Art. 61. 



THE GRAPHIC METHOD OF SECTIONS. 



83 



From the similar triangles formed by rays 2 and 6 and 

 strings 2 and 6 with R and t/ 5 , we have 



R ~f-T 



Hence U 2 d = IIy r> . 



Thus we get a value for the sum of the moments of the exter- 

 nal forces to the left of any section ~by scaling an ordinate be- 

 tween two strings, for may be so chosen that // is some conven- 

 ient quantity like 100 or 1000 Ibs. 



This is not true for non-parallel forces unless a string poly- 

 gon is drawn for each section, which would be very laborious. 

 For parallel forces H is the same for any resultant. 



H, the perpendicular distance from the pole to any force, 

 is called the fiole distance of the force, although it is really a 

 force; the product Hy 5 will be the same, no matter which is 

 called the force or the distance, so long as the scale of forces is 

 used in the force polygon and the scale of distances in the string 

 polygon or space diagram. 



To find U 2 then, it is simply a matter of scaling y 5 , locating 

 the decimal point, and dividing by d (the lever arm of U 2 ). U. z 

 may also be found by constructing any two similar triangles, 

 f or U 2 : H : : y. : d. 



For L 2 , the section is the same as for U 2 and, therefore, R 

 will be the same ; the center of moments is joint 4 and L 2 d = Hy. 



For L 3 , the external forces are R lt P t , and P 2 , whose result- 

 ant is nc; since 3 and 6 are components of nc, the ordinate y Q will 

 be measured between strings 3 and 6 on a line through the center 

 of moments which is at joint 6. 



Since R^ is always one of the external forces, the ordinate 

 y will always be measured from the closing line to that string 

 which is parallel to the other component of the resultant of the 

 forces. Thus if the moment of R : about joint 6 were wanted, 

 the ordinate would extend from the closing line to string 1 pro- 

 duced. 



For the truss of Fig. 61, the diagonal stresses can not be 

 found (the center of moments being at infinity) unless the chord 

 stresses are found first and then used in the equation of equilib- 

 rium for the diagonal stress. If the centers of moments for the 

 diagonals are taken at the middle of the top or bottom panels, 

 their lever arms will be d'=dsinO. For # 4 , D 4 Xd'-\-L 2 Xd=JI>/.. 



