®
Autodesk
™
Robot Structural Analysis
Professional
VERIFICATION MANUAL
FOR NORWEGIAN CODES
March 2014
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
INTRODUCTION .................................................................................................................................................................................. 1
STEEL ................................................................................................................................................................................................... 2
1. NS3472:2001 .................................................................................................................................................................................... 3
VERIFICATION EXAMPLE 1
VERIFICATION EXAMPLE 2
VERIFICATION EXAMPLE 3
VERIFICATION EXAMPLE 4
VERIFICATION EXAMPLE 5
VERIFICATION EXAMPLE 6
VERIFICATION EXAMPLE 7
- COMBINED WEAK AXIS BENDING AND AXIAL COMPRESSION ............................................................... 4
- IPE SECTION SUBJECTED TO AXIAL COMPRESSION WITH BUCKLING .................................................. 8
- HEA PROFILE SUBJECTED TO AXIAL COMPRESSION ........................................................................ 12
- BENDING WITH LATERAL/TORSIONAL BUCKLING EFFECT.................................................................. 16
- NON-SYMMETRICAL BEAM OF CLASS 4 SUBJECTED TO BENDING ..................................................... 20
- HEB PROFILE SUBJECTED TO BENDING AND AXIAL COMPRESSION .................................................. 24
- COMBINED STRONG AXIS BENDING AND AXIAL COMPRESSION ......................................................... 28
CONCRETE ........................................................................................................................................................................................ 32
1. NS 3473: 2003 – RC COLUMNS................................................................................................................................................... 33
VERIFICATION EXAMPLE 1 - COLUMN SUBJECTED TO AXIAL LOAD AND BIAXIAL BENDING ............................................................. 34
LITERATURE.................................................................................................................................................................................. 40
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
INTRODUCTION
This verification manual contains numerical examples for structures prepared and originally calculated
by Autodesk Robot Structural Analysis Professional version 2013. The comparison of results is
still valid for the next versions.
All examples have been taken from handbooks that include benchmark tests covering fundamental
types of behaviour encountered in structural analysis. Benchmark results (signed as “Handbook”) are
recalled, and compared with results of Autodesk Robot Structural Analysis Professional (signed further
as “Robot”).
Each example contains the following parts:
- title of the problem
- specification of the problem
- Robot solution of the problem
- outputs with calculation results and calculation notes
- comparison between Robot results and exact solution
- conclusions
- hand calculations notes (only Norwegian code).
March 2014
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
STEEL
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
1. NS3472:2001
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
VERIFICATION EXAMPLE 1
- Combined weak axis bending and axial compression
is based on the expert hand-calculations
of examples given from the course Prosjektering av stalkonstruksjoner,
Beregnings-og konstruksjonregler etter ny revidert NS3472, ons 28.3.2001 Oslo held by Norsk
Forening for Stalkonsttruksjoner.
TITLE:
Combined weak axis bending and axial compression.
SPECIFICATION:
Check HEA 400 section used as a beam-column subjected to the axial compressive force N=2000 kN
and weak axis moment Mz = 190 kNm. As the column is fully supported at the bottom end and pinned
at the top, the effective length Lkz = 0.7* Lz = 0.7*4.0 = 2.8 m. Assume that the column is made of
S275 steel.
SOLUTION:
For analysed member pre-defined type of COLUMN member may be used. It can be set in Member
type combo-box. Press the Parameters button in DEFINITION-MEMBERS tab, which opens the
MEMBER DEFINITION – PARAMETERS dialog box. Type a new name Column1 in the Member
Type editable field. Then select Buckling length coef Z icon. In Buckling type diagrams dialog choose
the third icon for setting buckling length coefficient on 0.7. Save the newly-created type of member.
March 2014
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
In the CALCULATIONS dialog box set Member Verification option for member 1 and switch off Limit
State – Serviceability (only Ultimate Limit State will be analysed). Start the calculations by pressing
Calculations button.
Member Verification dialog box with most significant results data will appear on the screen. Pressing
the line with results for member 1 opens the RESULTS dialog box with detailed results for the
analysed member.
The view of the RESULTS window is presented below. Moreover, the printout note containing the
same results data as in Simplified results tab of the RESULTS window is added.
