7. Conclusions & Recommendations
7.2 Recommendations
The Eurocode does not provide explicit design rules for the combination of bending moment, normal force and shear force. The principles of the Eurocode is used to propose an analytical solution. The results of the simulations with Abaqus were compared with this. The results of analytical calculation and Abaqus are comparable, but there is no certainty that these results are good. Therefore, it is advised to conduct experimental research and compare the results with the analytical calculation. If the results then match, the analytical calculation is also reliable.
The analytical solution proposed in the current investigation exists of a 3 dimensional graph which is formed from more 2 dimensional graphs. The formulas from the analytical solution should be extended to one formula which describes the bending moment, normal force and shear force interaction. For example by using of a 3D curve fitting technique.
Bending moment, shear and normal force interaction of I-shaped steel cross-sections
82
References
[1] NEN-EN 1993 1-1, Eurocode 3: Design of steel structures part 1-1, General rules and rules for buildings, Brussel, 2011.
[2] Dekker, R.W.A. and Snijder, H.H. Survey of Design Rules and Available Experiments for Cross-sectional Resistance, Department of the Built Environment, TU/e, Eindhoven 2015.
[3] Snijder, H.H. and Steenbergen, H.M.G.M., Krachtswerking, grondslagen voor het berekenen en toetsen van staalconstructies voor gebouwen volgens Eurocode 0, 1 en 3. Bouwen met Staal, Zoetermeer 2011.
[4] Sherbourne, A.N. and Oostrom Van, J. Plastic analysis of castellated beams- Interaction of moment, shear and axial force, Computers & Structures, 2, 79-109, 1972.
[5] Goczek, J. and Supel, L., Resistance of steel cross-sections subjected to bending, shear and axial forces, Engineering Structures, 70, 271-277, 2014.
[6] Neal, B.G., Effect of shear and normal forces on the fully plastic moment of an I-beam, Brown University, March 1961.
[7] Rombouts, I.M.J., Bending-normal force interaction of I-shaped cross-sections, Part A:
Literature Survey, Eindhoven University of Technology, August 2014.
[8] Rombouts, I.M.J., Bending-normal force interaction of I-shaped cross-sections, Part B:
Experimental, numerical and statistical investigation, Department of the Built Environment, Eindhoven University of Technology, Eindhoven, 2015.
[9] ABAQUS/CAE user manual, version 6.13.
[10] Sariç, I, Shear resistance of I-shaped steel beams and the influence of shear on the bending resistance, Department of the Built Environment, TU/e, Eindhoven 2014.
[11] NEN-EN 1993 1-5, Eurocode 3: Design of steel structures part 1-5, Plated structural elements, Brussel, CEN, 2012.
[12] National Board of Housing, Building and Planning, Swedish Regulations for Steel Structures, BSK 99, Stockholm, Sweden, 2003.
[13] NEN 6770, TGB 1990 - Steel structures – Basic requirements and basic rules for calculation of predominantly statically loaded structures, Delft, The Netherlands, 1997.
[14] da Silva, L.S; et al., Statistical evaluation of the lateral torsional buckling resistance of steel I-beams, Part2: Variability of steel properties, Journal of Constructional steel Research 65 2009 [15] Taras, A; et al., Guideline for the Safety Assessment of Design Rules for Steel Structures in Line with EN 1990, (SAFEBRICTILE: Standardization of Safety Assessment Procedures across Brittle to Ductile Failure Modes)
Bending moment, shear and normal force interaction of I-shaped steel cross-sections
83
APPENDIX
Appendix A: Python script
Appendix B: Spreadsheet analytical solution Appendix C: Length of the beam
Appendix D: Equilibrium check Appendix E: Script Matlab Appendix F: Statistical results
Appendix F1: Spreadsheet statistical analysis HEA240 S235 Appendix F2: Regression line of all investigated subsets
Bending moment, shear and normal force interaction of I-shaped steel cross-sections
84 Appendix A: Python script for Abaqus
# PYTHON SCRIPT FOR ABAQUS CAE 6.13-1
# M-N-V interaction of I-shaped cross-section
# Cross-section (HEA240, HEB200, HEM160, IPE330) Cross_section = 'HEA240'
# Steel grade (S235, S355, S460) Material = 'S235'
# Element Type (C3D8R, C3D8I, C3D20R) Element_type = 'C3D8R'
from abaqusConstants import
*
Bending moment, shear and normal force interaction of I-shaped steel cross-sections
85
mdb.models['Model-1'].sketches['__profile__'].geometry[2])
mdb.models['Model-1'].sketches['__profile__'].Line(point1=(b/2.0, h/2.0), point2=
(b/2.0, h/2.0-tf))
mdb.models['Model-1'].sketches['__profile__'].VerticalConstraint(addUndoState=
False, entity=mdb.models['Model-1'].sketches['__profile__'].geometry[3]) mdb.models['Model-1'].sketches['__profile__'].PerpendicularConstraint(
addUndoState=False, entity1=
mdb.models['Model-1'].sketches['__profile__'].geometry[2], entity2=
mdb.models['Model-1'].sketches['__profile__'].geometry[3])
mdb.models['Model-1'].sketches['__profile__'].Line(point1=(b/2.0, h/2.0-tf), point2=
(tw/2.0+r, h/2.0-tf))
mdb.models['Model-1'].sketches['__profile__'].HorizontalConstraint(
addUndoState=False, entity=
mdb.models['Model-1'].sketches['__profile__'].geometry[4]) mdb.models['Model-1'].sketches['__profile__'].PerpendicularConstraint(
addUndoState=False, entity1=
mdb.models['Model-1'].sketches['__profile__'].geometry[3], entity2=
Bending moment, shear and normal force interaction of I-shaped steel cross-sections
86
mdb.models['Model-1'].sketches['__profile__'].geometry[4])
mdb.models['Model-1'].sketches['__profile__'].Line(point1=(tw/2.0, h/2.0-tf-r), point2=
(tw/2.0, -h/2.0+tf+r))
mdb.models['Model-1'].sketches['__profile__'].VerticalConstraint(addUndoState=
False, entity=mdb.models['Model-1'].sketches['__profile__'].geometry[6]) mdb.models['Model-1'].sketches['__profile__'].TangentConstraint(addUndoState=
False, entity1=mdb.models['Model-1'].sketches['__profile__'].geometry[5], entity2=mdb.models['Model-1'].sketches['__profile__'].geometry[6])
mdb.models['Model-1'].sketches['__profile__'].ArcByCenterEnds(center=(tw/2.0+r, h/2.0+tf+r), direction=COUNTERCLOCKWISE, point1=(tw/2.0,
-h/2.0+tf+r), point2=(tw/2.0+r,
mdb.models['Model-1'].sketches['__profile__'].geometry[8])
mdb.models['Model-1'].sketches['__profile__'].TangentConstraint(addUndoState=
False, entity1=mdb.models['Model-1'].sketches['__profile__'].geometry[7], entity2=mdb.models['Model-1'].sketches['__profile__'].geometry[8])
mdb.models['Model-1'].sketches['__profile__'].Line(point1=(b/2.0, -h/2.0+tf), point2=(b/2.0, -h/2.0))
mdb.models['Model-1'].sketches['__profile__'].VerticalConstraint(addUndoState=
False, entity=mdb.models['Model-1'].sketches['__profile__'].geometry[9]) mdb.models['Model-1'].sketches['__profile__'].PerpendicularConstraint(
addUndoState=False, entity1=
mdb.models['Model-1'].sketches['__profile__'].geometry[8], entity2=
mdb.models['Model-1'].sketches['__profile__'].geometry[9])
mdb.models['Model-1'].sketches['__profile__'].Line(point1=(b/2.0, -h/2.0), point2=(-b/2.0, -h/2.0))
mdb.models['Model-1'].sketches['__profile__'].HorizontalConstraint(
addUndoState=False, entity=
mdb.models['Model-1'].sketches['__profile__'].geometry[10]) mdb.models['Model-1'].sketches['__profile__'].PerpendicularConstraint(
addUndoState=False, entity1=
mdb.models['Model-1'].sketches['__profile__'].geometry[9], entity2=
mdb.models['Model-1'].sketches['__profile__'].geometry[10])
mdb.models['Model-1'].sketches['__profile__'].ArcByCenterEnds(center=(tw/2.0+r, h/2.0-tf-r), direction=COUNTERCLOCKWISE, point1=(tw/2.0+r, h/2.0-f), point2=(tw/2.0, h/2.0-tf-r))
Bending moment, shear and normal force interaction of I-shaped steel cross-sections
87
mdb.models['Model-1'].sketches['__profile__'].Line(point1=(-b/2.0, -h/2.0), point2=(-b/2.0, -h/2.0+tf))
mdb.models['Model-1'].sketches['__profile__'].VerticalConstraint(addUndoState=
False, entity=mdb.models['Model-1'].sketches['__profile__'].geometry[11]) mdb.models['Model-1'].sketches['__profile__'].PerpendicularConstraint(
mdb.models['Model-1'].sketches['__profile__'].geometry[12]) mdb.models['Model-1'].sketches['__profile__'].PerpendicularConstraint(
addUndoState=False, entity1=
mdb.models['Model-1'].sketches['__profile__'].geometry[11], entity2=
mdb.models['Model-1'].sketches['__profile__'].geometry[12])
mdb.models['Model-1'].sketches['__profile__'].ArcByCenterEnds(center=(-tw/2.0-r,
-h/2.0+tf+r), direction=COUNTERCLOCKWISE, point1=(-tw/2.0-r, -h/2.0+tf), point2=(-tw/2.0,
False, entity=mdb.models['Model-1'].sketches['__profile__'].geometry[14]) mdb.models['Model-1'].sketches['__profile__'].TangentConstraint(addUndoState=
False, entity1=mdb.models['Model-1'].sketches['__profile__'].geometry[13], entity2=mdb.models['Model-1'].sketches['__profile__'].geometry[14])
mdb.models['Model-1'].sketches['__profile__'].ArcByCenterEnds(center=(-tw/2.0-r,
h/2.0-tf-r), direction=COUNTERCLOCKWISE, point1=(-tw/2.0, h/2.0-tf-r), point2=(-tw/2.0-r,
mdb.models['Model-1'].sketches['__profile__'].geometry[16])
mdb.models['Model-1'].sketches['__profile__'].TangentConstraint(addUndoState=
Bending moment, shear and normal force interaction of I-shaped steel cross-sections
88
False, entity1=mdb.models['Model-1'].sketches['__profile__'].geometry[15], entity2=mdb.models['Model-1'].sketches['__profile__'].geometry[16])
mdb.models['Model-1'].sketches['__profile__'].Line(point1=(-b/2.0, h/2.0-tf), point2=(-b/2.0, h/2.0))
mdb.models['Model-1'].sketches['__profile__'].VerticalConstraint(addUndoState=
