292 



PRACTICAL MATHEMATICS 



But the figures bch and gkc are similar, 



be he 11 

 _ = _ = 



7 f~\ T~ 



gh gC R 



TT 



rtenrp 



Then the strain in db = ^- where R is the radius of curvature 



measured from the neutral surface. 



But stress = E x strain, where E is Young's Modulus, 



Then 



Stress in ab = E 



or 



FIG. 



Let AB (Fig. 98) be any section of a beam, and considering a 

 thin horizontal strip of that section, the breadth of the strip 

 being Sz/, the length of the strip z, and y the height above the 

 neutral axis, 



Then 



Stress at height y 



y 



Total force on the strip = Stress x Area 



E 



where 8A = z y = Area of the strip. 



E 



Total force acting on the whole section = > y SA 



^ -s i 



E 



*-* 4 



