152 CONTINUOUS GffiDER. [CHAP. X. 



In a similar manner we find for the left support 



$=1 the span is completely covered, and we have, 

 then, right and left 



24 a 



If we compare this value with those for partial loading, we 

 see that they differ only by certain coefficients, and that these 

 coefficients depend only upon the length of the loaded portion. 

 If, then, we have the distance between the cross-lines for total 

 load, we have only to multiply by certain factors to obtain the 

 distances for partial loading. For uniform or total load over 



1 / A 4 

 the whole span, this distance is given by -p X 2 I - 1 (Art. 98). 



4: \ A./ 



If we divide this distance in certain proportions we have at 

 once the distances for partial loading. These proportions are 

 given by (2 /S 2 ) /S 2 for the right support, and (2 /3) 2 /3 for the 

 left, under the supposition that the load comes on from the 

 right. The reverse is the case for load coming on from left. 



113 



If we take ft = -, -, - of the span, we can calculate these pro- 

 portions once for all. We thus have the following table : 



Support under load Support for wnloaded end 



(2-(3<>)/3. (2-/3) 3 /3. 



1 span loaded ^- = 0.1211 . . . .-JL = 0.1914. 



4 2ob 256 



1 span loaded -JL = 0.4375 .... -2 = 0.5625. 



2 16 16 



907' 99^ 



^ span loaded ~L = 0.8086. . v --|Sr 0.8789. 



The division of the distance between the cross-lines for uni- 

 form load over the whole span into these proportions is easily 

 accomplished graphically. Thus, from the end of the line to 

 be divided, draw a line in any direction, and lay off upon it the 

 BIX numbers above, to any convenient scale. Join the end of 

 the last division with the end of the line to be divided, and 

 then draw parallels through the other points. 



It is important to observe some definite system 'of numera- 

 tion, otherwise, especially in the first attempt at construction, 

 confusion is apt to arise. 



