CHAPTER X 



ARCHES AND ARCHED RIBS 

 I. GRAPHICAL ANALYSIS OF FORCES 



130. Composition of forces. In determining the effect which a 

 given system of forces has upon a body, it is often convenient to 

 iv]. resent the forces by directed lines and calculate the result graphic- 

 ally. In this method of representation the length of the line denotes 

 the magnitude of the force laid off to any given scale, and the direc- 

 tion of the line indicates the direction in which the force acts, or its 

 line of action. 



\V1 idi the lines of action of a system of forces all pass through 

 the same point, the forces are said to be concurrent. The simplest 

 method of dealing with such a system is to find the amount and line 

 of action of a single force which would have the same effect as the 

 given system of forces upon the motion of the point at which they 

 act. This single force is called the resultant of the given system. 

 When each of a system of forces acting on a body balances the others 

 so that the body shows no tendency to move, 

 the forces are said to be in equilibrium, and in 

 this case it is obvious that their resultant must 

 be zero. 



The resultant of two forces acting at a point 

 is found by drawing the forces to scale in both 

 magnitude and direction, and constructing a 

 parallelogram upon these two lines as adjacent 

 sides ; the diagonal of this parallelogram is then the required resultant 

 (V\^. 112). This construction can be verified experimentally by fas- 

 tening a string at two points A and B and suspending a weight R 

 from it at any point C (Fig. 113). Then if two forces equal in magni- 

 tude to the tension in AC and BC are laid off parallel to AC and BC 



159 



FIG. 112 



