Civil Engineering Reference
In-Depth Information
corners, so that it is always 2
d
from the face of the column.
Figure 17.6
provides a design fl ow chart for punching shear.
17.5.5.2 Slabs
Assuming there is no prestress in the slab, then the shear
resistance of the slab can be obtained from
Table 17.7
. This
can be compared at the applied design shear stress. The table
has been produced for a concrete strength,
f
ck
of 25 MPa; for
higher concrete strengths factors are provided at the foot of
the table. Designers who are familiar with BS 8110 should
note that there is no limit on the maximum effective depth.
For depths over 500 mm, the shear resistance,
v
Rd,c
should be
calculated using Cl. 6.2.2(1) of Eurocode 2.
17.5.6 Defl ection
Defl ection of reinforced concrete is a complex subject; it varies
with a whole range of parameters. In essence, the more sophis-
ticated the analysis, the closer to the actual defl ection the predi-
cation is likely to be. The factors that affect defl ection are:
■
elastic modulus
■
tensile strength
17.5.5.3 Punching shear
As has already been seen for column design, as well as vertical
loads applied to a column, there will also be a moment. For
punching shear calculations this is important as it effectively
increase the shear stress in the slab, over part of the shear per-
imeter. This can be considered by applying a factor, which in
Eurocode 2 is
■
creep
■
loading sequence
■
cracking
■
shrinkage curvature
β .
There are numerous Expressions provided in
Eurocode 2 to allow
β
to be calculated, these include:
Designers should be aware that however sophisticated the
analysis, it is the input data that has a signifi cant impact on
the predicted defl ection. Of greatest signifi cance is the elastic
modulus, which is highly dependent on the type of aggregates
used. The elastic modulus will vary by ± 25% depending on
the aggregate type. Defl ection is directly proportional to elastic
modulus and therefore the actual defl ection can vary by similar
percentages. The loading sequence and long-term loading re-
gime are also diffi cult to predict, but will affect the actual
defl ection.
In this chapter, only simplifi ed methods will be presented
due to space limitations, but further guidance can be found in
How to Design Concrete Structures to Eurocode 2
(Brooker
et al
., 2006). Eurocode 2 has a simplifi ed method based on
the use of span-to-effective-depth ratios. Designers should
note that unlike some codes of practice, Eurocode 2 allows
internal rectangular column
■
■
internal circular column
internal rectangular column with biaxial loading
■
■
edge columns
corner columns
■
More simply, for a braced frame where the spans are
approximately equal (say within 15% of the longest span), the
factors in
Table 17.8
can be used.
The design shear stress is then,
v
Ed
=
β V
Ed
/(
u
i
d
eff
). The shear
stress is checked at the column face and then at perimeters
around the column. The basic control perimeter is at 2
d
from
the column face and for a rectangular column has rounded
Effective depth,
d
(mm)
A
A
b
bd
ρ
=
ρ
ρ
≤
200
225
250
275
300
350
400
500
0.25%
0.495
0.474
0.456
0.441
0.428
0.407
0.390
0.365
0.50%
0.557
0.541
0.528
0.516
0.506
0.489
0.475
0.455
0.75%
0.638
0.619
0.604
0.591
0.579
0.560
0.544
0.520
1.00%
0.702
0.682
0.665
0.650
0.637
0.616
0.599
0.573
1.25%
0.756
0.734
0.716
0.700
0.687
0.664
0.645
0.617
1.50%
0.803
0.780
0.761
0.744
0.730
0.705
0.686
0.656
1.75%
0.846
0.821
0.801
0.783
0.768
0.742
0.722
0.690
0.884
0.859
0.837
0.819
0.803
0.776
0.755
0.722
≥
2.00%
This table has been prepared for
f
ck
= 25 MPa, for other values use the following:
f
ck
28
30
32
35
40
45
50
Factor
1.038
1.063
1.086
1.119
1.170
1.216
1.260
Table 17.7
Values for v
Rd,c
