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D8.A.2.7 Combined Interaction Check

Members subjected to various forces – axial, shear, moment, torsion - are checked against combined interaction check.

Limit State Method

This interaction check is done taking care of two aspects:

  • Section strength

  • Overall member strength

Section strength interaction ratio is calculated as per sec. 9.3.1 of the code.

Overall Member Strength interaction ratio is calculated as per sec. 9.3.2, taking care of the design parameters PSI, CMX, CMY, and CMZ

Working Stress Method

The following interactions are considered:

  1. Combined Bending and Shear — No reduction in allowable stresses for the interaction of bending and shear is considered.

  2. Combined Axial Compression and Bending — The following formulas are intended to require member stability:

    fc/facy + 0.6·Ky(Cmyfbcy/fabcy) + KLTfbcz/fabcz ≤ 1.0

    fc/facz + 0.6·Ky(Cmyfbcy/fabcy) + Kzfbcz/fabcz ≤ 1.0

    fc/(0.6fy) + fbcy/fabcy + fbcz/fabcz ≤ 1.0

    where
    fc
    =
    Actual axial compressive stress.
    facy, facz
    =
    Allowable compressive stress, governed by buckling, about the local Y and Z axis, respectively.
    fbcy, fbcz
    =
    Actual bending compressive stress about minor and major axes, respectively.
    fabcy, fabcz
    =
    Allowable bending compressive stress about minor and major axes, respectively.

    Ky = 1 + (λy - 0.2)·ny ≤ 1 + 0.8·ny

    Kz = 1 + (λz - 0.2)·nz ≤ 1 + 0.8·nz

    KLT = 1 - 0.1·λLT·ny/(CmLT - 0.25) ≥ 0.1·ny/(CmLT - 0.25)

  3. Combined Axial Tension and Bending — The following formulas are intended to require member stability:

    ft/fat + fbty/fabty + fbtz/fabtz ≤ 1.0

    where
    ft
    =
    Actual axial tensile stress.
    fat
    =
    Allowable axial tensile stress.
    fbty, fbtz
    =
    Actual bending tensile stress about minor and major axes, respectively.
    fabty, fabtz
    =
    Allowable bending tensile stress about minor and major axes, respectively.