The AISC specification for allowable stress design for buildings includes three interaction formulas for combined axial compression and bending.

When the ratio of computed axial stress to allowable axial stress f /F a exceeds 0.15, both of the following equations must be satisfied:

( f a / F a ) + ( C m x f b x ) / (1– f a /F ‘ e x ) F b x + C m y f b y / (1 – f a / F ‘ e y ) F b y ? 1

f a / 0.60F y + f b x /F b x + f b y / F b y ? 1

when f a /F a ? 0.15, the following equation may be used instead of the preceding two:

f a / F a + f b x / F b x + f b y / F b y ? 1

In the preceding equations, subscripts x and y indicate the axis of bending about which the stress occurs, and

In the preceding equations, subscripts x and y indicate the axis of bending about which the stress occurs, and

F a = axial stress that would be permitted if axial force alone existed, ksi (MPa)

F b = compressive bending stress that would be permitted if bending moment alone existed, ksi (MPa)

F ‘ e = 149,000 / ( Kl b / r b ) 2 , ksi (MPa); as for F a , F b , and 0.6F y , F ‘ e may be increased one-third for wind and seismic loads

Lb = actual unbraced length in plane of bending, in (mm)

r b = radius of gyration about bending axis, in (mm)

K = effective-length factor in plane of bending

f a = computed axial stress, ksi (MPa)

f b = computed compressive bending stress at point under consideration, ksi (MPa)

C m = adjustment coefficient