DIAGRAMS. 



the diagram we substitute for the actual weight of the different parts of the 

 Imk. two weights which have the same resultant acting at the extremities of 



thf link. 



We mar now treat the diagram of the frame as composed of links without 

 but loaded at each joint with a weight made up of portions of the 

 of all the links which meet in that joint. 



If any link has more than two joints we may substitute for it in tlu> 

 diagram an imaginary stiff frame, consisting of links, each of which has only 



two joints. 



The diagram of the frame is now reduced to a system of points, certain 

 pairs of which are joined by straight lines, and each point is in general acted 

 on by a weight or other force acting between it and some point external to 



the system. 



To complete the diagram we may represent these external forces as links, 

 that is to say, straight lines joining the points of the frame to points external 



lie frame. Thus each weight may be represented by a link joining the 

 point of application of the weight with the centre of the earth. 



Hut we can always construct an imaginary frame having its joints in the 

 lines of action of these external forces, and this frame, together with the real 

 frame and the links representing external forces, which join points in the one 

 frame to points in the other frame, make up together a complete self-strained 

 system in equilibrium, consisting of points connected by links acting by pressure 

 or tension. We may in this way reduce any real structure to the case of a 



in of points with attractive or repulsive forces acting between certain pairs 

 t' these points, and keeping them in equilibrium. 



The direction of each of these forces is sufficiently indicated by that of 

 the line joining the points, so that we have only to determine its magnitude. 



We might do this by calculation, and then write down on each link the 

 pressure or the tension which acts in it. 



We should in this way obtain a mixed diagram in which the stresses 

 are represented graphically as regards direction and position, but symbolically 

 as regards magnitude. 



But we know that a force may be represented in a purely graphical 

 manner by a straight line in the direction of the force containing as many 

 units of length as there are units of force in the force. The end of this line 

 is marked with an arrow head to shew in which direction the force acts. 



