Contents Eurocode 2 04 RC PN 001

User Manual: Eurocode 2-04 RC-PN-001

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EXAMPLE EUROCODE 2-04 RC-PN-001 - 1
EXAMPLE EUROCODE 2-04 RC-PN-001
Slab Punching Shear Design
PROBLEM DESCRIPTION
The purpose of this example is to verify slab punching shear design in SAFE
The numerical example is a flat slab that has three 8-m spans in each direction, as
shown in Figure 1.
4
A
3
2
1
BC D
X
Y
0.3 m
0.3 m 8 m8 m8 m
0.6 m
0.6 m
0.25 m thick flat slab
Loading
DL = Self weight + 1.0 kN/m
2
LL = 4.0 kN/m
2
Columns are 0.3 m x 0.9 m
with long side parallel
to the Y-axis, typical
Concrete Properties
Unit weight = 24 kN/m
3
f'c = 30 N/mm
2
8 m
8 m
8 m
4
A
3
2
1
BC D
X
Y
0.3 m
0.3 m 8 m8 m8 m
0.6 m
0.6 m
0.25 m thick flat slab
Loading
DL = Self weight + 1.0 kN/m
2
LL = 4.0 kN/m
2
Columns are 0.3 m x 0.9 m
with long side parallel
to the Y-axis, typical
Concrete Properties
Unit weight = 24 kN/m
3
f'c = 30 N/mm
2
8 m
8 m
8 m
Figure 1: Flat Slab for Numerical Example
The slab overhangs beyond the face of the column by 0.15 m along each side of
the structure. The columns are typically 0.3 m x 0.9 m with the long side parallel
to the Y-axis. Thick plate properties are used for the slab.
The concrete has a unit weight of 24 kN/m3 and a f'c of 30 N/mm2. The dead load
consists of the self weight of the structure plus an additional 1 kN/m2. The live
load is 4 kN/m2.
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EXAMPLE EUROCODE 2-04 RC-PN-001 - 2
TECHNICAL FEATURES OF SAFE TESTED
Calculation of punching shear capacity, shear stress and D/C ratio.
RESULTS COMPARISON
Table 1 shows the comparison of the punching shear capacity, shear stress ratio
and D/C ratio obtained from SAFE with the punching shear capacity, shear stress
ratio and D/C ratio obtained by the analytical method. They match exactly for
this problem.
Table 1 Comparison of Design Results for Punching
Shear at Grid B-2
National Annex
Method
Shear
Stress
(N/mm2)
Shear
Capacity
(N/mm2) D/C
ratio
CEN Default, Norway,
Slovenia and Sweden SAFE 1.100 0.578 1.90
Calculated 1.099 0.578 1.90
Finland, Singapore and UK SAFE 1.100 0.5796 1.90
Calculated 1.099 0.5796 1.90
Denmark SAFE 1.100 0.606 1.82
Calculated 1.099 0.606 1.81
COMPUTER FILE: EUROCODE 2-04 RC-PN-001.FDB
CONCLUSION
The SAFE results show an acceptable comparison with the independent results.
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EXAMPLE EUROCODE 2-04 RC-PN-001 - 3
HAND CALCULATION
Hand Calculation for Interior Column using SAFE Method
= 218 mm
Refer to Figure 2.
u1 = u = 2•300 + 2•900 + 2•π•436 = 5139.468 mm
450
450
150 436
X
Y
1772
1172
Side 3
Column
Side 1
Side 4
436 150
436
436
Note: All dimensions in millimeters
X
Y
Side 2
AB
C
D
Critical section for
punching shear
shown dashed.
Center of column is
point (x1, y1). Set
this equal to (0,0).
450
450
150 436
X
Y
1772
1172
Side 3
Column
Side 1
Side 4
436 150
436
436
Note: All dimensions in millimeters
X
Y
Side 2
AB
C
D
Critical section for
punching shear
shown dashed.
Center of column is
point (x1, y1). Set
this equal to (0,0).
450
450
150 436
X
Y
1772
1172
Side 3
Column
Side 1
Side 4
436 150
436
436
Note: All dimensions in millimeters
X
Y
Side 2
AB
C
D
Critical section for
punching shear
shown dashed.
Center of column is
point (x1, y1). Set
this equal to (0,0).
450
450
150 436
X
Y
1772
1172
Side 3
Column
Side 1
Side 4
436 150
436
436
Note: All dimensions in millimeters
X
Y
Side 2
AB
C
D
Critical section for
punching shear
shown dashed.
Center of column is
point (x1, y1). Set
this equal to (0,0).
Figure 2: Interior Column, Grid B-2 in SAFE Model
From the SAFE output at Grid B-2:
VEd = 1112.197 kN
k2MEd2 = 41.593 kN-m
k3MEd3 = 20.576 kN-m
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EXAMPLE EUROCODE 2-04 RC-PN-001 - 4
Maximum design shear stress in computed in along major and minor axis of column:
2 ,2 1 3 ,3 1
1,2 1,3
1
Ed Ed
Ed
Ed
Ed Ed
kM u kM u
V
vud VW VW

