Buckling of Steel Arches

Steel arches may be useful in the exam for designing tied arch road bridges, or suspension footbridges.

The cheat sheet below describes how to determine some key arch geometry and section properties, and use it to check the following buckling modes using methods consistent with the Eurocodes:

• In-plane buckling (collapse of the arch in-plane, without lateral deflection)
• Out of plane buckling without lateral bracing between arches (i.e. for road bridges where the rise is too shallow and bracing would obstruct the arch)
• Out of plane buckling with bracing between arches. This method checks the bottom part of the arch as the leg of a portal frame. This graph provided in the cheat sheet assumes that there is no transverse moment fixity at the base of the arch; EN1993-2 Table D.1 contains another graph for where there is transverse moment fixity at the base, but this is unlikely to be the case for a tied arch and it is conservative to assume there will be less restraint.

All of the methods provided work by calculating an effective length factor 𝛽, which is used to determine the critical buckling load Ncr, which can be used to calculate a non-dimensional slenderness and buckling reduction factor 𝜒.