Tension members - The Behaviour and Design of Steel Structures to EC3 - page 34

Load N

N u

Strain-hardening
Fracture

N pl

E , A

N N

Plastic

L

e

Elastic

Not to scale
Axial extension e
(b) Axial extension e

e y e st

(a) Tension member

Figure 2.1 Load-extension behaviour of a perfect tension member.

samewayasdoestheaveragestrain ε = e / L withtheaveragestress σ = N / A ,and
sotheload-extensionrelationshipforthemembershowninFigure2.1bissimilar
to the material stress-strain relationship shown in Figure 1.6. Thus the extension
at first increases linearly with the load and is equal to

e = NL

EA ,

(2.1)

where E is theYoung's modulus of elasticity. This linear increase continues until
the yield stress f y of the steel is reached at the general yield load

N pl = Af y (2.2)

whentheextensionincreaseswithlittleornoincreaseinloaduntilstrain-hardening
commences.After this, the load increases slowly until the maximum value

N u = Af u

(2.3)

is reached, in which f u is the ultimate tensile strength of the steel. Beyond this,
a local cross-section of the member necks down and the load N decreases until
fracture occurs.
Thebehaviourofthetensionmemberisdescribedasductile,inthatitcanreach
and sustain the general yield load while significant extensions occur, before it
fractures. The general yield load N pl is often taken as the load capacity of the
member.
Ifthetensionmemberisnotinitiallystressfree,buthasasetofresidualstresses
induced during its manufacture such as that shown in Figure 2.2b, then local
yieldingcommencesbeforethegeneralyieldload N pl isreached(Figure2.2c),and
the range over which the load-extension behaviour is linear decreases. However,
the general yield load N pl at which the whole cross-section is yielded can still
be reached because the early yielding causes a redistribution of the stresses. The