# Fix-fix Arch Approximate Static Analysis

## Main Question or Discussion Point

Hey there,

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

MLL= - 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.

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.

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The moment (ha ha pun intended) you bring bending into it, you should be treating your structure as a curved beam, not an arch.

If you are trying to do more than MEXE or ARCHIE then you will need FE analysis.

not sure what ARCHIE or MEXE is ... but the point is not to use FE analysis ... i can be doing 2D/3D FE models all day, not a problem, but I really need an approximate solution, because the FE packages are not available at locations where we are trying to implement this ...

worst case scenario i´ll have analyse 30-40 arch bridges and come out with span/height/load carrying capacity tables :-/ (here I run into the problem that I dont have that many as-builts)

not sure that I can treat an fix-fix arch 40m long, 10m high as a curved beam ...

not sure that I can treat an fix-fix arch 40m long, 10m high as a curved beam ...
Sur you can. That is what it is if it carries bending.

not sure what ARCHIE or MEXE is ... but the point is not to use FE analysis ... i can be doing 2D/3D FE models all day, not a problem, but I really need an approximate solution, because the FE packages are not available at locations where we are trying to implement this ...
That is what MEXE and ARCHIE were developed for.

MEXE was originally developed in pre computer days as a quick field method for assessing arch bridges for load carrying capacity. It is very quick and easy. There are computer implementations these days. There is a UK Department of Transport on the subject. If I remember correctly, it is also discussed in Picard - The Masonry Arch.

ARCHIE is a PC implementation of theory developed bz Prof Harvey, during his tenure at the University of Strathclyde. It is available commercially for a small fee. It performs a similar function to MEXE.

ok, i might have misunderstood what you meant by a curved beam, i was assuming a line element with small deflection angles :-)

Cool, I gotta look up MEXE and ARCHIE then, especially MEXE sounds interesting to me. Thanks for the info.