EXTERNAL FORCES 



33 



from either end a and that from the other end 6. Then under 

 each load (for the load only) 



M 



L, 



Through each load drop a perpendicular and set off the bending 

 moment on each line 

 for the load above 

 that line. Connect the 

 ends of the lines to the 

 ends of the center line 

 of the beam, thus mak- 

 ing two triangles. Un- 

 der each load is the 

 moment due to the 

 load, plus the moment 

 due to the other load 

 shown by the inter- 

 cepts, Pb and PI&I. 

 From a set off ac = Pb 

 and from a\ set off 

 aici - PI&L The total 

 moment under P = PC 

 and under P\ = PiCi. 

 Connect the points by 

 the lines mcc\B, thus 

 forming a bending mo- 

 ment diagram (for the 

 loads only). The bend- 

 ing moment at any 

 point on the beam is 

 obtained by measuring 

 from the center line 

 (AB), of the beam to the bounding line of the bending moment 

 curve. 



In Fig. 27 is illustrated the application of the method just 

 described to three loads. Any number of loads may be similarly 

 treated, no matter how unequal in weight nor how unevenly spaced. 



Assume any number of equal loads equally spaced as in Fig. 28. 

 This amounts to a uniform load, and, triangles being drawn as 

 shown, for each load, a bending moment diagram is formed of which 



Fig. 27 Graphical Method for Several Loads 

 on a Beam 



