# Shakir-Khalil and Zeghiche 1989

Tests were conducted on 7 full-scale rectangular CFT columns, 1 axial, 4 in uniaxial bending (2 about the major axis, 2 about the minor axis), and 2 in biaxial bending. The results were compared with the predictions of a finite element analysis and the BS5400 predicted failure loads. Studies were also conducted to study the amount of bond in CFTs. A number of graphs and tables illustrated the results of the tests in detail.

## Contents

## Experimental Study, Discussion, and Results

Loading was applied in increments of 10% of the maximum load until some relatively large non-linearity was observed. Failure was considered to have occurred when the columns shed off any additional load increment.

*Bond* Bond tests were performed using a push-out test (i.e., the concrete was loaded by a steel ram and could move vertically when the bond failed). The relationship between load and slip was linear up to about 90% of failure, after which the load-slip curve became nonlinear as the slip showed a continuous increase with the addition of load. The bond strength of the tested specimens varied from only 38 to 54 psi. These values are relatively low compared to reinforcement bars and even circular CFT sections. The combination of shrinkage and the relative flexibility of the rectangular tube walls versus a circular tube has an adverse effect on the amount of bond strength developed.

*Long Column Tests* The failure mode of all the columns was overall flexural buckling. No local buckling was observed. The results show that the moment due to the eccentricity played a significant role in columns subjected to small eccentricities. For larger eccentricities, the secondary moment due to P-* effects could become larger than the primary moment caused by the eccentric loading. The need to incorporate initial out-of-straightness was recognized, although it was not considered in the paper. Strains across the cross section showed a linear variation up to 96% of the failure loads for all of the specimens. The yield strain was reached in the compression zones at loads varying from 80% to 90% of ultimate. Beyond this point, the strains increased rapidly with very small increases in the load. The strains in the tensile zones reached yield after failure as the column underwent large lateral displacements and were subjected to high bending moments.

## Theoretical Discussion

*Axially Loaded CFT's* The behavior of axially loaded CFT columns depends mainly on the column's effective buckling length, the minimum dimension of its cross section, and the mechanical properties of the steel and concrete. These properties may be combined to define the column as 'short' (stocky), 'medium' length, or 'long' (slender). Short columns fail by steel yielding and concrete crushing. Medium length columns exhibit inelastic behavior and fail by overall flexural buckling. The failure mechanism is characterized by partial steel yielding, crushing of the concrete on the compression face, and concrete cracking on the tensile face, which are caused by the induced bending moment in the column as it deforms laterally. Long columns behave elastically and fail by flexural buckling. Their behavior may be accurately predicted using the Euler approach.

*Eccentrically Loaded CFT's* Short columns under eccentric loading exhibit a linear load-moment relationship up to failure (i.e., lateral displacement of the section is insignificant compared to the applied moment). As the column length increases, the secondary moment due to the mid-height lateral deflection becomes larger than the moment caused by the applied eccentricity. This causes the column to fail by buckling or bending rather than by compression.

## Analytical Study

The first step in the numerical analysis was to develop moment-thrust-curvature diagrams. Following that, the analysis to determine the ultimate load was carried out by a finite element method and also by an approximate method using a sine curve to model the deflection with equilibrium maintained at mid-height. The moment-thrust-curvature curves were developed under the following assumptions: complete interaction between the steel and concrete, plane sections remain plane, the steel stress-strain relationship was elastic-perfectly plastic, and strain hardening of steel and tension in the concrete were ignored. The curves were constructed by establishing the neutral axis in the cross section for a given set of axial load and curvature. The moment to maintain equilibrium was established for each variation in curvature, then the process was repeated for a different axial load. The sine-curve deflected shape procedure first assumed an initial axial load and corresponding mid-height displacement. Using the moment-thrust-curvature relationship, external and internal bending moments were computed and their difference compared to a preset tolerance. This iterative process continued until a specified maximum number of iterations was exceeded. The load at this point was taken as the failure load. In the finite element analysis, the column was discretized into 10 beam elements with equilibrium and compatibility satisfied at each of the 11 nodes. The relationship between the external moment and the bending moment at each node was given as follows:

where E*I is the flexural rigidity of the section (not defined by the authors) and P is the axial load. The authors began the analysis by setting the end force and lateral mid-height displacement. The moment-thrust-curvature relationship was generated and then the stiffness matrix was formulated from which the curvature vectors could be obtained. Like the sine-curve approach, internal and external moments were computed based on curvatures and compared in an iterative process until a solution was found.

## Further Research

The authors emphasized in conclusion that many more tests must be performed to validate the results of their investigation. They suggested that initial out-of-straightness should be measured and incorporated into the analytical formulation. Finally, more tests regarding the validity of the BS5400 predictions should be performed, especially concerning minor axis bending.

## References

Shakir-Khalil, H. and Zeghiche, Z. (1989). “Experimental Behavior of Concrete-Filled Rolled Rectangular Hollow-Section Columns,” The Structural Engineer, Vol. 67, No. 19, pp. 345-353.