Steel checks to AS 4100

The steel design check supports the AS 4100-1998 version

Input data

All cases provided to the checker are assumed to be ultimate limit state (i.e. the member forces are fully factored). Any non ULS cases – e.g. unfactored wind load – will be treated as if they are ULS, and so will result in non-conservative utilisations.

Effective section properties

Members subjected to bending are classified as compact, non-compact and slender sections in accordance with AS4100:1998, clause 5.2 and table 5.2. The effective section modulus is computed using the appropriate clause from AS4100:1998 5.2.3, 5.2.4 and 5.2.5.

Members subjected to axial compression are classified as compact, non-compact and slender sections in accordance with AS4100:1998, clause 6.2.3

Local checks

Sections are checked at the ends of every sub-span of the member for the moments and forces acting on it.

Shear

Shear is checked according to AS4100:1998, clause 5.11. While calculating the shear strength, steel checker assumes that the section web is unstiffened.

The shear area is calculated based on clear web depth between flanges for the welded sections, and based on full web depth for rolled sections. For RHS and box sections the shear area is based on two clear web depths.

Shear capacities are reduced to account for moment in the direction of shear force according to AS4100:1998 5.12.3

Bending moment

Moment capacity at a section is calculated in accordance AS4100:1998, clause 5.2.1. See Effective section properties for details on calculation of effective section modulus.

Axial force

Compression capacity at a section is calculated in accordance with AS4100:1998, clause 6.2.1. See Effective section properties for details on calculation of effective area of a section.

Tension capacity at a section is calculated in accordance with AS4100:1998 clause 7.2 and 7.3. Sections in tension use the user defined net area ratio.

Torsion

At present, any significant torsional moment (greater than 5% of the torsional capacity) produces a warning.

Combined local effects

The section is checked against all the applied forces using the equations in AS4100:1998, clause 8.3.4. The choice of equations used depends on the section shape and the section’s local buckling class.

Moments used in the local interaction check include the moments due to eccentricity in axial force. Eccentricity may be due to an end connection and to a shift in neutral axis, in the case of unsymmetrical slender sections.

Buckling checks

Axial buckling

The member is checked along its length for major axis axial buckling and minor axis axial buckling according to AS4100:1998, clause 6.3.3.

Unsymmetrical sections are also checked for torsional and flexural torsional buckling according to AS4100:1998, clause 6.3.3. A lambda value will be computed in accordance with clause 6.3.4.

At present the effective length of the member is calculated from the factors available in AS4100:1998, figure 4.6.3.2.

Lateral torsional buckling

Members with full lateral restraint are checked for lateral torsional buckling in according to AS4100:1998, clause 5.3. Lateral restraints are verified in accordance with AS4100:1998, clause 5.3.2.

Lateral torsional buckling is checked in accordance with AS4100:1998, clause 5.6.1 and 5.6.2(i) for the member without continuous restraints. Effective lengths for lateral torsional buckling are calculated according to AS4100:1998, clause 5.6.3.

If the member has an equivalent uniform moment factor override specified, this is used in place of $\alpha_m$ in lateral torsional buckling calculations.

Buckling interaction

Interaction checks are carried out according to AS4100:1998, clause 8.4.5.1 and 8.4.5.2 for compression and tension members respectively. Reduced moments used in compression member checks are calculated using the simplified equations in AS4100:1998, clause 8.4.2.2 and 8.4.4.1.

Moment amplifications

The member moment demand will be amplified by the moment amplification factor for all member utilisation checks in accordance to clause 4.4.2.2.

If a member is subjected to compressive force, the member moments from linear analysis need to be amplified by a moment amplification factor. The amplified moments will be used in the member capacity checks and member designs.

The automatically calculated moment amplification factor can also be overridden in member definition. If it is overridden, the explicitly defined moment amplification factor will be used in the design, and the calculation of the moment amplification factors will be skipped. This may be of interest if alternative analysis methods are used to account for P-delta effects (ie. running a P-Delta analysis with at least one intermediate node in compression memebers).

Moment amplification factor

Moment amplification factors are calculated based on:

• The elastic buckling load capacity of the member (span)
• The axial force on the member (span) and
• The loading conditions on the member

A member can have several spans depending on the restraint conditions, e.g., if a member has one intermediate restraint in the major axis direction, the member will have two spans and two moment amplification factors in the major axis direction. As the restraint conditions may be different in major and minor axis directions, the moment amplification factors are calculated separately for the two directions. The calculation of the moment amplification factors is based on clause 4.4.2.2 of the design code.

If a member effective length has been overridden in a major or minor axis direction, there will be only one span and one moment amplification factor for that direction.

The moment amplification factor is only applied to the members with compressive force no matter the moment amplification factor is calculated or from user input.

The calculation of moment amplification factor

According to clause 4.4.2.2 of the design code, moment amplification factor is calculated from:

$$\delta_{\mathrm{b}}=\frac{\mathrm{C}_{\mathrm{m}}}{1-\left(\frac{\mathrm{N}^*}{\mathrm{~N}_{\mathrm{omb}}}\right)} \geq 1.0$$

Where:

$C_{\mathrm{m}}=0.6-0.4 \beta_{\mathrm{m}} \leq 1.0$

$N^*$ - the compressive force of the span

$\mathrm{N}_{\mathrm{omb}}=\frac{\pi^2 \mathrm{EI}}{\mathrm{L}_{\mathrm{e}}^2}$ - the elastic buckling load capacity of the span

$\beta_m$ is calculated based on the following two conditions

1. If a span has no span loading

   $\beta_m$ is the ratio of the smaller to the larger bending moment at the ends of the span, taken as positive when the member is bent in reverse curvature

2. If a span has span loading

$$\beta_m=1-\left(\frac{2 \Delta_{c t}}{\Delta_{c m}}\right)$$

with -1.0 ≤ $\beta_m$ ≤1.0

$\Delta_{c t}$ is mid-span deflection of the span resulting from the transverse loading together with both end bending moments as determined by the analysis

$\Delta_{c w}$ is mid-span deflection of the span resulting from the transverse loading together with only those end bending moments which produce a mid-span deflection in the same direction as the transverse load

$\Delta_{c t}$ and $\Delta_{c w}$ are calculated numerically in GSA using Gauss numerical integration based on the member properties and the moments along the span.