Thermal Bowing Moment - Beam - Temperature Gradient

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Thermal Bowing Moment - Beam - Temperature Gradient

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Hi All,
 
 I am doing thermal bowing/displacement of a cantilever beam subjected to temperature gradient.
 
 What I noticed was the bowing is independent of the profile/beam cross section. It always takes the cross section maximum distance from face-face as unity.
 
 Could anyone explain it, please? The displacement is inversely proportional to the face-face distance actually
 
 Thank you
 
 Regards,
 
 Vishnu