8 FORCES IN TIII-: SAMP: PLANE. [CHAP. i. 



10 tons. We lay off therefore 10 tons downward from e, Fig. 

 5 (i), and follow down from e around the polygon. We thu.- 

 lind B tension and 3 compression. Then 4 and F are found as 

 before for apex <?, 4 tension and F compression ; and then we 

 come to the next apex and the next weight. This is laid off 

 downwards from the end of the preceding, and then we follow 

 round, finding C tension and 5 compression ; and so on. 

 1C. As another example, let ns take the 



ROOF TRUSS, 



given in Fig. 6, PI. 2. This truss is given by Stoney, Vol. I., 

 page 128. Dimensions : span, 80 ft. : rise of top and bottom 

 flanges, 16 and 10 ft. respectively. Radii, 58 and 85 ft. The 

 figure shows two different kinds of bracing. In the left-hand 

 part the extreme bay of the lower flange is half as long again 

 as the others. The upper flange is divided into 4 equal bays. 

 In the right-hand section, both flanges are divided into 4 equal 

 bays, and every alternate brace is therefore nearly radial. Each 

 upper apex in both cases is supposed to sustain a weight of 

 one ton. 



The strains in the various pieces are given in Fig. 6 (a). 



We form the force polygon by laying off the weights from 

 to 7 and then laying off the reactions 3.5 apiece, upwards, we 

 come back to 0, and the force polygon is closed as it should be,) 

 since the sum of the reactions must be equal and opposite to 

 the sum of the weights. Starting then with the reaction at the 

 left support A, we go through from apex to apex in a manner 

 precisely similar to the previous case. The operation is so 

 simple that it is hardly necessary to detail it again, but we 

 recommend the reader to go over it with the aid of Fig. 6 (a), 

 lettering the figure as he proceeds. The dotted part gives the 

 strains for the right-hand half. 



DIAGRAM FOR WIND FORCE. 



11. It is of considerable importance to investigate the influ- 

 ence of a partial load, such as that caused by the wind blowing 

 on one side of the roof, and this by the aid of our method we 

 can easily do. 



From the experimental formulae of Hutton,* 



* Iron Bridges and Roofs. TJnwin. p. 120. 



