Contents Italian NTC 2008 RC PN 001

User Manual: Italian NTC 2008 RC-PN-001

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Software Verification
PROGRAM NAME:
SAFE
REVISION NO.:
0
EXAMPLE Italian NTC 2008 RC-PN-001 - 1
EXAMPLE Italian NTC 2008 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 Italian NTC 2008 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
Method Shear Stress
(N/mm2) Shear Capacity
(N/mm2) D/C ratio
SAFE 1.100 0.578 1.90
Calculated 1.099 0.578 1.90
COMPUTER FILE: ITALIAN NTC 2008 RC-PN-001.FDB
CONCLUSION
The SAFE results show an acceptable comparison with the independent results.
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EXAMPLE Italian NTC 2008 RC-PN-001 - 3
HAND CALCULATION
Hand Calculation for Interior Column using SAFE Method
( ) ( )
[ ]
250 26 250 38 2
= −+ −d
= 218 mm
Refer to Figure 2.
u1 = u = 2•300 + 2•900 + 2•π•436 = 5139.468 mm
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 Italian NTC 2008 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
1,2 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
ccRd
C
γ
18.0
,
=
= 0.18/1.5 = 0.12 (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)
200
1 2.0kd
=+≤
= 1.9578 (EC2 6.4.4(1))
k1 = 0.15. (EC2 6.2.2(1))
Software Verification
PROGRAM NAME:
SAFE
REVISION NO.:
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EXAMPLE Italian NTC 2008 RC-PN-001 - 5
ρ
1 = d
b
A
w
s1 ≤ 0.02
Area of reinforcement at the face of column for design strip are as follows:
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
21
23
min
035.0
ck
fk=
ν
=
( ) ( )
3/2 1/2
0.035 1.9578 30
= 0.525 N/mm2
()

=• • •+

13
,0.12 1.9578 100 0.004955 30 0
Rd c
v
= 0.5777 N/mm2
max
,
1.099
Shear Ratio 1.90
0.5777
Rd c
v
v
= = =

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