180 GRAPHIC AND ANALYTIC [ciTAP. XIT. 



found abundantly accurate to assume the curve for i between 

 the required limits, as a parabola whose equation is i = x = 



T-J - The greatest error for a = - will then be about 



- of the span, and decreases both ways to a = o and a = -. 

 100 2 



From a = to a = I the parabola coincides closely with the 



3 1 



true curve. The difference for a = I is only I, and we 



have, therefore, a very simple practical construction for both 

 reactions and moments. We have only (Fig. 82) to erect a 

 vertical at the centre support B and make it equal to I, and 

 then construct a parabola passing through B whose ordinate 



c d = - I. The horizontal ordinates to this parabola for any 



vertical value of #, give the distance out from B of the inflection 

 points. For the load in first span A B, of course this parabola 

 lies on the other side of B c, and b e is laid off to the left. The 

 remainder of the construction is as in Art. 118 for the reactions 

 and moments. When great accuracy is required, we can find 

 the reactions from the equations of Art. 118. In any case, the 

 reactions being given, we can follow them through the structure 

 by the method of Art. 114, and thus determine the strains in 

 every piece due to every position of each apex load. A tabu- 

 lation of these strains will then give by inspection the maximum 

 strain in any piece due to the live load. All the weights taken 

 as acting simultaneously will then give the strains due to uni- 

 form total live load. The strains due to dead load will be 

 multiples or sub-multiples of these. Thus if total live load 

 causes, say, 100 tons compression in a certain piece, and- if the 



O ft 



dead load is - of the live load, then we shall have - of 100 = 

 2 2i 



150 tons compression in the same piece due to the dead load 

 alone. If now the live load causes a maximum tension in the 

 same piece of 200 tons, then the piece must be made to resist 

 both tensile strain of 200 150 = 50 tons and compressive 

 strain of 150 + 100 = 250 tons. If a diagonal, the counter tic 

 is strained 50 tons, while the maximum strain on the diagonal 



