194 GRAPHIC AND ANALYTIC [CHAP. XII. 



6th spans loaded, and should have considered the other " ex- 

 terior" spans as causing compression in the upper flange. 

 This, although true for the end flanges, and indeed all upper 

 flanges as far as the inflection points, is not strictly true for the 

 flanges between the inflection points. The error is not great, 

 more especially as even the strains thus found can never be 

 realized in practice. It is exceedingly improbable that moving 

 trains will ever in practice occupy just such positions as those 

 supposed. We recommend, then, the above method as giving 

 safe and reliable results, while it makes the table much srnaller 

 and economizes much labor. 



In order to find the trite maximum strains, we must find the 

 strains in every piece of the span in question due to load over 

 each exterior span. We thus have a column in our table for 

 each of these spans, or, in the present case, six columns, instead 

 of only two, as by the above method. We leave the reader to 

 adopt this method or not, as he chooses, and shall content our- 

 selves with illustrating by an example the method of finding 

 the true maximum strains. This method, though more labori- 

 ous than the above, is by no means more difficult. We have 

 only to consider the effect of each exterior span by itself, instead 

 of the combined effect of several. 



127. Example. Let us take, as an illustration of the pre- 

 ceding, the girder shown in Fig. 87, of seven equal spans, and 

 seek the maximum strains which can ever occur in the middle 

 span D E. Let Fig. 88, PI. 23, represent the span D E length 

 80 feet, divided into 4 panels ; and let the live load per panel 

 be 40 tons,* the uniform load being half as much, or 20 tons 

 per panel. Height of truss, 10 ft. 



Now the quantities, which for the present we must suppose 

 known or already found, we give below. How these quantities 

 are found will be the subject of the next chapter. 

 For 1st span loaded moment = + 61.55 ft. tons at D. 



shear at D = + 0.97 tons. 

 For 2d span loaded moment at D = 184.65 ft. tons. 



shear at D = 4.74 tons. 

 For 3d span loaded moment at D = + 677.05 ft. tons. 



shear at D = + 10.67 tons. 



* A very great load : half the resulting strains would give more nearly the 

 strains in a single truss. 



