CHAPTER IX 



CURVED PIECES: HOOKS, LINKS, AND SPRINGS 



123. Erroneous analysis of hooks and links. In calculating the 

 strength of a curved piece whose axis is a plane curve, such as a hook 

 or a link of a chain, many engineers are accustomed to assume that 

 the distribution of stress is the same as in a straight beam subjected 

 to an equal bending moment and axial load. For example, in calcu- 

 lating the strength of a hook, such as shown in Fig. 101, the practice 

 has been to take a section AB where the 

 bending moment is a maximum, and cal- 

 < -ulate the unit stress p on AB by the 

 formula 



FIG. 101 



where tin- first term denotes the direct 

 stress on the section AB of area /', and 

 the second term represents the bending 

 stress due to a moment Pd calculated 

 from the formula for straight beams. 



The bending formula for straight 

 beams, however, does not apply to curved 

 pieces, as will be shown in what follows. 

 Moreover, experiment has conclusively shown that a curved piece 

 breaks at the point of sharpest curvature, whereas the above formula 

 takes no account whatever of the curvature. The above formula is 

 therefore not even approximately correct, and is cited as a popular 

 error against \vhi<-li the student is warned. 



124. Bending strain in curved piece. Consider a curved piece 

 which is subjected t<> pure bending strain, and assume that the axis 

 of the piece is a plane curve and also that the radius of curvature is 

 not very large as compared with the thickness of the piece. Hooke's 

 law and Bernoulli's assumption will be taken as the starting point 



146 