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
Robot RESULTS:
STEEL DESIGN
---------------------------------------------------------------------------------------------------------------------------------------CODE: Norsk Standard NS 3472:2001
ANALYSIS TYPE: Member Verification
---------------------------------------------------------------------------------------------------------------------------------------CODE GROUP:
MEMBER: 1
POINT: 1
COORDINATE: x = 0.00 L = 0.00 m
---------------------------------------------------------------------------------------------------------------------------------------LOADS: Governing Load Case: 1 STA1
---------------------------------------------------------------------------------------------------------------------------------------MATERIAL
S275J2G3
fy = 275.00 MPa
fu = 410.00 MPa
E = 210000.00 MPa
G = 80000.00 MPa
gM1 = 1.10
gM2 = 1.25
---------------------------------------------------------------------------------------------------------------------------------------SECTION PARAMETERS: HEA 400
h=39.0 cm
b=30.0 cm
Ay=114.000 cm2
Az=57.350 cm2
Ax=159.000 cm2
tw=1.1 cm
Iy=45069.400 cm4
Iz=8563.830 cm4
Ix=190.000 cm4
tf=1.9 cm
Wply = 2561.970 cm3
Wplz = 872.880 cm3
---------------------------------------------------------------------------------------------------------------------------------------INTERNAL FORCES AND CAPACITIES:
Nf = 2000.00 kN
Mfz = -190.00 kN*m
Vfy = -47.50 kN
Ncd = 3975.00 kN
Md,z = 218.22 kN*m
Vd,y = 1645.45 kN
n = 0.50
MNd,z = 197.65 kN*m
Section class = 1
mz = 0.87
---------------------------------------------------------------------------------------------------------------------------------------LATERAL BUCKLING PARAMETERS:
---------------------------------------------------------------------------------------------------------------------------------------BUCKLING PARAMETERS:
About Y axis:
About Z axis:
Lky = 4.00 m
Xy = 0.98
Lkz = 2.80 m
Xz = 0.91
Lamb,y = 23.76
Nkd,y = 3909.71 kN
Lamb,z = 38.15
Nkd,z = 3617.64 kN
Lamb_y = 0.27
ny = 0.51
Lamb_z = 0.44
nz = 0.55
Fi,y = 0.55
Xz = 0.91
kz = 0.82
---------------------------------------------------------------------------------------------------------------------------------------VERIFICATION FORMULAS:
Section check
Mfz/MNd,z = 0.96 < 1.00 (NS 12.2.6)
Vfy/Vd,y = 0.03 < 1.00 (NS 12.2.5)
Member stability check
nmax + kz*mz = 1.27 > 1.00 (NS 12.3.4.2)
----------------------------------------------------------------------------------------------------------------------------------------
Incorrect section !!!
COMPARISON:
Resistance, interaction expression
1. Plastic moment capacity Md,z [kNm]
2. Plastic moment capacity reduced by axial force MNd,z [kNm]
3. Axial capacity Nd [kN]
4. Buckling coefficient about Z-axis z [1]
5. Axial buckling capacity about Z-axis Nkd,z [kN]
March 2014
Robot
218.22
197.65
3975.00
0.910
3617.64
HAND CALCUL.
214.00
193.6
3975.00
0.910
3618.00
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
CONCLUSION:
Small differences are caused by different way of rounding-off the cross sectional properties (cross
sectional area, section modulus, moment of inertia).
HAND MADE CALCULATIONS:
March 2014
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
VERIFICATION EXAMPLE 2
- IPE section subjected to axial compression with buckling
is based on the expert hand calculations
of examples given from the course Prosjektering av stalkonstruksjoner,
Beregnings-og konstruksjonregler etter ny revidert NS3472, ons 28.3.2001 Oslo held by Norsk
Forening for Stalkonsttruksjoner.
TITLE:
IPE section subjected to axial compression with buckling.
SPECIFICATION:
The column shown aside is pinned at the both ends about y-y and z-z axes. Additionally, it is restraint
about weak Z axis at mid-height (Lkz = 0.5*Lz = 0.5*6.0 = 3.0 m). The effective length Lky along strong
Y axis is 1.0*Ly = 6.0 m. Calculate the buckling capacity of the column made of S235 steel. It has been
suggested that IPE 300 section may be considered.
SOLUTION:
For analysed member pre-defined type of COLUMN member may be used. It can be set in Member
type combo-box. Press the Parameters button in DEFINITION-MEMBERS tab, which opens MEMBER
DEFINITION – PARAMETERS dialog box. Type a new name Column 1 in the Member Type editable
field. Then select Buckling length coef Z icon. In Buckling type diagrams dialog choose the last icon
opens Internal bracing dialog box. Type 0.5 in the Coordinate of the existing bracing edit box and
select Relative radio-button. Save the newly-created type of member.
March 2014
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
In the CALCULATIONS dialog box set Member Verification option for member 1 and switch off Limit
State – Serviceability (only Ultimate Limit State will be analysed). Now, start the calculations by
pressing Calculations button.
Member Verification dialog box with most significant results data will appear on screen. Pressing the
line with results for member 1 opens the RESULTS dialog box with detailed results for the analysed
member.
The view of the RESULTS window is presented below. Moreover, the printout note containing the
same result data as in Simplified results tab of the RESULTS window is added.
March 2014
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
Robot RESULTS:
STEEL DESIGN
---------------------------------------------------------------------------------------------------------------------------------------CODE: Norsk Standard NS 3472:2001
ANALYSIS TYPE: Member Verification
---------------------------------------------------------------------------------------------------------------------------------------CODE GROUP:
MEMBER: 1
POINT: 1
COORDINATE: x = 0.00 L = 0.00 m
---------------------------------------------------------------------------------------------------------------------------------------LOADS:
Governing Load Case: 1 STA1
---------------------------------------------------------------------------------------------------------------------------------------MATERIAL
S235
fy = 235.00 MPa
fu = 340.00 MPa
E = 210000.00 MPa
G = 80000.00 MPa
gM1 = 1.100
gM2 = 1.250
---------------------------------------------------------------------------------------------------------------------------------------SECTION PARAMETERS: IPE 300
h=30.0 cm
b=15.0 cm
Ay=32.100 cm2
Az=25.680 cm2
Ax=53.810 cm2
tw=0.7 cm
Iy=8356.000 cm4
Iz=603.800 cm4
Ix=20.200 cm4
tf=1.1 cm
Wply = 628.000 cm3
Wplz = 125.000 cm3
---------------------------------------------------------------------------------------------------------------------------------------INTERNAL FORCES AND CAPACITIES:
Nf = 720.00 kN
Ncd = 1149.58 kN
n = 0.626
Section class = 2
---------------------------------------------------------------------------------------------------------------------------------------LATERAL BUCKLING PARAMETERS:
---------------------------------------------------------------------------------------------------------------------------------------BUCKLING PARAMETERS:
About Y axis:
About Z axis:
Lky = 6.00 m
Xy = 0.920
Lkz = 3.00 m
Xz = 0.627
Lamb,y = 48.149
Nkd,y = 1057.94 kN
Lamb,z = 89.558
Nkd,z = 720.40 kN
Lamb_y = 0.513
ny = 0.681
Lamb_z = 0.954
nz = 0.999
Fi,y = 0.664
Xz = 0.627
---------------------------------------------------------------------------------------------------------------------------------------VERIFICATION FORMULAS:
Section check
Nf/Ncd = 0.626 < 1.000 (NS 12.2.3.2)
Member stability check
Nf/min(Nkd,y;Nkd,z) = 0.999 < 1.000 (NS 12.3.2.1)
----------------------------------------------------------------------------------------------------------------------------------------
Section OK !!!