False, entity=mdb.models['Model-1'].sketches['__profile__'].geometry[17]) mdb.models['Model-1'].sketches['__profile__'].PerpendicularConstraint(
addUndoState=False, entity1=
mdb.models['Model-1'].sketches['__profile__'].geometry[16], entity2=
mdb.models['Model-1'].sketches['__profile__'].geometry[17])
mdb.models['Model-1'].Part(dimensionality=THREE_D, name=Cross_section, type=
DEFORMABLE_BODY)
'''half_length'''
mdb.models['Model-1'].parts[Cross_section].BaseSolidExtrude(depth=half_length, sketch=
mdb.models['Model-1'].sketches['__profile__'])
# Partitions
mdb.models['Model-1'].parts[Cross_section].cells.getSequenceFromMask(('[#1 ]', ), ), datumPlane=mdb.models['Model-1'].parts[Cross_section].datums[2])
mdb.models['Model-1'].parts[Cross_section].PartitionCellByDatumPlane(cells=
mdb.models['Model-1'].parts[Cross_section].cells.getSequenceFromMask(('[#1 ]', ), ), datumPlane=mdb.models['Model-1'].parts[Cross_section].datums[3])
mdb.models['Model-1'].parts[Cross_section].PartitionCellByDatumPlane(cells=
mdb.models['Model-1'].parts[Cross_section].cells.getSequenceFromMask(('[#8 ]', ), ), datumPlane=mdb.models['Model-1'].parts[Cross_section].datums[4])
mdb.models['Model-1'].parts[Cross_section].PartitionCellByDatumPlane(cells=
mdb.models['Model-1'].parts[Cross_section].cells.getSequenceFromMask(('[#3f ]',
Bending moment, shear and normal force interaction of I-shaped steel cross-sections
89
), ), datumPlane=mdb.models['Model-1'].parts[Cross_section].datums[5])
'''Horizontal partitions'''
mdb.models['Model-1'].parts[Cross_section].PartitionCellByPlanePointNormal(cells=
mdb.models['Model-1'].parts[Cross_section].cells.getSequenceFromMask(('[#294 ]', ), ), normal=mdb.models['Model-1'].parts[Cross_section].edges[37], point=
mdb.models['Model-1'].parts[Cross_section].vertices[61])
mdb.models['Model-1'].parts[Cross_section].PartitionCellByPlanePointNormal(cells=
mdb.models['Model-1'].parts[Cross_section].cells.getSequenceFromMask((
'[#2046 ]', ), ), normal=mdb.models['Model-1'].parts[Cross_section].edges[67], point=mdb.models['Model-1'].parts[Cross_section].vertices[66])
# Material
if Material == 'S235':
mdb.models['Model-1'].Material(name='S235_bilinear')
mdb.models['Model-1'].materials['S235_bilinear'].Elastic(table=((210000.0,0.3), mdb.models['Model-1'].materials['S235_bilinear'].Plastic(table=((235.263, 0.0),))
if Material == 'S355':
mdb.models['Model-1'].Material(name='S355_bilinear')
mdb.models['Model-1'].materials['S355_bilinear'].Elastic(table=((210000.0,0.3), )) mdb.models['Model-1'].materials['S355_bilinear'].Plastic(table=((355.6, 0.0), ) if Material == 'S460':
mdb.models['Model-1'].Material(name='S460_bilinear')
mdb.models['Model-1'].materials['S460_bilinear'].Elastic(table=((210000.0,0.3), )) mdb.models['Model-1'].materials['S460_bilinear'].Plastic(table=((461.008, 0.0), ))
# Section
if Material == 'S235':
mdb.models['Model-1'].HomogeneousSolidSection(material='S235_bilinear', name=
'S235_bilinear', thickness=None)
if Material == 'S355':
mdb.models['Model-1'].HomogeneousSolidSection(material='S355_bilinear', name=
'S355_bilinear', thickness=None)
if Material == 'S460':
mdb.models['Model-1'].HomogeneousSolidSection(material='S460_bilinear', name=
'S460_bilinear', thickness=None)
# Section_assignment if Material == 'S235':
mdb.models['Model-1'].parts[Cross_section].SectionAssignment(offset=0.0, offsetField='', offsetType=MIDDLE_SURFACE, region=Region(
cells=mdb.models['Model-1'].parts[Cross_section].cells.getSequenceFromMask(
Bending moment, shear and normal force interaction of I-shaped steel cross-sections
90
mask=('[#fffff ]', ), )), sectionName='S235_bilinear', thicknessAssignment=
FROM_SECTION) if Material == 'S355':
mdb.models['Model-1'].parts[Cross_section].SectionAssignment(offset=0.0, offsetField='', offsetType=MIDDLE_SURFACE, region=Region(
cells=mdb.models['Model-1'].parts[Cross_section].cells.getSequenceFromMask(
mask=('[#fffff ]', ), )), sectionName='S355_bilinear', thicknessAssignment=
FROM_SECTION)
if Material == 'S460':
mdb.models['Model-1'].parts[Cross_section].SectionAssignment(offset=0.0, offsetField='', offsetType=MIDDLE_SURFACE, region=Region(
cells=mdb.models['Model-1'].parts[Cross_section].cells.getSequenceFromMask(
mask=('[#fffff ]', ), )), sectionName='S460_bilinear', thicknessAssignment=
FROM_SECTION)
mdb.models['Model-1'].rootAssembly.instances[Cross_section].InterestingPoint(
mdb.models['Model-1'].rootAssembly.instances[Cross_section].edges[21], MIDDLE)) '''RP2'''
mdb.models['Model-1'].rootAssembly.ReferencePoint(point=
mdb.models['Model-1'].rootAssembly.instances[Cross_section].InterestingPoint(
mdb.models['Model-1'].rootAssembly.instances[Cross_section].edges[26], MIDDLE))
# Create set '''RF2'''
mdb.models['Model-1'].rootAssembly.Set(name='RF2', referencePoints=(
mdb.models['Model-1'].rootAssembly.referencePoints[4], )) '''U2'''
mdb.models['Model-1'].rootAssembly.Set(name='U2', referencePoints=(
mdb.models['Model-1'].rootAssembly.referencePoints[5], )) '''RF3'''
mdb.models['Model-1'].rootAssembly.Set(name='RF3', referencePoints=(
mdb.models['Model-1'].rootAssembly.referencePoints[5], )) '''U3'''
mdb.models['Model-1'].rootAssembly.Set(name='U3', referencePoints=(
mdb.models['Model-1'].rootAssembly.referencePoints[4], ))
Bending moment, shear and normal force interaction of I-shaped steel cross-sections
91
'''RM1'''
mdb.models['Model-1'].rootAssembly.regenerate()
mdb.models['Model-1'].rootAssembly.Set(name='RM1', referencePoints=(
mdb.models['Model-1'].rootAssembly.referencePoints[5], ))
# Step
mdb.models['Model-1'].StaticRiksStep(dof=2, maxNumInc=50, maximumDisplacement=
-80.0, minArcInc=1e-15, name='Step-1', nlgeom=ON, nodeOn=ON, previous=
'Initial', region=mdb.models['Model-1'].rootAssembly.sets['U2'])
# History output
mdb.models['Model-1'].historyOutputRequests.changeKey(fromName='H-Output-1', toName='RF2')
mdb.models['Model-1'].historyOutputRequests['RF2'].setValues(rebar=EXCLUDE, region=mdb.models['Model-1'].rootAssembly.sets['RF2'], sectionPoints=
DEFAULT, variables=('RF2', ))
mdb.models['Model-1'].HistoryOutputRequest(createStepName='Step-1', name='U2', rebar=EXCLUDE, region=mdb.models['Model-1'].rootAssembly.sets['U2'], sectionPoints=DEFAULT, variables=('U2', ))
mdb.models['Model-1'].HistoryOutputRequest(createStepName='Step-1', name='RF3', rebar=EXCLUDE, region=mdb.models['Model-1'].rootAssembly.sets['RF3'], sectionPoints=DEFAULT, variables=('RF3', ))
mdb.models['Model-1'].HistoryOutputRequest(createStepName='Step-1', name='U3', rebar=EXCLUDE, region=mdb.models['Model-1'].rootAssembly.sets['U3'], sectionPoints=DEFAULT, variables=('U3', ))
mdb.models['Model-1'].HistoryOutputRequest(createStepName='Step-1', name='RM1', rebar=EXCLUDE, region=mdb.models['Model-1'].rootAssembly.sets['RM1'], sectionPoints=DEFAULT, variables=('RM1', ))
# Rigid body '''Rigid body1'''
mdb.models['Model-1'].RigidBody(name='Constraint-1', pinRegion=Region(
faces=mdb.models['Model-1'].rootAssembly.instances[Cross_section].faces.
getSequenceFromMask(
mask=('[#110030 #80000000 #40001031 ]', ), )), refPointRegion=Region(
referencePoints=(mdb.models['Model-1'].rootAssembly.referencePoints[4], ))) '''Regig body2'''
mdb.models['Model-1'].RigidBody(name='Constraint-2', pinRegion=Region(
faces=mdb.models['Model-1'].rootAssembly.instances[Cross_section].faces.
getSequenceFromMask(
mask=('[#c0c00 #30000000 #80000580 ]', ), )), refPointRegion=Region(
referencePoints=(mdb.models['Model-1'].rootAssembly.referencePoints[5], )))
Bending moment, shear and normal force interaction of I-shaped steel cross-sections
92
# Applying loads '''S235'''
if Cross_section == 'HEA240' and Material == 'S235':
V_pl = 341635.5 N_pl = 1805740.0
if Cross_section == 'HEB200' and Material == 'S235':
V_pl = 337158.1 N_pl = 1835350.0
if Cross_section == 'HEM160' and Material == 'S235':
V_pl = 418700.2 N_pl = 2281850.0
if Cross_section == 'IPE180' and Material == 'S235':
V_pl = 152012.9 N_pl = 561650.0 '''S355'''
if Cross_section == 'HEA240' and Material == 'S355':
V_pl = 516087.6 N_pl = 2727820.0
if Cross_section == 'HEB200' and Material == 'S355':
V_pl = 509324.0 N_pl = 2772550.0
if Cross_section == 'HEM160' and Material == 'S355':
V_pl = 632504.5 N_pl = 3447050.0
if Cross_section == 'IPE180' and Material == 'S355':
V_pl = 229636.5 N_pl = 848450.0
'''S460'''
if Cross_section == 'HEA240' and Material == 'S460':
V_pl = 668733.3 N_pl = 3534640.0
if Cross_section == 'HEB200' and Material == 'S460':
V_pl = 659969.1 N_pl = 3592600.0
if Cross_section == 'HEM160' and Material == 'S460':
V_pl = 819583.3 N_pl = 4466600.0
if Cross_section == 'IPE180' and Material == 'S460':
V_pl = 297557.1 N_pl = 1099400.0
V = n_V*1000000.0
N = ((n_N*N_pl)/V_pl)*1000000.0
Bending moment, shear and normal force interaction of I-shaped steel cross-sections
93
'''Vertical load'''
mdb.models['Model-1'].ConcentratedForce(cf2=-V, createStepName='Step-1',
distributionType=UNIFORM, field='', localCsys=None, name='Vertical load', region=Region(referencePoints=(
mdb.models['Model-1'].rootAssembly.referencePoints[5], )))
'''Horizontal load'''
mdb.models['Model-1'].ConcentratedForce(cf3=-N, createStepName='Step-1',
distributionType=UNIFORM, field='', localCsys=None, name='Horizontal load', region=Region(referencePoints=(
mdb.models['Model-1'].rootAssembly.referencePoints[4], )))
# Boundary conditions '''U1=0'''
mdb.models['Model-1'].DisplacementBC(amplitude=UNSET, createStepName='Step-1', distributionType=UNIFORM, fieldName='', fixed=OFF, localCsys=None, name=
'U1 = 0', region=Region(
edges=mdb.models['Model-1'].rootAssembly.instances[Cross_section].edges.
