International Journal of Mechanical Sciences 41 (1999) 209—233 A theoretical analysis for the quasi-static axial crushing of top-hat and double-hat thin-walled sections M.D. White , N. Jones *, W. Abramowicz   Impact Research Centre, Department of Engineering, The University of Liverpool, Liverpool L69 3GH, UK  Impact Design, Europe ul. 3 Maja 18, Michalowice 05-816, Warsaw, Poland Received 2 May 1997; received in revised form 22 May 1998 Abstract A theoretical analysis, using superfolding elements (SE), has been carried out to determine the mean crushing loads for the quasi-static axial loading of top-hat and double-hat, spot-welded mild steel sections. The theoretical predictions compare favourably with experimental results reported in a companion article and with the experimental and numerical predictions of other authors.  1998 Elsevier Science Ltd. All rights reserved. Keywords: top-hat; double-hat; quasi-static; axial crushing; superfolding elements; mildsteel Notation A  , A  , A  , A  , A  constants in Eq. (1), governing solution for a superfolding element [27] a width of a top-hat or double-hat specimen a  a  a  variables in Eq. (11(a) — (c)) b depth of a top-hat or double-hat specimen b  effective width b  width of square section member C length of a superfolding element E modulus of elasticity E  energy absorbed by the folding of a plate E  internal energy absorbed by a SE in asymmetric folding mode E  total energy dissipation for the formation of one layer of superfolding elements f flange size 2H height of a superfolding element, as shown in Fig. 5 * Corresponding author. Tel.: 00 44 151 794 4858; fax: 00 44 151 794 4848; e-mail:njones@mechnet.liv.ac.uk. 0020-7403/99/$ — see front matter  1998 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 0 - 7 4 0 3 ( 9 8 ) 0 0 0 4 8 - 4