CHAP. XI.] CATTSINO MAXIMUM STRAINS. 163 



4. It is evidently unnecessary to actually draw all the vari- 

 ous lines. We need only to mark the different points of inter- 

 section. 



5. The construction for dead and live loads can be per- 

 formed at once, thus avoiding the necessity of a subsequent 

 addition. 



1O7. Approximate Practical Constructions. If the suc- 

 cessive steps of the preceding development are carefully fol- 

 lowed, the method will be found simple and easy of appli- 

 cation. Indeed, the complete and accurate solution of the 

 difficult problem of the continuous girder by a method purely 

 graphical, is the most important extension of the system since 

 the date of Culmann's treatise, and well illustrates the power 

 and practical value of the Graphical Method. 



Humber gives the following constructions, "which may "be 

 relied upon for safety without extravagance." * As rapid 

 means of obtaining approximate results, they may not be with- 

 out value to the practical engineer, and we therefore append 

 them here. It must be remembered that the constructions 

 hold good ONLY for end spans three-fourths the length of the 

 others. 



I. Beam of Uniform Strength, continuous over one 

 Pier, forming two equal Spans, subject to a fixed Load 

 uniformly distributed, and also to a moving Load, 

 maximum moments.* PI. 18, Fig. 73. 



The greatest moment at the pier (positive) will be when both 

 spans are fully loaded. 



The greatest negative moment will obtain in the loaded span 

 when the other span bears only the fixed load. 



(A moment is positive when the upper fibres or flanges are 

 extended, negative when the upper flange is com/pressed^) 



Construction. Let A B C be the beam. On A B draw the 



Z 2 

 parabola whose centre ordinate D E is (p + m) -g, and on 



V ft 

 B C the parabola whose centre ordinate G P is *g. 



At the pier B erect the perpendicular B H = ^ , 



and make B L = . - . Join AH, A L, and L C. 



\2t \ 



* " Strains in Girders, calculated by Formulas and Diagrams." Humber. 

 New York : D. Van Nostrand, publisher. 



