1.52 KANSAS UNIVERSITY QUARTERLY. 



., dMr (1— z) i 2xk'z x2z I" X2 X 1 I 



Also -— - = -~ W -j 2X — 6-— — 10 yr- /" 



dx 2I ( 2I 2I L l^ F I ) 

 -*- ...(37) 



Equating the values of z in (36) and (37) and simplifying we have 



I X I ^ I X I ^ ( X I ^ I X I '' r X I " 



.10 [ -p j —45 I ~Y I +50 I -1-- I +37 I ~j- I —75 I Y I +^5 



=0 (38) 



One root of (38) is ——=.58-)- and it makes Mj. a maximum. 

 Substituting this value of - in (36) we have 



z=.7661 

 Substituting for x and z their values in (26) we have 



(Mi.)max= — .0165WI2 (39) 



To find the maximum moment under the load we have 

 ( wx^ ) wz2 wx^ wx^ 



dM, wx2 ( k' I w i x2 ) 



^-=wx-^^-^i^-[---^i--k ^^z=o 



i X f k' 1 

 ^ = ^2 (40) 



This value of z in (40) is the same as that in (35)' and hence gives 



minimum values of z instead of maximum values. 



If in (27) we substitute for x and z values in terms of 1 it reduces 



to the form 



Mi=Cwl2 (41) 



In (41) C is a constant for given values of x and z. 



X z 



Table III gives values of C in (41) for values of ^p- and — r-. 



