EXTERNAL FORCES 



17 



In Fig. 7 is shown the actual shear when the loads have a defi- 

 nite width and when the beam rests on a support of a definite 

 width. At the face of the 

 support the shear is a maxi- 

 mum and it is zero at the 

 end of the support. It is not 

 usual to show this in shear 

 diagrams, for it complicates 

 the drafting work without 

 enough benefit to pay for the 

 trouble. The slight difference 

 increases the factor of safety. 



T 



Manieni Diagram 



Beams Resting on Two 

 Supports 



To determine bending mo- 

 ments on beams on two or 

 more supports, it is necessary 

 to find first the amount of 

 the reactions. 



In Fig. 8 a concentrated 

 load is carried on a beam 

 resting freely on two supports. 

 For convenience we adopt the 

 conventional method of be- 

 ginning at the left end as in 

 reading. The word "conven- 

 tional " has the same root form 

 as the word "convenience" 

 so may be easily remembered. 



Common sense assures us 

 that if the load is in the 

 middle one-half will be carried 

 by each support. Let us imagine the concentrated load to be 

 stationary and the ends of the beam pushed up by the reactions. 

 The reactions being equal to the load, there is no movement, but 

 the forces actually exist. 



Each reaction being one-half of P, then Ri - % and #, - - 



2 2 



This gives two cantilever beams with moments acting about 



Shear Diagram 



Fig. 6 A Cantilever Beam Carrying 

 Two Concentrated Loads 



