13 



FORCES IN THE SAME PLANE. 



[CHAP, 



any intermediate weight. Thus scaling off the strains in Fig, 

 7 (a) and (i), we can tabulate them under PX and P 7 , as shown 

 liv the table. 



Now the reaction at the left abutment due to P 6 is twice 

 as great as that due to P 7 . Hence the values in the column 

 for P 6 will be twice as great ; in the column for P 5 three times 

 as great, and so on. For similar reasons the strain in 5 for 

 P 2 will be twice that for P t . In column P 2 , then, from 5 

 down we multiply the strains in P t by 2. In P 8 from 7 down 

 by 3. Thus we fill out the table of strains completely, and find 

 the maximum tension and compression. A similar procedure 

 will give the flanges.* 



APPLICATION TO AN AKCH. 



13. For a " braced arch " (Stoney, p. 136) as represented in 

 Fig. 5 (c) PI. 2, the strains in every piece due to any load are 

 in similar manner easily found by first finding the components 

 of the load acting at the abutments, and then proceeding as 

 above. Thus for a load P 2 , the left half of the arch is in equi- 

 librium with the forces acting upon it ; viz., a horizontal and a 

 downward force at a, and a horizontal and an upward force at 

 A. The resultant of the forces at a must then pass through 



* The reader not familiar with the above method of tabulation will find it 

 further illustrated in Art. 7 of the Appendix. He cannot do better than tc 

 refer to it here and now. 



