Introduction - The Behaviour and Design of Steel Structures to EC3 - page 9

steel type are significantly higher than the nearly static rates often encountered in
actual structures.
For design purposes, a 'minimum' yield stress is identified for each differ-
entsteelclassification.ForEC3,theseclassificationsaremadeonthebasisofthe
chemicalcompositionandtheheattreatment,andsotheyieldstressesineachclas-
sificationdecreaseasthegreatestthicknessoftherolledsectionorplateincreases.
The minimum yield stress of a particular steel is determined from the results of
a number of standard tension tests. There is a significant scatter in these results
because of small variations in the local composition, heat treatment, amount of
working, thickness, and the rate of testing, and this scatter closely follows a nor-
mal distribution curve. Because of this, the minimum yield stress f y quoted for
a particular steel and used in design is usually a characteristic value which has
a particular chance (often 95%) of being exceeded in any standard tension test.
Consequently, it is likely that an isolated test result will be significantly higher
than the quoted yield stress. This difference will, of course, be accentuated if the
test is made for any but the thickest portion of the cross-section. In EC3 [8], the
yieldstresstobeusedindesignislistedinTable3.1forhot-rolledstructuralsteel
and for structural hollow sections for each of the structural grades.
The yield stress f y determined for uniaxial tension is usually accepted as being
valid for uniaxial compression. However, the general state of stress at a point in
a thin-walled member is one of biaxial tension and/or compression, and yielding
under these conditions is not so simply determined. Perhaps the most generally
accepted theory of two-dimensional yielding under biaxial stresses acting in the
1 2 plane is the maximum distortion-energy theory (often associated with names
ofHuber,vonMises,orHencky),andthestressesatyieldaccordingtothistheory
satisfy the condition

σ 1 − σ 1 σ 2 + σ 2 + 3 σ 1 2 = f y ,

(1.1)

in which σ 1 , σ 2 are the normal stresses and σ 1 2 is the shear stress at the point.
Forthecasewhere1 and2 aretheprincipalstressdirections1and2,equation1.1
takes the form of the ellipse shown in Figure 1.7, while for the case of pure shear
(σ 1 = σ 2 = 0, so that σ 1 =− σ 2 = σ 1 2 ) , equation 1.1 reduces to
σ 1 2 = f y / √ 3 = τ y ,

(1.2)

which defines the shear yield stress τ y .

1.3.2 Fatigue failure under repeated loads

Structural steel may fracture at low average tensile stresses after a large number
of cycles of fluctuating load. This high-cycle fatigue failure is initiated by local
damagecausedbytherepeatedloads,whichleadstotheformationofasmalllocal
crack.Theextentofthefatiguecrackisgraduallyincreasedbythesubsequentload
repetitions, until finally the effective cross-section is so reduced that catastrophic