# Tomii and Sakino 1979 c

The objectives of this paper are twofold--1) to clarify the elasto-plastic behavior of CFT columns subjected to combined axial and shearing forces, and 2) to present a practical analytical model to predict the behavior of such columns.

## Experimental Study, Discussion, and Results

Forty tests were conducted in five series. Each series contained different material properties and tube thickness (D/t). The variable parameters within each series were the shear span ratio (a/D) and the axial load ratio (P/Po). The tubes were annealed to remove residual stresses. The test setup simulated fixed end conditions and induced a double-curvature deformation in the specimen.

The paper includes numerous V-R curves, where R is the translation angle, measured as the midheight deflection divided by the length. Each curve included the point of observed local buckling, which typically occurred at or near the peak shear stress, but well in advance of the maximum rotation. Two types of behavior were recognized based on the a/D ratio. For a shear span ratio of 0.83 or 1.0, diagonal shear cracking was observed in all specimens except the one without an axial load. The column with a high D/t ratio behaved in a brittle manner under a high axial load. For a shear span ratio of 2.0 or 3.0, all of the columns failed in flexure.

## Analytical Study

The relationship between shear force and rotation was determined following the same assumptions proposed in Tomii and Sakino (1979a). Additionally, the fracture zone was assumed to occur in a region at the member end with a length of 0.6*D. Shearing deformation is accounted for by using an effective shear modulus of the concrete and steel. Additional moments due to the P-Δ effect (end offset) were considered using a Column Deflection Curve method, which was not discussed in any detail. Also, the descending branch of the concrete stress-strain diagram was adjusted to account for the additional ductility provided by the presence of a moment gradient. The analytical results agreed well with the experimental except for the shear span ratio of 2.0. The authors believe the discrepancy lies in the perfect bond assumption and an overestimate of the shearing rigidity of the section.

## References

Tomii, M. and Sakino, K. (1979c). “Experimental Studies on Concrete Filled Square Steel Tubular Beam-Columns Subjected to Monotonic Shearing Force and Constant Axial Force,” Transactions of the Architectural Institute of Japan, No. 281, July, pp. 81-90.