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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

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Kanwarjot Singh

Kanwarjot Singh is the founder of Civil Engineering Portal, a leading civil engineering website which has been awarded as the best online publication by CIDC. He did his BE civil from Thapar University, Patiala and has been working on this website with his team of Civil Engineers.

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