MECHANICS 101 



or beam must be zero, and (2) the resultant moment of all 

 the forces about any point must be zero. 



The forces acting on a beam are the forces due to loads on 

 the beam and the weight of the beam itself, if that is con- 

 sidered, and then there are the reactions of the supports on 

 the beam. Now, all the loads act vertically downwards and 

 the reactions act vertically upwards. They are therefore 

 parallel; and as they are opposite, the sum of the loads must 

 equal the sum of the reactions. 



A beam with two supports will be considered. The sum 

 of the reactions is known from the loads, but the value of 

 each reaction is not known. To find this, it is necessary to 

 resort to the second condition, namely, that the resultant 

 moment of all the forces about any point must be zero. 

 Any point can be assumed, but it is found convenient to 

 choose the reaction of one support as the point about which 

 to take moments. The moment of the reaction at the point 

 is zero, because the arm of the moment is zero. It is there- 

 fore necessary that the sum of the moments of the loads about 

 one point of support and the moment of the other reaction 

 about the same point shall equal zero. 



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FIG. 6 



A practical example will now be considered. In Fig. 6 

 let it be required to find the reactions RI and R? at the points 

 of support a and b. (In all the subjoined problems, RI and 

 R 2 represent the reactions.) The center of moments may 

 be taken at either RI or R z . Let the point b be taken in 

 this case. The three loads are forces acting in a downward 



