4.2.1.5. CSA S16-24 - Steel Design - PM Interaction

The following can be used to determine the compression / moment interaction capacity of a steel W or Hss section.

Contains functions for managing sections specific to CSAo86-19

Note, right now all limits are calculated at once BEFORE the

class Omega1LoadConditions(value)[source]

An enumeration that represents possible loading cases for omega from 13.8.6 1 = No loads 2 = uniformly distributed loads, or regularly spaced point loads 3 = concentrated loads applied at to the member.

checkBeamColumnCombined(beamColumn: BeamColumnSteelCsa24, Cf: float, Mfx: float, Mfy: float = 0, n: float = 1.34, omegax1: float = 1.0, omegax2: float = 1.0, isBracedFrame=False)[source]

Checks the 4 cases required to assess a steel element in combined bending and shear: cross section strength (c.l. 13.8.2a); Overall member strength (c.l. 13.8.2b); Lateral Torsional Buckling (c.l. 13.8.2c); and biaxial bending (c.l. 13.8.2d).

Parameters

  • beamColumn (BeamColumnSteelCsa24) – The beamcolumn to check.

  • Cf (float) – The applied compressive load (N).

  • Mfx (float) – The applied moment in the strong axis direction (Nm).

  • Mfy (float, optional) – The applied moment in the strong weak direction (Nm). The default is 0.

  • n (float, optional) – The parameter for compressive resistance. The default is 1.34, but the parameter can be increased for certain section types per c.l. 13.3.1.1.

  • omegax1 (float, optional) – Omega 1 calculated as per 13.8.6. It has a default value of is 1.0, which represents a constant moment in single curvature..

  • isBracedFrame (bool, optional) – A flag that specifies if the beam is in a braced frame. The default is False.

Returns

  • u1 (float) – The utilization in case 1, cross section strength.

  • u2 (float) – The utilization in case 2, overall member strength.

  • u3 (float) – The utilization in case 3, Lateral Torsional Buckling.

  • u4 (float) – The utilization in case 4, biaxial bending.

checkCombinedCaseA(beamColumn: BeamColumnSteelCsa24, Cf: float, Mfx: float, Mfy: float, n: float, omega1: float)[source]

Checks the cross sectional member strength, where:

  • Clause 13.8.2 a

  • beta = 0.6

  • lamda = 0

  • Mr is calculated as normal

  • U1x/U2x are specified in 13.8.5 >= 1

Parameters

  • beamColumn (BeamColumnSteelCsa24) – The beamcolumn to check.

  • Cf (float) – The applied compressive load (N).

  • Mfx (float) – The applied moment in the strong axis direction (Nm).

  • Mfy (float, optional) – The applied moment in the strong weak direction (Nm). The default is 0.

  • n (float, optional) – The parameter for compressive resistance. The default is 1.34, but the parameter can be increased for certain section types per c.l. 13.3.1.1.

  • omegax1 (float, optional) – Omega 1 calculated as per 13.8.6. It has a default value of is 1.0, which represents a constant moment in single curvature..

Returns

u – The the output utilziation

Return type

float

checkCombinedCaseB(beamColumn: BeamColumnSteelCsa24, Cf: float, Mfx: float, Mfy: float, n: float, omega1: float, isBracedFrame: bool = False)[source]

Overall member strength Unbraced moment Moment is amplified due to p-delta in the axis of bending only. Assumes the following: - Clause 13.8.2 b - k = 1 for compression, based on axis of bending only. - If there is uniaxial bending, use calulate Cr in that direction. - Mr is calculated as if the column is braced - U1x/U2x are taken as 1, unless the system is in a braced frame - If the system is a braced frame, it is calcualted with 13.8.5

Parameters

  • beamColumn (BeamColumnSteelCsa24) – The beamcolumn to check.

  • Cf (float) – The applied compressive load (N).

  • Mfx (float) – The applied moment in the strong axis direction (Nm).

