The Design of Modern Steel Bridges - TEDI

154 The Design of Modern Steel Bridges
Yielding check – Hencky–Mises equivalent stress at top edge:
se ¼f150 2 þ 3 60 2 g 0:5 ¼ 182:5N=mm 2
Reference [2] allows for some plastic redistribution of the bending
component of the longitudinal stress by taking only 0.77 times the bending
stress. The top panel is subjected to 107 N/mm 2 direct compression and 43 N/
mm 2 bending stress. Hence
se ¼fð107 þ 0:77 43Þ 2 þ 3 60 2 g 0:5 ¼ 176:4N=mm 2
Bottom edge:
se ¼f280 2 þ 3 60 2 g 0:5 ¼ 298:7N=mm 2
With plastic redistribution of bending stress in bottom panel
se ¼fð176:8 þ 0:77 103:2Þ 2 þ 3 60 2 g 0:5 ¼ 276:5N=mm 2
Limiting value of
se ¼ 355=ð1:1 1:05Þ ¼307:4N=mm 2
Hence the design is satisfactory for yielding.
Buckling check
(1) Top panel: to check if the panel can be deemed restrained for compressive
and shear stresses. To take compression first
BT 2 f
b2 500 252
¼
t 5002 ¼ 0:125
10
which is greater than the minimum required as calculated below
sf ¼ 152:15 1:1 1:05 ¼ 175:7N=mm 2
S ¼ b
t
rffiffiffiffiffi
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
sy 355
¼ 50 ¼ 2:08
E 205 000
0:024ðS 1Þfs 2 yf =ðs2yf s2f Þg ¼ 0:024 1:08 1:325 ¼ 0:0343
For shear, also, the slenderness ratio is such that the plate can be taken as
restrained.
The panel is subjected to 107 N/mm 2 compressive, 43 N/mm 2 bending and
60 N/mm 2 shear stresses. Buckling stress coefficients are obtained from
Reference [2] for
rffiffiffiffiffiffiffi
b sy
¼ 50 and f ¼ 3
t 355
as follows:
K1 ¼ coefficient for axial compression ¼ 0.675
Kb ¼ coefficient for pure bending ¼ 1.205
(a value higher than 1.0 recognises plastic redistribution of bending
stress at ultimate state)
Kq ¼ coefficient for shear ¼ 0.966.