552 STRUCTURAL MECHANICS. CHAP. XVI. 



STRESSES IN FRAMED STRUCTURES. 



Loads. The stresses in roof trusses are due to (i) the dead load, (2) the snow load, (3) the 

 wind load, and (4) concentrated and moving loads. Data for dead loads, snow loads, wind 

 loads, crane loads and other loads to be carried on trusses are given in Chapter I to Chapter IV, 

 inclusive. The loads on roof trusses are commonly given as a certain number of Ib. per sq. ft. 

 of horizontal projection of the roof. The loads are assumed to be transferred to the truss by 

 means of purlins acting as simple beams, the joint loads being equal to the purlin reactions. 



Methods of Calculation. The determination of the reactions of simple framed structures 

 usually requires the use of the three fundamental equations of equilibrium 



2 horizontal components of forces = o (a) 



'Z vertical components of forces = o (b) 



S moments of forces about any point = o (c) 



Having completely determined the external forces, the internal stresses may be obtained 

 by either equations (a) and (b) (resolution), or equation (c) (moments). These equations may 

 be solved] by graphics or by algebra. There are, therefore, four methods of calculating stresses: 



, , . , T-, f Graphic Method 



Resolution of Forces < .. . ,, . 



l_ Algebraic Method 



,, , ~ J" Graphic Method 



Moments of Forces -s . . . , , . 



L Algebraic Method 



The stresses in any simple framed structure can be calculated by using any one of the four 

 methods. The method of calculating the stresses in roof trusses by means of graphic resolution 

 will be explained in detail. For the calculation of the stresses in roof trusses and other framed 

 structures by algebraic resolution and by algebraic and graphic moments the reader is referred 

 to the author's " The Design of Steel Mill Buildings." 



Graphic Resolution. In Fig. i the reactions RI and RZ are found by means of the force and 

 equilibrium polygons as shown in (6) and (c). The principle of the force polygon is then applied 

 to each joint of the structure in turn. Beginning at the joint LQ, the forces are shown in (c), 

 and the force triangle in (d). The reaction RI is known and acts up, the upper chord stress i-x 

 acts downward to the left, and the lower chord stress i-y acts to the right, closing the polygon. 

 Stress i-x is compression and stress l-y is tension, as can be seen by applying the arrows to the 

 members in (c). The force polygon at joint U\ is then constructed as in (f). Stress l-x acting 

 toward joint U\ and load PI acting downward are known, and stresses 1-2 and 2-x are found by 

 completing the polygon. Stresses 2-x and 1-2 are compression. The force polygons at joints 

 Li and Uz are constructed, in the order given, in the same manner. The known forces at any 

 joint are indicated in direction in the force polygon by double arrows, and the unknown forces 

 are indicated in direction by single arrows. 



The stresses in the members of the right segment of the truss are the same as in the left, and 

 the force polygons are, therefore, not constructed for the right segment. The force polygons for 

 all the joints of the truss are grouped into the stress diagram shown in (&). Compression in the 

 stress diagram and truss is indicated by arrows acting toward the ends of the stress lines and toward 

 the joints, respectively, and tension is indicated by arrows acting away from the ends of the 

 stress lines and away from the joints, respectively The first time a stress is used a single arrow, 

 and the second time the stress is used a double arrow is used to indicate direction. The stress 

 diagram in (&) Fig. I is called a Maxwell diagram or a reciprocal polygon diagram, *. e., areas' 

 in the truss diagram become points in the stress diagram. The notation used is known as Bow's 

 notation. The method of graphic resolution is the method most commonly used for calculating 

 stresses in roof trusses and in simple framed structures with inclined chords. 



STRESSES IN ROOF TRUSSES. The methods of calculating dead load, snow load, and 

 wind load stresses in roof trusses by graphic resolution will be briefly described. 



