| | Nearly three centuries ago, Couplet proposed the problem of finding the
minimum thickness of a uniform semicircular arch subjected to its own weight, and it
was Serbian scholar Milutin Milankovitch who first gave the complete and correct
solution almost two centuries later. After remarkable mathematical elaboration
concerning thrust line theory, searching for the expression more appropriate for
iterative procedure, Milankovitch finds the solution numerically. Since iterations may be
easily done by using computer programs nowadays, the mathematical calculation which
concerns the finding of the minimum value of equation by the mean of differentiating can
be omitted, and the iterative procedures can be done at the earlier stage of the
computation, i.e. with the more complex expressions. Recently, the minimum thickness of
elliptical arches has been computed, as well. However, there are very few contemporary
researches dealing with the mechanical behaviour of pointed arches.
In this paper, on the basis of the appropriate correlation between the shape of an arch
and corresponding collapse mode, particular iterative procedures have been derived. In
order to determine the minimum thickness of the chosen arch, the appropriate collapse
mode and corresponding iterative procedure have been adopted, and the thickness, as
well as the position of the application point of the horizontal thrust force at the crown or
of the reaction force at the springing, have been modified, regarding the distance of
thrust line from the intrados or extrados at the critical sections. The analysis has been
conducted on pointed arches having various eccentricities and embrace angles,
including both incomplete and overcomplete arches, and the numerical values for the
minimum thickness of more than hundred arches have been provided for the first time.
Developed procedures may be applied in the analysis regarding maximum and minimum
thrust, span to thickness ratio or weight to span ratio, as well as in the analyses
concerning the different types of employed stereotomy. |
