I wanted to derive a formulae to give a value of fx in the region beteween ε1 and ε2, which has a quadratic overlay with a point of contraflexure. We know f2, ε1,ε2 and S2, but not f1. Just to clarify E0 is the initial tangent stiffness at (0,0) and S2 is the secant line between points (ε1,f1) and (ε2,f2), where the slope is 0.
In a similar way I figured out that the formulae for fx in the qadratic range between 0 to ε1 is:
fx=εx (E0+(S1-E0)εx/ε0)
where S1 is the secant line betwee points (0,0) and (ε1,f1).
I tried to derive a similar formulae for region between ε0 and ε1 but I couldn't figure it out. Could someone help me? Apologies for the dreadful drawing.
Thanks
In a similar way I figured out that the formulae for fx in the qadratic range between 0 to ε1 is:
fx=εx (E0+(S1-E0)εx/ε0)
where S1 is the secant line betwee points (0,0) and (ε1,f1).
I tried to derive a similar formulae for region between ε0 and ε1 but I couldn't figure it out. Could someone help me? Apologies for the dreadful drawing.
Thanks
