In-plane bending of beams - The Behaviour and Design of Steel Structures to EC3 - page 155

Cut

Shear
connector

Solid section Rolled section

Reverse

Composite beam

Weld

Tapered I-beam

Weld

Cut

Thin-walled
open section

Fabricated
section

Displace

Weld

Weld
Compound
section

Thin-walled
closed section

Encased beam

Castellated I-beam

Figure 5.1 Beam types.

f y f y f y f y

2

d w

2

d x

Elastic First

yield

Elastic-
plastic

Fully
plastic

Strain-
hardened

1 2 4

3 5

(c) Stress distributions

Rigid plastic assumption

M

5

3

M p
M y

First yield 2

4

Effect of residual stresses

1 2

d w

2

d x

(d) Moment-curvature relationships

Figure 5.2 Moment-curvature relationships for steel beams.

I-beams this margin varies between 10 and 20% approximately. The attainment
of the first plastic hinge forms the basis for the traditional method of design of
beams in which the bending moment distribution is calculated from an elastic
analysis.