222 CONTINUOUS GIRDER. [CHAP. HIL 



ever}* weight, cr by giving the proper value to m in our for- 

 mulae, we may find the moment at any support we please. 



The moments at the supports of the loaded span being found; 

 the moments at the other supports may be obtained according 

 to tiie rule given in Art. 140 for uniform live load over single 

 span. 



146. Triangle of Momenta The reader may also by the 

 aid of the formulae above form a triangle similar to those al- 

 ready given, containing the coefficients of P I for the moments 

 at the supports of the loaded span. 



Thus for two spans, for moment at left support, we should 

 obtain and \ [2 k 3 #* + #] P I, and this last value will 

 run down the right diagonal column without change, except in 

 its coefficient , which will become successively -j^, f , -/$, 

 for three, four and five spans respectively. For three spans 

 we shalfhave, 0, ^ [7 & 12 1& + 5 %?] P I, and, as above, 

 & [2 k 3 #> + J^\ P I. The second of these will run down 

 the second diagonal column from the right without change, 

 except in its coefficient, which will be T \, 3*^, etc., for five 

 and six spans. 



So, for four spans we have 



0,-h [26 & - 45 &* + 19 >] PI, ^ [7&-12F + 5& 3 ] PZ, 

 [2 k - 3 # + #] P I, 



for moments at left, for load in 1st, 2d, 3d and 4th span re. 

 spectively. The second of these runs down the third diagonal 

 column from the right, changing coefficient as above. 



If the triangle be now drawn, and these expressions properly 

 inserted, we shall observe that along the diagonal columns 

 sloping down and to the left, the values of k in the parenthesis, 

 as also the denominators of the outside fractions, follow the law 

 of the Clapeyroniau numbers. The numerators of these out- 

 side fractions in these columns remain unchanged. The outer 

 left column is of course always zero. 



Another triangle must be found for moments to the right of 

 load, and then the moments at the unloaded supports may be 

 found by the rule of Art. 140. 



All the moments may also be found from a couple of tables 

 formed similarly to those of that Art. It is unnecessary to 

 give such tables here. From the above the reader can form 

 them for himself, if desired. The formulas for moments given 



