I currently have the moment-rotation curve from several experiments. But I could not find the guidance in Eurocode on how to get the rotational stiffness from the experimental M-rotation curve? Are there any guidances available like finding the concrete's modulus using the secant slope from zero to 40% of the ultimate strength?
It depends on which stiffness do you need - the initial or secant. If you need the initial stiffness you may use the curve in the truly linear range (in your figure up to 30-40 units on the Y-axis). You may use the elastic range up to 2/3Mmax, there you'll have limited non-linearity. You should use some regression (MLE or least squares).
Hello Zequan
For the initial stiffness, you may use the tangent to the moment-rotation curve at the initial stage when the curve is fairly linear.
Best wishes
Thank you very much for your answers. In the end, I chose to use the 2/3Mmax as suggested by Mr. Andreev. As this will lead to a more conservative initial rotational stiffness. I am also working on the following option suggested by one friend from Quora from the paper by Xue & Yang (2010) " Seismic tests of precast concrete, moment- resisting frames and connections."
Mr Ziquan, the plot you linked shows the procedure of the N2-method by Fajfar et al for displacement based seismic design. It was developed for whole buildings which could be simplified to SDOF systems. You may use something like this as proposed in EN 1993-1-8 (see attached picture).
Best regard,
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