Steel Checks to BS 5950-1

The steel design check supports the BS 5950-1:2005 edition.

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 utilizations.

This section explains particular (non-obvious) significances of input data to the BS5950-1:2000 member checker. See Step By Step Guide: Steel Design and the Steel Member Design chapter for general steel design input requirements.

Max Plastic/Elastic Ratio

In order to limit the effects of plasticity at the serviceability limit state (SLS), the design code limits the maximum benefit that can be obtained at the ultimate limit state from allowing the section to become plastic in bending. To comply with BS5950-1:2000 4.2.5.1, the limit should be set to 1.2 for simply supported members and cantilevers, and 1.5 for members with moment continuity between spans. If the ratio is set to 0, the checker will assume 1.2 (which is the more conservative choice available).

Single Angle Struts

BS5950-1:2000 4.7.10.2 and Table 25 make reference to the A-A, B-B and V-V axes in relation to axial buckling. The V-V axis is the minor principal axis. The AA and BB axes are the X-X and Y-Y axes, but which is which depends on the design of the connections of the member to the rest of the structure. The checker only knows about the applied member restraints.

The rotational restraint applied by a two bolt group in clearance holes in one leg ( clause 4.7.10.2 (a) ) should be represented by restraining the section:

• fully about the axes of the bolts, and
• partially about an axis perpendicular to the bolts and the member.

The rotational restraints applied by a two bolt group, one of which uses a kidney shaped hole should be represented by restraining the section:

• partially about an axis perpendicular to the bolts and the member.

The rotational restraint applied by a single bolt group should be represented by leaving the member free about both the X-X and Y-Y axes.

The local capacity check needs to know which legs are connected at the location of the check ( clause 4.6.3.1 ). This information is partly provided by the rotational restraints if they are applied as above. In cases of ambiguity, the connection restraint settings are used. Restraint settings “A” and “B” imply that legs A and B respectively are connected. Where both legs are connected, both “A” and “B” should be set. Even if “A” and/or “B” are not set, the checker can often make assumptions using the rotational restraints alone. Examples of connections requiring use of “A” and “B” include all those consisting of a single bolt through either leg.

Local Checks

At each end of each subspan (LH and RH), the member’s section is checked for the moments and forces applied to it.

Plastic, compact. semi-compact and slender sections are supported.

Allowance for slenderness is made by the use of effective section properties, and the full design stress, which is considerably less conservative than the adoption of a lowered design stress in conjunction with the gross section properties (as used by the Blue Book [19]).

Depending on the section’s properties, the method of checking may vary. For example, if the section is doubly-symmetric and compact or plastic, biaxial bending may be checked using the Mrx and Mry method which reduces the moment capacities with increasing axial load.

Shear

Shear is checked only if the section’s web(s) are not slender. Warning is given if the section is slender in shear.

Bending moments

Moments are conservatively enhanced if slenderness leads to the effective centroid of the section moving, and axial force is present.

Mcx and Mcy are always calculated (reduced by coincident shears in either direction), and compared with the applied moments. The interaction of transverse shear is not covered by BS5950-1:2000 (which is therefore potentially non-conservative). This deficiency is rectified by the use of a Von Mises type capacity reduction. Shear force parallel to webs in bending is considered in accordance with BS5950-1:2000.

Mrx and Mry (moment capacities with coincident axial force) are calculated for plastic and compact doubly symmetric sections, and compared with the applied moments. They are not reduced by coincident shears. For this reason, their use is inhibited by “high” shears: (Fv>0.6Pv) in either direction.

Axial force

Sections in tension use the user controllable Net Area Ratio to determine net area.

Slenderness is calculated differently for sections in overall tension, than for sections in compression.

Torsion

At present, any significant torsional moment (greater than 5% of the torsional capacity) causes a warning, because torsion is not explicitly catered for by the code. The torsional capacity is calculated as follows: (1) CHS - thin wall theory is used; (2) RHS - thin wall theory is used but warping restraint is ignored; (3) I section - based on formulas in Table 10.7 in the book of “Roark’s Formulas for Stress and Strain”.

Combined local effects

The section is checked against all the applied forces (except torsion) using the appropriate equations in BS5950-1:2000 4.8.2 and 4.8.3. The choice of equations depends on the section shape and the section’s local buckling class.

Buckling Checks

The member is checked along its length for major axis axial buckling, minor axis axial buckling and LT buckling in turn. Once complete, relevant interactions of the buckling modes are considered.

Individual buckling mode checks

Each buckling mode check searches for appropriate buckling spans using the design restraints that have been applied to the member. Each buckling span is checked individually. Cantilever spans at either end of members are recognized and catered for.

The effective buckling length calculated can be overridden to either a multiple of the member length or to an absolute length. If this is done, the whole member length is used for determination of buckling parameters, such as equivalent uniform moment factors and applied axial forces.

If a member has an Equivalent Uniform Moment Factor override specified, this is used in place of $m_{LT}$ for lateral torsional buckling check and design.

Buckling interaction

During checks for the simple buckling modes (axial/major axis, axial minor axis, and LT) note is made of various parameters needed later when the buckling interaction check is carried out. These parameters are stored for each sub-span of the member. (See BS5950-1:2000 4.8.3.3)

The parameters are:

• $F_{cx}$ – maximum axial compression in the major axis buckling span
• $F_{cy}$ – maximum axial compression in the minor axis buckling span
• $M_{b1}$ – major axis bending moment capacity in the LT span
• $M_{b2}$ – opposite sense moment capacity in the LT span (for reverse curvature spans)
• $M_{LT1}$ – maximum applied major axis bending moment in the LT span
• $M_{LT2}$ – opposite sense major axis bending moment in the LT span (for reverse curvature spans)
• $M_{x}$ – maximum major axis moment in the major axis buckling span
• $M_{y}$ – maximum minor axis moment in the minor axis buckling span
• $P_{cx}$ – major axis axial buckling capacity
• $P_{cy}$ – minor axis axial buckling capacity
• $Z_{x}$ – section modulus about major axis
• $Z_{y}$ – section modulus about minor axis
• $m_{LT}$ – equivalent uniform moment factor for major axis moment in relevant LT span
• $m_{x}$ – equivalent uniform moment factor for major axis moment in the major axis axial span
• $m_{y}$ – equivalent uniform moment factor for minor axis moment in the minor axis axial span
• $m_{yx}$ – equivalent uniform moment factor for minor axis moment in the major axis axial span
• $p_{y}$ – design stress for the section

The checker steps through the sub-spans looking at this interaction data. It only carries out an interaction check once for each permutation of buckling spans, to reduce the volume of output.

Interaction is carried out according to clauses BS5950-1:2000 4.8.3.3.1, 4.8.3.3.2 and 4.8.3.3.3 depending on the section shape. The variant (c) that allows biaxial bending moments is always used, even when there is only bending about a single axis.

Limitations

• Torsion not fully considered.
• Unsymmetrical sections not yet supported.
• Mixed steel grades in single section not yet supported.
• Weld material disregarded in assessment of section properties.
• Web high-shear buckling treated conservatively in respect of web capacity.
• Whole structure stability issues are not considered, since the checker only knows about one member at a time. Users must construct their models to account for these effects if appropriate.