304 



PRACTICAL MATHEMATICS 



M + SM. Considering a fibre situated at a distance y from the 

 neutral axis, z being the breadth of this fibre. 



FIG. 106, 

 For the section CD, if p is the stress in the fibre, 



Th M 



Then p = y y 



Thrust on the fibre = pz by 



M 



= -j yz sy 



If AB is a fixed line in the section drawn parallel to the neutral 

 axis, at a distance y l from it, and if R 2 be the resultant thrust 

 on that part of the section above AB, 



^1M 



Then 



and this may be taken as acting from left to right. 

 For the section CjDj, if p is the stress in the fibre, 



M+SM 

 Then p= j y 



Thrust on the fibre = pz &y 



M+SM 



and if Rj is the resultant thrust on that part of the section 

 above AB, Vt) 



<m. 



Then R, 



and this may be taken as acting from right to left. 



Hence the small portion of the beam contained by the two 

 parallel sections C 1 D 1 and CD, &r apart, and a horizontal plane 