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
COMPARISON:
Resistance, interaction expression
1. Buckling coefficient about Y-axis y [1]
2. Buckling coefficient about Z-axis z [1]
3. Axial buckling capacity Nkd [kN]
Robot
0.920
0.627
720.4
HAND CALCUL.
0.92
0.63
720
HAND MADE CALCULATIONS:
March 2014
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
VERIFICATION EXAMPLE 3
- HEA profile subjected to axial compression
is based on the expert hand calculations
of examples given from the course Prosjektering av stalkonstruksjoner,
Beregnings-og konstruksjonregler etter ny revidert NS3472, ons 28.3.2001 Oslo held by Norsk
Forening for Stalkonsttruksjoner.
TITLE:
HEA profile subjected to axial compression.
SPECIFICATION:
Check a steel column for the 2-storey building. The buckling length Lkz is determined by a separate
calculations so that Lkz = 0.92*Lz = 0.92*3.5 = 3.22 m. The effective length Lky along strong Y axis is
1.0*Ly = 7.0 m. For the design value of the compressive force Lkz = 2700 kN check the column made
of S355 steel. It has been suggested that HEA 300 section may be considered.
SOLUTION:
For analysed member pre-defined type of COLUMN member may be used. It can be set in Member
type combo-box. Press the Parameters button in DEFINITION-MEMBERS tab, which opens MEMBER
DEFINITION – PARAMETERS dialog box. Type a new name Column 1 in the Member Type editable
field. Then, select the Member length Ly - Real radio-button and type 7.0. Set the length Lz =3.5 m the
same way as for Ly. In Buckling length coefficient Z editable field type 0.92. Save the newly-created
type of member.
March 2014
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
In the CALCULATIONS dialog box set Member Verification option for member 1 and switch off Limit
State – Serviceability (only Ultimate Limit State will be analysed). Now, start the calculations by
pressing Calculations button.
Member Verification dialog box with most significant results data will appear on the screen. Pressing
the line with results for member 1 opens the RESULTS dialog box with detailed results for the
analysed member.
The view of the RESULTS window is presented below. Moreover, the printout note containing the
same result data as in Simplified results tab of the RESULTS window is added.
March 2014
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
Robot RESULTS:
STEEL DESIGN
---------------------------------------------------------------------------------------------------------------------------------------CODE: Norsk Standard NS 3472:2001
ANALYSIS TYPE: Member Verification
---------------------------------------------------------------------------------------------------------------------------------------CODE GROUP:
MEMBER: 1
POINT: 1
COORDINATE: x = 0.00 L = 0.00 m
---------------------------------------------------------------------------------------------------------------------------------------LOADS:
Governing Load Case: 1 STA1
---------------------------------------------------------------------------------------------------------------------------------------MATERIAL
S355J2G3
fy = 355.00 MPa
fu = 490.00 MPa
E = 210000.00 MPa
G = 80000.00 MPa
gM1 = 1.100
gM2 = 1.250
---------------------------------------------------------------------------------------------------------------------------------------SECTION PARAMETERS: HEA 300
h=29.0 cm
b=30.0 cm
Ay=84.000 cm2
Az=37.250 cm2
Ax=112.500 cm2
tw=0.9 cm
Iy=18263.500 cm4
Iz=6309.560 cm4
Ix=85.600 cm4
tf=1.4 cm
Wely = 1259.552 cm3
Welz = 420.637 cm3
---------------------------------------------------------------------------------------------------------------------------------------INTERNAL FORCES AND CAPACITIES:
Nf = 2700.00 kN
Ncd = 3630.68 kN
n = 0.744
Section class = 3
---------------------------------------------------------------------------------------------------------------------------------------LATERAL BUCKLING PARAMETERS:
---------------------------------------------------------------------------------------------------------------------------------------BUCKLING PARAMETERS:
About Y axis:
About Z axis:
Lky = 7.00 m
Xy = 0.773
Lkz = 3.22 m
Xz = 0.807
Lamb,y = 54.939
Nkd,y = 2806.02 kN
Lamb,z = 42.996
Nkd,z = 2930.90 kN
Lamb_y = 0.719
ny = 0.962
Lamb_z = 0.563
nz = 0.921
Fi,y = 0.847
Xz = 0.807
---------------------------------------------------------------------------------------------------------------------------------------VERIFICATION FORMULAS:
Section check
Nf/Ncd = 0.744 < 1.000 (NS 12.2.3.2)
Member stability check
Nf/min(Nkd,y;Nkd,z) = 0.962 < 1.000 (NS 12.3.2.1)
----------------------------------------------------------------------------------------------------------------------------------------
Section OK !!!
