Alkxandke — Maximum Bending-moments on Short Girders. 19 



seen that the point 6 feet to the right of the middle and the middle point 

 of the span itself are equidistant about the axis of the parabola, so that the 

 bending-moment is the same at the two points when the wheel Wi arrives 

 at them respectively. 



Fio. 2. 

 To find the locus of the apex 0, fig. 1, the locomotive should be shifted till 

 the wheel ^^3= 11 tons is 2 feet to the left of the centre, when will coincide 

 with ^3, fig. 2 ; and the height S^ A3 will be, calculating from the left end, 



tons ft. 



ail/, = 19 X 19 - (5 X 8 + 5 X 13) = 2.56 foot-tons. 

 For a movement of one foot left or right the moment has the common 

 value 



tons ft. tons ft. 



^Mi = 20 X 18 - 105 and ,iM, = IS x 20 - 105. 



