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determine a suitable grade S275 steel universal beam section

From what i have worked out so far:

imposed load = 5.0kNm-2 x 4.2m

=21kN/m

dead load = 4.2m x 0.18m x 24kN/m3

=18.14kN/m

to select a suitable UB section:

214x1.6x7+18.14x1.4x7

=413kN

design shear force:

413/2= 206.5

desing BM:

m=wl sqaured / 8 =

18.14x1.4+21x1.6 x 7sqaured / 8 = 361.4

section selection:

S=m/py

=361.4/275

=1314cm cubed

this is where im lost need to find UB with plastic section modulus

do i use UB 406 x 178 x 67

if somone could help me with this question and make sure im doing this example right

thank you