COMPARISON:
Resistance, interaction expression
1.Buckling coefficient about Y-axis y [1]
2.Buckling coefficient about Z-axis z [1]
3.Axial buckling capacity about Nkd [kN]
4.Check of the formula (Nf/Nkd) < 1.00
(Stability check – see paragraph 12.3.2)
March 2014
Robot
0.773
0.807
2806.02
0.962
HAND CALCUL.
0.77
0.81
2783.0
0.97
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
CONCLUSION:
Small differences are caused by different way of rounding-off the cross-section properties (crosssection area, section modulus, moment of inertia).
HAND MADE CALCULATIONS:
March 2014
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
VERIFICATION EXAMPLE 4
- Bending with lateral/torsional buckling effect
is based on the expert hand calculations
of examples given from the course Prosjektering av stalkonstruksjoner,
Beregnings-og konstruksjonregler etter ny revidert NS3472, ons 28.3.2001 Oslo held by Norsk
Forening for Stalkonsttruksjoner.
TITLE:
Bending about strong Y axis with lateral-torsional buckling effect.
SPECIFICATION:
IPE 500 simply supported beam over a span of 10.0 m is laterally restraint at both ends and is not
laterally restraint between supports. For the concentrated force Q z = 125 kN applied in the mid-span,
check a beam in Grade S355. The load is applied on the bottom edge of the cross-section.
SOLUTION:
For analysed member pre-defined type of BEAM member may be used. It can be set in Member type
combo-box. Press the Parameters button in DEFINITION-MEMBERS tab, which opens MEMBER
DEFINITION – PARAMETERS dialog box. Type a new name Beam 1 in the Member Type editable
field. Then select Load level icon. In Load level dialog choose the last icon for setting appropriate load
level (bottom flange). For defining a proper load type press More button. Chose the icon for Load
parameters:Y and double click the third icon (Concentrated force in the middle). Save the newlycreated type of member.
March 2014
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
In the CALCULATIONS dialog box set Member Verification option for member 1 and switch off Limit
State – Serviceability (only Ultimate Limit State will be analysed). Now, start the calculations by
pressing Calculations button. Member Verification dialog box with most significant results data will
appear on the screen. Pressing the line with results for member 1 opens the RESULTS dialog box
with detailed results for the analysed member.
The view of the RESULTS window is presented below. Moreover, the printout note containing the
same results data as in Simplified results tab of the RESULTS window is added.
March 2014
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
Robot RESULTS:
STEEL DESIGN
---------------------------------------------------------------------------------------------------------------------------------------CODE: Norsk Standard NS 3472:2001
ANALYSIS TYPE: Member Verification
---------------------------------------------------------------------------------------------------------------------------------------CODE GROUP:
MEMBER: 1
POINT: 3
COORDINATE: x = 0.50 L = 5.00 m
---------------------------------------------------------------------------------------------------------------------------------------LOADS:
Governing Load Case: 1 STA1
---------------------------------------------------------------------------------------------------------------------------------------MATERIAL
S355J2G3
fy = 355.00 MPa
fu = 490.00 MPa
E = 210000.00 MPa
G = 80000.00 MPa
gM1 = 1.100
gM2 = 1.250
---------------------------------------------------------------------------------------------------------------------------------------SECTION PARAMETERS: IPE 500
h=50.0 cm
b=20.0 cm
Ay=64.000 cm2
Az=59.852 cm2
Ax=115.500 cm2
tw=1.0 cm
Iy=48200.000 cm4
Iz=2142.000 cm4
Ix=89.700 cm4
tf=1.6 cm
Wply = 2190.000 cm3
Wplz = 336.000 cm3
---------------------------------------------------------------------------------------------------------------------------------------INTERNAL FORCES AND CAPACITIES:
Mfy = 312.50 kN*m
Md,y = 706.77 kN*m
Vfz = -62.50 kN
Section class = 1
Vd,z = 1115.20 kN
---------------------------------------------------------------------------------------------------------------------------------------LATERAL BUCKLING PARAMETERS:
zg = -0.250 m
C1 = 1.365
Mcr = 380.23 kN*m
kLT = 1.000
Ld_upp = 10.00 m
C2 = 0.553
XLT = 0.414
Mb,d = 292.79 kN*m
---------------------------------------------------------------------------------------------------------------------------------------BUCKLING PARAMETERS:
About Y axis:
About Z axis:
--------------------------------------------------------------------------------------------------------------------------------------VERIFICATION FORMULAS:
Section check
Mfy/Md,y = 0.442 < 1.000 (NS 12.2.4)
Vfz/Vd,z = 0.056 < 1.000 (NS 12.2.5)
Member stability check
Mfy/Mb,d = 1.067 > 1.000 (NS 12.3.4.1)
----------------------------------------------------------------------------------------------------------------------------------------
Incorrect section !!!
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
COMPARISON:
Resistance, interaction expression
1.Lateral buckling critical moment Mcr [kNm]
2.Lateral buckling coefficient LT [1]
3.Lateral buckling moment capacity Mbd [kNm]
4.Check of the formula (Mfy/Mb,d) < 1.00
(Stability check – see paragraph 12.3.4.1)
Robot
380.23
0.414
292.79
1.067
HAND CALCUL.
383.0
0.40
287.00
1.089
CONCLUSION:
Small differences are caused by different way of rounding-off the cross-section properties (crosssection area, section modulus, moment of inertia).
