Combined Axial Compression Or Tension And Bending

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