getSequenceFromMask(
faces=mdb.models['Model-1'].rootAssembly.instances[Cross_section].faces.
getSequenceFromMask(
mask=('[#c0c00 #30000000 #80000580 ]', ), ), referencePoints=(
mdb.models['Model-1'].rootAssembly.referencePoints[5], )))
''Support'''
mdb.models['Model-1'].DisplacementBC(amplitude=UNSET, createStepName='Step-1', distributionType=UNIFORM, fieldName='', fixed=OFF, localCsys=None, name=
'Support', region=Region(referencePoints=(
mdb.models['Model-1'].rootAssembly.referencePoints[4], )), u1=UNSET, u2=0.0 , u3=UNSET, ur1=UNSET, ur2=UNSET, ur3=UNSET)
# Mesh
'''Assign Element Type''' if Element_type == 'C3D8R':
mdb.models['Model-1'].parts[Cross_section].setElementType(elemTypes=(ElemType(
elemCode=C3D8R, elemLibrary=STANDARD, secondOrderAccuracy=OFF, kinematicSplit=AVERAGE_STRAIN, hourglassControl=DEFAULT,
distortionControl=DEFAULT), ElemType(elemCode=C3D6, elemLibrary=STANDARD), ElemType(elemCode=C3D4, elemLibrary=STANDARD)), regions=(
mdb.models['Model-1'].parts[Cross_section].cells.getSequenceFromMask((
'[#fffff ]', ), ), )) if Element_type == 'C3D8I':
mdb.models['Model-1'].parts[Cross_section].setElementType(elemTypes=(ElemType(
elemCode=C3D8I, elemLibrary=STANDARD, secondOrderAccuracy=OFF,
Bending moment, shear and normal force interaction of I-shaped steel cross-sections
94
kinematicSplit=AVERAGE_STRAIN, hourglassControl=DEFAULT,
distortionControl=DEFAULT), ElemType(elemCode=C3D6, elemLibrary=STANDARD), ElemType(elemCode=C3D4, elemLibrary=STANDARD)), regions=(
mdb.models['Model-1'].parts[Cross_section].cells.getSequenceFromMask((
'[#fffff ]', ), ), ))
if Element_type == 'C3D20R':
mdb.models['Model-1'].parts[Cross_section].setElementType(elemTypes=(ElemType(
elemCode=C3D20R, elemLibrary=STANDARD, secondOrderAccuracy=OFF, kinematicSplit=AVERAGE_STRAIN, hourglassControl=DEFAULT,
distortionControl=DEFAULT), ElemType(elemCode=C3D15, elemLibrary=STANDARD), ElemType(elemCode=C3D10, elemLibrary=STANDARD)), regions=(
mdb.models['Model-1'].parts[Cross_section].cells.getSequenceFromMask((
'[#fffff ]', ), ), ))
'''Assign Mesh Controls'''
mdb.models['Model-1'].parts[Cross_section].setMeshControls(algorithm=MEDIAL_AXIS, regions=mdb.models['Model-1'].parts[Cross_section].cells.getSequenceFromMask((
'[#2949c ]', ), ), technique=SWEEP) minSizeFactor=0.1, size=L_imp_part)
'''Seed edges'''
'''In longitudinal direction'''
Bending moment, shear and normal force interaction of I-shaped steel cross-sections
95
mdb.models['Model-1'].parts[Cross_section].seedEdgeBySize(constraint=FINER, deviationFactor=0.1, edges=
mdb.models['Model-1'].parts[Cross_section].edges.getSequenceFromMask((
'[#8000230 #80000600 #148a0000 #a1421141 #4a000 ]', ), ), minSizeFactor=0.1 , size=L_imp_part)
mdb.models['Model-1'].parts[Cross_section].seedEdgeBySize(constraint=FINER, deviationFactor=0.1, edges=
mdb.models['Model-1'].parts[Cross_section].edges.getSequenceFromMask((
'[#10040a #40000110 #a0500000 #4628ca28 #10020 ]', ), ), minSizeFactor=0.1, size=50.0)
'''H_fl'''
mdb.models['Model-1'].parts[Cross_section].seedEdgeByNumber(constraint=FINER, edges=
mdb.models['Model-1'].parts[Cross_section].edges.getSequenceFromMask((
'[#21024000 #12222000 #40044892 #10100402 #a14 ]', ), ), number=int(H_fl)) '''H_w'''
mdb.models['Model-1'].parts[Cross_section].seedEdgeByNumber(constraint=FINER, edges=
mdb.models['Model-1'].parts[Cross_section].edges.getSequenceFromMask((
'[#800009c5 #ec ]', ), ), number=int(H_w))
'''B_fl'''
mdb.models['Model-1'].parts[Cross_section].seedEdgeBySize(constraint=FINER, deviationFactor=0.1, edges=
mdb.models['Model-1'].parts[Cross_section].edges.getSequenceFromMask((
'[#40842000 #21111000 #820b56c #8812094 #2554b ]', ), ), minSizeFactor=0.1, size=B_fl)
'''B_w'''
mdb.models['Model-1'].parts[Cross_section].seedEdgeBySize(constraint=FINER, deviationFactor=0.1, edges=
mdb.models['Model-1'].parts[Cross_section].edges.getSequenceFromMask((
'[#4280000 #3 #2010200 #0 #80 ]', ), ), minSizeFactor=0.1, size=B_w) '''roots'''
mdb.models['Model-1'].parts[Cross_section].seedEdgeByNumber(constraint=FINER, edges=
mdb.models['Model-1'].parts[Cross_section].edges.getSequenceFromMask((
'[#12419000 #cccc800 #1000001 #40000 ]', ), ), number=int(roots))
'''mesh part'''
mdb.models['Model-1'].parts[Cross_section].generateMesh()
# Job
mdb.Job(atTime=None, contactPrint=OFF, description='', echoPrint=OFF,
explicitPrecision=SINGLE, getMemoryFromAnalysis=True, historyPrint=OFF, memory=90, memoryUnits=PERCENTAGE, model='Model-1', modelPrint=OFF, multiprocessingMode=DEFAULT, name=Job_name, nodalOutputPrecision=SINGLE, numCpus=4, numDomains=4, numGPUs=0, queue=None, scratch='', type=ANALYSIS, userSubroutine='', waitHours=0, waitMinutes=0)
Bending moment, shear and normal force interaction of I-shaped steel cross-sections
96 Appendix B: Spreadsheet analytical solution
Region I
Geometry Exact calculation y-y axis
Profi l e HEA240 y-a s A Ned nN W My,Ed nM Aroots Wr
Npl ,Rd 1805.6 kN mm mm² kN - mm³ kNm - mm² mm³
Mpl ,y,Rd 175.0 kNm 1.68 0.0 0.00 0.00 744605.0 174.98 1.00 web
1.87 2.9 0.69 0.00 744599.8 174.98 1.00 web
Wpl ,y 744626 mm³ 2.07 5.9 1.38 0.00 744594.0 174.98 1.00 web
2.27 8.8 2.07 0.00 744587.6 174.98 1.00 web
Av 2517.56 mm² 2.46 11.8 2.76 0.00 744580.7 174.98 1.00 web
Vpl ,Rd 341.6 kN 2.66 14.7 3.45 0.00 744573.2 174.97 1.00 web
2.85 17.6 4.14 0.00 744565.1 174.97 1.00 web
Wv = 21.1 mm³ 3.05 20.6 4.83 0.00 744556.4 174.97 1.00 web
nV = 0.01 3.25 23.5 5.52 0.00 744547.1 174.97 1.00 web
3.44 26.4 6.22 0.00 744537.3 174.97 1.00 web
3.64 29.4 6.91 0.00 744526.9 174.96 1.00 web
3.83 32.3 7.60 0.00 744515.9 174.96 1.00 web
4.03 35.3 8.29 0.00 744504.4 174.96 1.00 web
4.23 38.2 8.98 0.00 744492.3 174.96 1.00 web
4.42 41.1 9.67 0.01 744479.6 174.95 1.00 web
A = 7684 mm² 4.62 44.1 10.36 0.01 744466.3 174.95 1.00 web
h = 230 mm 4.81 47.0 11.05 0.01 744452.4 174.95 1.00 web
5.01 50.0 11.74 0.01 744438.0 174.94 1.00 web
b = 240 mm 5.20 52.9 12.43 0.01 744423.0 174.94 1.00 web
tw = 7.5 mm 5.40 55.8 13.12 0.01 744407.4 174.94 1.00 web
tf = 12 mm 5.60 58.8 13.81 0.01 744391.2 174.93 1.00 web
r = 21 mm 5.79 61.7 14.50 0.01 744374.5 174.93 1.00 web
5.99 64.6 15.19 0.01 744357.2 174.92 1.00 web
y-y a xi s 6.18 67.6 15.88 0.01 744339.3 174.92 1.00 web
Aw 1545 mm² 6.38 70.5 16.57 0.01 744320.9 174.92 1.00 web
Af 5760 mm² 6.58 73.5 17.26 0.01 744301.8 174.91 1.00 web
Ar 378.56 mm² 6.77 76.4 17.95 0.01 744282.2 174.91 1.00 web
6.97 79.3 18.65 0.01 744262.0 174.90 1.00 web
hw = 206 mm 7.16 82.3 19.34 0.01 744241.3 174.90 1.00 web
d = 164 mm 7.36 85.2 20.03 0.01 744219.9 174.89 1.00 web
hf = 218 mm 7.56 88.2 20.72 0.01 744198.0 174.89 1.00 web
7.75 91.1 21.41 0.01 744175.5 174.88 1.00 web
7.95 94.0 22.10 0.01 744152.4 174.88 1.00 web
8.14 97.0 22.79 0.01 744128.8 174.87 1.00 web
8.34 99.9 23.48 0.01 744104.6 174.86 1.00 web
8.54 102.9 24.17 0.01 744079.8 174.86 1.00 web
8.73 105.8 24.86 0.01 744054.4 174.85 1.00 web
8.93 108.7 25.55 0.01 744028.5 174.85 1.00 web
9.12 111.7 26.24 0.01 744002.0 174.84 1.00 web
