In-plane bending of beams - The Behaviour and Design of Steel Structures to EC3 - page 192

b 1 b 1 × t 1

t 1

a a

t 2

b 2 × t 2

b 3 × t 3

(a) Actual cross-section (b) Thin-walled approximation

Figure 5.34 Thin-walled cross-section assumption.

The area A of a thin-walled section composed of a series of thin rectangles b n
wide and t n thick ( b n t n ) is given by

A =

A d A =

A n (5.55)

n

in which A n = b n t n . This approximation may make small errors of the order of
( t / b ) 2 at some junctions.
The centroid of a cross-section is defined by

y d A = z d A = 0

A A

and for a thin-walled section these conditions become

A n y n = A n z n = 0 (5.56)

n n

in which y n , z n are the centroidal distances of the centre of the rectangular ele-
ment, as demonstrated in Figure 5.35a. The position of the centroid can be found
by adopting any convenient initial set of axes y i , z i as shown in Figure 5.35a,
so that

y n = y in − y ic
z n = z in − z ic