AISC 341-16 and AISC 341-10

Columns in OMF and OCBF – No additional requirements.

Columns in IMF – Columns must satisfy the requirements of clause D1.1b for “moderately ductile” members.

Columns in SMF and SCBF – Columns must satisfy the requirements of clause D1.1b for “highly ductile” members.

The loading conditions affect the seismic classification in the following way,

• Axial tension only – no classification required.
• Any other loading condition – the appropriate rules in the section classification table are applied.

See: AISC 341-16 and AISC 341-10 seismic classification - all members

AISC 341-05

Columns in OMF and OCBF – No additional requirements.

Columns in IMF – Columns must satisfy clause 8.2a i.e. the requirements for Compact sections to AISC 360-05 in Table B4.1.

Columns in SMF and SCBF – Columns must satisfy Clause 8.2b for “seismically compact” sections.

The loading conditions affect the seismic classification in the following way,

• Axial tension – no classification required.
• Any other loading condition – the appropriate rules in the section classification table are applied.

See: AISC 341-05 seismic classification - all members

This check consists of two analyzes of the column - one that uses the 'amplified seismic load' and a second that uses a 'capacity analysis' as an upper bound. The moments and shears in the column are ignored and the column is designed for axial load only.

Overstrength seismic load

P_amp, the required axial strength (either tension or compression) including the “overstrength seismic load” is given by,

P_amp = P_r + f_E/ρ * P_E * (Ω_o - ρ)

Where;

P_r = the axial force (-ve for tension and +ve for compression) determined from the analysis of the seismic load combination (LRFD or ASD). This may be the result of a first or second order analysis.

P_E = the axial force (-ve for tension and +ve for compression) determined from the analysis of the seismic loadcase(s) associated with the seismic load combination.

f_E = the strength load factor associated with the seismic load in the seismic load combination (base combination factor x ρ) (for example, 0.683 in the ASD combination, D + 0.75 L + 0.75 Lr + 0.683 E).

ρ = the redundancy factor, ρ₁ when the column is assigned to Direction 1 and r2 when the column is assigned to Direction 2 (from the Seismic Wizard).

Ω_o = the overstrength factor, Ω_o1 when the column is assigned to Direction 1 and Ω_o2 when the column is assigned to Direction 2 (from the Seismic Wizard...).

Design condition

For each stack, the required axial strength, P_r is compared with the nominal axial strength, P_n, i.e. the design condition is,

P_r ≤ ɸ x P_n (LRFD) or P_n/Ω (ASD)

Where

P_n = the nominal axial strength in tension or compression as appropriate to the sign of P_r

ɸ = the resistance factor for tension or compression as appropriate

Ω = the safety factor for tension or compression as appropriate

This check consists of two analyzes of the column - one that uses the 'amplified seismic load' and a second that uses a 'capacity analysis' as an upper bound. The moments and shears in the column are ignored and the column is designed for axial load only.

Amplified seismic load

P_amp, the required axial strength (either tension or compression) including the “amplified seismic load” is given by,

P_amp = P_r + f_E/ρ * P_E * (Ω_o - ρ)

Where;

P_r = the axial force (-ve for tension and +ve for compression) determined from the analysis of the seismic load combination (LRFD or ASD). This may be the result of a first or second order analysis.

P_E = the axial force (-ve for tension and +ve for compression) determined from the analysis of the seismic loadcase(s) associated with the seismic load combination.

f_E = the strength load factor associated with the seismic load in the seismic load combination (base combination factor x ρ) (for example, 0.683 in the ASD combination, D + 0.75 L + 0.75 Lr + 0.683 E).

ρ = the redundancy factor, ρ₁ when the column is assigned to Direction 1 and r2 when the column is assigned to Direction 2 (from the Seismic Wizard).

Ω_o = the overstrength factor, Ω_o1 when the column is assigned to Direction 1 and Ω_o2 when the column is assigned to Direction 2 (from the Seismic Wizard...).

Capacity analysis

At any level on a column there can be SFRS members and non-SFRS members. The principle of this check is that the former might be operating at their “capacity” in an earthquake and so they are likely to apply more force to the column than the global analysis would indicate. “Capacity” in this context also includes the possibility that the material is stronger than its specified yield (typical).

The capacity calculation involves establishing the capacities of the incoming SFRS members at each node (level) in the column – these might be zero if there are only non-SFRS members at that level. The capacities so determined are then resolved into the local x-axis of the column. The capacities are calculated for beams and braces only, not the columns themselves.

The end result of the capacity analysis is that for each stack there is an axial force, P_cap which can be compression or tension. This will be included in the results and used in this design check to D1.4a but will only govern if smaller than that from the “Amplified seismic load” analysis.

Design condition

For each stack, the required axial strength, P_r (the smaller of P_cap or P_amp) is compared with the nominal axial strength, P_n, i.e. the design condition is,

P_r ≤ ɸ x P_n (LRFD) or P_n/Ω (ASD)

Where

P_n = the nominal axial strength in tension or compression as appropriate to the sign of P_r

ɸ = the resistance factor for tension or compression as appropriate

Ω = the safety factor for tension or compression as appropriate

At each level in a column where an SMF beam connects into the strong axis of the column (i.e. into the flange), a check is performed for each seismic combination to ensure that the plastic moment capacity of the column is greater than the plastic moment capacity of the incoming beams.

The design condition is,

∑ M_pcol / ∑ M_pbeam > 1.0

Design condition

Moments in the column are permitted to be ignored as per F2.3 (1) and so only the axial check (compression or tension) is required.

For each stack, the required axial strength, P_r, is compared with the nominal axial strength, P_n, i.e. the design condition is,

P_r ≤ ɸ x P_n (LRFD) or P_n/Ω (ASD)

Where P_r = the required axial strength, P_cap

P_n = the nominal axial strength in tension or compression as appropriate to the sign of P_r

ɸ = the resistance factor for tension or compression as appropriate

Ω = the safety factor for tension or compression as appropriate

The calculations for this check are exactly the same as those for the AISC 341-10, D1.4a Required Strength check except that they are only performed when the required axial force exceeds a certain limit as described below.

P_r > 0.4 x ɸ_c x P_n (LRFD)

P_r > 0.4 x P_n / Ω_c (ASD)

Where

ɸ_c = 0.90

Ω_c = 1.67

P_n = the nominal axial strength of the stack in compression or tension as appropriate to the sign of P_r

Either,

P_r = P_u

= the maximum axial force in the stack from the current (LRFD) seismic combination

Or,

P_r = P_a

= the maximum axial force in the stack from the current (ASD) seismic combination

At each level in a column where an SMF beam connects into the strong axis of the column (i.e. into the flange), a check is made to ensure that for each seismic combination the plastic moment capacity of the column is greater than the plastic moment capacity of the incoming beams. The calculations for this check are exactly the same as those for the AISC 341-10, E3.4a Moment Ratio check.