EXTERNAL FORCES 27 



Third. The moment due to the concentrated load must 

 be subtracted. The load is multiplied by the distance from 



the middle of the beam to the load -f -^ - aj; this giving P x 

 ( a) =- y- + Pa, and as this is to be subtracted the minus 



sign is placed before -75 



2i 



Fourth. The whole expression now appears, 



L PL wU 



M-^X-g + Pa--^ 



When adding positive and negative quantities add each kind 

 separately. Take the difference of the sums and prefix the sign 

 of the greater sum. By inclosing the two negative quantities in 

 a parenthesis the sign of the second is changed, so the full expression 

 may be written 



The arithmetical work is simple, as here shown 



q v ooc;\ 

 M = (300 x 5 + 367.5 x 7.5) - (300 x 7.5 + * ) = 1753 ft. Ibs. 



o / 



Graphical Methods 



To divide a line into any number of equal parts use the geo- 

 metrical principle of similar triangles. 



2 3 4 5 6 7 



Fig. 20 Division of Line into Equal Parts 



In Fig. 20 let AC represent a line that is to be divided into any 

 number of equal parts. The length is such that no regular scale 

 can be used readily for the purpose. Set off from one end a line, 

 AB, at any angle. This line is drawn to some scale and divided 

 into as many equal parts as it is desired to divide the line AC. 

 Connect B to C and through the divisions on the line AB draw 

 lines parallel to BC, as shown. 



