SCfi NOTE TO CHAP. V. [APPENDIX. 



NOTE TO CHAPTER V., ART. 51. 



15. In Fig. YIII. (Append!*) we have given the construction 

 referred to in Art. 51 of the text for a system of loads of given 

 intensities. The span s 8 is supposed to shift to s t s ly S 2 *2? e tc., 

 and a certain cross-section fc to shift with it to & 15 3, etc. The 

 intersections of the respective closing lines with verticals 

 through k$, k^ &%, etc., gives us a curve between which and the 

 polygon the greatest ordinate gives the maximum moment for 

 the assumed cross-section. The place of this ordinate is the 

 position of the cross-section from which we determine the ends 

 of the span, and thus have its position with reference to the 

 loading when the moment in & is the greatest possible. 



Thus if this greatest ordinate is at the angle YIII. in the Fig., 

 the weight P 8 must rest upon the cross-section. The distance 

 then from P 8 to the left end of span s, is the distance from s 

 to &o on left, and to right end of span s, is the distance from 

 to 8 on right. 



The ends 8 and a being thus found, perpendiculars through 

 them determine the closing line L, and the parallel to this in 

 the force polygon gives the end reactions L and 20 L for the 

 position of span which makes moment at Jc a maximum. 



