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American Institute of Steel Construction has this graph, (AISC Spec E2), for columns that are not crooked and do not have residual manufacturing stress, and are doubly symmetrical. There are safety factors that take into consideration a variety of imperfections and apply according to the specific load combinations. The vertical axis is $F_{cr}/F_y \ $ and ...


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When a column is stressed beyond yield, the strain increases rapidly with small changes in stress, at this stage, the stress-strain curve is no longer linear, and the tangent modulus decreases. The tangent modulus is the slope of the stress-strain curve; in the linear elastic range, it is called "elastic modulus, $E$"; beyond yield, it is called &...


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Equation 6.18 is the "design plastic shear resistance", and equation 6.19 is the limiting shear stress for the "design elastic shear resistance. Hope this clears the confusion.


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