Contents NTC 2008 Example 001

User Manual: NTC 2008 Example 001

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NTC 2008 Example 001 - 1
NTC 2008 Example 001
WIDE FLANGE SECTION UNDER COMBINED COMPRESSION & BENDING
EXAMPLE DESCRIPTION
In this example a continuous beam-column is subjected to factored axial load P =
1400 kN and major-axis bending moment M = 200 kN-m. The beam is
continuously braced to avoid any buckling effects. This example was tested using
the Italian NTC-2008 steel frame design code. The design capacities are
compared with independent hand calculated results.
GEOMETRY, PROPERTIES AND LOADING
L = 0.4 m
TECHNICAL FEATURES TESTED
Section compactness check (beam-column)
Section compression capacity
Section shear capacity
Section bending capacity with compression & shear reductions
Interaction capacity, D/C
Material Properties
E = 210x103 MPa
v = 0.3
G = 80769 MPa
Loading
P = 1400 kN
M = 200 kN-m
Design Properties
P
L
A
A
Section A-A
M
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NTC 2008 Example 001 - 2
RESULTS COMPARISON
Independent results are taken from hand calculations based on the CSI steel
design documentation contained in the file “SFD-NTC-2008.pdf,” which is
available through the program “Help” menu.
Output Parameter
SAP2000
Independent
Percent
Difference
Compactness
Class 2
Class 2
0.00%
Section Compression Resistance,
Nc,Rd (kN)
2797.6
2797.6
0.00%
Section Shear Resistance,
Vc,Rd,y (kN)
719.2
719.2
0.00%
Section Plastic Bending Resistance,
Mc,y,Rd (kN-m)
499.1
499.1
0.00%
Section Bending Resistance Axially
Reduced,
MN,y,Rd (kN-m)
310.8
310.8
0.00%
Section Bending Resistance Shear
Reduced,
MV,y,Rd (kN-m)
481.3
481.3
0.00%
Interaction Capacity, D/C
0.741
0.741
0.00%
COMPUTER FILE: NTC 2008 EX001
CONCLUSION
The results show an exact comparison with the independent results.
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NTC 2008 Example 001 - 3
HAND CALCULATION
Properties:
Material: S275 Steel
E = 210000 MPa
fy = 235 MPa
Section: 457x191x98 UB
A = 12,500 mm2
b = 192.8 mm, tf = 19.6 mm, h = 467.2 mm, tw = 11.4 mm, r = 10.2 mm
2 467.2 2 19.6 428mm
wf
h h t  
 
 
2 467.2 2 19.6 10.2 407.6mm
f
d h t r  
2192.8 11.4 2 10.2 80.5mm
22
w
b t r
c  
 
Wpl,y = 2,230,000 mm3
Other:
01.05
M

Loadings:
1400kNP
axial load
200 kN-m
y
M
bending load at one end
Results in the following internal forces:
1400 kN
Ed
N
500 kN
Ed
V
,200 kN-m
y Ed
M
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NTC 2008 Example 001 - 4
Section Compactness:
235 235 1
235
y
f
  
1
1 1 1
22
Ed
wy
N
ht f

 



1 1,400,000
1 2.7818 1, so
2 2 467.2 11.4 235

 

 

1.0
Localized Buckling for Flange:
For the tip in compression under combined bending & compression
.1
9 9 1 9
1
cl

- 
80.5 4.11
19.6
e
f
c
t
- 
.1
4.11 9
e cl
-  -
So Flange is Class 1 in combined bending and compression
Localized Buckling for Web:
0.5, so
.1
396 396 1 33.00
13 1 13 1 1
cl

- 
 
for combined bending & compression
407.6 35.75
11.4
e
w
d
t
- 
.1
35.75 33.00
e cl
-  -
.2
456 456 1 38.00
13 1 13 1 1
cl

- 
 
.2
35.75 38.00
e cl
-  -
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NTC 2008 Example 001 - 5
So Web is Class 2 in combined bending & compression.
Since Web is Class 2, Section is Class 2 in combined bending & compression.
Section Compression Capacity
,,
0
12,500 235
1.05
y
c Rd pl Rd
M
Af
NN
 
,2797.6kN
c Rd
N
Section Shear Capacity
 
,2 2 12,500 2 192.8 19.6 19.6 11.4 2 10.2
V y f f w
A A bt t t r    
2
,5,565.5mm
Vy
A
,,
0
235 5,565.5
3 1.05 3
y
c Rd y vy
M
f
VA  
,, 719.2kN
c Rd y
V
1.0
467.1 72 235 72 235
37.5 72
11.4 1.0 235
wy
h
tf
 
So no shear buckling needs to be checked.
Section Bending Capacity
,
, , , ,
0
2,230,000 235
1.05
pl y y
c y Rd pl y Rd
M
Wf
MM
 
,, 499.1kN-m
c y Rd
M
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NTC 2008 Example 001 - 6
with Shear Reduction
,
500kN 0.5 359.6kN
Ed c Rd
VV  
Shear Reduction is needed
2
467.2 11.4 4,879.2mm
vw
A ht 
22
,
22 500
1 1 0.1525
719.2
Ed
c Rd
V
V


   





22
,
, , , ,
0
0.1525 4879.2
2,230,000 235
44 11.4
1.05
v
pl y yk
w
y V Rd y c Rd
M
A
Wf
t
MM





 
 
,, 481.3kN-m
V r Rd
M
with Compression Reduction
,
1400 0.50
2797.6
Ed
pl Rd
N
nN
 
212,500 2 192.8 19.6 0.40 0.5
12,500
f
A bt
aA
 
 
, , , ,
1 1 0.5
499.1
1 0.5 1 0.5 0.4
N y Rd pl y Rd
n
MM a

 
 
,, 310.8kN-m
N y Rd
M
Interaction Capacity: Compression & Bending
Section Bending & Compression Capacity
Formula NTC 4.2.39
252
,,
,
, , , , , ,
200 0 0.414 0.644
310.8
n
y Ed y Ed
z Ed
N y Rd N z Rd N y Rd
MM
M
D
C M M M



 








0.644
D
C
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NTC 2008 Example 001 - 7
Member Bending & Compression Capacity: Method B
k factors used are taken from the software, and determined from Method 2 in
Annex B of Eurocode 3.
0.540
yy
k
0.420
yz
k
0.600
zy
k
0.700
zz
k
Formula NTC 4.2.37
,,
,,
1 1 1
y Ed z Ed
Ed yy yz
y yk pl y yk pl z yk
LT
M M M
MM
N
Dkk
Af W f W f
C 
 
1,400 200
0.54 0
1 12,500 235 2,230,000 235
1
1.05 1.05
 
 
D
C
0.5 0.22 0
D
C 
0.717
D
C
Formula NTC 4.2.38
,,
,,
1 1 1
y Ed z Ed
Ed zy zz
z yk pl y yk pl z yk
LT
M M M
MM
N
Dkk
Af W f W f
C 
 
1,400 200
0.600 0
1 12,500 235 2,230,000 235
1
1.05 1.05
D
C  
 
0.5 0.24 0
D
C 
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NTC 2008 Example 001 - 8
0.741
D
C
(Governs)

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