EUROCODE 2 WORKED EXAMPLES - Federbeton

EC2 – worked examples 6-55
6.15.4 Verification at Serviceability Limit State
The verification at serviceability limit state is relative to the following conditions:
− stress limitation at tensioning;
− stress limitation at service;
− crack widths;
− deformation.
Table of Content
Verification at tensioning
At time of tensioning, no tensile stress should be present in the extreme fibres of the slab
and the maximum compressive stress should not exceed the limit value of 0.6 × fck = 21
MPa. For the sake of simplicity, one reports the verification related to the four elements
showed in fig ii, as subjected to the higher stress level.
The external actions are calculated adopting the rare combination with only the load steps
1 and 2. From FEM analysis, the value of n22 , m22 , n33 , m33 , n23 , m23 are evaluated so that
it results:
n22 6 m 22
σyt , = σ22,
t=
− 2
h h
;
n22 6 m 22
σyb , = σ22,
b=
+ 2
h h
n33 6 m 33
σxt , = σ33,
t = − 2
h h
;
n33 6 m 33
σxb , = σ33,
b=
+ 2
h h
n23 6 m 23
σxy, t = σ23,
t = − 2
h h
; σxy, b = σ23,
b
n23 6 m 23
= + 2
h h
where the subscripts t and b indicate respectively top and bottom fibre. The angles of
principal directions (for which is σxy = 0) are:
θ
1
=
1
2
⎛ 2 σ23
⎜
⎝ σ − σ
⎞
atan ⎟ ; θ2 = θ1 + 90°
22 33 ⎠
and the principal stresses result:
2
2
σ = σ cos ( θ ) + σ sin ( θ ) + σ sin(
2θ
)
1,/ t b 22,/
t b 1 33,/
t b 1 23,/ t b
1
2
2
σ = σ cos ( θ ) + σ sin ( θ ) + σ sin(
2θ
)
2,/ t b 22,/
t b 2 33,/
t b 2 23,/ t b
2
Referring to the elements marked in Fig.6.32 one obtains:
Table 6.7
Elem. h n 22 n 33 n 23 m 22 m 33 m 23
[m] [kN/m] [kN/m] [kN/m] [kNm/m] [kNm/m] [kNm/m]
648 1.5 -3091 -13159 6 -225 -2176 0
93 0.963 -7806 -8526 75 743 456 -51
320 1.5 -3516 -10418 1 -45 -812 0
589 1.5 -4280 -10007 -67 653 1945 20
Table 6.8