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Bi-axial bending of concrete beam

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While the book by Paulay and Park present a physically correct solution,
it might be a bit tedious to use. A simple initial approximation would be to say
 
r = MY/MY0 + MZ/MZ0
 
where MY and MX are the individual bending moments,
and bending capacities, separately calculated ,are in the denominators.
r is the usage factor. If r < 1, the beam is OK.
 
Sincerely
Gregory from Oz