Beam-columns - The Behaviour and Design of Steel Structures to EC3 - page 343

µ z
1 − N Ed / N cr , y

1
C zy 0.6

w y
w z = 0.990

k zy = C my C mLT

0.746
1 − 200 / 1417 ×

1
0.716 × 0.6 ×

1.115
1.5

× 1.287 × = 0.800 TA.1

µ z
1 − N Ed / N cr , z

1
C zz = 0.804 ×

0.746
1 − 200 / 584.4 ×

1
0.888 = 1.027
TA.1

k zz = C mz

N b , y , Rd + k yy M y , Ed

N Ed

M b , Rd + k yz M z , Ed M z , Rd = 200 900 + 1.508 × 45.0 121.4

+ 1.115 × 8.1

32.7 = 0.222 + 0.559 + 0.276 = 1.057 > 1

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

N Ed

M b , Rd + k zz M z , Ed M z , Rd = 200 449 + 0.800 × 45.0 121.4 + 1.027

× 8.1

32.7 = 0.445 + 0.296 + 0.254 = 0.995 < 1

and the member resistance appears to be inadequate.

7.8 Unworked examples

7.8.1 Example 6 - non-linear analysis

Analyse the non-linear elastic in-plane bending of the simply supported beam-
column shown in Figure 7.20a, and show that the maximum moment M max may
be closely approximated by using the greater of M max = qL 2 / 8 and

M max = 9 qL 2
128

( 1 − 0.29 N / N cr , y )
( 1 − N / N cr , y )

in which N cr , y = π 2 EI y / L 2 .

7.8.2 Example 7 - non-linear analysis

Analyse the non-linear elastic in-plane bending of the propped cantilever shown
in Figure 7.20b, and show that the maximum moment M max may be closely
approximated by using

qL 2 / 8 ≈ ( 1 − 0.18 N / N cr , y )

M max

( 1 − 0.49 N / N cr , y )

in which N cr , y = π 2 EI y / L 2 .