EUROCODE 2 WORKED EXAMPLES - Federbeton

EC2 – worked examples 11-3
EXAMPLE 11.2 [EC2 Clause 11.3.1 – 11.3.5 – 11.3.6 – 11.4 – 11.6]
The maximum moment that the reinforced concrete section of given dimensions, made of
type 1 lightweight concrete, described in the previous example, is able to withstand when
the reinforcement steel achieves the design elastic limit. The dimensions of the section are:
b=30 cm, h=50cm and d=47cm.
The section in question is shown in Fig. 11.1 together with the strain diagram related to the
failure mode recalled, which implies the simultaneous achievement of maximum
contraction side concrete and of the strain corresponding to the design yield stress of the
tensioned reinforcement steel.
In case one chooses, like in the previous example, to use the bilinear diagram to calculate
the compressive strength on concrete, the limits of strain by compression have values εlc3 =
1,75‰ and εlcu3 = 3,5η1 = 2,98‰.
The design strain corresponding to steel yielding, for fyk= 450 MPa, is εyd = fyd /(1,15 x Es)
= 450/(1,15 x 200000) = 1,96‰. The distance of the neutral axis from the compressed
upper edge is therefore x = 28,3 cm.
Two areas can be distinguished in the compressed zone: the first one is comprised between
the upper edge and the chord placed at the level where the contraction is εlc3 = 1,75‰. The
compressive stress in it is constant and it is equal to flcd = 0,85 flck/γc = 19,8 MPa; the
second remaining area is the one where compression on concrete linearly decreases from
the value flcd to zero in correspondence of the neutral axis.
The resultant of compression forces is placed at a distance of around 10,5 cm from the
compressed end of the section and is equal to C = 1185 kN. For the condition of
equilibrium the resultant of compressions C is equal to the resultant of tractions T, to
which corresponds a steel section As equal to As = T/fyd = 3030 mm 2 . The arm of internal
forces is h’ = d – 10,5 cm = 36,5 cm, from which the value of the moment resistance of the
section can eventually be calculated as MRd = 1185 x 0,365 = 432,5 kNm.
Fig.11.1 Deformation and tension diagram of r.c. section, build up with lightweight concrete
(flck = 35 MPa, ρ = 1650 kg/m 3 ), for collapse condition in which maximum resisting bending moment is
reached with reinforcement at elastic design limit.
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