CHAP. I.] COMMON POINT OF APPLICATION. 15 



we take the direction of rotation of the forces on the left of the 

 section when in the direction of the hands of a watch as posi- 

 tive, and tind the moment of strain in D negative, it shows 

 negative rotation about a, and the strain in D to resist this rota- 



O ' 



tion must act away from J, or be tensile. If the resultant 

 rotation of the outer forces is on the other hand positive, the 

 strain in D must act toward b, and D is therefore compressed. 



This method of calculation, it will be observed, is both sim- 

 ple and general. It can be applied to any structure, when the 

 outer forces are completely known, and only three pieces are 

 cut by the ideal section. 



15. It is unnecessary to give here further applications of our 

 graphical method. The reader can easily apply it for himself 

 to the " bowstring girder," bent crane, etc., and satisfy himself 

 as to its accuracy, and the ease ,with which the desired results 

 are obtained. 



Enough has been said to indicate the many important appli- 

 cations which even at the very commencement of our develop- 

 ment of the graphical method we are enabled to make, and 

 here we shall close our discussion of forces lying in the same 

 plane and having a common point of application. As we pass 

 on to forces having different points of application, we shall 

 have occasion to develop new principles and relations not less 

 fruitful and useful in their practical results.* 



* We refer the reader here to the Appendix to this chapter for further 

 illustrations of the application of the above principles, as well as for informa- 

 tion upon several points of considerable practical importance. We would also 

 remind him here once for all, that the Appendix to this work was NOT in- 

 tended to b disregarded, but has been thought desirable in order to avoid 

 encumbering the general principles with too much of detail in the text. We 

 earnestly request him to neglect no reference to it which may be made in the 

 text. 



He will do well in the present case, after first making himself familiar with 

 the above points, to solve for himself with scale and dividers a number of 

 similar problems, checking his results always by the method of moments. 

 He will thus in a very short time master the method, and be able to solve 

 readily and accurately every problem of usual occurrence in practice. 

 Though the method is very simple, actual practice with the drawing board it 

 lure indispensable. 



