stress distribution in concrete

huangyhg

stress distribution in concrete
i have a hp12x53 embedded in a concrete slab.  hp12x53 has a horizontal load.  how do i determine the stress distribution in concrete.  can i assume a triangular distribution with the hinge at the top of the slab (ie zero stress at top)?.  i know that the hinge forms at certain depth below the top surface, but is the assumption of triangular distribution of load still valid?  if so, would the maximum occur at the bottom as it happens in soil?
if this is the problem of a cantilever embedment, a contrary pair of forces will develop in the concrete. other than going to very complex models, one merley would be seeking simplified pairs within the concrete by whichever the assumption of the assumed shape of the stresses, and then verify the stress is acceptable, designing reinforcement as the case requires, but one shouldn't acept as high compressive stresses as to need to reinforce for spalling, whatever the to be laid rebar is. not forgetting to check the steel   
yes, this is analogous to a cantilever beam.  how do i determine the embedment of the beam?  i thought bearing stress in concrete along embedded length would be the good limiting factor.  also, pull-out due to flexural stresses (tension in extreme fiber) has to be considered.  is there a definite way to determine the embedment other than these two?
modern fem packages having compression only springs enable us to somewhat automatize the response. however it is unlikely such model represents reality. in my view, the easy and safe way is to use plastified stresses in the concrete at the opposed ends of the embedded member and first judge if low enough to not give problems. typically one shouldn't want the working service level stresses but at much about half the specified strength of the concrete.
then, any of the compressed parts may be near a face or edge; if such is the case proper anchor of the equilibrating force in the lever needs be accounted by a tie or convenient rebar against the induced action.
last, and for moderate concurrent tensile axial force, i would only count friction in proportion to the total amount of the resultant of both compression blocks at the end of the embedded lever.
for this case, only if axial tension is very big i would start to think in bond to the structural embedded part.
as a final comment, everything pertaining to high forces applied in small areas in concrete may be needed to be considered if our case approaches such extremes of application of force.