 
217-8 
165-4 
206-4 
1537 
3990 
331-3 
283-0 
247-0 
219  0 
196-7 
178-5 
163  3 
L50-6 
139-7 
