The allowable stess falls rapidly depending on the unbraced length of the beam top flange. The beam will fail in lateral-buckling before it fails in bending, especially in a configuration like a bridge crane. It is dangerous to use elastic stress analysis without taking into account the allowable stress reductions for the un-braced length. For a W14x22, the allowabale stress needs to be reduced for unsupported lengths over 5.6'. In other words, the W14x22 used as a bridge crane beam for spans over 5.6' will fail due to lateral buckling, not bending.
The allowable stress for a W14x22 spanning 21' between lateral supports has an allowable stress of 5.7ksi, which is approximately 25% of the allowable stress for the same member laterally supported at 5.6' intervals, assuming A36steel.
Reference AISC (American Institute of Steel Construction), Allowable Stress Design, 9th edition.
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