Lateral buckling of beams - The Behaviour and Design of Steel Structures to EC3 - page 279

Elastic buckling moment.
The beam is fully restrained at mid-span, and so consists of two equal length
segments 12 and 23. By inspection, the check will be controlled by segment 23
whichhasthelowermomentgradient,andthereforethelowervalueof α m .Using
Figure 6.7, α m = 1.75.
Using equation 6.3,

π 2 × 210000 × 571 × 10 4
4500 2

Nmm

M zx =

81000 × 15.3 × 10 4 + π 2 × 210000 × 0.0857 × 10 12
4500 2

×

= 111.2kNm.

Using equation 6.4,

M cr = 1.75 × 111.2 = 194.6kNm.

(Using the computer program PRFELB [18] on the segment 23 alone leads to
M cr = 204.5kNm. Using PRFELB on the complete beam leads to M cr =
237.9kNm,whichindicatestheincreasecausedbytherestraintofferedbysegment
12 to segment 23. The increased elastic buckling moment may be approxi-
mated by using the improved method given in Section 6.8.2, as demonstrated
in Section 6.15.5.)

Member resistance.

Using equation 6.25, λ LT = √ ( 132.8 / 194.6 ) = 0.826

h / b = 256 / 146.4 = 1.75 < 2

Using the EC3 simple general method with β = 1.0, λ LT ,0 = 0.2 (Clause 6.3.2.2)
and α LT = 0.21 (Tables 6.4 and 6.3), and equation 6.27,

Φ LT = 0.5 { 1 + 0.21 ( 0.826 − 0.2 ) + 1.0 × 0.826 2 }= 0.907

Using equation 6.26,

M b , Rd = 132.8 / { 0.907 + √ ( 0.907 2 − 0.826 2 ) } kNm
= 103.7kNm < 122.5kNm = M Ed

and the beam appears to be inadequate.