216 CONTENTIOUS GIRDER. [CHAP. 



This table, it will be observed, can be produced to include 

 any number of supports desired. The law of the Clapeyronian 

 numbers runs both horizontally and vertically. The smaller 

 table gives the denominator, the larger the numerator of the 

 coefficient of w P for any case. Thus, for seven spans we have 

 four times 2911 = 11644 for the common denominator. For 

 load on second span from right, moment at sixth support from 



627 

 left, we have then directly - w P ; for fourth support from 



45 



, TT-TTT w PI the same as above. 

 11644 



For load in fifth span from right, the table gives us at once 



-1 K O />H \ 



0? ~ -,-1 QA A W P an d + TTrrrr w P, fc> r supports 1, 2 and 3. 

 11644 11644 



For the other supports, since if now we were to continue count- 

 ing from left we should have to pass a loaded support, we 

 must count the loaded span from left, and count the supports 

 in reverse order. For fifth support from right, then, the num- 

 ber required is at intersection of III. (instead of Y.) and 5, or 



/>-i n 



--TTTTI w P, as found above. Thus the tables above cover all 

 11644 



cases, giving supports at loaded span itself, as also right and 

 left of this span. We have only to remember to count sup- 

 ports from left, and loaded span from right, for all supports 

 left of load, and inversely for all supports right of load. [The 

 reader should always, when using Table, make a sketch of the 

 given number of spans, indicate the loaded span, and number 

 the supports.] 



141. Reaction at Supports Live Load over single pan. 

 For the reactions at ends of loaded span, we have 



, r + . 



For reactions at extreme ends, when end spans are loaded, or 

 whenr = lorr=, Rj = _ ^? + i > Z, R B =-??! + -i 



v A (t a 



When any other spans are loaded, or 



when r>l and <, 1^=-??? R a + 1 =_!. 



