of  Loaded  and  Unloaded  Bars.  363 
equating  the  values  for-^  and  y  when  x  =  a,we  get  for  x<a, 
y=  |^  |  ^(lx" -ax^a\v - 2al2x  +  ZaHx)  +  p^  {^'01011905l7x 
4.  -0lGFa*—-0Q8iPafi  +  -00238095^7- -00059524a?8) }  . 
Whilst  for  x>a  the  first  term  in  the  brackets  is 
-r-(laz  —  a*x  —  axz — '2al2x  +  Salx2) . 
In  either  case 
^=EI.P; 
where 
-p.    ,       ma262   ,  pco 
P_1-  ~3T  +  a  (~'01011905Z7a  +  -016Z5a3--0083?3a5 
+  '00238095/a7  -  -00059524a8) . 
§  16.  In  the  second  approximation,  for  x<a 
:g  =  Jm^-/H»^Jox(*-*)sf^ 
y(l—a)dx+  j  /(/—*)<&]. 
EI 
+pM¥J 
If  .v  >  a,  the  second  expression  on  the  right  hand  must  be 
written 
I/"  LJo  J  «  J 
and  the  term  —  mya(x—a)  must  be  added. 
By  the  method  already  indicated  we  find  the  inclinations 
of  the  ends  to  be 
at  x  =  0  : 
dV       y'a[m(an       a3       al2\       pwV  C  .nnmn~Qr      m 
dx=mlj{Y-  -6-yJ+^-t.00010386^F 
mA/      17^      la       aH*      a3Z4      ±alQY\  " 
+   6/  \~  420  +  30  +  60  ~  45  +  315/J  J; 
dx=Will\-^-T)+   A~}  00010386/^ 
wiA/       17a7       a5/2      ^'/l       4aZ6\  \  "I 
+    6/  \~420+  60  ""45  + 315/J J 
at  x  —  l 
2B  S 
