angumar verdie ellysabeta
Boyan Atanaschev
This article describes the verification of steel members subject to shear, bending moments and axial forces. The member must provide adequate compression, tension, bending and shear resistance. Where the member is subjected to axial and bending simultaneously, additional resistance checks will be required, taking into account the combination of these loading effects.
The class of the cross section is determined from Table 5.2 of BS EN 1993-1-1[1] , where a cross section is classified according to the highest (least favourable) class of its parts subject to compression. See also SCI P362 .
Section classification is also given in resistance tables, such as SCI P363 (the 'Blue Book' ). SCI P363 gives axial load ratios where (under increasing levels of axial load) a section becomes Class 3 and Class 4. The level of axial load at which a section becomes Class 2 is not required because the same section properties (the gross area and plastic modulus) are used in the resistance calculations for both Class 1 and Class 2 sections.
The design value of an action effect in each cross-section should not exceed the corresponding resistance and if several action effects act simultaneously, the combined effect should not exceed the resistance for that combination. As a conservative approximation for all cross-sections, a linear summation of the utilization ratios for each resistance may be used. For the combination of NEd, My,Ed and Mz,Ed this method may be applied using the following criteria:
More generally, the Eurocodes provide specific clauses for common combined effects (for example bending and shear, bending and axial force and bending, shear and axial force) which should be used in preference to this simplified approach.
According to the UK National Annex to BS EN 1993-1-1[2], yield strength fy and ultimate strength fu must be taken from the product standard, not Table 3.1 of the design standard. Moreover, if a range of ultimate strengths is given in the product standard, the lowest value must be adopted. Yield strengths and ultimate strengths for hot-rolled steelwork are given in BS EN 10025-2[3].
The properties of the gross cross-section should be determined using the nominal dimensions. Holes for fasteners need not be deducted, but allowance should be made for larger openings. Splice materials should not be included.
The net area of a cross section should be taken as its gross area less appropriate deductions for all holes and other openings. For calculating net section properties, the deduction for a single fastener hole should be the gross cross-sectional area of the hole in the plane of its axis. For countersunk holes, appropriate allowance should be made for the countersunk portion.
Beams subject to loads which do not act through the point on the cross-section known as the shear centre normally suffer some twisting. For doubly symmetrical sections such as UB or UC, the shear centre coincides with the centroid, while for channels it is situated on the opposite side of the web from the centroid.
If torsion cannot be avoided, a torsionally stiff section, such as a hollow section, is recommended. The twist of an open section may be very significant and must be considered if this type of section is used.
Where VEd > 0.5Vpl,Rd, the design resistance of the cross-section to combinations of moment and axial force should be calculated using a reduced yield strength, as given for bending and shear.
Open sections (UB, UC) (bi-symmetric sections) are not subject to torsional flexural buckling. Open sections do exhibit torsional buckling, but for any given length, minor axis flexural buckling is critical. SCI P363 (the Blue Book) provides flexural buckling resistances in both axes and the torsional buckling resistance.
For angles, an effective slenderness should be calculated from Annex BB.1.2 of BS EN 1993-1-1[1]. A similar effective slenderness can be calculated for channels which are only connected through the web.
The imperfection factor α corresponding to the appropriate buckling curve is obtained from the table below. The choice of buckling curve is obtained from the table to the right. For S460 steel consult Table 6.2.
For members of structural systems, verification of buckling resistance of doubly symmetric cross-sections may be carried out on the basis of the individual single span members regarded as cut out of the system. Second order effects of the sway system (P-Δ effects) should be taken into account, either by the end moments of the member or by means of appropriate buckling lengths about each axis for the global buckling mode.
In some cases, a conservative value of the k factors may be sufficient for initial design. The following table gives maximum values, based on Annex B of the Standard, and assuming the sections are susceptible to torsional deformations, i.e. not hollow sections.
The equations to calculate the interaction factors are given in SCI P362 Appendix D. A series of graphs are provided in SCI P362 from which accurate values of the interaction factors may be determined as an alternative to calculation.
Design of columns in simple construction is based on NCCI document SN048 in which a column in simple construction subject to nominal bending moments and axial compression may be verified using simplified interaction criteria.
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