Art. 63. THE STRING POLYGON AS A MOMENT DIAGRAM. 87 



63. The String Polygon as a Moment Diagram. 



When the forces acting on a structure are all parallel, as in 

 Fig. 61, H is constant and the moment at any section is pro- 

 portional to the ordinate of the string polygon. The string 

 polygon is, therefore, quite similar to the moment diagram, 

 especially if the pole is chosen on a horizontal line through 

 n, so that the closing line will be horizontal. For example, if 

 H = 10000 Ibs. and y scales 34.5 ft., the moment is 345000 ft. 

 Ibs., while in the moment diagram the moment would be scaled 

 directly and this scaled distance would have exactly the same 

 length as y if the scales were properly chosen. 



The string polygon is of greater importance in theory than 

 in practice; it furnishes a graphic representation of the varia- 

 tion of the moment. 



64. The Graphic Method of Sections for Uniform Loads, 



According to Art. 57 (Fig. 55) the bending moment at any sec- 

 tion of a beam distant x from the left support is, for uniform 

 load, M x = R. L x ~L/2 WX ~' This shows that if x may be represented 



wL 



Fig. 63. 



by ordinates to a parabola whose maximum ordinate is at the 

 middle of the beam and is equal to 



The parabola may be constructed by the method shown for 

 the right half of the beam, Fig. 63, or by constructing a string 

 polygon as shown. The load is divided into a number of equal 

 parts, and each part is considered as a concentrated load acting 

 at its center of gravity. This is equivalent to the procedure for 

 finding the moment at any of the sections of division and, there- 

 fore, the string polygon will give the correct moments at these 