fy = 235 N/mm² 9.32 114.6 26.93 0.01 743974.9 174.83 1.00 web
9.51 117.5 27.62 0.02 743947.2 174.83 1.00 web
9.71 120.5 28.31 0.02 743918.9 174.82 1.00 web
9.91 123.4 29.00 0.02 743890.1 174.81 1.00 web
10.10 126.4 29.69 0.02 743860.7 174.81 1.00 web
Bending moment, shear and normal force interaction of I-shaped steel cross-sections
97
75.34 1104.9 259.65 0.14 702056.2 164.98 0.94 web
75.54 1107.9 260.34 0.14 701834.5 164.93 0.94 web
75.73 1110.8 261.04 0.14 701612.3 164.88 0.94 web
75.93 1113.7 261.73 0.14 701389.4 164.83 0.94 web
76.12 1116.7 262.42 0.15 701166.0 164.77 0.94 web
76.32 1119.6 263.11 0.15 700942.1 164.72 0.94 web
76.51 1122.5 263.80 0.15 700717.5 164.67 0.94 web
76.71 1125.5 264.49 0.15 700492.4 164.62 0.94 web
76.91 1128.4 265.18 0.15 700266.7 164.56 0.94 web
77.10 1131.4 265.87 0.15 700040.4 164.51 0.94 web
77.30 1134.3 266.56 0.15 699813.5 164.46 0.94 web
77.49 1137.2 267.25 0.15 699586.1 164.40 0.94 web
77.69 1140.2 267.94 0.15 699358.1 164.35 0.94 web
77.89 1143.1 268.63 0.15 699129.5 164.30 0.94 web
78.08 1146.1 269.32 0.15 698900.3 164.24 0.94 web
78.28 1149.0 270.01 0.15 698670.6 164.19 0.94 web
78.47 1151.9 270.70 0.15 698440.3 164.13 0.94 web
78.67 1154.9 271.39 0.15 698209.4 164.08 0.94 web
78.87 1157.8 272.08 0.15 697977.9 164.02 0.94 web
79.06 1160.7 272.78 0.15 697745.9 163.97 0.94 web
79.26 1163.7 273.47 0.15 697513.2 163.92 0.94 web
79.45 1166.6 274.16 0.15 697280.0 163.86 0.94 web
79.65 1169.6 274.85 0.15 697046.3 163.81 0.94 web
79.85 1172.5 275.54 0.15 696811.9 163.75 0.94 web
80.04 1175.4 276.23 0.15 696577.0 163.70 0.94 web
80.24 1178.4 276.92 0.15 696341.5 163.64 0.94 web
80.43 1181.3 277.61 0.15 696105.4 163.58 0.93 web
80.63 1184.3 278.30 0.15 695868.8 163.53 0.93 web
80.82 1187.2 278.99 0.15 695631.6 163.47 0.93 web
81.02 1190.1 279.68 0.15 695393.8 163.42 0.93 web
81.22 1193.1 280.37 0.16 695155.4 163.36 0.93 web
81.41 1196.0 281.06 0.16 694916.5 163.31 0.93 web
81.61 1198.9 281.75 0.16 694676.9 163.25 0.93 web
81.80 1201.9 282.44 0.16 694436.8 163.19 0.93 web
82.00 1204.8 283.13 0.16 694196.2 163.14 0.93 roots
82.20 1223.1 287.42 0.16 692696.5 162.78 0.93 15.26 1253.4 roots 82.40 1240.1 291.42 0.16 691296.1 162.45 0.93 29.24 2406.803 roots 82.60 1256.2 295.21 0.16 689958.7 162.14 0.93 42.40 3496.77 roots 82.80 1271.7 298.86 0.17 688671.0 161.84 0.92 54.90 4536.317 roots 83.00 1286.7 302.37 0.17 687425.7 161.55 0.92 66.84 5532.955 roots 83.20 1301.1 305.76 0.17 686217.6 161.26 0.92 78.28 6491.746 roots 83.40 1315.1 309.04 0.17 685043.0 160.99 0.92 89.26 7416.402 roots 83.60 1328.7 312.23 0.17 683899.2 160.72 0.92 99.83 8309.796 roots 83.80 1341.8 315.33 0.17 682783.6 160.45 0.92 110.01 9174.241 roots 84.00 1354.6 318.34 0.18 681694.5 160.20 0.92 119.82 10011.65 roots 84.20 1367.1 321.27 0.18 680630.2 159.95 0.91 129.30 10823.63 roots 84.40 1379.3 324.13 0.18 679589.4 159.70 0.91 138.46 11611.59 roots 84.60 1391.1 326.92 0.18 678570.7 159.46 0.91 147.31 12376.73 roots 84.80 1402.7 329.63 0.18 677573.2 159.23 0.91 155.87 13120.13 roots 85.00 1414.0 332.28 0.18 676595.9 159.00 0.91 164.15 13842.73 roots 85.20 1425.0 334.87 0.19 675637.9 158.77 0.91 172.17 14545.41 roots 85.40 1435.7 337.40 0.19 674698.5 158.55 0.91 179.92 15228.94 roots 85.60 1446.3 339.87 0.19 673776.9 158.34 0.90 187.44 15894.02 roots 85.80 1456.5 342.29 0.19 672872.5 158.13 0.90 194.72 16541.33 roots 86.00 1466.6 344.65 0.19 671984.7 157.92 0.90 201.76 17171.45 roots 86.20 1476.4 346.96 0.19 671112.9 157.71 0.90 208.59 17784.94 roots 86.40 1486.0 349.22 0.19 670256.6 157.51 0.90 215.21 18382.33 roots 86.60 1495.4 351.43 0.19 669415.3 157.31 0.90 221.61 18964.11 roots 86.80 1504.6 353.59 0.20 668588.6 157.12 0.90 227.82 19530.72 roots 87.00 1513.7 355.71 0.20 667776.1 156.93 0.90 233.84 20082.59 roots 87.20 1522.5 357.78 0.20 666977.2 156.74 0.90 239.66 20620.14 roots 87.40 1531.1 359.82 0.20 666191.7 156.56 0.89 245.30 21143.75 roots 87.60 1539.6 361.80 0.20 665419.2 156.37 0.89 250.77 21653.78 roots 87.80 1547.9 363.75 0.20 664659.3 156.19 0.89 256.06 22150.57 roots 88.00 1556.0 365.66 0.20 663911.7 156.02 0.89 261.19 22634.46 roots 88.20 1564.0 367.53 0.20 663176.1 155.85 0.89 266.15 23105.77 roots 88.40 1571.8 369.37 0.20 662452.2 155.68 0.89 270.95 23564.79 roots 88.60 1579.4 371.16 0.21 661739.6 155.51 0.89 275.60 24011.82 roots 88.80 1586.9 372.93 0.21 661038.2 155.34 0.89 280.10 24447.14 roots 89.00 1594.3 374.65 0.21 660347.6 155.18 0.89 284.45 24871.01 roots 89.20 1601.5 376.35 0.21 659667.7 155.02 0.89 288.65 25283.69 roots 89.40 1608.5 378.01 0.21 658998.0 154.86 0.89 292.72 25685.45 roots 89.60 1615.5 379.64 0.21 658338.4 154.71 0.88 296.65 26076.51 roots 89.80 1622.3 381.23 0.21 657688.7 154.56 0.88 300.45 26457.12 roots 90.00 1628.9 382.80 0.21 657048.7 154.41 0.88 304.12 26827.5 roots 90.20 1635.5 384.34 0.21 656418.0 154.26 0.88 307.67 27187.87 roots 90.40 1641.9 385.85 0.21 655796.5 154.11 0.88 311.09 27538.45 roots 90.60 1648.2 387.33 0.21 655184.0 153.97 0.88 314.39 27879.46 roots 90.80 1654.4 388.78 0.22 654580.3 153.83 0.88 317.57 28211.09 roots 91.00 1660.5 390.21 0.22 653985.1 153.69 0.88 320.64 28533.54 roots 91.20 1666.4 391.61 0.22 653398.3 153.55 0.88 323.60 28847.02 roots 91.40 1672.3 392.98 0.22 652819.7 153.41 0.88 326.45 29151.71 roots 91.60 1678.0 394.33 0.22 652249.2 153.28 0.88 329.19 29447.8 roots 91.80 1683.7 395.66 0.22 651686.4 153.15 0.88 331.83 29735.47 roots 92.00 1689.2 396.96 0.22 651131.2 153.02 0.87 334.37 30014.91 roots 92.20 1694.6 398.24 0.22 650583.6 152.89 0.87 336.81 30286.29 roots 92.40 1700.0 399.49 0.22 650043.2 152.76 0.87 339.15 30549.78 roots 92.60 1705.2 400.73 0.22 649509.9 152.63 0.87 341.40 30805.56 roots 92.80 1710.4 401.94 0.22 648983.6 152.51 0.87 343.56 31053.8 roots 93.00 1715.5 403.13 0.22 648464.0 152.39 0.87 345.63 31294.66 roots 93.20 1720.4 404.30 0.22 647951.1 152.27 0.87 347.62 31528.3 roots 93.40 1725.3 405.46 0.22 647444.6 152.15 0.87 349.52 31754.88 roots 93.60 1730.2 406.59 0.23 646944.4 152.03 0.87 351.33 31974.57 roots 93.80 1734.9 407.70 0.23 646450.3 151.92 0.87 353.07 32187.53 roots 94.00 1739.6 408.80 0.23 645962.2 151.80 0.87 354.73 32393.9 roots 94.20 1744.1 409.87 0.23 645480.0 151.69 0.87 356.31 32593.85 roots 94.40 1748.6 410.93 0.23 645003.4 151.58 0.87 357.82 32787.52 roots 94.60 1753.1 411.98 0.23 644532.4 151.47 0.87 359.26 32975.07 roots 94.80 1757.5 413.00 0.23 644066.7 151.36 0.86 360.63 33156.64 roots 95.00 1761.8 414.01 0.23 643606.3 151.25 0.86 361.93 33332.39 roots 95.20 1766.0 415.01 0.23 643150.9 151.14 0.86 363.16 33502.46 roots 95.40 1770.2 415.99 0.23 642700.4 151.03 0.86 364.33 33667 roots 95.60 1774.3 416.95 0.23 642254.8 150.93 0.86 365.44 33826.16 roots 95.80 1778.3 417.90 0.23 641813.8 150.83 0.86 366.49 33980.07 roots 96.00 1782.3 418.84 0.23 641377.3 150.72 0.86 367.48 34128.88 roots 96.20 1786.2 419.77 0.23 640945.1 150.62 0.86 368.41 34272.74 roots 96.40 1790.1 420.68 0.23 640517.2 150.52 0.86 369.29 34411.79 roots 96.60 1793.9 421.58 0.23 640093.3 150.42 0.86 370.12 34546.16 roots 96.80 1797.7 422.46 0.23 639673.3 150.32 0.86 370.89 34676 roots 97.00 1801.4 423.34 0.23 639257.2 150.23 0.86 371.61 34801.46 roots 97.20 1805.1 424.20 0.23 638844.7 150.13 0.86 372.29 34922.66 roots 97.40 1808.7 425.06 0.24 638435.7 150.03 0.86 372.92 35039.75 roots 97.60 1812.3 425.90 0.24 638030.1 149.94 0.86 373.51 35152.88 roots 97.80 1815.9 426.73 0.24 637627.7 149.84 0.86 374.05 35262.17 roots 98.00 1819.4 427.55 0.24 637228.4 149.75 0.86 374.55 35367.77 roots 98.20 1822.8 428.37 0.24 636832.0 149.66 0.86 375.02 35469.81 roots 98.40 1826.3 429.17 0.24 636438.5 149.56 0.85 375.44 35568.44 roots
