EUROCODE 2 WORKED EXAMPLES - Federbeton

EC2 – worked examples 7-16
0.1687 ⎛ 0.0223 ⎞
σ s,cr = 0.6⋅3.086⋅ ⋅ ⎜1+ 15⋅ ⎟=
41.78 MPa
0.0223 ⎝ 0.1687 ⎠
160 ⎛ 41.78 ⎞ ⎛ 0.1687 ⎞
w k = ⋅ 1 3.4 50 0.17 26 0.12 mm
5 ⎜ − ⎟⋅⎜ ⋅ + ⋅ ⋅ ⎟=
2 ⋅10 ⎝ 160 ⎠ ⎝ 0.0223 ⎠
The obtained values are in good agreement with those evaluated within the design.
The values from the verification are slightly larger because of the fact that in the considered
section the internal drive lever arm is lower than the approximated value 0.9d assumed in the
approximated design procedure. In fact, being h0/d the adimensional lever arm in units of
effective height d, in the three case we have
kw = 1 h0/d = (43.70 – 19.59/3) / 43.70 = 0.85
kw = 2/3 h0/d = (43.70 – 21.46/3) / 43.70 = 0.836
kw = 1/3 h0/d = [(18·160·18.99 + 3·160·13.79 2 /18.99) / (18·160 + 3·160·13.79/18.99) +
+ 2/3·24.71] / 43.70 ≅ 0.8
Let’s remark that the presence of a compressed reinforcement is highly recommended to
make ductile the section in the ultimate limit state. The reinforcement increase the lever arm
of the section reducing the difference between the approximated values and those coming
from the verification. The approximated method previously discussed can be successfully
applied in the design of the ultimate crack state.
The obtained results are reported in the Tables 7.1 and 7.2 and they are shown in Figure 7.9.
Table 7.3 and Figure 7.10 report numerical values and graphs for the maximal diameter and
the required reinforcement expressed as a function of fixed values for σs. Stating a suitable
precision for the approximated method, those values are evaluated using the (7.16) (7.14).
Table 7.1. Approximated method. Table 7.2. Exact method.
w k (mm) A s (mm 2 ) σ s (MPa) h 0/d A s (mm 2 ) w k (mm) σ s (MPa) h 0/d
0.1 11151 140 0.9 11151 0.120 160 0.811
0.2 6903 221 0.9 6903 0.213 238 0.836
0.3 5310 190 0.9 5310 0.306 304 0.85
Table of Content
Fig. 7.9. Comparison between the exact and approximated methods.