EXTERNAL FORCES 



35 



as above and measure the ordinate to the curve at the point 

 where the desired bending moment is to be found. 



In Fig. 29 is shown the effect of concentrated loads plus the 

 uniform load due to the weight of the beam. The moment due to 

 the uniform weight of the beam is computed and a center line 

 measured upward to 

 represent this mo- 

 ment. Construct a 

 parabola. 



Below the center 

 line of the beam con- i / x-x , s~^ 



struct a moment dia- V ^ J \ vV 



gram representing the 

 effects of the concen- 

 trated loads. The 

 bending moment at 

 any point is shown 

 by the line intercept- 

 ed by the upper and 

 lower boundaries of 

 the moment curves. 

 For example, at a dis- 

 tance y from the left 

 end of the beam the 

 bending moment is 

 shown by the length 

 of the line xx\. 



In Fig. 29 the re- 

 actions are drawn to 

 scale so that ac and bd 



each represent one-half the uniform load. Draw the horizontal 

 line ab and connect c to d. The two triangles represent the 

 shear to scale at all points on the beam. The horizontal measure- 

 ments are lengths and the vertical measurements are loads. Since 

 beams usually weigh much less than any load they carry it is com- 

 monly stated that the maximum moment and zero shear, or point 

 where shear passes through zero, occur always under a concen- 

 trated load. The student can see that this statement must be 

 qualified when the uniform load is considerable. The combined 

 shear diagram in Fig. 29 is obtained by adding the end reactions 



Combined Shear 



Fig. 29 Graphical Method for Combination of 



Concentrated and Uniformly Distributed 



Loads on a Beam 



