Technical
NSC 29
July/Aug 19
Mcr must be calculated, using the gross properties. Ltbeam is a
convenient software to use. With a UDL causing compression on
the web, Mcr = 67 kNm.
Verification then proceeds in the usual way, using the general case
of clause 6.3.2.2. A tee section is taken to be an “other cross section”
in Table 6.4. The intermediate values are therefore:
λLT = 0.41
αLT = 0.76
φLT = 0.66
χLT = 0.84
and finally MbRd = 9.5 kNm
Method 4 – BS EN effective section method
Having found the section is class 4, the effective length of the web
may be determined from BS EN 1993-1-5.
If kσ = 0.616 then from clause 4.4(2)
p = b / t = = 1.39
28.4 k
25.2
28.4 × 0.81 × 0.616
Because λp > 0.748 then
= = = 0.622 p – 0.188
p
2
1.39 – 0.188
1.392
The effective length of the web from the neutral axis is therefore
0.622 × 168.8 = 105 mm and the overall depth of the effective
section is now 163.7 mm.
This change of section means that the original assumptions
about c/t ratio, position of neutral axis etc are now invalid. The
process must be repeated (by spreadsheet preferably!) until a
final solution is found. A final solution is found when there is no
further reduction needed to the web (i.e. all the reduced section
is effective). This happens when ρ = 1 (no reduction), which, with
reference to BS EN 1993-1-5, happens when λp =0.748
Probably, there would be a neat way to determine this point
by calculation, but it is easy to complete a number of cycles to
discover the point when the entire reduced section becomes
effective. The final section, with an overall depth of 130 mm,
is shown in Figure 4. The Eurocode effective section appears
reassuringly similar to that according to BS 5950, in Figure 2.
Having found the final section, the section properties can be
determined and the resistance determined in the normal way, as
Method 3. The intermediate values are:
Wel = 37.3 cm3
λLT =0.44
αLT = 0.76
φLT = 0.69
Figure 4: EN 1993 effective section
χLT = 0.82
and finally MbRd = 10.8 kNm
Summary
The various resistances are shown below:
BS 5950 reduced design strength 11.3 kNm
BS 5950 effective section 12.3 kNm
BS EN 1993-1-1 reduced design strength 9.5 kNm
BS EN 1993-1-1 effective section 10.8 kNm
Note that according to BS 5950, the maximum moment should
be limited to Mb /mLT , so the BS 5950 values above should be
increased by 1 ⁄ 0.925 to provide a proper comparison. The shape
of the bending moment diagram – due to a UDL – is already
included in the Eurocode resistances by virtue of the Mcr value.
Conclusions
Firstly, it is not easy to calculate the correct resistance. It took
some time and the assistance of two colleagues at SCI to reach a
consensus. The Eurocode approach has the benefit of software to
calculate Mcr , but the easier solution (method 3, reduced design
strength) is conservative. The less conservative method 4, effective
section, is painful because of the loops required to calculate the
effective section.
The second observation is that perhaps the guidance in BS 5950
could be clearer.
The final observation is that tees have their place - but
preferably not as unrestrained members in bending.
link
/www.rainhamsteel.co.uk