Date : 2016-06-23 12:24:21

A crane hook is a curved beam and the simple theory of straight, shallow beam bending does not apply.

The stress distribution across the depth of such a beam, subject to pure bending, is nonlinear (actually hyperbolic) and the position of the neutral surface is displaced from the centroidal surface towards the centre of curvature.

A rigorous solution is quite complex and some simplifying assumptions are made in practice. 
The diagrams below show the nomenclature used:


In the expressions below 
h = the depth of the beam. 
A = the beam cross section area. 
co = distance from the neutral surface to outer fibre. 
ci = distance from the neutral surface to inner fibre.

2 Suggested Simple Approach 
The stress distribution due to the moment only can be found by balancing the externally applied moment against the internal resisting moment. The result is:

sigma = M y/ (A e (rn - y))

The critical stresses occur at the inner and outer surfaces:

sigma = M ci/ (A e ri) and sigma = M co/ (A e ro)


The difficult part is evaluating(or rn). e = R - rn Values that can be used for common sections are given below: 


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