HAND MADE CALCULATIONS:
March 2014
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
VERIFICATION EXAMPLE 5
- Non-symmetrical beam of class 4 subjected to bending
is based on the expert hand calculations
of examples given from the course Prosjektering av stalkonstruksjoner,
Beregnings-og konstruksjonregler etter ny revidert NS3472, ons 28.3.2001 Oslo held by Norsk
Forening for Stalkonsttruksjoner.
TITLE:
Non-symmetrical beam of class 4 subjected to bending about Y axis.
SPECIFICATION:
Non-symmetrical (upper flange 200x15, lower flange 500x30, web 1000x6) simply supported beam
over a span of 15.0 m is fully laterally restraint between supports. For the concentrated force Q z = 200
kN applied in the mid-span, check a beam in Grade S235.
SOLUTION:
For analysed member pre-defined type of MEMBER member may be initially opened. It can be set in
Member type combo-box. Any additional changes in MEMBER parameters set are not necessary.
In the CALCULATIONS dialog box set Member Verification option for member 1 and switch off Limit
State – Serviceability (only Ultimate Limit State will be analysed). Now, start the calculations by
pressing Calculations button.
March 2014
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
Member Verification dialog box with most significant results data will appear on the screen. Pressing
the line with results for member 1 opens the RESULTS dialog box with detailed results for the
analysed member.
The view of the RESULTS window is presented below. Moreover, the printout note containing the
same results data as in Simplified results tab of the RESULTS window is added.
March 2014
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
Robot RESULTS:
STEEL DESIGN
---------------------------------------------------------------------------------------------------------------------------------------CODE: Norsk Standard NS 3472:2001
ANALYSIS TYPE: Member Verification
---------------------------------------------------------------------------------------------------------------------------------------CODE GROUP:
MEMBER: 1
POINT: 3
COORDINATE: x = 0.50 L = 7.50 m
---------------------------------------------------------------------------------------------------------------------------------------LOADS:
Governing Load Case: 1 STA1
---------------------------------------------------------------------------------------------------------------------------------------MATERIAL
S235
fy = 235.00 MPa
fu = 340.00 MPa
E = 210000.00 MPa
G = 80000.00 MPa
gM1 = 1.100
gM2 = 1.250
---------------------------------------------------------------------------------------------------------------------------------------SECTION PARAMETERS: IASYM_1
h=104.5 cm
b=20.0 cm
Ay=180.000 cm2
Az=62.700 cm2
Aeff=240.000 cm2
tw=0.6 cm
Iy=364926.641 cm4
Iz=32251.800 cm4
Ix=461.593 cm4
tf=1.5 cm
Weff,y = 3915.181 cm3
Weff,z = 1290.072 cm3
---------------------------------------------------------------------------------------------------------------------------------------INTERNAL FORCES AND CAPACITIES:
Mfy = 750.00 kN*m
Md,y = 836.43 kN*m
Vfz = -100.00 kN
Section class = 4
Vd,z = 773.36 kN
---------------------------------------------------------------------------------------------------------------------------------------LATERAL BUCKLING PARAMETERS:
---------------------------------------------------------------------------------------------------------------------------------------BUCKLING PARAMETERS:
About Y axis:
About Z axis:
----------------------------------------------------------------------------------------------------------------------------------VERIFICATION FORMULAS:
Section check
Mfy/Md,y = 0.897 < 1.000 (NS 12.2.4)
Vfz/Vd,z = 0.129 < 1.000 (NS 12.2.5)
Member stability check
Not analyzed
----------------------------------------------------------------------------------------------------------------------------------------
Section OK !!!
March 2014
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
COMPARISON:
Resistance, interaction expression
1.Effective section modulus for class 4 section W eff,y [cm3]
2.Moment capacity Mb,d [kNm]
3.Check of the formula (Mfy/Md,y) < 1.00
(Section check – see paragraph 12.2.4)
Robot
3915.2
836.43
0.897
HAND CALCUL.
3940
842
0.891
CONCLUSION:
Small differences are caused by different way of rounding-off the cross-section properties (crosssection area, section modulus, moment of inertia).
HAND MADE CALCULATIONS:
March 2014
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
VERIFICATION EXAMPLE 6
- HEB profile subjected to bending and axial compression
is based on the expert hand-calculations
of examples given from the course Prosjektering av stalkonstruksjoner,
Beregnings-og konstruksjonregler etter ny revidert NS3472, ons 28.3.2001 Oslo held by Norsk
Forening for Stalkonsttruksjoner.
TITLE:
HEB profile subjected to bending and axial compression.
SPECIFICATION:
The column shown aside is pinned at the both ends about Y and Z axes. The effective lengths along
both axes are Lky = Lkz = 1.0*L = 1.0*4.0 = 4.0 m. For the design value of the compressive force Nf =
800 kN and two equal end moments Mfy = 200 kNm check the column made of S355 steel. It has been
suggested that HEB 260 section may be considered.
SOLUTION:
For analysed member pre-defined type of COLUMN member may be initially opened. It can be set in
Member type combo-box. Press the Parameter button in DEFINITION-MEMBERS tab, which opens
MEMBER DEFINITION – PARAMETERS dialog box. Type a new name Column1 in the Member
Type editable field. Switch Lateral buckling check box on. Save the newly created type of member.
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
In the CALCULATIONS dialog box set Member Verification option for member 1 and switch off Limit
State – Serviceability (only Ultimate Limit State will be analysed). Now, start the calculations by
pressing Calculations button.
Member Verification dialog box with most significant results data will appear on the screen. Pressing
the line with results for member 1 opens the RESULTS dialog box with detailed results for the
analysed member.
