CHAPTER V. 



APPLICATION OF THE LAWS OF EQUILIBRIUM TO A PART 

 OF A STRUCTURE. 



STRESSES. 



49. Stresses. The stresses in the members of a truss 

 are found by applying the laws of equilibrium to parts of the 

 truss. These parts may be single joints or larger portions of 

 the structure. 



As explained in Art. 40, the application of the equations of 

 equilibrium to one joint of a truss at a time, involves only con- 

 current forces. Graphically, we deal with force polygons only. 

 Any j oint may be treated graphically or algebraically, but there 

 is usually nothing to be gained by using both methods for one 

 truss. 



When larger portions of the structure are considered in 

 calculating stresses, it is called the method of sections. The 

 stresses in the members cut by the section dividing the truss 

 into two parts are obtained. This method is of considerable 

 importance, especially the algebraic application, on account of 

 its ready application to the forms of trusses usually used. This 

 is the only method applicable for finding stresses in solid beams 

 and girders. 



When a single joint of a truss is considered, there are but 

 two independent equations of equilibrium, the forces being 

 concurrent. The solution must therefore begin at a joint where 

 there are but two unknown quantities. 



The reactions are first determined by the methods of Chapter IV. 



50. Stresses in the Simplest Form of Truss. Stress 

 Diagrams. Fig. 48 shows a triangular truss carrying a single load 

 at its apex. To find the stresses (the reactions being known) 

 it is only necessary to draw a force polygon for each joint. In 

 this case, there are three forces at each joint, two being un- 

 known. Laying out P to some suitable scale and drawing a 

 force triangle for joint 2, stresses D^ and D 2 are determined. 

 Since these three forces are in equilibrium the direction of the 

 arrows is clockwise as determined by the known direction 



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