Bending moment, shear and normal force interaction of I-shaped steel cross-sections
98
100.80 1865.0 438.29 0.24 631885.1 148.49 0.85 378.22 36536.22 roots 101.00 1868.1 439.01 0.24 631515.5 148.41 0.85 378.30 36603.12 roots 101.20 1871.2 439.73 0.24 631146.8 148.32 0.85 378.37 36668.56 roots 101.40 1874.3 440.45 0.24 630778.8 148.23 0.85 378.43 36732.69 roots 101.60 1877.3 441.16 0.24 630411.3 148.15 0.85 378.47 36795.65 roots 101.80 1880.3 441.88 0.24 630044.3 148.06 0.85 378.50 36857.58 roots 102.00 1883.4 442.59 0.25 629677.5 147.97 0.85 378.53 36918.63 roots 102.20 1886.4 443.30 0.25 629310.9 147.89 0.85 378.54 36978.94 roots 102.40 1889.4 444.00 0.25 628944.3 147.80 0.84 378.55 37038.66 roots 102.60 1892.4 444.71 0.25 628577.5 147.72 0.84 378.56 37097.93 roots 102.80 1895.4 445.41 0.25 628210.4 147.63 0.84 378.56 37156.9 roots 103.00 1898.4 446.12 0.25 627842.9 147.54 0.84 378.56 37215.73 fl a nge
103.20 1994.4 468.68 0.26 617945.3 145.22 0.83 fl a nge
103.40 2090.4 491.24 0.27 608028.5 142.89 0.82 fl a nge
103.60 2186.4 513.80 0.28 598092.5 140.55 0.80 fl a nge
103.80 2282.4 536.36 0.30 588137.3 138.21 0.79 fl a nge
104.00 2378.4 558.92 0.31 578162.9 135.87 0.78 fl a nge
104.20 2474.4 581.48 0.32 568169.3 133.52 0.76 fl a nge
104.40 2570.4 604.04 0.33 558156.5 131.17 0.75 fl a nge
104.60 2666.4 626.60 0.35 548124.5 128.81 0.74 fl a nge
104.80 2762.4 649.16 0.36 538073.3 126.45 0.72 fl a nge
105.00 2858.4 671.72 0.37 528002.9 124.08 0.71 fl a nge
105.20 2954.4 694.28 0.38 517913.3 121.71 0.70 fl a nge
105.40 3050.4 716.84 0.40 507804.5 119.33 0.68 fl a nge
105.60 3146.4 739.40 0.41 497676.5 116.95 0.67 fl a nge
105.80 3242.4 761.96 0.42 487529.3 114.57 0.65 fl a nge
106.00 3338.4 784.52 0.43 477362.9 112.18 0.64 fl a nge
106.20 3434.4 807.08 0.45 467177.3 109.79 0.63 fl a nge
106.40 3530.4 829.64 0.46 456972.5 107.39 0.61 fl a nge
106.60 3626.4 852.20 0.47 446748.5 104.99 0.60 fl a nge
106.80 3722.4 874.76 0.48 436505.3 102.58 0.59 fl a nge
107.00 3818.4 897.32 0.50 426242.9 100.17 0.57 fl a nge
107.20 3914.4 919.88 0.51 415961.3 97.75 0.56 fl a nge
107.40 4010.4 942.44 0.52 405660.5 95.33 0.54 fl a nge
107.60 4106.4 965.00 0.53 395340.5 92.91 0.53 fl a nge
107.80 4202.4 987.56 0.55 385001.3 90.48 0.52 fl a nge
108.00 4298.4 1010.12 0.56 374642.9 88.04 0.50 fl a nge
108.20 4394.4 1032.68 0.57 364265.3 85.60 0.49 fl a nge
108.40 4490.4 1055.24 0.58 353868.5 83.16 0.48 fl a nge
108.60 4586.4 1077.80 0.60 343452.5 80.71 0.46 fl a nge
108.80 4682.4 1100.36 0.61 333017.3 78.26 0.45 fl a nge
109.00 4778.4 1122.92 0.62 322562.9 75.80 0.43 fl a nge
109.20 4874.4 1145.48 0.63 312089.3 73.34 0.42 fl a nge
109.40 4970.4 1168.04 0.65 301596.5 70.88 0.41 fl a nge
109.60 5066.4 1190.60 0.66 291084.5 68.40 0.39 fl a nge
109.80 5162.4 1213.16 0.67 280553.3 65.93 0.38 fl a nge
110.00 5258.4 1235.72 0.68 270002.9 63.45 0.36 fl a nge
110.20 5354.4 1258.28 0.70 259433.3 60.97 0.35 fl a nge
110.40 5450.4 1280.84 0.71 248844.5 58.48 0.33 fl a nge
110.60 5546.4 1303.40 0.72 238236.5 55.99 0.32 fl a nge
110.80 5642.4 1325.96 0.73 227609.3 53.49 0.31 fl a nge
111.00 5738.4 1348.52 0.75 216962.9 50.99 0.29 fl a nge
111.20 5834.4 1371.08 0.76 206297.3 48.48 0.28 fl a nge
111.40 5930.4 1393.64 0.77 195612.5 45.97 0.26 fl a nge
111.60 6026.4 1416.20 0.78 184908.5 43.45 0.25 fl a nge
111.80 6122.4 1438.76 0.80 174185.3 40.93 0.23 fl a nge
112.00 6218.4 1461.32 0.81 163442.9 38.41 0.22 fl a nge
112.20 6314.4 1483.88 0.82 152681.3 35.88 0.21 fl a nge
112.40 6410.4 1506.44 0.83 141900.5 33.35 0.19 fl a nge
112.60 6506.4 1529.00 0.85 131100.5 30.81 0.18 fl a nge
112.80 6602.4 1551.56 0.86 120281.3 28.27 0.16 fl a nge
113.00 6698.4 1574.12 0.87 109442.9 25.72 0.15 fl a nge
113.20 6794.4 1596.68 0.88 98585.3 23.17 0.13 fl a nge
113.40 6890.4 1619.24 0.90 87708.5 20.61 0.12 fl a nge
113.60 6986.4 1641.80 0.91 76812.5 18.05 0.10 fl a nge
113.80 7082.4 1664.36 0.92 65897.3 15.49 0.09 fl a nge
114.00 7178.4 1686.92 0.93 54962.9 12.92 0.07 fl a nge
114.20 7274.4 1709.48 0.95 44009.3 10.34 0.06 fl a nge
114.40 7370.4 1732.04 0.96 33036.5 7.76 0.04 fl a nge
114.60 7466.4 1754.60 0.97 22044.5 5.18 0.03 fl a nge
114.80 7562.4 1777.16 0.98 11033.3 2.59 0.01 fl a nge
115.00 7658.4 1799.72 1.00 2.9 0.00 0.00 fl a nge
Bending moment, shear and normal force interaction of I-shaped steel cross-sections
99
Region II
Geometry Exact calculation y-y axis
Profi l e HEA240 y-a s A Ned nN W My,Ed,web nM Aroots Wr
Npl ,Rd 1805.6 kN mm mm² kN - mm³ kNm - mm² mm³
Mpl ,y,Rd 175.0 kNm 82.3226 0.0 0.00 0.00 691829.6 162.58 0.93 23.94 1969.006 roots 82.37 4.2 0.99 0.00 691480.9 162.50 0.93 27.41 2255.381 roots Wpl ,y 744626.1515 mm³ 82.42 8.4 1.97 0.00 691136.3 162.42 0.93 30.82 2537.638 roots 82.47 12.5 2.94 0.00 690795.5 162.34 0.93 34.19 2816.049 roots
Av 2517.55764 mm² 82.52 16.6 3.90 0.00 690458.3 162.26 0.93 37.51 3090.842 roots
Vpl ,Rd 341.6 kN 82.57 20.6 4.85 0.00 690124.5 162.18 0.93 40.78 3362.21 roots
82.63 24.6 5.78 0.00 689793.9 162.10 0.93 44.01 3630.319 roots
Wv = 52796.6 mm³ 82.68 28.6 6.71 0.00 689466.4 162.02 0.93 47.20 3895.317 roots
nV = 0.5 82.73 32.5 7.63 0.00 689141.8 161.95 0.93 50.35 4157.333 roots
Av,rec 4.84 mm² 82.78 36.3 8.54 0.00 688820.1 161.87 0.93 53.47 4416.482 roots
Av,res t 28.78 mm² 82.83 40.2 9.44 0.01 688501.0 161.80 0.92 56.54 4672.868 roots
di fference 0.00 mm² 82.88 44.0 10.33 0.01 688184.6 161.72 0.92 59.59 4926.587 roots 82.93 47.7 11.22 0.01 687870.8 161.65 0.92 62.59 5177.724 roots 82.98 51.5 12.09 0.01 687559.4 161.58 0.92 65.57 5426.359 roots 83.03 55.2 12.96 0.01 687250.4 161.50 0.92 68.51 5672.563 roots
A = 7684 mm² 83.08 58.8 13.82 0.01 686943.7 161.43 0.92 71.42 5916.405 roots
h = 230 mm 83.13 62.5 14.68 0.01 686639.3 161.36 0.92 74.30 6157.947 roots
83.18 66.1 15.53 0.01 686337.1 161.29 0.92 77.15 6397.247 roots
b = 240 mm 83.23 69.7 16.37 0.01 686037.1 161.22 0.92 79.97 6634.36 roots
tw = 7.5 mm 83.28 73.2 17.20 0.01 685739.1 161.15 0.92 82.77 6869.337 roots
tf = 12 mm 83.33 76.7 18.03 0.01 685443.2 161.08 0.92 85.53 7102.226 roots
r = 21 mm 83.38 80.2 18.85 0.01 685149.3 161.01 0.92 88.27 7333.072 roots
83.43 83.7 19.67 0.01 684857.3 160.94 0.92 90.98 7561.918 roots
y-y a xi s 83.48 87.1 20.48 0.01 684567.3 160.87 0.92 93.67 7788.804 roots
Aw 1545 mm² 83.53 90.5 21.28 0.01 684279.2 160.81 0.92 96.33 8013.769 roots
