Tension members - The Behaviour and Design of Steel Structures to EC3 - page 35

c

1 Residual stress
( N = 0)

b t

c

t
(a) Section

2 First yield

Load N

f y

3 N pl

2 3 4

e y e st

Extension e

4 Fully yielded

( N = N p l )

1

(b) Stress
distributions

(c) Load-extension behaviour

Figure 2.2 Effect of residual stresses on load-extension behaviour.

w

N N

N = 0 N = 0

w 0

(a) Initial crookedness (b) Deflection under load

Figure 2.3 Tension member with initial crookedness.

residualstressesalsocauselocalearlystrain-hardening,andwhiletheplasticrange
is shortened (Figure 2.2c), the member behaviour is still regarded as ductile.
If, however, the tension member has an initial crookedness w 0 (Figure 2.3a),
theaxialloadcausesittobendanddeflectlaterally w (Figure2.3b).Theselateral
deflectionspartiallystraightenthemembersothatthebendingactioninthecentral
regionisreduced.Thebendinginducesadditionalaxialstresses(seeSection5.3),
which cause local early yielding and strain-hardening, in much the same way as
do residual stresses (see Figure 2.2c). The resulting reductions in the linear and
plasticrangesarecomparativelysmallwhentheinitialcrookednessissmall,asis
normally the case, and the member behaviour is ductile.

2.2.2 Members with small holes

The presence of small local holes in a tension member (such as small bolt holes
used for the connections of the member) causes early yielding around the holes,
so that the load-deflection behaviour becomes non-linear. When the holes are
small, the member may reach the gross yield load (see equation 2.2) calculated