30 \OTES ON PLATE-GIRDER DESK A 



tin- .-hearing resistances of tho right surface above a, 



V L is the sum of tin .-hearing resistances of the left surface 



above n. 



IF-(P, +10 + 1IV "tnl load Ix'tween the two 



;med piano above the point a, and /l=the area in 



square inches of the horizontal surface through a. Then 



I V H -W+p u A-0, 



Can must be taken in giving the proper signs to I / and 



r, 



Having a method for finding p T , p y and <y for any 

 point in a beam, there remains to be found the plane 

 in \\liieli their combined action has the greatest intensity. 



Th- s per square inch p r , p v and 7 may be pro- 



duced in any manner, even in an arbitrary manner or p, 

 and q, and p v and 7 may be tin rectangular components into 

 \vhich the actual stresses on any elementary parallelopiped 

 have been resolved, as far as the following argument is 

 concerned. 



I/'t Fig. 6d be a redrawing of 6a. Let tin- plane OP 

 be passed through the elementary particle perpendicular 

 to the face and making the angle with AA' . con>id<-r 

 the elementary figure to have a dimension of unity per- 

 pendicular to the plane of the drawing. 



Let it be required to find so that the Cresses on 

 OP will l>e normal and therefor, cither the maximum or 

 minimum stresses in tin- bodv. 



