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STRENGTH OF MATERIALS 



points on the beam shown in Fig. 3 are as follows: At W\ 



FIG. 3 



The bending moment varies, de- 

 pending on the shear, and attains 

 a maximum value at the point where 

 the shear changes sign. If the 

 loads are concentrated at several 

 points, the maximum bending mo- 

 ment will be under the load at which 



the sum of all the loads between one support up to and inclu- 

 ding the load in question first becomes equal to, or greater 

 than, the reaction at the support. Hence, to find the maximum 

 bending moment in any simple beam: 



Rule. Compute the reactions and determine the point where 

 the shear changes sign. Calculate the moment about this point 

 of either reaction, and of each load bet-ween the reaction and the 

 point, and subtract the sum of the latter moments from the former. 



EXAMPLE. What is the maximum bending moment of the 

 beam loaded as shown in Fig. 4? 



FIG. 4 



SOLUTION. The reactions due to the uniform load are equal 

 to half of the load; those due to the concentrated loads are 

 computed by the principle given under Reactions. Both added 

 give R\ = 18,170 Ib. and Ri= 14,330 Ib. Beginning at Ri and 

 subtracting the loads in succession, it is found that the shear 

 just to the left of the load d is 18,170-16,500; and just to 

 right of the load d it becomes negative. Hence, the shear 