Af 5760 mm² 83.58 93.9 22.08 0.01 683992.9 160.74 0.92 98.97 8236.85 roots
Ar 378.56 mm² 83.63 97.3 22.87 0.01 683708.4 160.67 0.92 101.58 8458.081 roots
83.68 100.6 23.65 0.01 683425.7 160.61 0.92 104.16 8677.495 roots
hw = 206 mm 83.73 104.0 24.43 0.01 683144.8 160.54 0.92 106.72 8895.123 roots
d = 164 mm 83.79 107.3 25.21 0.01 682865.5 160.47 0.92 109.26 9110.997 roots
hf = 218 mm 83.84 110.5 25.98 0.01 682588.0 160.41 0.92 111.78 9325.145 roots
83.89 113.8 26.74 0.01 682312.1 160.34 0.92 114.27 9537.594 roots 83.94 117.0 27.50 0.02 682037.8 160.28 0.92 116.74 9748.372 roots 83.99 120.2 28.25 0.02 681765.2 160.21 0.92 119.19 9957.503 roots 84.04 123.4 29.00 0.02 681494.1 160.15 0.92 121.62 10165.01 roots 84.09 126.6 29.74 0.02 681224.6 160.09 0.91 124.02 10370.93 roots 84.14 129.7 30.48 0.02 680956.6 160.02 0.91 126.41 10575.26 roots 84.19 132.8 31.21 0.02 680690.2 159.96 0.91 128.77 10778.05 roots 84.24 135.9 31.94 0.02 680425.2 159.90 0.91 131.11 10979.3 roots
fy = 235 N/mm² 84.29 139.0 32.67 0.02 680161.7 159.84 0.91 133.44 11179.04 roots
84.34 142.1 33.38 0.02 679899.7 159.78 0.91 135.74 11377.29 roots 84.39 145.1 34.10 0.02 679639.1 159.72 0.91 138.02 11574.07 roots 84.44 148.1 34.81 0.02 679379.9 159.65 0.91 140.29 11769.39 roots 84.49 151.1 35.51 0.02 679122.1 159.59 0.91 142.53 11963.28 roots 84.54 154.1 36.21 0.02 678865.7 159.53 0.91 144.76 12155.75 roots 84.59 157.1 36.91 0.02 678610.7 159.47 0.91 146.96 12346.82 roots 84.64 160.0 37.60 0.02 678357.0 159.41 0.91 149.15 12536.5 roots 84.69 162.9 38.29 0.02 678104.6 159.35 0.91 151.32 12724.82 roots 84.74 165.8 38.97 0.02 677853.6 159.30 0.91 153.47 12911.78 roots 84.79 168.7 39.65 0.02 677603.8 159.24 0.91 155.61 13097.4 roots Shams Hamidi:
Bending moment, shear and normal force interaction of I-shaped steel cross-sections
100
101.18 637.4 149.78 0.08 631175.5 148.33 0.85 378.37 36663.52 roots 101.23 638.1 149.96 0.08 631082.6 148.30 0.85 378.38 36679.83 roots 101.29 638.9 150.14 0.08 630989.8 148.28 0.85 378.40 36696.06 roots 101.34 639.7 150.32 0.08 630897.0 148.26 0.85 378.41 36712.22 roots 101.39 640.4 150.50 0.08 630804.2 148.24 0.85 378.42 36728.29 roots 101.44 641.2 150.68 0.08 630711.5 148.22 0.85 378.44 36744.29 roots 101.49 642.0 150.86 0.08 630618.8 148.20 0.85 378.45 36760.22 roots 101.54 642.7 151.04 0.08 630526.2 148.17 0.85 378.46 36776.08 roots 101.59 643.5 151.22 0.08 630433.5 148.15 0.85 378.47 36791.87 roots 101.64 644.3 151.40 0.08 630341.0 148.13 0.85 378.48 36807.59 roots 101.69 645.0 151.58 0.08 630248.4 148.11 0.85 378.49 36823.25 roots 101.74 645.8 151.76 0.08 630155.8 148.09 0.85 378.49 36838.85 roots 101.79 646.6 151.94 0.08 630063.3 148.06 0.85 378.50 36854.39 roots 101.84 647.3 152.12 0.08 629970.8 148.04 0.85 378.51 36869.87 roots 101.89 648.1 152.30 0.08 629878.3 148.02 0.85 378.51 36885.3 roots 101.94 648.9 152.48 0.08 629785.9 148.00 0.85 378.52 36900.68 roots 101.99 649.6 152.66 0.08 629693.4 147.98 0.85 378.53 36916 roots 102.04 650.4 152.84 0.08 629600.9 147.96 0.85 378.53 36931.28 roots 102.09 651.1 153.02 0.08 629508.5 147.93 0.85 378.53 36946.52 roots 102.14 651.9 153.20 0.08 629416.0 147.91 0.85 378.54 36961.71 roots 102.19 652.7 153.37 0.08 629323.6 147.89 0.85 378.54 36976.86 roots 102.24 653.4 153.55 0.09 629231.2 147.87 0.85 378.54 36991.98 roots 102.29 654.2 153.73 0.09 629138.7 147.85 0.84 378.55 37007.05 roots 102.34 654.9 153.91 0.09 629046.3 147.83 0.84 378.55 37022.1 roots 102.39 655.7 154.09 0.09 628953.8 147.80 0.84 378.55 37037.11 roots 102.45 656.5 154.27 0.09 628861.4 147.78 0.84 378.55 37052.1 roots 102.50 657.2 154.44 0.09 628768.9 147.76 0.84 378.55 37067.06 roots 102.55 658.0 154.62 0.09 628676.4 147.74 0.84 378.55 37081.99 roots 102.60 658.7 154.80 0.09 628583.9 147.72 0.84 378.56 37096.9 roots 102.65 659.5 154.98 0.09 628491.3 147.70 0.84 378.56 37111.8 roots 102.70 660.2 155.16 0.09 628398.8 147.67 0.84 378.56 37126.68 roots 102.75 661.0 155.33 0.09 628306.2 147.65 0.84 378.56 37141.54 roots 102.80 661.8 155.51 0.09 628213.6 147.63 0.84 378.56 37156.39 roots 102.85 662.5 155.69 0.09 628121.0 147.61 0.84 378.56 37171.23 roots 102.90 663.3 155.87 0.09 628028.3 147.59 0.84 378.56 37186.07 roots 102.95 664.0 156.05 0.09 627935.7 147.56 0.84 378.56 37200.9 roots 103.00 664.8 156.22 0.09 627842.9 147.54 0.84 378.56 37215.73 roots
103.07 664.8 156.22 0.09 627730.5 147.52 0.84 fl a nge
103.15 699.7 164.43 0.09 624131.1 146.67 0.84 fl a nge
103.22 734.6 172.63 0.10 620529.1 145.82 0.83 fl a nge
103.29 769.5 180.83 0.10 616924.6 144.98 0.83 fl a nge
103.36 804.4 189.04 0.10 613317.5 144.13 0.82 fl a nge
103.44 839.3 197.24 0.11 609707.9 143.28 0.82 fl a nge
103.51 874.2 205.45 0.11 606095.8 142.43 0.81 fl a nge
103.58 909.1 213.65 0.12 602481.1 141.58 0.81 fl a nge
103.65 944.1 221.85 0.12 598863.9 140.73 0.80 fl a nge
103.73 979.0 230.06 0.13 595244.1 139.88 0.80 fl a nge
103.80 1013.9 238.26 0.13 591621.8 139.03 0.79 fl a nge
103.87 1048.8 246.46 0.14 587997.0 138.18 0.79 fl a nge
103.95 1083.7 254.67 0.14 584369.6 137.33 0.78 fl a nge
104.02 1118.6 262.87 0.15 580739.7 136.47 0.78 fl a nge
104.09 1153.5 271.07 0.15 577107.3 135.62 0.78 fl a nge
104.16 1188.4 279.28 0.15 573472.3 134.77 0.77 fl a nge
104.24 1223.3 287.48 0.16 569834.7 133.91 0.77 fl a nge
104.31 1258.2 295.69 0.16 566194.7 133.06 0.76 fl a nge
104.38 1293.1 303.89 0.17 562552.1 132.20 0.76 fl a nge
104.45 1328.1 312.09 0.17 558906.9 131.34 0.75 fl a nge
104.53 1363.0 320.30 0.18 555259.2 130.49 0.75 fl a nge
104.60 1397.9 328.50 0.18 551609.0 129.63 0.74 fl a nge
104.67 1432.8 336.70 0.19 547956.3 128.77 0.74 fl a nge
104.75 1467.7 344.91 0.19 544301.0 127.91 0.73 fl a nge
104.82 1502.6 353.11 0.20 540643.1 127.05 0.73 fl a nge
104.89 1537.5 361.31 0.20 536982.8 126.19 0.72 fl a nge
104.96 1572.4 369.52 0.20 533319.8 125.33 0.72 fl a nge
105.04 1607.3 377.72 0.21 529654.4 124.47 0.71 fl a nge
105.11 1642.2 385.93 0.21 525986.4 123.61 0.71 fl a nge
105.18 1677.1 394.13 0.22 522315.9 122.74 0.70 fl a nge
105.25 1712.1 402.33 0.22 518642.8 121.88 0.70 fl a nge
105.33 1747.0 410.54 0.23 514967.2 121.02 0.69 fl a nge
105.40 1781.9 418.74 0.23 511289.0 120.15 0.69 fl a nge
105.47 1816.8 426.94 0.24 507608.3 119.29 0.68 fl a nge
105.55 1851.7 435.15 0.24 503925.1 118.42 0.68 fl a nge
105.62 1886.6 443.35 0.25 500239.3 117.56 0.67 fl a nge
105.69 1921.5 451.55 0.25 496551.0 116.69 0.67 fl a nge
105.76 1956.4 459.76 0.25 492860.2 115.82 0.66 fl a nge
105.84 1991.3 467.96 0.26 489166.8 114.95 0.66 fl a nge
105.91 2026.2 476.17 0.26 485470.9 114.09 0.65 fl a nge
105.98 2061.1 484.37 0.27 481772.4 113.22 0.65 fl a nge
106.05 2096.1 492.57 0.27 478071.4 112.35 0.64 fl a nge
106.13 2131.0 500.78 0.28 474367.9 111.48 0.64 fl a nge
106.20 2165.9 508.98 0.28 470661.8 110.61 0.63 fl a nge
106.27 2200.8 517.18 0.29 466953.2 109.73 0.63 fl a nge
106.35 2235.7 525.39 0.29 463242.1 108.86 0.62 fl a nge
106.42 2270.6 533.59 0.30 459528.4 107.99 0.62 fl a nge
