164 METHODS OF LOADING [CHAP. XI. 



Then the vertical distances between the parabolic arc A E B 

 and the lines A H and A L, the greatest being taken, will give 

 the maximum moments positive in the first case and negative 

 in the last. The points of inflection approach as near the pier 

 as K and recede as far as M. 



If ^r- is less than - , the beam must be latched 



A \.i 



down at the abutments. The load comes on from the left; 

 p and m are the loads per unit of length of the permanent or 

 fixed and the moving or live loads. 



Shearing Forces (PI. 18, Fig. 74). The maximum shearing 

 force at either abutment will obtain when its span only sus- 

 tains the moving load. The maximum shear at the centre pier 

 will obtain when both spans are fully loaded. 



Construction. Lay off A C = (p + 5 ra) and A D = 



- (p + m). At B lay off B F = twice A D. Take a point 



M distant -J I from A, and join D and F to M. Draw C N 

 parallel to D M. Sketch in a curve similar to that dotted in 

 the figure, giving an additional depth to the ordinates at the 



point of minimum shear of m -. Then the vertical ordinates 



between A B and C O P F may be considered to give the 

 maximum shearing force for either span. 



II. Beam as above continuous over three or more 

 Piers, li = end spans. I = the other spans. 



Moments. 



The maximum moment (positive) will obtain when only the 

 two adjacent spans, and every alternate span from them, are 

 simultaneously loaded with the total load the remaining spans 

 sustaining only the fixed load. 



The maximum moment at the centre of any span will obtain 

 when it and the alternate spans from it are fully loaded the 

 remaining spans sustaining only the fixed load. 



Construction (PI. 18, Fig. 75). Let A B C be part of the 

 beam. On B O draw the parabola whose centre ordinate E F 



= ^ - , and on A B the parabola whose centre ordi- 



o 



nate C D = (P + m W, A t B and C make B H = C L = 

 8 



