 # G.17.4.1.6.1 Calculation of QCE

The expected flexural strength is evaluated by the following means for beam or column elements.

## Beams

The strength of elements of structural steel under flexural actions with negligible axial load present is calculated in accordance with this section.

The expected flexural strength, QCE, of beam components is determined using equation 1-6-3. For nonlinear procedure flexural actions of beams is considered deformation controlled. Permissible plastic rotation deformation is as indicated in equations 1-6-1 and 1-6-2 (Ref. Sections 5.5.2.2.2 and 5.5.2.3.2 of FEMA 356).

## Columns

This section is used to evaluate flexural and axial strengths of structural steel elements with non-negligible axial load present. These actions shall be considered force controlled.

The lower-bound strength, QCL, of steel columns under axial compression is taken to be the lowest value obtained for the limit states of column buckling, local flange buckling, or local web buckling. The effective design strength or the lower-bound axial compressive strength, PCL, shall be calculated in accordance with the LRFD method, taking φ = 1.0 and using the lower-bound strength, FyLB, for yield strength. The expected axial strength of a column in tension, QCE, is computed in accordance with equation (1-6-1-1) (Ref. Section 5.5.2.3.2 of FEMA 356):

 QCE = TCE = AcFye (1-6-1-1)

where
 Ac = Area of column Fye = Expected yield strength of column TCE = Expected tensile strength of column FyLB = Lower-bound yield strength

Flexural loading of columns, with axial loads at a target displacement less than 50% of PCL shall be considered deformation controlled and maximum permissible plastic rotation demands on columns, in radians, shall be as indicated in tables 1.5.1 and 1.5.2, dependent on the axial load present and the compactness of the section.

Flexural loading of columns, with axial loads at the target displacement greater than or equal to 50% of PCL, shall be considered force-controlled and shall conform to equation (1-6-1-2) (Ref. Section 5.5.2.4.2 of FEMA 356).

 PUF/(2·PCL) + Mx/(mxMCEx) + My/(myMCEy) ≤ 1.0 (1-6-1-2)

where
 PUF = Axial force in the member PCL = Lower bound compression strength of the column Mx = Bending moment in the member for the x-axis My = Bending moment in the member for the y-axis MCEx = Expected bending strength of the column for the x-axis MCEy = Expected bending strength of the column for the y-axis mx = Value of m for the column bending about the x-axis in accordance with Table 5-5 of FEMA 365 my = Value of m for the column bending about the y-axis in accordance with Table 5-5 of FEMA 365