Acta Mechanica

, Volume 230, Issue 3, pp 909–928 | Cite as

Circumferential gap and partial debonding effects on buckling loads and modes of slender CFST circular columns

  • Simon SchnablEmail author
  • Igor Planinc
Original Paper


This paper presents a new mathematical model for analytical investigation of global buckling behavior of slender concrete-filled steel tubular (CFST) columns with circumferential gaps and partial debonding between the concrete core and the steel tube. The analytical buckling load of circular and slender CFST columns with circumferential gaps and partial debonding is derived for the first time. The critical buckling load decreases as the magnitude and length of the circumferential gap increases. Nevertheless, it is shown that if the length of the circumferential gap is smaller than the length of the CFST column, this effect is less than 4%. On the other hand, for a fully delaminated CFST column, this effect can be up to approximately 40%. Similarly, the first buckling shape modes proved to be notably affected by the circumferential gap only if its length is greater than 75% of the CFST column length. The results can be used as a benchmark solution for the buckling problem of slender circular CFST columns with circumferential gaps and partial debonding between the materials.

List of symbols


Cross-sectional area (cm\(^2\))


Outer diameter of the steel tube (cm)

\(D_{\sigma }\)



Elastic modulus (kN/cm\(^{2}\))


Moment of inertia (cm\(^4\))

\(K_{x}, K_{y}, K_{z}\)

Tangent, radial, and circumferential contact stiffness (kN/cm\(^2\))


Column length (cm)


Delamination length (cm)

\(L_{1}, L_{2}\), and \(L_{3}\)

Length of segments 1–3 (cm)


Cross-sectional bending moment (kNcm)


Experimental axial capacity (kN)


Centrally applied point force (kN)


Critical buckling load (kN)


Full debonding arc-length ratio

\(p_{X}, p_{Y}, p_{Z}\)

X, Y, and Z component of the contact traction (kN/cm)

\(R_X, R_Z\)

X and Z component of the cross-sectional equilibrium force (kN)


Wall thickness of the steel tube (cm)


Axial displacement (cm)


Deflection (cm)

Greek letters

\(\omega \)

Debonding angle (rad)

\(\delta \)

Variational operator

\(\varDelta _{x}, \varDelta _{y}, \varDelta _{z}\)

Generalized slip in tangential, radial, and circumferential direction (cm)

\(\varDelta _{X},\varDelta _{Y},\varDelta _{Z}\)

Generalized slip in XY, and Z direction (cm)

\(\varepsilon \)

Extensional strain

\(\varepsilon _\mathrm{cr}\)

Critical axial strain

\(\kappa \)

Pseudocurvature (rad/m)

\(\lambda \)

Column slenderness ratio

\(\sigma \)

Stress (kN/cm\(^2\))

\(\varphi \)

Rotation (rad)

Subscripts and superscripts


Layer or material


Concrete core


Steel tube


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The authors acknowledge the financial support from the Slovenian Research Agency (research core Funding No. P2-0260).


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Chemistry and Chemical TechnologyUniversity of LjubljanaLjubljanaSlovenia
  2. 2.Faculty of Civil and Geodetic EngineeringUniversity of LjubljanaLjubljanaSlovenia

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