OHAP. IV."j MOMENT OF ROTATION OF FORCES. 33 



CHAPTER IV. 



MOMENT OF ROTATION OF FORCES IN THE SAME PLANE. 



35. The " Moment " of a Force about any Point is the 



product of the force into the perpendicular distance from that 

 point to the line of direction of the force. The importance 

 and application of the " moment " in the determination of the 

 strains in the various pieces of any structure will be evident by 

 referring to Art. 14, where Ritter's " method of sections " is 

 alluded to. In general, when the moments of all the exterior 

 forces acting upon a framed structure are known, the interior 

 forces, or the strains in the various pieces, can be easily ascer- 

 tained. 



As we shall immediately see, these moments are given 

 directly in any case by the " equilibrium polygon" 



36. Culmanii's Principle. If a force P be resolved into 

 two components in any directions as b C, b C^ (Fig. 19, PI. 5), 

 and these components be prolonged, it is evident that the 

 moment of P with reference to any point as a situated any- 

 where in the line c d parallel to P, is P x 5 a. But if from C 

 we draw the perpendicular H to P, then by similar triangles, 



P : H ; ; G d : b a ; 



Pxb a = fixed. 



That is, the moment ofP with respect to any point a is equal 

 to a certain constant H multiplied by the ordinate c d, paral- 

 lel to P and limited by the components prolonged. The con- 

 stant H we call the "pole distance." 



This holds good for any point whatever, and we have only to 

 remember that if we assume the ordinates to the right of P as 

 positive, those to the left are negative. 



We can choose the pole C where we please, and thus obtain 

 various values for H, but for any one value the corresponding 

 ordinates are proportional to the moments. 