The view of the RESULTS window is presented below. Moreover, the printout note containing the
same results data as in Simplified results tab of the RESULTS window is added.
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
Robot RESULTS:
STEEL DESIGN
---------------------------------------------------------------------------------------------------------------------------------------CODE: Norsk Standard NS 3472:2001
ANALYSIS TYPE: Member Verification
---------------------------------------------------------------------------------------------------------------------------------------CODE GROUP:
MEMBER: 1
POINT: 1
COORDINATE: x = 0.00 L = 0.00 m
---------------------------------------------------------------------------------------------------------------------------------------LOADS:
Governing Load Case: 1 STA1
---------------------------------------------------------------------------------------------------------------------------------------MATERIAL
S355J2G3
fy = 355.00 MPa
fu = 490.00 MPa
E = 210000.00 MPa
G = 80000.00 MPa
gM1 = 1.10
gM2 = 1.25
---------------------------------------------------------------------------------------------------------------------------------------SECTION PARAMETERS: HEB 260
h=26.0 cm
b=26.0 cm
Ay=91.000 cm2
Az=37.550 cm2
Ax=118.400 cm2
tw=1.0 cm
Iy=14920.000 cm4
Iz=5135.000 cm4
Ix=124.000 cm4
tf=1.8 cm
Wply = 1280.000 cm3
Wplz = 602.000 cm3
---------------------------------------------------------------------------------------------------------------------------------------INTERNAL FORCES AND CAPACITIES:
Nf = 800.00 kN
Mfy = -200.00 kN*m
Ncd = 3821.09 kN
Md,y = 413.09 kN*m
n = 0.21
MNd,y = 369.34 kN*m
Section class = 1
my = 0.48
---------------------------------------------------------------------------------------------------------------------------------------LATERAL BUCKLING PARAMETERS:
zg = 0.00 m
C1 = 1.00
Mcr = 1144.71 kN*m
kLT = 1.00
Ld_low = 4.00 m
C2 = 0.00
XLT = 0.93
Mb,d = 383.72 kN*m
---------------------------------------------------------------------------------------------------------------------------------------BUCKLING PARAMETERS:
About Y axis:
About Z axis:
Lky = 4.00 m
Xy = 0.90
Lkz = 4.00 m
Xz = 0.67
Lamb,y = 35.63
Nkd,y = 3434.51 kN
Lamb,z = 60.74
Nkd,z = 2542.36 kN
Lamb_y = 0.47
ny = 0.23
Lamb_z = 0.79
nz = 0.31
Fi,y = 0.65
ky = 1.15
Xz = 0.67
---------------------------------------------------------------------------------------------------------------------------------------VERIFICATION FORMULAS:
Section check
Mfy/MNd,y = 0.54 < 1.00 (NS 12.2.6)
Member stability check
nmax + ky*my = 0.87 < 1.00 (NS 12.3.4.2)
n/Xz + kLT*my/XLT = 0.84 < 1.00 (NS 12.3.4.2)
----------------------------------------------------------------------------------------------------------------------------------------
Section OK !!!
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
COMPARISON:
Resistance, interaction expression
1.Buckling coefficient about Y-axis y [1]
2.Axial buckling capacity about Y-axis Nkd,y [kN]
3.Buckling coefficient about Z-axis z [1]
4.Axial buckling capacity about Z-axis Nkd,z [kN]
5.Lateral buckling critical moment Mcr [kNm]
6.Lateral buckling coefficient LT [1]
7.Lateral buckling moment capacity Mbd [kNm]
8.Check of the formula n/Xz + kLT*my/XLT
(Stability check – see paragraph 12.3.4.2)
Robot
0.90
3434.5
0.67
2542.4
1144.7
0.93
383.72
0.84
HAND CALCUL.
0.90
3430
0.65
2477
1144
0.89
332
0.92
CONCLUSION:
The differences are caused by the fact that in hand calculations elastic moment capacity for obtaining
lateral buckling LT, Mbd,kLT, Mi,LT was used.
HAND MADE CALCULATIONS:
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
VERIFICATION EXAMPLE 7
- Combined strong axis bending and axial compression
is based on the expert hand-calculations
of examples given from the course Prosjektering av stalkonstruksjoner,
Beregnings-og konstruksjonregler etter ny revidert NS3472, ons 28.3.2001 Oslo held by Norsk
Forening for Stalkonsttruksjoner.
TITLE:
Combined strong axis bending and axial compression.
SPECIFICATION:
Check HEA140 section used as the beam-column subjected to compressive force Nf = 250 kN and
uniform distributed load q = 4.0 kN/m (caused bending about strong axis). The column is fully restraint
at the bottom and is pinned at the top end. It is also fully restraint against lateral buckling. The
effective length, after separate analysis, should by taken as follows - Lky = 1.1*0.7*L = 1.0*0.7*6.0 =
4.62 m. It has been suggested that column is made of S355 steel.
SOLUTION:
For analysed member pre-defined type of member COLUMN may be used. It can be set in Member
type combo-box. Press the Parameters button in DEFINITION-MEMBERS tab, which opens MEMBER
DEFINITION – PARAMETERS dialog box. Type a new name Column 1 in the Member Type editable
field. In Buckling length coefficient Y editable field type 0.77. Switch buckling about Z axis off by
choosing icon X in Buckling type diagrams dialog. For defining a proper load type press More button.
Chose the icon for Load type Y and double click the last icon. Save the newly-created type of member.
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
In the CALCULATIONS dialog box set Member Verification option for member 1 and switch off Limit
State – Serviceability (only Ultimate Limit State will be analysed). Now, start the calculations by
pressing Calculations button.
