Art. 50. STRESSES IN THE SIMPLEST TRUSS. 



ing whatever to do with the signs in the equations of equilibrium. 

 In this book the + sign is used to denote compression, and the 

 - sign to denote tension. This convention is often reversed: 

 practice is not uniform on this point. In mechanics, the + sign 

 is nearly always used to denote tension. 



In drawing a stress diagram, it is not necessary to draw it 

 joint by joint. The method of procedure is as follows : 



1. Lay out the force polygon for the external forces. This 

 will be a straight line for parallel forces but, since the polygon 

 must close, the line will be traversed twice in going over all loads 

 and reactions. 



2. Draw lines parallel to the outer members (upper and 

 lower chords) ; these will go through the points in the force 

 polygon in which the adjacent outer forces in the truss diagram 

 meet. If a number of members lie between two adjacent forces, 

 the lines parallel to them in the stress diagram will all go through 

 the same point. See Figs. 48 to 53. 



3. Complete the stress diagram by drawing a succession of 

 lines parallel to the inner members. 



4. Determine the character of each stress by going around 

 the force polygon for each joint, starting with a konwn force or 

 stress. The character of each stress, together with its scaled 

 amount should be put on the truss diagram. 



It will be found that, if the external forces have been laid 

 out in a clockwise direction, the order of the forces at any joint 

 will be in a clockwise direction, as determined by the force poly- 

 gon, and vice versa. 



Algebraically, we have 

 At joint 1, D! cos 6 = R^ DI = 



D i sinO = L = R 1 tan 

 Or considering joint 1, with a center of moments at joint 2, 



T T-) 2f' _ 



and with a center of moments at joint 3, 

 M 3 = Rip -Dip cos 6 = 



= R sec 



The stresses DI and L were first determined by two resolu- 

 tion equations and then by two moment equations. They may 

 nlso be gotten by means of one resolution and one moment equa- 

 tion. It is to be noted that the equation in M 2 determines an 



