where Mmax is the maximum moment at a zero shear section.
Utilizing this general expression, the arch shape can be
easily formulated for a beam subjected to various types of
loadings, such as uniform loaded beams or eccentrically
loaded columns, on condition that an appropriate a is
known. Now it becomes clear that the crux of the present
approach is the assignment of a value to the factor-a, and the
value can be determined from the gross compatibility condition of Eq. (4).
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