HOOKS, LINKS, AND SPRINGS 



155 



of the mean fiber BC is at A. Therefore, if A denotes the thickness 

 of the piece, the radius of curvature of BC is 



p = Consequently, 



p + h 2h 



g = c ' 



and hence formula (99) becomes 



k 



d = p = -* 



FIG. 109 



Therefore the neutral fiber passes through the ver- 

 tex of the angle A, and consequently a piece of 

 this kind can offer no resistance to bending. In other words, if a 

 piece is bent exactly at right angles on itself, the slightest bending 

 strain must produce incipient rupture. 



This example is useful, then, in pointing out the danger of sharp 

 curvature and showing how rapidly the strength decreases with the 

 radius of curvature. 



128. Maximum moment in circular piece. Consider a prismatic 

 piece with a circular axis, such as a ring or a section of pipe, 



and suppose that it is 

 subjected to two equal 

 and opposite forces 

 P, either of tension 

 or compression, act- 

 ing along a diameter 

 as shown in Fig. 110. 

 Draw a second diam- 

 eter MN at right an- 

 gles to the direction 

 in which the forces P 

 act. Since these two 

 diameters divide the 



figure into four symmetrical parts, it is only necessary to consider one 

 of these parts, say the upper left-hand quadrant. The forces acting on 



any section of this quadrant consist of a single force and a moment. 



p 

 On the base CD of the quadrant this single force is of amount > 



ft 



110 



