150 KANSAS UNIVERSITY QUARTERLY. 



The first term of the second factor of (29) is the ordinate of the 

 -moment curve on the right of the load, and since it is of the first 

 degree in z we see that the moment curve on the right for any position 

 of the loading is a straight line. 



Equation (27) can be put in the form 



,, wx2k' ( i6h r r wx2 1 wz2 1 ) ■ , ( i6h [ f 



Mi=^— - -—-; wx z y - ==H - — — , wx 



i6h ( wx^k L L 2I J 2 J ) ( wx^k L I 



wx 



M 



!l J 



T r (30'; 



From (30) we see that the moment curve under the load is a para- 

 bola whose equation is 



i6h ( wx^ i i6h 



wx r z — —-ttt-tZ^ (31) 



wx^k' ( 2I ) 2x^k' 



For x=i5 feet, h=io feel and 1= 50 feet, (31) reduces to 

 y'=i.97z— .o77z2 (32) 



The curve A R S T, Fig. 2., represents equation (32). 

 Substituting 1 for x in (32) we have 



y=p-(zi— z') 



that is, the moment curve under the loading coincides with the rib 

 when the load covers the whole span and, hence, the moment at every 

 point of the rib is zero for this case. 



To find the locus of the point of intersection of the two moment 

 curves: Let u denote the ordinate of any point on the locus. Then 



wx^ \ X \ 



M^ "^l'~Xi" i6h 



"==H^-- ^^' = lir^-^-"^ 



i6h 



u= — — — {33) 



We see from {33) that the shape of the locus is independent of the 

 Tnagnitude of w. , , . •, 



The curve D T C KB, Fig. 2, represents this locus for hrn^io feet 

 and 1=50 feet. 



Putting Mr=o in (26) we have 



