EUROCODE 2 WORKED EXAMPLES - Federbeton

EC2 – worked examples 7-5
EXAMPLE 7.2 Design of minimum reinforcement [EC2 clause 7.3.2]
Let’s consider the section in Figure 7.3 with the following geometry:
A = 1.925·10 6 mm 2 ; yG =809 mm; I = 71.82·10 10 mm 4 ;
Wi = 7.25·10 8 mm 3 ; r 2 = I/A =39.35·10 4 mm 2
Fig. 7.3. Box - section, design of minimum reinforcement.
Evaluate the minimum reinforcement into the bottom slab in the following cases:
•Application of the first cracking moment Mcr •Application of an axial compressive force N = -6000 kN, applied in the point P at 250
mm from the bottom border of the corresponding cracking moment.
Consider the following data:
fck = 45 MPa; fct,eff = 3.8 MPa; σs = 200 MPa; k =0.65 (hw > 1m)
The given statements imply:
α s = 250/1800 = 0.1388
α f = 300/1800 = 0.1667
β= 1−αs −α f = 0.6945
0
ρ s,min = 0.65⋅ 3.8/200 = 0.01235
Case a)
The application of cracking moment is associated to the neutral axis position yn = yG, and then
ξ = 809/1800 = 0.4494 .
It results also
1−αs
−α f = 0.4860 >ξ
2
and for the web
⎡ 3 0.6945 −2(1−0.1667 −0.4494)
⎤
ρ s,min = 0.01235⋅0.4 ⎢
1− ( 1−0.1667 − 0.4494) = 0.00208
⎣ 4 1− 0.4494 ⎥
⎦
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