# Difference between revisions of "Bode 1976"

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== Theoretical Discussion == | == Theoretical Discussion == | ||

− | ''Short Axially Loaded Columns''. The steel and the concrete in axially loaded short circular columns act independently until the concrete has reached a longitudinal strain of approximately 0.02. At this point, the concrete expands more than the steel tube. The steel is subjected to circumferential tensile stresses and the concrete is compressed triaxially resulting in a much larger strength than concrete loaded only in the axial direction. The increase in the capacity of the short column (the author defines a short circular column as a column with | + | ''Short Axially Loaded Columns''. The steel and the concrete in axially loaded short circular columns act independently until the concrete has reached a longitudinal strain of approximately 0.02. At this point, the concrete expands more than the steel tube. The steel is subjected to circumferential tensile stresses and the concrete is compressed triaxially resulting in a much larger strength than concrete loaded only in the axial direction. The increase in the capacity of the short column (the author defines a short circular column as a column with L/D ≤ 5) was given by the following formula originally published by Sen, 1972: |

<!-- <math>P_o=0.75A_sf_y+A_c(f'_c+\frac{3.5tf_y}{D-2t})</math> --> | <!-- <math>P_o=0.75A_sf_y+A_c(f'_c+\frac{3.5tf_y}{D-2t})</math> --> |

## Latest revision as of 20:34, 8 March 2018

This paper presented a brief overview of analytical methods for calculating the ultimate capacity of short and long columns, and columns subjected to combined axial load and bending moment. The author also discussed the long-term performance of concrete in CFT columns (i.e., creep and shrinkage). He enumerated a number of advantages of filling hollow steel tubes with concrete. These include: a higher critical buckling load due to the stiffening effect of the concrete; greater load-bearing capacity for the given external dimensions; higher resistance to transverse impact loads (e.g., vehicles); ideal use of relatively inexpensive concrete as a compression load-resisting element; simple connections capable of standardization; and the steel tube serving as the concrete formwork.

## Theoretical Discussion

*Short Axially Loaded Columns*. The steel and the concrete in axially loaded short circular columns act independently until the concrete has reached a longitudinal strain of approximately 0.02. At this point, the concrete expands more than the steel tube. The steel is subjected to circumferential tensile stresses and the concrete is compressed triaxially resulting in a much larger strength than concrete loaded only in the axial direction. The increase in the capacity of the short column (the author defines a short circular column as a column with L/D ≤ 5) was given by the following formula originally published by Sen, 1972:

The carrying capacity of a short circular column is also increased if the concrete alone is loaded. To prevent the steel from buckling locally prior to the steel reaching the yield strength, the ACI Building Code 318-71 specifies a minimum ratio of the diameter to thickness of the steel tube:

For short rectangular CFT columns (), the ultimate axial load is equal to the sum of the individual material strengths:

The ratio of the tube width to the tube thickness is also limited by the ACI formula:

*Long Axially Loaded Columns and Beam-Columns*. The author listed a number of characteristics of long, or slender, CFT columns that prohibit a direct calculation of the ultimate load: the materials do not conform to a linear stress-strain relationship; lateral buckling must be accounted for in the equilibration of forces; the steel may be plastic and elastic at different points on the cross-section; the concrete may be cracked; imperfections and residual stresses in the tube may exist; and the effects of creep and shrinkage of the concrete are uncertain. In light of this, the author very briefly described a fiber element method of analysis which has been shown to be quite accurate compared with experimental results. This method involves assigning stress-strain relations (specified by the German code DIN 1045) to fibers on the discretized cross-section. It was assumed that Bernoulli's law applies (i.e., plane sections remain plane for any amount of longitudinal strain). The ultimate combination of axial load and bending moment was obtained using this process for several load cases. Examples of the interaction between axial force and bending moment for different flexural stiffnesses and for different L/D ratios was illustrated for circular sections.

For purposes of design, the author restated an empirical experiment-calibrated equation proposed by Basu and Somerville to calculate the interaction between axial load and bending moment and proposed his own equation based upon the results of his computer analysis.

*Biaxially Loaded Beam-Columns*. For biaxially loaded beam-columns Basu and Somerville extended to rectangular CFTs the formula originally proposed by Bresler for reinforced concrete columns. The formula is a conservative calculation of the ultimate capacity of a section for a load applied with eccentricity about two axes:

where .

*Long-Term Concrete Performance*. The phenomena of creep and shrinkage are less severe in CFTs than in corresponding reinforced columns. Creep of the concrete may reduce the ultimate capacity of the section because it induces additional stress in the steel tube. This may be accounted for in design by adding the anticipated creep load to the dead load. Additionally, creep will reduce the overall stiffness of the CFT. This effect may be accounted for by using a reduced concrete elastic modulus. Shrinkage of concrete inside a steel tube is considerably less than the shrinkage of concrete exposed to the environment. The conditions inside the tube are more humid and shrinkage proceeds at a slower rate. However, care must be exercised if bond is assumed to exist between the steel and the concrete since shrinkage of the concrete may cause a breakdown in the steel/concrete bond.

## References

Bode, H. (1976). “Columns of Steel Tubular Sections Filled with Concrete Design and Applications,” Acier Stahl, No. 11/12, pp. 388-393.