106.49 2305.5 541.79 0.30 455812.1 107.12 0.61 fl a nge
Bending moment, shear and normal force interaction of I-shaped steel cross-sections
101
106.56 2340.4 550.00 0.30 452093.4 106.24 0.61 fl a nge
106.64 2375.3 558.20 0.31 448372.1 105.37 0.60 fl a nge
106.71 2410.2 566.41 0.31 444648.2 104.49 0.60 fl a nge
106.78 2445.1 574.61 0.32 440921.8 103.62 0.59 fl a nge
106.85 2480.1 582.81 0.32 437192.9 102.74 0.59 fl a nge
106.93 2515.0 591.02 0.33 433461.4 101.86 0.58 fl a nge
107.00 2549.9 599.22 0.33 429727.4 100.99 0.58 fl a nge
107.07 2584.8 607.42 0.34 425990.9 100.11 0.57 fl a nge
107.15 2619.7 615.63 0.34 422251.8 99.23 0.57 fl a nge
107.22 2654.6 623.83 0.35 418510.2 98.35 0.56 fl a nge
107.29 2689.5 632.03 0.35 414766.0 97.47 0.56 fl a nge
107.36 2724.4 640.24 0.35 411019.3 96.59 0.55 fl a nge
107.44 2759.3 648.44 0.36 407270.1 95.71 0.55 fl a nge
107.51 2794.2 656.65 0.36 403518.3 94.83 0.54 fl a nge
107.58 2829.1 664.85 0.37 399764.0 93.94 0.54 fl a nge
107.65 2864.1 673.05 0.37 396007.1 93.06 0.53 fl a nge
107.73 2899.0 681.26 0.38 392247.8 92.18 0.53 fl a nge
107.80 2933.9 689.46 0.38 388485.8 91.29 0.52 fl a nge
107.87 2968.8 697.66 0.39 384721.4 90.41 0.52 fl a nge
107.95 3003.7 705.87 0.39 380954.3 89.52 0.51 fl a nge
108.02 3038.6 714.07 0.40 377184.8 88.64 0.51 fl a nge
108.09 3073.5 722.27 0.40 373412.7 87.75 0.50 fl a nge
108.16 3108.4 730.48 0.40 369638.1 86.86 0.50 fl a nge
108.24 3143.3 738.68 0.41 365860.9 85.98 0.49 fl a nge
108.31 3178.2 746.89 0.41 362081.2 85.09 0.49 fl a nge
108.38 3213.1 755.09 0.42 358299.0 84.20 0.48 fl a nge
108.45 3248.1 763.29 0.42 354514.2 83.31 0.48 fl a nge
108.53 3283.0 771.50 0.43 350726.9 82.42 0.47 fl a nge
108.60 3317.9 779.70 0.43 346937.0 81.53 0.47 fl a nge
108.67 3352.8 787.90 0.44 343144.6 80.64 0.46 fl a nge
108.75 3387.7 796.11 0.44 339349.7 79.75 0.46 fl a nge
108.82 3422.6 804.31 0.45 335552.2 78.85 0.45 fl a nge
108.89 3457.5 812.51 0.45 331752.2 77.96 0.45 fl a nge
108.96 3492.4 820.72 0.45 327949.7 77.07 0.44 fl a nge
109.04 3527.3 828.92 0.46 324144.6 76.17 0.44 fl a nge
109.11 3562.2 837.13 0.46 320336.9 75.28 0.43 fl a nge
109.18 3597.1 845.33 0.47 316526.8 74.38 0.43 fl a nge
109.25 3632.1 853.53 0.47 312714.1 73.49 0.42 fl a nge
109.33 3667.0 861.74 0.48 308898.8 72.59 0.41 fl a nge
109.40 3701.9 869.94 0.48 305081.0 71.69 0.41 fl a nge
109.47 3736.8 878.14 0.49 301260.7 70.80 0.40 fl a nge
109.55 3771.7 886.35 0.49 297437.8 69.90 0.40 fl a nge
109.62 3806.6 894.55 0.50 293612.4 69.00 0.39 fl a nge
109.69 3841.5 902.75 0.50 289784.5 68.10 0.39 fl a nge
109.76 3876.4 910.96 0.50 285954.0 67.20 0.38 fl a nge
109.84 3911.3 919.16 0.51 282121.0 66.30 0.38 fl a nge
109.91 3946.2 927.37 0.51 278285.4 65.40 0.37 fl a nge
109.98 3981.1 935.57 0.52 274447.3 64.50 0.37 fl a nge
110.05 4016.1 943.77 0.52 270606.7 63.59 0.36 fl a nge
110.13 4051.0 951.98 0.53 266763.5 62.69 0.36 fl a nge
110.20 4085.9 960.18 0.53 262917.8 61.79 0.35 fl a nge
110.27 4120.8 968.38 0.54 259069.6 60.88 0.35 fl a nge
110.35 4155.7 976.59 0.54 255218.8 59.98 0.34 fl a nge
110.42 4190.6 984.79 0.55 251365.5 59.07 0.34 fl a nge
110.49 4225.5 992.99 0.55 247509.6 58.16 0.33 fl a nge
110.56 4260.4 1001.20 0.55 243651.2 57.26 0.33 fl a nge
110.64 4295.3 1009.40 0.56 239790.2 56.35 0.32 fl a nge
110.71 4330.2 1017.61 0.56 235926.8 55.44 0.32 fl a nge
110.78 4365.1 1025.81 0.57 232060.7 54.53 0.31 fl a nge
110.85 4400.1 1034.01 0.57 228192.2 53.63 0.31 fl a nge
110.93 4435.0 1042.22 0.58 224321.1 52.72 0.30 fl a nge
111.00 4469.9 1050.42 0.58 220447.4 51.81 0.30 fl a nge
111.07 4504.8 1058.62 0.59 216571.2 50.89 0.29 fl a nge
111.15 4539.7 1066.83 0.59 212692.5 49.98 0.29 fl a nge
111.22 4574.6 1075.03 0.60 208811.3 49.07 0.28 fl a nge
111.29 4609.5 1083.23 0.60 204927.5 48.16 0.28 fl a nge
111.36 4644.4 1091.44 0.60 201041.1 47.24 0.27 fl a nge
111.44 4679.3 1099.64 0.61 197152.3 46.33 0.26 fl a nge
111.51 4714.2 1107.85 0.61 193260.9 45.42 0.26 fl a nge
111.58 4749.1 1116.05 0.62 189366.9 44.50 0.25 fl a nge
111.65 4784.1 1124.25 0.62 185470.4 43.59 0.25 fl a nge
111.73 4819.0 1132.46 0.63 181571.4 42.67 0.24 fl a nge
111.80 4853.9 1140.66 0.63 177669.8 41.75 0.24 fl a nge
111.87 4888.8 1148.86 0.64 173765.7 40.83 0.23 fl a nge
111.95 4923.7 1157.07 0.64 169859.1 39.92 0.23 fl a nge
112.02 4958.6 1165.27 0.65 165949.9 39.00 0.22 fl a nge
112.09 4993.5 1173.47 0.65 162038.2 38.08 0.22 fl a nge
112.16 5028.4 1181.68 0.65 158123.9 37.16 0.21 fl a nge
112.24 5063.3 1189.88 0.66 154207.1 36.24 0.21 fl a nge
112.31 5098.2 1198.09 0.66 150287.8 35.32 0.20 fl a nge
112.38 5133.1 1206.29 0.67 146365.9 34.40 0.20 fl a nge
112.45 5168.1 1214.49 0.67 142441.5 33.47 0.19 fl a nge
112.53 5203.0 1222.70 0.68 138514.5 32.55 0.19 fl a nge
112.60 5237.9 1230.90 0.68 134585.0 31.63 0.18 fl a nge
112.67 5272.8 1239.10 0.69 130653.0 30.70 0.18 fl a nge
112.75 5307.7 1247.31 0.69 126718.4 29.78 0.17 fl a nge
112.82 5342.6 1255.51 0.70 122781.3 28.85 0.16 fl a nge
112.89 5377.5 1263.71 0.70 118841.7 27.93 0.16 fl a nge
112.96 5412.4 1271.92 0.70 114899.5 27.00 0.15 fl a nge
113.04 5447.3 1280.12 0.71 110954.7 26.07 0.15 fl a nge
113.11 5482.2 1288.33 0.71 107007.5 25.15 0.14 fl a nge
113.18 5517.1 1296.53 0.72 103057.7 24.22 0.14 fl a nge
113.25 5552.1 1304.73 0.72 99105.3 23.29 0.13 fl a nge
113.33 5587.0 1312.94 0.73 95150.4 22.36 0.13 fl a nge
113.40 5621.9 1321.14 0.73 91193.0 21.43 0.12 fl a nge
113.47 5656.8 1329.34 0.74 87233.1 20.50 0.12 fl a nge
113.55 5691.7 1337.55 0.74 83270.6 19.57 0.11 fl a nge
113.62 5726.6 1345.75 0.75 79305.5 18.64 0.11 fl a nge
113.69 5761.5 1353.95 0.75 75338.0 17.70 0.10 fl a nge
113.76 5796.4 1362.16 0.75 71367.8 16.77 0.10 fl a nge
113.84 5831.3 1370.36 0.76 67395.2 15.84 0.09 fl a nge
113.91 5866.2 1378.57 0.76 63420.0 14.90 0.09 fl a nge
113.98 5901.1 1386.77 0.77 59442.3 13.97 0.08 fl a nge
114.05 5936.1 1394.97 0.77 55462.0 13.03 0.07 fl a nge
114.13 5971.0 1403.18 0.78 51479.2 12.10 0.07 fl a nge
114.20 6005.9 1411.38 0.78 47493.8 11.16 0.06 fl a nge
114.27 6040.8 1419.58 0.79 43505.9 10.22 0.06 fl a nge
114.35 6075.7 1427.79 0.79 39515.5 9.29 0.05 fl a nge
114.42 6110.6 1435.99 0.80 35522.5 8.35 0.05 fl a nge
114.49 6145.5 1444.19 0.80 31527.0 7.41 0.04 fl a nge
114.56 6180.4 1452.40 0.80 27529.0 6.47 0.04 fl a nge
114.64 6215.3 1460.60 0.81 23528.4 5.53 0.03 fl a nge
114.71 6250.2 1468.81 0.81 19525.3 4.59 0.03 fl a nge
114.78 6285.1 1477.01 0.82 15519.6 3.65 0.02 fl a nge
114.85 6320.1 1485.21 0.82 11511.4 2.71 0.02 fl a nge
114.93 6355.0 1493.42 0.83 7500.7 1.76 0.01 fl a nge
115.00 6389.9 1501.62 0.83 3487.4 0.82 0.00 fl a nge
Bending moment, shear and normal force interaction of I-shaped steel cross-sections
102
Region III
Geometry Exact calculation y-y axis
Profi l e HEA240 y-a s A Ned nN W My,Ed,web nM
Npl ,Rd 1805.6 kN mm mm² kN - mm³ kNm
-Mpl ,y,Rd 175.0 kNm 103.00 0.0 0.00 0.00 618481.3 145.34 0.83 fl a nge1
103.02 8.0 1.87 0.00 617660.8 145.15 0.83 fl a nge1