=++



(EC2 6.4.4(2))
22
1
1 12 2 1
4 16 2
2
c
W c c c d d dc
π
=++ + +
22
1,2
900 300 900 4 300 218 16 218 2 218 900
2
W
π
= + • +• • + • + • •
1,2 2,929,744.957
W=
mm2
22
1,3
900
3 900 300 4 900 218 16 218 2 218 300
2
W
π
= + • +• • + • + • •
1,2
2,271,104.319
W=
mm2
2 ,2 1 3 ,3 1
1 1,2 1,3
1
Ed Ed
Ed
Ed
Ed Ed
kM u kM u
V
vud VW VW

=++



36 6
33
1112.197 10 41.593 10 5139.468 20.576 10 5139.468
1
5139.468 218 1112.197 10 2929744.957 1112.197 10 2271104.319
Ed
v
• •• ••
=++

• •• ••

Ed
v=
1.099 N/mm2
Thus vmax = 1.099 N/mm2
For CEN Default, Finland, Norway, Singapore, Slovenia, Sweden and UK:
ccRd
C
γ
18.
0
,
=
= 0.18/1.5 = 0.12 (EC2 6.4.4)
For Denmark:
,
0.18
Rd c c
C
γ
=
= 0.18/1.45 = 0.124 (EC2 6.4.4)
The shear stress carried by the concrete, VRd,c, is calculated as:
( )
ρσ

= +

13
,, 1 1
100
Rd c Rd c ck cp
V Ck f k
(EC2 6.4.4)
with a minimum of:
( )
, min 1Rd c cp
v vk
σ
= +
(EC2 6.4.4)
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EXAMPLE EUROCODE 2-04 RC-PN-001 - 5
200
1 2.0kd
=+≤
= 1.9578 (EC2 6.4.4(1))
k1 = 0.15. (EC2 6.2.2(1))
ρ
1 =
db
A
w
s1
≤ 0.02
Area of reinforcement at the face of column for design strip are as follows:
For CEN Default, Norway, Slovenia and Sweden:
As in Strip Layer A = 9204.985 mm2
As in Strip Layer B = 8078.337 mm2
Average As =
( )
9204.985 8078.337 2+
= 8641.661 mm2
ρ
1 =
( )
8641.661 8000 218•
= 0.004955 ≤ 0.02
For Finland, Singapore and UK:
As in Strip Layer A = 9319.248 mm2
As in Strip Layer B = 8174.104 mm2
Average As =
( )
9319.248 8174.104 2+
= 8746.676 mm2
ρ
1 =
()
8746.676 8000 218•
= 0.005015 ≤ 0.02
For Denmark:
As in Strip Layer A = 9606.651 mm2
As in Strip Layer B = 8434.444 mm2
Average As =
( )
9606.651 8434.444 2+
= 9020.548 mm2
ρ
1 =
( )
9020.548 8000 218•
= 0.005172 ≤ 0.02
Software Verification
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EXAMPLE EUROCODE 2-04 RC-PN-001 - 6
For CEN Default, Denmark, Norway, Singapore, Slovenia, Sweden and UK:
21
23
min
035.0
ck
fk=
ν
=
( ) ( )
3/2 1/2
0.035 1.9578 30
= 0.525 N/mm2
For Finland:
2/3 1 2
min
0.035
ck
kf
ν
=
=
() ( )
2/3 1/2
0.035 1.9578 30
= 0.3000 N/mm2
For CEN Default, Norway, Slovenia and Sweden:
( )

=• • •+

13
,0.12 1.9578 100 0.004955 30 0
Rd c
v
= 0.5777 N/mm2
For Finland, Singapore, and UK:
( )
13
,0.12 1.9578 100 0.005015 30 0
Rd c
v
=• • •+

= 0.5796 N/mm2
For Denmark:
( )
13
,0.124 1.9578 100 0.005015 30 0
Rd c
v
= • • •+

= 0.606 N/mm2
For CEN Default, Norway, Slovenia and Sweden:
max
,
1.092
Shear Ratio 1.90
0.5777
Rd c
v
v
= = =
For Finland, Singapore and UK:
max
,
1.092
Shear Ratio 1.90
0.5796
Rd c
v
v
= = =
For Denmark:
max
,
1.092
Shear Ratio 1.81
0.606
Rd c
v
v
= = =

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