308 



PRACTICAL MATHEMATICS 



For any section q = r= (9 w ) 

 . ao 3 i 



6F 



9 U-C 



= fc (9 y ), where k = -yj 



162. The following method for investigating the distribution oi 

 shear stress over a section will be found to give a very convenient 

 relation to use providing the section is such that the height oi 

 centroid of any portion of it above the neutral axis can be easily 

 determined. It can therefore be used with great advantage to 

 any beam section which can be taken as being made up oi 

 rectangles. 



Referring to Fig. 106 and considering the section CD. 



If P! is the stress at AB and p is the stress at KL 



Then 



P Pi A Pi 



* = ". and p = 11 



y 2/1 2/1 " 



Thrust on the fibre KL = pz y 



and if R 2 is the resultant thrust on that part of the section 

 above AB, Vn 



Then R, = ^ 



= Afl where A is the area of that 

 2/i 



part of the section above AB and y is the height of the centroid 

 of that part of the section above the neutral axis. 



Considering the section CjD^ if p z is the stress at A 1 B 1 and p 

 is the stress at KL 



Then 



y 2/1 



2/1 



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

 above A. 1 B 1 



