DEFLECTION OF BEAMS. 



35 



OB!_ C B 

 O A F A ' 

 A B C B - F A 



01 



OA 



FA 



But 



CB-FA f 

 FA ~E 



where f is the stress in the fibre and E the modulus of 



elasticity of the material of the beam, 



and 



Therefore 



or 



But 

 wherefore 



O A~R 



!_/ 



R~E' 



R~EY* 



Y = I ' 



1 M 

 R = El 



. . (XXV.) 



FIG. 10. 



The beam, as a whole, is shown in Fig. 16. A horizon- 

 tal tangent to the curved neutral surface A B is drawn at 

 O ; the deflection at the centre is C B or 8. 



Now, from the properties of curves, it is known that 



