Introduction - Composite Structures of Steel and Concrete - page 11

Concrete reaches its maximum compressive stress at a strain of between
0.002 and 0.003, and at higher strains it crushes, losing almost all of its
compressive strength. It is very brittle in tension, having a strain capacity
of only about 0.0001 (i.e., 0.1 mm per metre) before it cracks. Figure 1.1
also shows that the maximum stress reached by concrete in a beam or
column is well below its cube strength.
Steel yields at a strain similar to that given for the maximum stress in
concrete, but on further straining the stress continues to increase slowly,
until (for a typical structural steel) the total strain is at least thirty times
the yield strain. Its subsequent necking and fracture is of little significance
for composite members because the useful resistance of a cross-section is
reached when all of the steel has yielded, when steel in compression
buckles, or when concrete crushes.
Resistances of cross-sections are determined using plastic analysis wher-
ever possible because results of elastic analyses are unreliable, unless
careful account is taken of the cracking, shrinkage, and creep of concrete
(which is difficult), and also because plastic analysis is simpler and leads
to more economical design.
The use of a higher value of γ M for concrete than for steel (Table 1.2)

includes allowance for the higher variability of the strength of test speci-
mens, and the variation in the strength of concrete over the depth of a
member, due to migration of water before setting. It also allows for the
larger errors in the dimensions of cross-sections, particularly in the posi-
tions of reinforcing bars.
Brief comments are now given on individual materials.

Concrete
In EN 1992, a typical strength class for normal-density concrete is denoted
C25/30, where the specified characteristic compressive strengths at age 28
days are f ck 30 N/mm 2 (cube test). The

design formulae in EN 1994 use f cd , which is f ck /

= 25 N/mm 2 (cylinder test) and f cu =

γ C . The normal-density
concrete used in worked examples here is 'Grade 30' (in British terminology),
with f ck taken as 25 N/mm 2 . It is used for the columns and for encasement
of beam webs. The floor slabs are constructed with lightweight-aggregate
concrete of grade LC25/28, with oven-dry density 1800 kg/m 3 . Other
properties for these two concretes are given in Table 1.4.
For densities, EN 1991-1-1 uses kN/m 3 units, and so gives densities about
2% higher than those of EN 1992-1-1, since 1800 kg/m 3 is 17.65 kN/m 3 .
The higher values are used here.

Reinforcing steel
Strength grades for reinforcing steel are given in EN 10080 [20] in terms
of a characteristic yield strength f sk . The value used here is 500 N/mm 2 ,