41. The derivation of Equation 2 assumes that plane sections remain 

 plane during bending and that the material obeys Hooke ' s law (stress is pro- 

 portional to strain). This relation therefore assumes a linear stress dis- 

 tribution across the section. While the FEM model has shown the stress dis- 

 tribution to be nonlinear, it appears that this analysis method provides a 

 reasonable approximation of the maximum principal stresses; but further veri- 

 fication of this hypothesis is necessary (Melby, Rosson, and Tedesco 1990). 

 Also, because the flexural shearing strains, and therefore stresses, are 

 generally maximum at the section center and decrease to near zero at the outer 

 fibers, they have been neglected in this measurement and analysis scheme. 

 Although the FEM results above show this assumption to be invalid, Burcharth 

 and Liu (1990) have shown this to be a reasonable assumption for the extreme 

 stress states in which the designer is interested. Here also, further 

 research is necessary. 



42. The torque is combined with the bending stress to yield the planar 

 principal stresses for an element at the outer surface as given below. 





(o„) 



43. The torsional shear stress r is given by 



Tr 

 J 



where 



T = torque 



r = radius of the member 



J = polar moment of inertia 

 Although these relations are derived for a circular cross section, they appear 

 to be reasonably accurate if one assumes an effective diameter for the octago- 

 nal dolos cross section. The preceding assumptions indicate that this princi- 

 pal stress is an approximation to the actual stress state within the dolosse. 



44. Melby, Rosson, and Tedesco (1990) also showed that, although axial 

 stresses are in general compressive, they can be tensile and add significantly 

 to the maximum tensile stress. It was shown that two prototype dolosse had 



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