554 



STRUCTURAL MECHANICS. 



CHAP. XVI. 



The ambiguity at joint P 3 is removed by means of the dotted member, as in the case of the 

 dead load stress diagram, ft will be seen that there are no stresses in the dotted web members 

 in the right segment of the truss. It is necessary to carry the solution entirely through the 

 truss, beginning at the left reaction and checking up at the right reaction. It will be seen that 

 the load PI lias no effect on the stresses in the truss in this case, the left reaction being simply 

 reduced if PI is omitted. 



ao' so' 



tdj 



Joint Lo 



FIG. i. 



Wind Load Stresses : Rollers. Trusses longer than 70 ft. are usually fixed at one end, and 

 are supported on rollers at the other end. The reaction at the roller end is then vertical the hori- 

 zontal component of the external wind force being all taken by the fixed end. The wind may 

 come on either side of the truss, giving rise to two conditions: (i) rollers leeward and (2) rollers 

 windward, each requiring a separate solution. 



Rollers Leeward. The wind load stresses in a triangular Pratt truss with rollers under the 

 leeward side are calculated by graphic resolution in (c) Fig. 2. 



The reactions in (c) Fig. 2 were first determined by means of force and equilibrium polygons, 

 on the assumption that they were parallel to each other and to the resultant of the external loads. 

 Then since the reaction at the roller end is vertical and the horizontal component at the fixed end 

 is equal to the horizontal component of the external wind forces, the true reactions were obtained 

 by closing the force polygon. 



In order that the truss be in equilibrium under the action of the three external forces, RI, R 2 

 and the resultant of the wind loads, the three external forces must meet in a point if produced. 

 This furnishes a method for determining the reactions, where the direction and line of action of 

 one and a point in the line of action of the other are known, providing the point of intersection 

 of the three forces comes within the limits of the drawing board. 



The stress diagram is constructed in the same way as the stress diagram for dead loads. 

 It will be seen that the load Pi has no effect on the stresses in the truss in this case. Heavy lines 

 in truss and stress diagram indicate compression, and light lines indicate tension. 



Rollers Windward. The wind load stresses in the same triangular Pratt truss as shown in 

 (c) Fig. 2, with rollers under the windward side of the truss are calculated by graphic resolution 

 in (d) Fig. 2. 



The true reactions were determined directly by means of force and equilibrium polygons. 

 The direction of the reaction RI is known to be vertical, but the direction of the reaction R? is 

 unknown, the only known point in its line of action being the right abutment. The equilibrium 

 polygon is drawn to pass through the right abutment and the direction of the right reaction is 

 determined by connecting the point of intersection of the vertical reaction RI and the line drawn 

 through O parallel to the closing line of the equilibrium polygon, with the lower end of the load line. 



