50 COMPARISON OF METHODS. Art. 43 



2 j 3 30 3 = 27 = number of members. If another mem- 

 ber were added without adding any more joints, it would be 

 indeterminate. The stresses in this case are easily gotten by us- 

 ing a combination of the second method with the method of 

 sections (56). 



Statically indeterminate structures are generally avoided. 

 The distribution of stress in them depends upon the relative 

 stiffness of their parts. The stresses are determined by means of 

 the principle of virtual work or least work. See Chapter XVIII. 1 



43. Comparison of Graphic and Algebraic Methods. In 



comparing graphic and algebraic methods, it should be under- 

 stood that the slide rule is used in the latter by all experienced 

 calculators, and that the matter of relative accuracy is unimpor- 

 tant, excepting certain graphic solutions. If two lines make an 

 acute intersection with each other, the point of intersection can 

 not be accurately located, and the resulting error may be too 

 great. The same objection holds for intersections found by means 

 of long lines whose directions may be slightly in error. These 

 objections arise particularly in the use of the string polygon, but 

 the force polygon is its own check, for it will not close if the work 

 is not accurate. With careful work, proper instruments, and 

 proper scales, it is seldom necessary to redraw a force polygon. 



The greater the number of different inclinations of forces 

 (external and internal) to be dealt with, the more the use of the 

 graphic method is to be commended, and the greater the liability 

 to error in the algebraic method. The more angles there are to 

 deal with, the more laborious the algebraic methods become, while 

 this has no effect in the graphic method, except as it makes the 

 diagrams somewhat more irregular or complicated. 



An experienced calculator will use the graphic methods less 

 than an inexperienced one, because he is familiar with the method 

 of calculating stresses in certain kinds of structures and is there- 

 fore less liable to make mistakes and errors, and because it re- 

 quires considerable time to get paper, instruments, etc. ready to 

 use the graphic methods. 



Graphically, the method of application of the equations of 

 equilibrium to any one joint is, by far, the most important, be- 

 cause it deals with force polygons, and the method of sections is 

 the least important. 



' l Prof. Heller died before the completion of this book. 



