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Calculation of flange stresses for underhung trolleys

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The December 1999 issue of Modern Steel Construction's Steel Interchange 
(page 9), had a question concerning the design calculation of the lower 
flange loading capacity of a steel beam to be used to support an underhung 
crane.  It further asked if there are any published ASD or LRFD design 

The answer given by David T. Ricker of Javelina Explorations of Payson, Az., 
investigates capacity based on tensile stress and on bending stress.

The capacity based on tensile stress in the web is determined by using 3.5 x 
k times the web thickness as the effective area of the member.  This seems 
like a reasonable way to proceed.  The capacity of the member would then be 
the effective area times the allowable AISC tensile stress.

He further investigates the capacity based on flange bending using the 
section modulus of an  "equivalent cantilever" beam whose effective width is 
2xe (e is the eccentricity of the load measured from the k1 point as 
presented in the AISC Manual) and whose depth is equal to the thickness of 
the flange.  The allowable moment is equal to the section modulus times the 
AISC bending allowable.  The length of the "equivalent cantilever" beam is 
the eccentricity plus the edge distance, although it does not enter into the 
calculation.  The "equivalent cantilever" beam is considered to have free 
unsupported longitudinal edges.  The moment is equal to the local load times 
the eccentricity.  The stress calculation results in e cancelling out in the 
numerator and denominator and is thus independent of the eccentricity.  In 
other words, as the eccentricity decreases, the effective width also 
decreases.  The result is a very low capacity and seems to be unrealistic and 
very conservative.  It would seem that taking into account the continuity of 
the longitudinal edge of the beam (instead of assuming it to be a cantilever 
slice) would dramatically influence the capacity calculation. It would also 
seem to be more realistic to use a greater effective width of the "equivalent 
cantilever" member.  Possibly, something more like the 3.5 x k value used in 
determining the tensile effective area.

Is there a more realistic assessment of the flange bending capacity which 
accounts for the continuity of the "equivalent cantilever" beam's edge 
restraint?  More importantly, is there a prescribed ASD or LRFD procedure? 

Tom Ahl