BENDING. 



33 



It should be observed that, if the neutral axis has been 

 correctly drawn through the centre of gravity of the 

 original figure, and the construction of the modulus figure 





FIG. 14 (b). 



has been accurately performed, the area of that part of the 

 modulus figure above the neutral axis will be equal to that 

 below. This will serve as a check on the correctness of the 

 work. The most convenient way of ascertaining the areas 

 is by means of an Amsler planimeter. 



Let the area of that part of the modulus figure which 

 is above the neutral axis be A x ; and that of the part 

 below be A 2 . 



And let the distance of the centre of gravity of the first 

 from the neutral axis be x\, and that of the second x 2 . 



The modulus of the section will be 



But as 



or if we call the distance, perpendicular to the axis, of one 

 centroid from the other, X, then we shall have 



It is usual to take inches and square inches as units, 

 where the moments are expressed in " inch-tons " or " inch- 

 pounds," and the stresses in tons or pounds per square inch. 

 D2 