Member Verification dialog box with most significant results data will appear on the screen. Pressing
the line with results for member 1 opens the RESULTS dialog box with detailed results for the
analysed member.
The view of the RESULTS window is presented below. Moreover, the printout note containing the
same results data as in Simplified results tab of the RESULTS window is added.
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
Robot RESULTS:
STEEL DESIGN
---------------------------------------------------------------------------------------------------------------------------------------CODE: Norsk Standard NS 3472:2001
ANALYSIS TYPE: Member Verification
---------------------------------------------------------------------------------------------------------------------------------------CODE GROUP:
MEMBER: 1
POINT: 1
COORDINATE: x = 0.00 L = 0.00 m
---------------------------------------------------------------------------------------------------------------------------------------LOADS:
Governing Load Case: 1 STA1
---------------------------------------------------------------------------------------------------------------------------------------MATERIAL
S355J2G3
fy = 355.00 MPa
fu = 490.00 MPa
E = 210000.00 MPa
G = 80000.00 MPa
gM1 = 1.10
gM2 = 1.25
---------------------------------------------------------------------------------------------------------------------------------------SECTION PARAMETERS: HEA 140
h=13.3 cm
b=14.0 cm
Ay=23.800 cm2
Az=10.127 cm2
Ax=31.420 cm2
tw=0.5 cm
Iy=1033.130 cm4
Iz=389.321 cm4
Ix=8.160 cm4
tf=0.9 cm
Wply = 173.506 cm3
Wplz = 84.850 cm3
---------------------------------------------------------------------------------------------------------------------------------------INTERNAL FORCES AND CAPACITIES:
Nf = 250.00 kN
Mfy = -18.00 kN*m
Ncd = 1014.01 kN
Md,y = 56.00 kN*m
n = 0.25
MNd,y = 48.01 kN*m
Vfz = 15.00 kN
Section class = 2
my = 0.32
Vd,z = 188.70 kN
---------------------------------------------------------------------------------------------------------------------------------------LATERAL BUCKLING PARAMETERS:
---------------------------------------------------------------------------------------------------------------------------------------BUCKLING PARAMETERS:
About Y axis:
About Z axis:
Lky = 4.62 m
Xy = 0.56
Lamb,y = 80.57
Nkd,y = 570.79 kN
Lamb_y = 1.05
ny = 0.44
Fi,y = 1.20
ky = 1.39
---------------------------------------------------------------------------------------------------------------------------------------VERIFICATION FORMULAS:
Section check
Mfy/MNd,y = 0.37 < 1.00 (NS 12.2.6)
Vfz/Vd,z = 0.08 < 1.00 (NS 12.2.5)
Member stability check
nmax + ky*my = 0.89 < 1.00 (NS 12.3.4.2)
----------------------------------------------------------------------------------------------------------------------------------------
Section OK !!!
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
COMPARISON:
Resistance, interaction expression
1.Buckling coefficient about Y-axis y [1]
2.Axial buckling capacity about Y-axis Nkd,y [kN]
3.Moment capacity Md,y [kNm]
4.Imperfection coefficient ky [1]
5.Check of the formula nmax + ky*my
(Stability check – see paragraph 12.3.4.2)
Robot
0.56
570.8
56.0
1.39
0.89
HAND CALCUL.
0.55
557
56
1.40
0.90
CONCLUSION:
Small differences are caused by different way of rounding-off the cross-section properties (crosssection area, section modulus, moment of inertia).
HAND MADE CALCULATIONS:
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
CONCRETE
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
1. NS 3473: 2003 – RC columns
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
VERIFICATION EXAMPLE 1
- Column subjected to axial load and biaxial bending
DESCRIPTION OF THE EXAMPLE:
Following example illustrates the procedure of dimensioning of biaxial bending of column, which is
non-sway in one direction, whereas sway in the other. The results of the program are accompanied by
the „manual” calculations.
1.
SECTION DIMENSIONS
2.
MATERIALS
Concrete:
Longitudinal reinforcement:
Transversal reinforcement:
3.
B20
B500C
B500C
fck = 25.00 (MPa)
fsk = 500.00 (MPa)
fsk = 500.00 (MPa)
BUCKLING MODEL
As can be seen the sway column is assumed for Z direction, and the non-sway column for Y direction.
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
4.
LOADS
NOTE: Let us assume, the moments in Y direction are linearly distributed along the height of the
column. Thus, we define only the ends’ moments for Y direction. In Z direction however, we assume
the mid-height moment is not a result of the linear distribution. For such a case, Robot let the user
define the moments in the mid-section explicitly.
5.
CALCULATED REINFORCEMENT:
Program generates the reinforcement 16  25.
6.
RESULTS OF THE SECTION CALCULATIONS:
The dimensioning combination is 1.2DL1+1.5WIND1
The dimensioning section (where the most unfavorable set of forces is found) is for that combination
the section in the mid-height of the column (marked as (C)).
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
Since the column is found as slender, in both direction the second-order effects are taken into
account.
In parallel the other sections (at the ends of the column) are checked for all combinations of loads.
NOTE: The second-order effects in Robot are taken into account dependent upon the section
and upon the parameter sway/non sway in a following way:
 in non-sway structures, M2f is added for the mid-height section only.
 in sway structures, M2f is added to each of three sections of column. Such addition is
carried out disregarding the distribution of the first-order moment.
All the results of total forces for each combination and each section of the column may be seen in the
table “Intersection” at the Column-results layout.
7.
