# D14.C.6.7 Member Strength and Stability

## Class 1 and Class 2 I-Shaped Sections

Members required to resist both bending moments and an axial compressive force shall be proportioned so that:

$C u C r + 0.85 U 1 x M u x M r x + β U 1 y M u y M r y ≤ 1.0$
where
 Cu and Mu = = the maximum load effects in compression and bending, respectively, including stability effects as defined in Cl. 8.7. β = = 0.6 + 0.4λy ≤ 0.85 λy = = the nondimensional slenderness parameter about the y-y axis

The capacity of the member shall be examined for:

1. cross-sectional strength (members in braced frames only), with β = 0.6, in which case:

• Cr is as define din Cl. 13.3 with the value of λ = 0.
• Mr is as defined in Cl. 13.5 (for the appropriate class of section), and
• U1x and U1y are as defined in 13.8.4 but not less than 1.0, and
2. overall member strength, in which case:

• Cr is as define din Cl. 13.3 with the value of K = 1, except that for strong-axis bending,
• Cr = Crx (see aslo 10.3.2),
• Mr is as defined in Cl. 13.5 (for the appropriate class of section), and
• U1x and U1y are as defined in 13.8.4 for members in braced frames, and
• U1x and U1y are taken as 1.0 for members in unbraced frames, and
3. lateral torsional bucking strength, when applicable, in which case:

• Cr is as define din Cl. 13.3, and is based on weak-axis or torsional-flexural buckling (see also 10.3.3),
• Mrx is as defined in 13.6 (for the appropriate class of section),
• Mry is as defined in 13.5 (for the appropriate class of section),
• U1x and U1y are as defined in 13.8.4 for members in braced frames, and
• U1x is as defined in 13.8.4 but not less than 1.0, for members in braced frames, and
• U1y is as defined in 13.8.4 for members in braced frames

There parameters SSY and SSZ are used to indicate the sidesway in the local Y and Z axes, respectively.

In addition, the member shall meet the following criteria:

$M u x M r x + M u y M r y ≤ 1.0$
where
 Mrx and Mry = = as described in 13.5 or 13.6, as appropriate

## All Other Sections

Members required to resist both bending moments and an axial compressive force shall be proportioned so that:

$C u C r + U 1 x M u x M r x + U 1 y M u y M r y ≤ 1.0$

where all terms are as defined in 13.8.2

The capacity of the member shall be examined for the following cases in a parallel manner to that in 13.8.2:

1. cross-sectional strength (members in braced frames and tapered members only),
2. overall member strength, and
3. lateral-torsional buckling strength.

## Section Values of U1

In lieu of a more detailed analysis, the value of U1 for the axis under consideration, accounting for the second-order effects due to the deformation of a member between its ends, shall be taken as:

$U 1 = ω 1 1 − C u / C e$
where
 ω1 = = for the axis under consideration as defined in 13.8.4 Ce = $= π 2 E I L 2$ for the axis under consideration