Beam-columns - The Behaviour and Design of Steel Structures to EC3 - page 340

N b , z , Rd + k zy M y , Ed

N Ed

M b , Rd = 200 449 + 0.793 × 45.0

121.4 = 0.445 + 0.294 = 0.739 < 1
6.3.3(4)

and the member out-of-plane resistance is adequate.

7.7.5Example - checking the biaxial bending capacity

Problem. The 9m long simply supported beam-column shown in Figure 7.19c
and d has a factored design axial compression force of 200kN, a factored design
concentrated load of 20kN (which includes an allowance for self-weight) acting
in the major principal plane, and a factored design uniformly distributed load
of 3.2kN/m acting in the minor principal plane. Lateral deflections v and twist
rotations φ are prevented at the ends and at mid-span. The beam-column is the
254 × 146UB37ofS275steelshowninFigure7.19a.Checktheadequacyofthe
beam-column.

Design bending moments.

M y , Ed = 45.0kNm ( Section 7.7.2 ) , M z , Ed = 8.1 kNm ( Section 7.7.3 )

Simplified approach for cross-section resistance.
Combining the calculations of Sections 7.7.2 and 7.7.3,

200 × 10 3

47.2 × 10 2 × 275 / 1.0 + 45.0 132.8 + 8.1 32.7 = 0.740 < 1

6.2.1(7)

and the cross-section resistance is adequate.

Alternative approach for cross-section resistance.
AsshowninSections7.7.2and7.7.3,theaxialloadissufficientlylowforthereisto
benoreductioninthemomentresistanceabouteitherthemajorortheminoraxis.

n = N Ed / N pl , Rd = 200 × 10 3 /( 47.2 × 10 2 × 275 / 1.0 ) = 0.154,
β = 5 n = 0.770

6.2.9.1(6)

M y , Ed
M N , y , Rd

α M z , Ed

M N , z , Rd

β 45.0

132.8

2 8.1

32.7

0.770

+ = + = 0.456 ≤ 1

6.2.9.1(6)

and the cross-section resistance is adequate.