152 



STRENGTH OF MATERIALS 



Problem 150. The dangerous section of a hook similar to that shown in Fi-. H j 

 has for its dimensions 6 = 2f , h - 6", n = If", r 2 = |", and OC = 2f" (Fig. KM;,. 

 Using a factor of safety of 4, find the safe load for the hook. 



* 126. Curved piece of rectangular cross section. If the cross 

 section of a curved piece is rectangular, the integrals in formulas 

 (96) and (97), Article 124, can be easily evaluated. These formulas 

 may therefore be used for calculating the strength of the piece in 

 preference to the graphical method explained in the preceding article. 



Let the cross section of the piece be a rec- 

 tangle of breadth b and depth h, and let p 

 denote the radius of curvature of the piece 

 at the section under consideration. From 

 formula (96), the distance of the neutral axis 

 of the section from the mean fiber, or gravity 



where y denotes the distance of the infinitesi- 

 mal area dF from the gravity axis. In i In- 

 present case dF = bdy ; hence 



A A 



C*ydy 

 J *y + p 



-- L J 



FIG. 106 



y 



= 1- 



By division, 



y + P y + p 



the above fraction becomes 



Consequently, the numerator of 



* For a brief course the remainder of this chapter may be omitted. 



