
Rectangle 
Trapezium 
Circle 
Area 
b d 
0.5 d(b_{i} b_{o}) 
3.14159 d^{2}/4 
R 
0.5 (r_{i} r_{o}) 
r_{i} (d/3)(b_{i} 2 b_{o})/(b_{i} b_{o}) 
0.5 (r_{i} r_{o}) 
r_{n} 
d/ln(r_{o}/r_{i}) 


The equations for the stress, sigma, are for pure bending and for a crane hook the bending moment is due to a force acting on one side of the cross section.
In this case the bending moment is calculated about the centroidal axis, not the neutral axis.
Also additional tensile and / or compressive stresses must be added to the bending stresses, given by the two equations above, to obtain the total stresses acting on the section.
The most highly stressed points in a typical crane hook area E and B, see diagram below:
sigma = F R c_{i}/ (A e r_{i}) F/A (tension) and
sigma =  F R c_{o}/ (A e r_{o}) F/A
The cross section of many crane hooks can be approximated to that of a trapezium giving rise to only a small error so the data given above can be used.