Art. 103. 



UNIFORM LIVE AND DEAD LOAD. 



167 



The dotted moment diagram is for full load; all ordinates are 

 longer than for partial load. 



The maximum shear in the beam occurs at the end, and is 

 equal to the reaction; it occurs under full load because a load 

 anywhere on the beam will increase R i or R 2 . 



The maximum shear at C occurs ivhen the load extends from 

 C to the farther support, for if there were any load to the left 

 of C, part of it would go to R l to increase it to //, while all of it 

 would be subtracted from R^ to give the shear at C; in other 



words, it decreases the shear more than it increases it $c==R/ 



wa. It may easily be proven analytically that a should be zero. 



It is often necessary to find the shear at an intermediate 

 section of a girder. 



103. Combination of Uniform Live and Uniform Dead 

 Load. Fig. 120 shows a girder of 50 ft. span; the dead load is 



600 Ibs. per foot and must, of 

 course, always be a full load; 

 the live load is 2300 Ibs. per 

 foot, and is taken as a full load 

 for all moments and for maxi- 

 mum end shear; it is taken as 

 Fig. 120. a partial load only for maxi- 



mum shear at an intermediate section (102). 



The reactions for full load are (2300+600)25 = 72500 Ibs., 

 and this is the maximum or end shear. The maximum moment 

 is, according to equation (42), 



i/ 8 WL = Vs2900X 50X50 = 906250 ft. Ibs. 

 The maximum moment at 16 ft. from one end is 

 72500X162900X16X8 = 788800 ft. Ibs. 

 The maximum shear at 16 ft. from the end is (partial load) 

 7^600 X 16 = 600 X 25+ J 2300X34 600X16 = 41600 Ibs. 

 At the middle of the span, the dead load shear is zero, and 

 the maximum live load shear is (for the load covering half the 

 span) 



12.5 



50 



2300X25 = 14375 Ibs. 



104. Maximum Live Load Shears in a Continuous Beam 

 of Two Spans. In a two span continuous beam (spans equal or 

 unequal), it is only necessary to consider one section (in th" 



