Art. 169. 



PORTAL WITH SIMPLE X-BRACING. 



337 



In case No.lb xi> xi and H'> H (Fig. 217), although a = a' 

 and c = c' . 



This case must be solved by approximation as indicated in 

 Art. 166. Having thus found x 1} xi', H, H' , V and V we find the 

 stresses exactly as in No. la. This will be illustrated by an ex- 

 ample. 



Let us take a single track through railroad bridge of 8 panels 

 at 24 ft., with a depth of 36.2 ft. and a width center to center 

 of trusses of 16.5 ft., end posts inclined. 



The dead load stress in the end post is 100,000 Ibs. and the 

 live load stress 212,000 Ibs. The portal is connected so that in 

 Fig. 219, c=43.5 ft., =31.5 ft, e=12.0 ft. C. to 0. of bearings 

 on top pin .^=20 in. C. to C. of bearings on bottom pin= 

 in. 



Wind Load per ft. 150 Ibs. on top chord. Wind Load per 



:P=3,600 Ibs., 72=21/2^=9,000 Ibs. J R+P=12,600 Ibs. 

 Top: 1/2/^=10X100,000=1,000,000 in. Ibs. =Z>. L. Mom. 



=10X212,000=2,120,000 in. Ibs. =L. L. Mom. 



3,120,000 in. Ibs. =TotaL 



This is at B. If the post is fixed at this point, it certainly will 

 be at B' also. 



Bottom : 



^10. 5X100,000=1,050,000 in. Ibs. =D. L. Mom. 

 10.5X212,000=2,230,000 in. lbs.=L. L. Mom. 



3,280,000 in. lbs.=Total. 

 From equation (121) . = - - (a x^), 



12600 



31.5(31.5+43.5) 

 94.5 _|_ 43.5 



(31.5-17.1)=45,300 ft. lbs.=544,000 in .Ibs. 



Since this is less than y%kj) above, the tops of the posts are 



fixed. 



, 2 =,y 2 (K+P)a: 1 =6,300Xl7.lXl2=l,290,000 in. Ibs. 



Since this is more than y 2 k z D under D. L., not considering 

 V which will make the difference still greater, the bottom of the 

 pest is partially fixed under dead load only. On account of the 

 large margin it will evidently be fixed when the live load is on 

 the bridge. We have then only the former case to consider here. 



