EXTERNAL FORCES 



21 



supports, this is always a positive (downward) moment, the beam 

 being in tension on the lower side and in compression on the 

 upper side between supports. 



Bending Moment at any Point on a Beam on Two Supports 



The loads are shown in position and amount in Fig. 13. First 

 find the reactions. 



ft,-- 748.+1 



ft 



-*--- 



751.56 



Fig. 13 Example of Uniform Load and Several Concentrated Loads on 

 Beam on Two Supports 



#, = (4.5x200) + (7.5 x 300) + (11.5x250) + (8x750) 



16 



Ri - (200 + 300 + 250 + 750) - 751.56 = 748.44 Ibs. 



Check for /&: 



(4.5x250) + (8.5x300) -I- (11.5x200) + (8 x 750) 



K\ =- 



lo 



In finding the reactions the weight of the beam = 15 x 50 = 750 

 Ibs. This was multiplied by half the length of the span, which 

 gave the quantity above, 8 X 750. 



What is the bending moment at the section xx? 



The section xx is 2 ft. from the face of the left support. 

 The span face to face of supports = 15 ft., but the length center 

 to center of bearings - 16 ft., assuming a bearing 1 ft. long on 

 each support. Therefore the moment arm from the section to 

 the reaction at the right end - 13.5 ft. The moment arms to the 

 loads from the section are marked on the figure. There is one 

 moment arm, however, of 6.5 ft. to be explained. It is the length 

 from the section to the center of gravity of that portion of the 

 beam lying between the section and the support at the right end. 

 The total clear span - 15 ft. and the section is 2 ft. from the left 



