Recently I tested concrete filled steel tube of 3.5m length for flexure load. When the maximum deflection at the center reaches to 20mm, the machine broke down. Now I want to check that whether the steel yielded or not?
It is a bit like reinforced concrete beams. The concrete inside the tube would have started to crack before the steel tube yielded. If you did not put any strain gauges on the tube, you use bending theory by calculating the maximum stress = M/Z, then compare this with the yield stress of the tube.
My deepest sympathies to the machine that was damaged! But clearly, you have made an interesting finding. Composites have tricky results to interpret but nonetheless, the same principles hold - Synergetic benefits are made possible.
Regarding application of flexure, concrete give a very high stiffness while steel behave in a ductile manner. A curve of your experiment's Stress vs strain will be helpful for me to comment further.
I agree with Samuel, it will be very interesting to see the stress-strain curve, as it will be quite revealing as to the composite behaviour of the tube.
If you have the lateral deflection of the column at more than three points along the column, you can plot a reasonable estimate of curvature. From this, you can estimate the maximum and minimum strains at the point of maximum deflection. If you have the stress strain curve of the steel, you can determine whether yielding has occurred.
Of course, it would be better still to correlate this with actual strain readings on the surface of the column.
I assume that local buckling of the compression side of the column has not occurred.