The convexity about ultimate bearing hypersurfaces of structures

doi:10.1007/s11709-016-0334-1

Front. Struct. Civ. Eng.

2016, Vol. 10

Issue (4) : 456-461 https://doi.org/10.1007/s11709-016-0334-1

RESEARCH ARTICLE

The convexity about ultimate bearing hypersurfaces of structures

Chengxi GUO(

),Tingting GUO

College of Civil Engineering, Institution of Architecture Design, Xi’an University of Architecture and Technology, Xi’an 710055, China

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Abstract

The relationship between the convexity on the ultimate bearing surface of a structure and the second-order 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.

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

Corresponding Author(s): Chengxi GUO

Online First Date: 04 November 2016 Issue Date: 29 November 2016

Cite this article:

Chengxi GUO,Tingting GUO. The convexity about ultimate bearing hypersurfaces of structures[J]. Front. Struct. Civ. Eng., 2016, 10(4): 456-461.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-016-0334-1
https://academic.hep.com.cn/fsce/EN/Y2016/V10/I4/456

Fig.1 convexity of G(P) = 0

Fig.2 Cantilever. (a) P=Ne1+Me2; (b) F1=Afye1+0e2; (c) F2=0e1+Zfye2

Fig.3 Frame structure. (a) P = pe1+ qe2+ se3; (b) F₁ = Pe₁ + 0e₂ + 0e₃; (c) F₂ = 0e₁ + Qe₂+ 0e₃; (d) F₃ = 0e₁ + 0e₂ + Se₃

Fig.4 Continuous beam

Fig.5 Scheme A

Fig.6 Scheme B

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