# Combined Axial Compression Or Tension And Bending

Posted in Building | Email This Post |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