34 DEFLECTION OF BEAMS. 



14. Deflection of Beams. In connection with testing 

 it is necessary to have a knowledge of the relation of 

 stress and strain, not only so far as the small portions 

 of beam sections are concerned, but to know how to deal 

 with loads as related to the strains they give rise to in 

 the beam as a whole. Loads upon a beam cause it to 

 assume a curved form, and the extent of departure, under 

 stress, of a portion of the neutral axis of the beam from its 

 originally straight position is termed the deflection. This 

 is the strain which it is generally most convenient and 

 easy to measure during a test, and it is necessary to 

 know how this deflection is connected with the intrinsic 

 properties of the beam, and with the loads upon it. 



FIG. 15. 



Let a portion of a beam be bent under stress. Two 

 plane sections B E and C D, which were parallel before 

 bending, are inclined after bending has taken place. If 

 these sections are taken near to one another, and if C D 

 and B E be continued, they will meet in a point O, which 

 is the centre of curvature. 



Let A = R = the radius of curvature of the neutral 

 surface. The neutral surface is under no stress, and is not 

 altered in length. 



Let C B be the length of an outside fibre, at a distance 

 Y from the neutral surface. 



Then, it will be easily seen that, 



