Civil Engineering Reference
In-Depth Information
Table 6.4
Strains and internal forces for determining force acting on end strap.
x
ε
L
ε
s
ε
c
F
LEd
F
sEd
F
cEd
m
mm/m
mm/m
mm/m
kN
kN
kN
0.892
1.11
1.02
0.43
37.61
630.59
668.08
V
Ed
489
:
0kN
V
Rd
;
c
;
LE
282
:
52 kN
=
m
The force acting on the end strap is calculated according to DAfStb guideline part 1
section RV 9.2.6:
1
1
:
67
22
:
5kN
where
F
LEd
is the
fictitious strip tensile force at the end of the strip plus the
F
LwEd
;
end
F
LEd
?
tan
θ
37
:
61
?
'
shift rule
'
.
This means that the strip force is required at the point
x
=
a
L
+
891.8
mm. This strip force and the associated strains are listed in Table 6.4 and were
determined iteratively without taking the prestrain into account because this has a
favourable effect here but it is not certain that the cross-section is cracked at this point.
The force acting on the end strap is carried by the end strap of the shear strengthening.
For this reason, this strap will be somewhat wider. The additional width necessary is
b
Lw
=
20mm and the additional resistance of the strap can be calculated with the
following equation:
F
LwRd
;
end
a
l
=
400
+
491.8
=
2
?
t
Lw
?
b
Lw
?
f
Lwd
2
?
6
?
20
?
141
33
:
84 kN
The resistance is greater than the action of 22.5 kN and so the design is veri
ed. To avoid
a concrete cover separation failure, the end strap of the shear strengthening must
therefore have dimensions of (
b
Lw
×
t
Lw
) 100
×
6mm.
6.7 Analyses for the serviceability limit state
Analyses of crack width and deformation are not carried out in this example. It is merely
verified that the necessary stresses are complied with. According to DAfStb guideline
part 1 section 7.2, described in Section 3.6 of this topic, the strains in the strip and the
reinforcing steel must be limited as follows for a rare load combination:
f
yk
E
s
500
200 000
2
:
5mm
=
m
ε
s
ε
L
2mm
=
m
Under a rare load combination, we get the following maximum moment at mid-span:
M
E
;
rare
680 kNm
=
m
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