44 PRACTICAL STRUCTURAL DESIGN 



distance from the concentrated load to the nearest support and 



call the result x. 



W L 



Example. A beam weighing 200 Ibs. on a span of 12 ft. carries 

 a concentrated load of 750 Ibs. 3 ft. from one end. What is the 

 equivalent distributed load? What is the bending moment? 



Pa(L - a) 750 x 3 X 9 

 Ans. M = - *-= - - = - - = 1687.5 ft. Ibs. 



LJ \ - 



y.W 8X 1687.5 



Ll 1- 



W _ 1125 _ 



= "~~ = 



L _ 12 _ 

 = a~ 3 " 



The equivalent distributed load producing a bending moment 

 equivalent to the bending moment produced by the concentrated 

 load = 1125 Ibs. and to this must be added the weight of the 

 beam, 200 Ibs. The total bending moment is 



,, WL 1325 x 12 



M = -5- = -- - -- = 1987.5 ft. Ibs. 



o o 



The student is advised to compute a table, following the above 

 example, with the concentrated load assumed to be placed at vari- 

 ous points on the beam, the table giving values of m and x, to be 

 used in shortening labor in future work. 



Such tables are in use giving values of m and x for a dozen or 

 more points on a beam. The following table gives these values 

 for ten points: 

 When x = 2 m = 2 



x = 3 m = 1.78 



x = 4 m = 1.5 



x = 5 m = 1.28 



x = 6 m = 1.11 



x = 7 m = 0.98 



x = 8 m = 0.875 



x = 9 m = 0.79 



x = 10 m = 0.72 



