EUROCODE 2 WORKED EXAMPLES - Federbeton

EC2 – worked examples 7-18
EXAMPLE 7.6 Verification of limit state of deformation
Evaluate the vertical displacement in the mid-spam of the beam in Figure 7.11 with constant
transversal section represented in Figure 7.12
Fig. 7.11. deflected beam, deformation limit state.
Assume the following values for the main parameters
f ck=30MPa; g+q=40kN/m; g=2q; l=10m; A s=3164mm 2 (7φ24) ;
Table of Content
Fig. 7.12. Transversal section.
and solve the problem firstly in a cumulative way, stating αe = Es/Ec=15. Referring to the stage I, as indicated in Figure 7.13,
A = 700⋅ 500 + 15⋅ 3164 = 397460mm
* 2
( 700⋅500⋅ 350 + 15⋅3164 ⋅650)
*
yG =
397460
= 385.8mm
I
500 ⋅700
12
500 700 35.8 15 3164 650 385.8 18.05 10 mm
9
* 18.05⋅10 7 3
Wi = = 5.745⋅10 mm
700 − 385,8
3
* 2 2
9 4
I = + ⋅ ⋅ + ⋅ ⋅( − ) = ⋅
From Table [3.2-EC2] we get
ctm
and then the cracking moment results
* 7 −6
cr ctm i
2 3
f = 0.30⋅ 30 = 2.9MPa
M = f W = 2.9⋅5.745⋅10 ⋅ 10 = 166.6kNm
Considering the whole applied load then
M 500
max λ= = =
Mcr 166.6
3
2
M 40 10
max = ⋅
8
= 500kNm
Fig. 7.13. Section at stage I.
In the stage II, as reported in Figure 7.13,