56 MOMENT OF ROTATION PARALLEL FORCES. [CHAP. V. 



tie line ^ 9, and seek the greatest ordinate between it and the 

 polygon. Tliis we find at 7, and directly above 7 the given 

 point must lie, and hence we have the position of the span, viz., 

 t t. If the scale of tons is ten tons to an inch, of distance 5 ft. 

 to an inch, and the pole distance H is assumed 12 ft. = 2 

 inches, the scale of moments will be 10 x 2.5 x 5, = 125 ft. tons 

 to an inch. 



As to the second question ; the position of the span required, 

 is that where the vertical through the given point of the system 

 S Fig. 32 (a), intersects the corresponding tie line at its point 

 of tangency with the parabola ; all other tie lines intersect this 

 vertical in a point between the tangent point and the polygon. 

 The middle of the span must then lie midway between the in- 

 tersection a of the outer polygon sides and the point s, where 

 the vertical through S meets the line X X. Thus the span has 

 the position t% t%. 



The third question, finally, is easily solved if the parabola en- 

 veloped by the tie lines is drawn. The greatest ordinate be- 

 tween this parabola and the polygon gives the greatest moment, 

 and the point and the position of span required, since the 

 middle of the span must be half-way between the point given 

 by this ordinate and a. 



The greatest moment is always found upon an ordinate 

 through an angle of the polygon. 



If, however, the parabola is not drawn, we find by trial at 

 several angles, drawing the tie lines and comparing the corre- 

 sponding ordinates, the ordinafe required. Here the following 

 considerations may aid : 



When the load is uniformly distributed, the maximum mo- 

 ment is in the middle of the span, and at the same time in the 

 vertical through the intersection a of the outer polygon sides. 

 The polygon itself becomes a parabola. The less uniform the 

 load is, the more this point approaches the heaviest loaded side, 

 as also the intersection a, though not in the same degree. For 

 loads not exceedingly unsymmetrical the point may be sought 

 for, then, in the neighborhood of a, i.e., near the resultant of the 

 forces acting upon the truss. Thus in our example we are jus- 

 tified in selecting the corner 7 of the polygon, nearest the point 

 of intersection a. 



5O. Mot unfavorable Position of Load upon a Beam of 

 given Span. The fourth question above requires a somewhat 



