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i´m dealing with a problem when I´m trying to analyze an arch bridge for approximate stresses in the arch. The normal force is quite easy to get for such structure.

The problem I´m running into is the fix-end moment for the arch under both dead load and live load (live load is approximated as one-half span length uniform load). Obviously, the stiffness plays an key issue. Is there an easy approximation formula that would get me the moment assuming fix-fix condition.

The following one for half-sided uniform load

M

_{LL}= - w L

^{2}/ 64

doesn´t really do the trick, since it grossly underestimates the moment at the opposite side support, thus underestimates the total stress in the arch.

And I don´t even have a formula for dead load moments.

Back to the topic of moment, assuming pin-pin condition only normal force gets tranferred into abutments, however, significant moment can develop withing the arch itself @ approximately 5/16L ... any good formula for estimating such moment?

I´ve searched multiple books, papers, etc but I haven´t had much luck.