# D3.B.5 Member Capacities

The basic measure of capacity of a beam is taken as the plastic moment of the section. This is a significant departure from the standard practice followed in BS449, in which the limiting condition was attainment of yield stress at the extreme fibers of a given section. With the introduction of the plastic moment as the basic measure of capacity, careful consideration must be given to the influence of local buckling on moment capacity. To assist this, sections are classified as either Class 1, plastic, Class 2, compact, Class 3, semi-compact or Class 4, slender, which governs the decision whether to use the plastic or the elastic moment capacity. The section classification is a function of the geometric properties of the section. STAAD is capable of determining the section classification for both hot rolled and built up sections. In addition, for slender sections, BS5950 recommends the use of a 'stress reduction factor' to reduce the design strength. This factor is again a function of the geometry of the section and is automatically determined by STAAD for use in the design process.

## D3.B.5.1 Axial  Tension

In members with axial tension, the tensile load must not exceed the tension capacity of the member. The tension capacity of the member is calculated on the basis of the effective area as outlined in Section 4.6 of the code. STAAD calculates the tension capacity of a given member per this procedure, based on a user supplied net section factor (NSF-a default value of 1.0 is present but may be altered by changing the input value - see D3.B.6 Design Parameters), proceeding with member selection or code check accordingly. BS5950 does not have any slenderness limitations for tension members.

## D3.B.5.2 Compression

Compression members must be designed so that the compression resistance of the member is greater than the axial compressive load. Compression resistance is determined according to the compressive strength, which is a function of the slenderness of the gross section, the appropriate design strength and the relevant strut characteristics. Strut characteristics take into account the considerable influence residual rolling and welding stresses have on column behavior. Based on data collected from extensive research, it has been determined that sections such as tubes with low residual stresses and Universal Beams and Columns are of intermediate performance. It has been found that I-shaped sections are less sensitive to imperfections when constrained to fail about an axis parallel to the flanges. These research observations are incorporated in BS5950 through the use of four strut curves together with a selection of tables to indicate which curve to use for a particular case. Compression strength for a particular section is calculated in STAAD according to the procedure outlined in Annex C of BS5950 where compression strength is seen to be a function of the appropriate Robertson constant ( representing Strut Curve) corresponding Perry factor, limiting slenderness of the member and appropriate design strength.

A departure from BS5950:1990, generally compression members are no longer required to be checked for slenderness limitations, however, this option can be included by specifying a MAIN parameter.  Note, a slenderness limit of 50 is still applied on double angles checked as battened struts as per clause 4.7.9.

## D3.B.5.3 Axially  Loaded  Members  With  Moments

In the case of axially loaded members with moments, the moment capacity of the member must be calculated about both principal axes and all axial forces must be taken into account. If the section is plastic or compact, plastic moment capacities will constitute the basic moment capacities subject to an elastic limitation. The purpose of this elastic limitation is to prevent plasticity at working load. For semi-compact or slender sections, the elastic moment is used. For plastic or compact sections with high shear loads, the plastic modulus has to be reduced to accommodate the shear loads. The STAAD implementation of BS5950 incorporates the procedure outlined in section 4.2.5 and 4.2.6 to calculate the appropriate moment capacities of the section.

For members with axial tension and moment, the interaction formula as outlined in section 4.8.2 is applied based on effective tension capacity.

For members with axial compression and moment, two principal interaction formulae must be satisfied – Cross Section Capacity check (4.8.3.2) and the Member Buckling Resistance check (4.8.3.3 ). Three types of approach for the member buckling resistance check have been outlined in BS5950:2000 - the simplified approach (4.8.3.3.1), the more exact approach (4.8.3.3.2) and Annex I1 for stocky members. As noted in the code, in cases where neither the major axis nor the minor axis moment approaches zero, the more exact approach may be more conservative than the simplified approach. It has been found, however, that this is not always the case and STAAD therefore performs both checks, comparing the results in order that the more appropriate criteria can be used.

Additionally the equivalent moment factors, mx my and myx, can be specified by the user or calculated by the program.

Members subject to biaxial moments in the absence of both tensile and compressive axial forces are checked using the appropriate method described above with all axial forces set to zero. STAAD also carries out cross checks for compression only, which for compact/plastic sections may be more critical. If this is the case, COMPRESSION will be the critical condition reported despite the presence of moments.

## D3.B.5.4 Shear

A member subjected to shear is considered adequate if the shear capacity of the section is greater than the shear load on the member. Shear capacity is calculated in STAAD using the procedure outlined in section 4.2.3, also 4.4.5 and Annex H3 if appropriate, considering the appropriate shear area for the section specified.

Since plastic moment capacity is the basic moment capacity used in BS5950, members are likely to experience relatively large deflections. This effect, coupled with lateral torsional buckling, may result in severe serviceability limit state. Hence, lateral torsional buckling must be considered carefully.

The procedure to check for lateral torsional buckling as outlined in section 4.3 has been incorporated in the STAAD implementation of BS5950. According to this procedure, for a member subjected to moments about the major axis, the 'equivalent uniform moment' on the section must be less than the lateral torsional buckling resistance moment. For calculation of the buckling resistance moment, the procedure outlined in Annex B.2 has been implemented for all sections with the exception of angles. In Annex B.2., the resistance moment is given as a function of the elastic critical moment, Perry coefficient, and limiting equivalent slenderness, which are calculated within the program; and the equivalent moment factor, mLT, which is determined as a function of the loading configuration and the nature of the load (stabilizing, destabilizing, etc).

## D3.B.5.6 RHS  Sections - Additional  Provisions

Rectangular Hollow sections are treated in accordance with S.C.I. recommendations in cases when the plastic axis is in the flange. In such cases, the following expressions are used to calculate the reduced plastic moduli:

For n ≥ 2t(D-2t)/A

$S r x = A 2 4 ( B − t ) ( 1 − n ) [ 2 D ( B − t ) A + n − 1 ]$

For n ≥ 2t(B-2t)/A

$S r y = A 2 4 ( D − t ) ( 1 − n ) [ 2 B ( D − t ) A + n − 1 ]$