D4.E.6.3 Members Subject to Combined Forces
Axial compression and bending
The member strength and stability for sections subjected to axial compression and uniaxial or biaxial bending is obtained through the use of interaction equations. In these equations, the additional bending caused by the action of the axial load is accounted for by using amplification factors (Cl. 13.8). ω1y and ω1z are calculated as per Cl. 13.8.5 or as specified in the CMY and CMZ design parameters, respectively.
-
For Class 1 and Class 2 sections of I-shaped members (Cl. 13.8.2): where
- Cf , Mf
= - the maximum load effects, including stability, as specified in Cl. 8.4.
- β
= - 0.6 + 0.4λy ≤ 0.85
The capacity of the member is investigated for the following:
- Cross sectional strength with β = 0.6, where
- Overall member
strength, where
- Cr as specified in Cl. 13.3 with K = 1, except for uniaxial bending, in which case Cr is based on the axis of bending
- Mr as specified in Cl. 13.5
- U1x and U1y are taken as 1.0 for members in an unbraced frame, and as specified in Cl. 13.8.4 for members in a braced frame. Design parameters SSY and SSZ are used to evaluate these coefficients.
- Lateral torsional
buckling strength, when applicable, where
- Cr as specified in Cl. 13.3
- Mrx as specified in Cl. 13.6
- Mry as specified in Cl. 13.5
- U1x and U1y are taken as 1.0 for members in an unbraced frame, and as specified in Cl. 13.8.4 for members in a braced frame (where U1x is not less than 1.0). Design parameters SSY and SSZ are used to evaluate these coefficients.
- For Class 1 and Class 2 square or circular HSS sections per S16-19 only (Cl.
13.8.3):
- For square sections:
- For circular sections:
-
For all other cases (Cl13.8.3 per S16-09 / 14 or Cl 13.8.4 of S16-19):
The capacity of the member is investigated for the following per Cl.13.8.2:
Axial tension and bending
Members subjected to axial tension and bending must satisfy the following equation (Cl. 13.9.1):
where= |
Additionally, the following equations must be satisfied for laterally unsupported members (Cl. 13.9.2 of S16-09 /14):
- for Class 1 and Class 2 sections
- for Class 3 and Class 4 sections
= |
The following equations must be satisfied for laterally unsupported members designed per S16-19 (Cl. 13.9.3 of S16-19):
- for Class 1 and Class 2 sections
- for Class 3 and Class 4 sections
= |
= |
Shear and Bending
For S16-09 / 14, to resist the combined effects of shear and bending, all of the following equations must be satisfied (Cl. 14.6):
(S16-09 / 14) |
= | ||
= |
For S16-19: for beams with webs with Fs > 0.60 Fy to resist the combined effects of shear and bending, the shear resistance, Vr, is multiplied by the following reduction factor (Cl. 14.6):
The shear resistance is not reduced below 0.60 ϕAwFy. Also, the shear resistance is not increased due to this calculation.