  • Mfy (float, optional) – The applied moment in the strong weak direction (Nm). The default is 0.

  • n (float, optional) – The parameter for compressive resistance. The default is 1.34, but the parameter can be increased for certain section types per c.l. 13.3.1.1.

  • omegax1 (float, optional) – Omega 1 calculated as per 13.8.6. It has a default value of is 1.0, which represents a constant moment in single curvature..

  • isBracedFrame (bool, optional) – A flag that specifies if the beam is in a braced frame. The default is False.

Returns

u – The the output utilziation

Return type

float

checkCombinedCaseC(beamColumn: BeamColumnSteelCsa24, Cf: float, Mfx: float, Mfy: float, n: float, omega1: float, omega2: float, isBracedFrame=False)[source]

Lateral Torsional Buckling Typically govens sections with strong axis loaded. Assumes the following:

  • Clause 13.8.2 with weak axis bending only.

  • Mrx is calculated as unbraced

  • Mry is calculated as braced

  • U1x/U1y = 1 for members in unbraced framses.

  • U1x is calcualted as in clause 13.8.5, but not less than 1.0 if braced

  • U1y is calculated as in clause 13.8.5

  • U1x/U2x are taken as 1, unless the system is in a braced frame

  • If the system is a braced frame, it is calcualted with 13.8.5

Parameters

  • beamColumn (BeamColumnSteelCsa24) – The beamcolumn to check.

  • Cf (float) – The applied compressive load (N).

  • Mfx (float) – The applied moment in the strong axis direction (Nm).

  • Mfy (float, optional) – The applied moment in the strong weak direction (Nm). The default is 0.

  • n (float, optional) – The parameter for compressive resistance. The default is 1.34, but the parameter can be increased for certain section types per c.l. 13.3.1.1.

  • omegax1 (float, optional) – Omega 1 calculated as per 13.8.6. It has a default value of is 1.0, which represents a constant moment in single curvature.

  • omegax2 (float, optional) – Omega 1 calculated as per 13.8.1. It has a default value of is 1.0, which represents a constant moment in single curvature.

  • isBracedFrame (bool, optional) – A flag that specifies if the beam is in a braced frame. The default is False.

Returns

u – The the output utilziation

Return type

float

checkCombinedCaseD(beamColumn: BeamColumnSteelCsa24, Cf, Mfx, Mfy, isBracedFrame=False)[source]

Biaxial Bending

Members are checked for biaxial bending, without considering compression. Compression is still passed to the function to determine section class.

Parameters

  • beamColumn (BeamColumnSteelCsa24) – The beamcolumn to check.

  • Cf (float) – The applied compressive load (N).

  • Mfx (float) – The applied moment in the strong axis direction (Nm).

  • Mfy (float, optional) – The applied moment in the strong weak direction (Nm). The default is 0.

  • n (float, optional) – The parameter for compressive resistance. The default is 1.34, but the parameter can be increased for certain section types per c.l. 13.3.1.1.

  • omegax1 (float, optional) – Omega 1 calculated as per 13.8.6. It has a default value of is 1.0, which represents a constant moment in single curvature..

  • isBracedFrame (bool, optional) – A flag that specifies if the beam is in a braced frame. The default is False.

getOmega1(loadCase: Omega1LoadConditions, Mmax=1, Mmin=-1)[source]

Calculates the amplifction factor when no transvers loads acts between supports. See c.l. 13.8.6 for details.

Parameters

  • loadCase (Omega1LoadConditions) –

    The load condition:

    1 if there are no intermediate loads 2 if there are uniformy distributed loads 3 if there are concentrated loads applied at to the member.

  • Mmax (TYPE, optional) – TYhe maximum load. The default is 1.

  • Mmin (TYPE, optional) – THe minimum load, negative if single curvature, positive if double curvature. The default is 1.

Returns

The output value of the factor.

Return type

float