Design procedure
(a) Calculate the factored load = 1.6 x imposed + 1.4 x dead, and then calculate the maximum factored bending moments (Mx) and the factored shear forces
(b) Calculate the second moment of area (/) required to satisfy the deflection limitations described in clause 2.6.2. For simply supported beams, use the method described in clause 4.2 (b).
(c) Determine the effective length LE from the two cases:
• Beams with lateral restraints at their ends only The effective length LE should be obtained from Table 7 according to the conditions of restraints at their ends. If the conditions of restraint differ at each end then a mean value of LE may be taken.
For cantilevers the effective length LE should be obtained from Table 8.
Table 7 Effective length of beams LE
conditions of restraint at the ends of the beams loading conditions normal destabilizing (see note 3)
compression flange laterally restrained; beam fully restrained against torsion both flanges fully restrained against rotation on plan
both flanges partially restrained against rotation on plan
0-85L
both flanges free to rotate on plan
1-0L
0-85L
1-0L
1-2L
compression flange laterally unrestrained; both flanges free to rotate on plan restraint against torsion provided only by positive connection of bottom flange to supports
restraint against torsion provided only by dead bearing of bottom flange on supports
Notes to Table 7
1. D is the depth of the beam.
2. L is the length of the beam between its ends.
3. It should be noted that destabilizing load conditions exist when a load is applied to the compression flange of a beam or the tension flange of a cantilever and both the load and the flange are free to deflect laterally (and possibly rotationally also) relative to the centroid of the beam.
Table 8 Effective length of cantilever LE
Restraint conditions
Loading conditions
At support
At tip
Normal
- Continuous with lateral restraint only
Free
Laterally restrained on top flange only
Torsionally restrained only
Laterally and torsionally restrained
2 1L
Continuous with lateral and torsional restraint
Free
Laterally restrained on top flange only Torsionally restrained only
Laterally and torsionally restrained
- Built-in laterally and torsionally
Free
Laterally restrained on top flange only
Torsionally restrained only
Laterally and torsionally restrained
- Face beams extending Braced laterally in at over several bays least one bay
Top flange restraint
Torsional restraint
Lateral and torsional restraint
Top flange restraint
Torsional restraint
Lateral and torsional restraint
Note : When values from this table are used for Lg the equivalent uniform moment _factor, m . and the slenderness correction factor, n , should be taken as 10
• Beams with effective intermediate lateral restraints as well as at their ends Provided that the lateral restraints have been designed to be adequate then the effective lengths LE of the parts of the beam may be obtained from the following:
(i) Part of beam between restraints
The effective length LE of this part of the beam should be taken as the actual distance between the restraints.
(ii) Part of the beam between the end of the beam and the first internal lateral restraint
The effective length LE should be taken as the mean of the value given by (i) and the value given by Table 7 for the conditions of restraint at the support, taking L as the distance between the restraint and the support in both cases.
It is most important to design the lateral restraints so that they have adequate stiffness and strength. Restraints may be deemed to provide adequate strength if they are capable of resisting a lateral force of not less than 21/2% of the maximum factored force in the compression flange or chord. Where several members share a common restraint, the minimum total lateral force may be taken as the sum of those derived from the largest three members.
When a series of two or more parallel beams require a lateral restraint at intervals, it is not adequate merely to tie the compression flanges together such that the members become mutually dependent. Adequate restraint to any beam will be achieved only if the beam supports and the restraining members are held by a robust part of the structure or held in a fixed relationship to each other by means of triangulated bracing.
(d) Choose a trial section and grade of steel and check that the maximum Afx on any portion of the beam between adjacent lateral restraints does not exceed the buckling resistance moment Mh of the section obtained from:
Mb = PbSx where pb is the bending strength of the member and
Sx is the plastic modulus of the section about the x-x axis. The bending strength pb of the trial section is obtained from the tables in Appendix B for the design strength py, the slenderness A and the torsional index x where p is the design strength obtained from Table 2 according to the grade of steel and thickness of the flange of the chosen section.
where LE is the effective length obtained in (c)
r is the radius of gyration of the section about its minor axis, and n for beams without intermediate lateral restraints may be taken as:
0.86 for central point loads 0.94 for all other loads
For beams with intermediate lateral restraints, cantilevers and beams subject to destabilizing loads n should be taken as 1.0.
Less conservative values of n may be obtained from Tables 12 or 13.
x is the torsional index which may be taken as the D/T ratio where D is the depth of the section and T is the thickness of the flange as obtained from the blue book. The buckling resistance moment Mb should be calculated for each portion of beam from Mb = pbSx. If this is less than the corresponding maximum Mx on that portion of beam a larger section or higher grade of steel should be chosen or additional restraints provided and the calculation repeated.
In Appendix A tables are provided that give the buckling resistance moments for commonly used UBs for a range of effective lengths LE. The tables also show the critical values of LE for each UB at which pb = p .
(e) Check that the beam complies with the requirements for bending and deflection using the procedure detailed in clauses 4.2 (b) and (c)
(f) Check that the shear capacity P, of the sections exceeds the factored shear forces (Fv) using the procedure detailed in clause A.2(d).
(g) Check for web bearing and buckling as detailed in clause 4.2(e).
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