On the buckling and imperfection-sensitivity of arches with and without prestress

Abstract

Shallow, essentially inextensional, simply-supported arches under central point load are used extensively to illustrate the cusped imperfection-sensitivity of an unstable-symmetric bifuraction. Often these are made in the laboratory by simply buckling a straight strut between fixed abutments, and are therefore prestressed. We give here a concise buckling and post-buckling analysis of such an arch with any degree of prestress, and show that the critical bifurcation load varies linearly with the prestress. The immediate use of the inextensibility greatly simplifies the analysis and leads to neat closed-form solutions which agree extremely well with the limited theoretical and experimental results available from other sources.