Frontiers of Structural and Civil Engineering

, Volume 10, Issue 4, pp 456–461 | Cite as

The convexity about ultimate bearing hypersurfaces of structures

  • Chengxi Guo
  • Tingting Guo
Research Article


The relationship between the convexity on the ultimate bearing surface of a structure and the secondorder effects of loads is discussed. All of generalized non-overload forces acted on a structure forms a convex set when ignoring the second-order effects (coupling effects between the generalized forces). It is true also when the Hessian matrix composed of the second-order partial derivatives on the hypersurface about the ultimate bearing of the structure is negative definite. The outward convexity is kept when the surface is expressed by certain dimensionless parameters. A series of properties based on the convexity are pointed out. Some applications in the analysis of bearing capacity of structures were illustrated with examples. The study shows that an evaluation about the bearing capacity state of a complex structure can be made on the basis of several points on the surface of the ultimate bearing of the structure.


service limit load ultimate bearing surface convexity generalized force generalized displacement frame structure 


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Copyright information

© Higher Education Press and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.College of Civil Engineering, Institution of Architecture DesignXi’an University of Architecture and TechnologyXi’anChina

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