Art. 169. 



PORTAL WITH SIMPLE X BRACING. 



339 



From equation (130) 



Stress in '=9,000+1,800+12,600=23,400 Ibs. 

 From equation (131) 



Horiz. Comp. 'P=23,400+1,800+15,100=40,300 Ibs. 

 From equation (134) 



Stress in PP'=7,430+15,100=22,530 Ibs. 

 The maximum stress in the posts occurs at a' but this comes 

 under case No. la, as the live load must be on the bridge. 



Case No. Ic. Posts Partially Fixed Top and Bottom. As in 

 the previous case we first test by equation (121) and (122) to 

 see whether or not either end of either post is fixed under any 

 condition of loading. We solve by approximation in a manner 

 exactly similar to the previous case, using equations of Art. 167. 

 This will be illustrated by an example. 



Let us consider a highway bridge of 150 ft. span with 9 

 panels at 16.67 ft. Depth=22 ft. 6=17.17. DL=630 Ibs. per 

 lin. ft. LL=1,600 Ibs. per lin. ft. End Posts inclined. 

 DL Stress in End Post=26,400 Ibs. 

 LL Stress in End Post=66,800 Ibs. 



93,200 Ibs. Total. 



c= 28 ft. =20 ft. e=S ft. ^=9 in. ,=91/2 in. 

 P=150Xl6f =2,500 Ibs. #+P=16.67Xl50X4=10,000 Ibs. 



Now let us test for fixity of the ends of the posts. 



Assuming the ends fixed, 



From equation (118) x^= 



20 (20 + 28) _ 20X48 



10.9 ft. 



60 + 28 88 



From equation (106) #=#'=% (12+P)=5,OOC Ibs. 



9Q 1 Q 



From equation (128) ^=1 X 5,000^ g -=8,500 lbs.=K/ 



From equation (126) V= YTT7 ( 10 00 Xl7.1+i X 17,000) 



=12,600 Ibs. 

 From equation (121) 3/ 1 =|X 8,500=22,600 ft. Ibs. 



=271,200 in. ibs. 



From equation (122) J1 2 =5,OOOX 10.9=54,500 ft. Ibs. 



=654,000 in. Ibs. 



Top : 1/2^7) =4.5X93,200=420,000 in. Ibs. at with LL on. 

 or =4.5X26,400=119,000 in. Ibs. at with DL only. 



