The yield stress fdetermined for uniaxial tension is usually accepted as beingvalid for uniaxial compression. However, the general state of stress at a point ina thin-walled member is one of biaxial tension and/or compression, and yieldingunder these conditions is not so simply determined. Perhaps the most generally accepted theory of two-dimensional yielding under biaxial stresses acting in the

plane is the maximum distortion-energy theory (often associated with namesof Huber, von Mises, or Hencky), and the stresses at yield according to this theorysatisfy the conditions21_

- s1_

s2_

+ s22_

+ 3s21_2_

= f2y

, (1.1)in which s1_

, s2_

are the normal stresses and s

is the shear stress at the point.For the case where 1_

and 2_1_2_

are the principal stress directions 1 and 2, equation 1.1takes the form of the ellipse shown in Figure 1.7, while for the case of pure shear(s1_

= s2_

= 0, so that s1

=-s2

= s), equation 1.1 reduces tos1_2_

= fy

/v3 = ty1_2_

, (1.2)which defines the shear yield stress ty

.