APPENDIX.] SUPPORTS OUT OF LEVEL. 383 



+ alf 6 A. E I, 



TUT 



when m > n, jVu. = 

 in which expressions 



A _ -1 



Ct v, <% _ i, 33 __ 



- , 4 - 7 7 



_ ^ (4 + d) &-i + ^)- 

 - - 



-d, etc. 



The reader who has learned the use of the formulae of Chap- 

 ter XIII. will have no difficulty in applying the above to any 

 particular case. In the same way as there explained, by mak- 

 ing li and 4 zero, we may fix the girder at the ends, etc. The 

 formulae for shear at any support are, of course, the same as 

 before (Art. 150). 



Ex. 1. Let a beam of two equal spans be uniformly loaded 

 throughout its whole length, and let the centre support be low- 



ered by an amount h% = *_. What are the moments and 



4o 



reactions f 



The moments due to the full load alone before the support is 



lowered are M x = 0, M 8 = ^?, M 3 = (Art. 150). For 



8 



the moment due to the lowering of the support alone, we have 

 from the above formulae, since 



3 wff ft ft 



H = , 5 = 2, m = n = 2, 



Hence the total moment is 



^ _ w & __ 

 ^~~8~ ' 6 



