BENDING. 



31 



and the modulus Z is the product of the area by the 

 distance of its centre of gravity from the neutral axis. In 

 the case in question, the area of the modulus figure, on 

 one side of the axis, is obviously 



I , d 



T ' b ' T ; 



2 d 



and the centre of gravity of the triangle is situated-^ ' -- 



from the neutral axis. So that the modulus of the section, 

 taking both sides of the neutral axis, is 



21- 



bd' 



which is what we obtained by the previous method. 



This principle can be extended to more complex and 

 difficult figures, and will be found of the greatest use for 

 such cases as rail sections, rolled joists and beams, and 

 awkward sections generally. 



Fig. 14. (a) 



On Figs. 14 are shown two examples of these. That 

 marked (a) is a solid circular section ; (6) is a section of a 