CALCULATIONS OF TOTAL MOMENT:
7.1. LOADS
For the dimensioning combination, the loads are:
DL1
LL1
N
(kN)
400
150
MyA
(kN*m)
150
120
MyB
(kN*m)
30
30
MyC
(kN*m)
102
84
MzA
(kN*m)
20
10
MzB
(kN*m)
30
20
MzC
(kN*m)
50*
40*
1.2DL1+1.5WIND1
705
360
81
248.4
66
39
120
Case
1
2
Dimensioning
combination
,where A, B and C denote upper, lower and mid-height sections of the column respectively.
* - the values are written “by hand” by the user (see point 4 – Loads)
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
7.2. THE INFLUENCE OF SLENDERNESS
Two independent calculations of the total moment for both directions are carried out.
Y DIRECTION
Slenderness analysis
Geometrical Slenderness
l0
= 74.82
i
Check if   80 1  4 t

 t  f sd As / f cd Ac = 1.310
80 1  4 t = 199.86
  74.82 < 199.86
- OK
Force dependent slenderness
 N   n f /(1  4 t ) = 16.24
n f  N f / f cd Ac = 0.2938
Check if
 N < 45
- OK
The slenderness limit for braced (non-sway) column:
N lim  18  8M 0 A / M 0 B = 16.20
 N   N lim
- the column is slender for Y direction
Calculation of unintended eccentricity – 12.2.3
ea  max( 0.02;h / 30; le / 300) = 0.036 (m)
Calculation of first-order eccentricity and first-order moment M1f
For the mid-height section, we have:
cm  0.6  0.4e0 A / e0 B = 0.69
e0 A = 81 / 705 = 0.115 (m)
e0 B = 360 / 705 = 0.511 (m)
e0  cm e0 B = 0.352 (m)
M 1 f  N f (e0  ea )  705  0.388 = 273.78 (kNm)
Calculation of critical force NE
N E   2 EJ cr / le = 8578 (kN)
EJ cr  0.6Eck I c  Esk I s = 101381 (kNm2)
2
Eck = 23336 (MPa)
Esk = 200000 (MPa)
I c = 416667 (cm4)
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
The moment of inertia of steel is calculated according to the scheme:
I s   As i  z i = 21520 (cm4)
i
l e = 10.8 (m)
Calculation of the long-term eccentricity aL
a L  e1L
0.8
= 0.026 (m)
N E / N L  1  0.4
N L  1.2  400  1  1.5  150  0 = 480 (kN)
e1L 

480
e0  ea  = 0.264 (m)
705
= 2.0
Calculation of the immediate eccentricity ae
ae  0.1  le2 / r = 0.143 (m)
1 f sk / E sk  0.003

= 0.0122
r
d
d = 0.45 (m)
for n f  0.5
Calculation of second-order moment M2f
M 2 f  N f (ae  a L )  705  0.169 = 119.20 (kNm)
The total moment My :
M y  M 1 f  M 2 f  392.98 (kNm)
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
Z DIRECTION
Slenderness analysis
Geometrical Slenderness
l0
= 51.96
i
Check if   80 1  4 t

 t  f sd As / f cd Ac = 1.310
80 1  4 t = 199.86
  51.96 < 199.86
- OK
Force dependent slenderness
 N   n f /(1  4 t ) = 11.28
n f  N f / f cd Ac = 0.2938
Check if
 N < 45
- OK
The slenderness limit for non-braced (sway) column:
 N lim = 10.00
 N   N lim
- the column is slender for Z direction
Calculation of unintended eccentricity – 12.2.3
ea  max( 0.02;b / 30; le / 300) = 0.02 (m)
Calculation of first-order eccentricity and first-order moment M1f
For the mid-height section, we have the moments defined directly, thus
e0  M 0 / N = 120/705 = 0.170 (m)
M 1 f  N f (e0  ea )  705  0.190 = 134.10 (kNm)
Calculation of critical force NE
N E   2 EJ cr / le = 16866 (kN)
EJ cr  0.6Eck I c  Esk I s = 61519 (kNm2)
2
Eck = 23336 (MPa)
Esk = 200000 (MPa)
I c = 266666 (cm4)
I s   As i  y i = 12090 (cm4)
i
l e = 6.0 (m)
Calculation of the long-term eccentricity aL
a L  e1L
0.8
= 0.006 (m)
N E / N L  1  0.4
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Autodesk Robot Structural Analysis Professional - Verification Manual for Norwegian Codes
N L  1.2  400  1  1.5  150  0 = 480 (kN)
e1L 

480
e0  ea  = 0.129 (m)
705
= 2.0
Calculation of the immediate eccentricity ae
ae  0.1  le2 / r = 0.057 (m)
1 f sk / E sk  0.003
= 0.0157

r
d
d = 0.35 (m)
for n f  0.5
Calculation of second-order moment M2f
M 2 f  N f (ae  a L )  705  0.063 = 44.33 (kNm)
The total moment Mz :
M z  M 1 f  M 2 f  178.43 (kNm)
7.3. FINAL RESULT
M y = 392.98 (kNm)
M z = 178.43 (kNm)
8.
CONCLUSIONS
The algorithm of calculations of the total moments (i.e. slenderness effects) in non-sway/sway column
has been presented. The results obtained with the program (see point 6 – Results of the Section
Calculations) are in agreement with the manual calculations (see point 7.3 – Final Result).
LITERATURE
[1] Norwegian Standard NS 3473.E. Concrete structures. Design and detailing rules. Standards
Norway, 2004.
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