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Collar Ties

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     I had occasion to evaluate the performance of collar ties installed in 
     a house with a roof that spanned approximately 45'.  My initial 
     evaluation using statics principals resulted in failure of the rafter 
     from bending moment.  The failure was far enough from allowable to 
     cause concern with out additional investigation, and not enough to 
     justify rework with out sharpening my pencil.  
     
     I modeled the collar tie in a 2D finite element analysis program with 
     an X and Y restraint at one end and a Y (vertical) only on the other 
     end.  The answer was the same I found with based on simple statics.  
     My next approach was to consider contribution by the wall and roof 
     diaphragm system in resisting the thrust.  I modeled a spring to 
     represent the amount of deflection I felt would be conservative for 
     the diaphragm and wall elements (double top plate with paneling on the 
     outside).  I found that by allowing the small amount of deflection (< 
     1/2") redistribution of loads occurred and the rafter was adequate.  I 
     further convinced myself that this was adequate by considering that 
     the live load was not highly likely to be seen again during the life 
     of the building as the roof slope was steep and the roofing system had 
     already been installed.
     
     I believe that the largest contribution to the stiffness of this system is 
     the roof diaphragm.  Whenever I've been called in the fix a roof of this 
     type that has pushed out the bearing walls, the failure has occurred prior 
     to installation of the roof diaphragm.
     
     What do you think about this approach?
     
     Scott
     Bechtel