Wpl ,y 744626.1515 mm³ 103.04 15.9 3.74 0.00 616840.1 144.96 0.83 fl a nge1
103.06 23.9 5.62 0.00 616019.3 144.76 0.83 fl a nge1
Av 2517.55764 mm² 103.08 31.9 7.49 0.00 615198.3 144.57 0.83 fl a nge1
Vpl ,Rd 341.6 kN 103.10 39.8 9.36 0.01 614377.1 144.38 0.83 fl a nge1
103.13 47.8 11.23 0.01 613555.8 144.19 0.82 fl a nge1
Wv = 126144.9 mm³ 103.15 55.8 13.10 0.01 612734.3 143.99 0.82 fl a nge1
nV = 0.8 103.17 63.7 14.97 0.01 611912.6 143.80 0.82 fl a nge1
103.19 71.7 16.85 0.01 611090.8 143.61 0.82 fl a nge1
103.21 79.7 18.72 0.01 610268.8 143.41 0.82 fl a nge1
103.23 87.6 20.59 0.01 609446.7 143.22 0.82 fl a nge1
δ 0.9140 mm 103.25 95.6 22.46 0.01 608624.3 143.03 0.82 fl a nge1
δ+hw/2 103.9140 mm 103.27 103.5 24.33 0.01 607801.8 142.83 0.82 fl a nge1
103.29 111.5 26.21 0.01 606979.2 142.64 0.82 fl a nge1
A = 7684 mm² 103.31 119.5 28.08 0.02 606156.4 142.45 0.81 fl a nge1
h = 230 mm 103.33 127.4 29.95 0.02 605333.4 142.25 0.81 fl a nge1
103.36 135.4 31.82 0.02 604510.2 142.06 0.81 fl a nge1
b = 240 mm 103.38 143.4 33.69 0.02 603686.9 141.87 0.81 fl a nge1
tw = 7.5 mm 103.40 151.3 35.56 0.02 602863.4 141.67 0.81 fl a nge1
tf = 12 mm 103.42 159.3 37.44 0.02 602039.7 141.48 0.81 fl a nge1
r = 21 mm 103.44 167.3 39.31 0.02 601215.9 141.29 0.81 fl a nge1
103.46 175.2 41.18 0.02 600391.9 141.09 0.81 fl a nge1
y-y a xi s 103.48 183.2 43.05 0.02 599567.8 140.90 0.81 fl a nge1
Aw 1545 mm² 103.50 191.2 44.92 0.02 598743.4 140.70 0.80 fl a nge1
Af 5760 mm² 103.52 199.1 46.80 0.03 597918.9 140.51 0.80 fl a nge1
Ar 378.56 mm² 103.54 207.1 48.67 0.03 597094.3 140.32 0.80 fl a nge1
Wr 37215.7 mm³ 103.56 215.1 50.54 0.03 596269.5 140.12 0.80 fl a nge1
hw = 206 mm 103.59 223.0 52.41 0.03 595444.5 139.93 0.80 fl a nge1
d = 164 mm 103.61 231.0 54.28 0.03 594619.3 139.74 0.80 fl a nge1
hf = 218 mm 103.63 239.0 56.15 0.03 593794.0 139.54 0.80 fl a nge1
103.65 246.9 58.03 0.03 592968.5 139.35 0.80 fl a nge1
103.67 254.9 59.90 0.03 592142.8 139.15 0.80 fl a nge1
103.69 262.9 61.77 0.03 591317.0 138.96 0.79 fl a nge1
103.71 270.8 63.64 0.04 590491.0 138.77 0.79 fl a nge1
103.73 278.8 65.51 0.04 589664.9 138.57 0.79 fl a nge1
103.75 286.7 67.39 0.04 588838.6 138.38 0.79 fl a nge1
103.77 294.7 69.26 0.04 588012.1 138.18 0.79 fl a nge1
103.79 302.7 71.13 0.04 587185.4 137.99 0.79 fl a nge1
fy = 235 N/mm² 103.82 310.6 73.00 0.04 586358.6 137.79 0.79 fl a nge1
103.84 318.6 74.87 0.04 585531.6 137.60 0.79 fl a nge1
103.86 326.6 76.74 0.04 584704.4 137.41 0.79 fl a nge1
103.88 334.5 78.62 0.04 583877.1 137.21 0.78 fl a nge1
103.90 342.5 80.49 0.04 583049.6 137.02 0.78 fl a nge1
103.92 351.0 82.50 0.05 582161.9 136.81 0.78 fl a nge2
103.94 361.1 84.85 0.05 581119.0 136.56 0.78 fl a nge2
103.96 371.1 87.21 0.05 580075.9 136.32 0.78 fl a nge2
103.98 381.1 89.57 0.05 579032.5 136.07 0.78 fl a nge2
104.00 391.2 91.93 0.05 577989.0 135.83 0.78 fl a nge2
104.02 401.2 94.29 0.05 576945.2 135.58 0.77 fl a nge2
104.05 411.3 96.64 0.05 575901.2 135.34 0.77 fl a nge2
104.07 421.3 99.00 0.05 574857.1 135.09 0.77 fl a nge2
104.09 431.3 101.36 0.06 573812.7 134.85 0.77 fl a nge2
104.11 441.4 103.72 0.06 572768.1 134.60 0.77 fl a nge2
104.13 451.4 106.08 0.06 571723.3 134.35 0.77 fl a nge2
Bending moment, shear and normal force interaction of I-shaped steel cross-sections
103
112.58 4509.5 1059.74 0.59 132001.3 31.02 0.18 fl a nge2
112.60 4519.5 1062.09 0.59 130875.3 30.76 0.18 fl a nge2
112.62 4529.5 1064.44 0.59 129749.2 30.49 0.17 fl a nge2
112.65 4539.5 1066.79 0.59 128622.8 30.23 0.17 fl a nge2
112.67 4549.5 1069.14 0.59 127496.3 29.96 0.17 fl a nge2
112.69 4559.5 1071.49 0.59 126369.5 29.70 0.17 fl a nge2
112.71 4569.5 1073.84 0.59 125242.5 29.43 0.17 fl a nge2
112.73 4579.5 1076.19 0.60 124115.3 29.17 0.17 fl a nge2
112.75 4589.5 1078.54 0.60 122987.9 28.90 0.17 fl a nge2
112.77 4599.5 1080.89 0.60 121860.3 28.64 0.16 fl a nge2
112.79 4609.5 1083.24 0.60 120732.5 28.37 0.16 fl a nge2
112.81 4619.5 1085.59 0.60 119604.5 28.11 0.16 fl a nge2
112.83 4629.5 1087.94 0.60 118476.3 27.84 0.16 fl a nge2
112.85 4639.5 1090.29 0.60 117347.8 27.58 0.16 fl a nge2
112.87 4649.5 1092.64 0.61 116219.2 27.31 0.16 fl a nge2
112.90 4659.5 1094.99 0.61 115090.3 27.05 0.15 fl a nge2
112.92 4669.5 1097.34 0.61 113961.3 26.78 0.15 fl a nge2
112.94 4679.5 1099.69 0.61 112832.0 26.52 0.15 fl a nge2
112.96 4689.5 1102.04 0.61 111702.5 26.25 0.15 fl a nge2
112.98 4699.5 1104.39 0.61 110572.8 25.98 0.15 fl a nge2
113.00 4709.5 1106.74 0.61 109442.9 25.72 0.15 fl a nge2
113.02 4719.5 1109.09 0.61 108312.8 25.45 0.15 fl a nge2
113.04 4729.5 1111.44 0.62 107182.5 25.19 0.14 fl a nge2
113.06 4739.5 1113.79 0.62 106052.0 24.92 0.14 fl a nge2
113.08 4749.5 1116.14 0.62 104921.3 24.66 0.14 fl a nge2
113.10 4759.5 1118.49 0.62 103790.3 24.39 0.14 fl a nge2
113.12 4769.5 1120.84 0.62 102659.2 24.12 0.14 fl a nge2
113.15 4779.5 1123.19 0.62 101527.8 23.86 0.14 fl a nge2
113.17 4789.5 1125.54 0.62 100396.3 23.59 0.13 fl a nge2
113.19 4799.5 1127.89 0.62 99264.5 23.33 0.13 fl a nge2
113.21 4809.5 1130.24 0.63 98132.5 23.06 0.13 fl a nge2
113.23 4819.5 1132.59 0.63 97000.3 22.80 0.13 fl a nge2
113.25 4829.5 1134.94 0.63 95867.9 22.53 0.13 fl a nge2
113.27 4839.5 1137.29 0.63 94735.3 22.26 0.13 fl a nge2
113.29 4849.5 1139.64 0.63 93602.5 22.00 0.13 fl a nge2
113.31 4859.5 1141.99 0.63 92469.5 21.73 0.12 fl a nge2
113.33 4869.5 1144.34 0.63 91336.3 21.46 0.12 fl a nge2
113.35 4879.5 1146.69 0.64 90202.8 21.20 0.12 fl a nge2
113.37 4889.5 1149.04 0.64 89069.2 20.93 0.12 fl a nge2
113.40 4899.5 1151.39 0.64 87935.3 20.66 0.12 fl a nge2
113.42 4909.5 1153.74 0.64 86801.3 20.40 0.12 fl a nge2
113.44 4919.5 1156.09 0.64 85667.0 20.13 0.12 fl a nge2
113.46 4929.5 1158.44 0.64 84532.5 19.87 0.11 fl a nge2
113.48 4939.5 1160.79 0.64 83397.8 19.60 0.11 fl a nge2
113.50 4949.5 1163.14 0.64 82262.9 19.33 0.11 fl a nge2
113.52 4959.5 1165.49 0.65 81127.8 19.07 0.11 fl a nge2
113.54 4969.5 1167.84 0.65 79992.5 18.80 0.11 fl a nge2
113.56 4979.5 1170.19 0.65 78857.0 18.53 0.11 fl a nge2
113.58 4989.5 1172.54 0.65 77721.3 18.26 0.10 fl a nge2
113.60 4999.5 1174.89 0.65 76585.3 18.00 0.10 fl a nge2
113.62 5009.5 1177.24 0.65 75449.2 17.73 0.10 fl a nge2
113.65 5019.5 1179.59 0.65 74312.8 17.46 0.10 fl a nge2
113.67 5029.5 1181.94 0.65 73176.3 17.20 0.10 fl a nge2
113.69 5039.5 1184.29 0.66 72039.5 16.93 0.10 fl a nge2
113.71 5049.5 1186.64 0.66 70902.5 16.66 0.10 fl a nge2
113.73 5059.5 1188.99 0.66 69765.3 16.39 0.09 fl a nge2
113.75 5069.5 1191.34 0.66 68627.9 16.13 0.09 fl a nge2
113.77 5079.5 1193.69 0.66 67490.3 15.86 0.09 fl a nge2
113.79 5089.5 1196.04 0.66 66352.5 15.59 0.09 fl a nge2
113.81 5099.5 1198.39 0.66 65214.5 15.33 0.09 fl a nge2
113.83 5109.5 1200.74 0.66 64076.3 15.06 0.09 fl a nge2
113.85 5119.5 1203.09 0.67 62937.8 14.79 0.08 fl a nge2
113.87 5129.5 1205.44 0.67 61799.2 14.52 0.08 fl a nge2
113.90 5139.5 1207.79 0.67 60660.3 14.26 0.08 fl a nge2
113.92 5149.5 1210.14 0.67 59521.3 13.99 0.08 fl a nge2
113.94 5159.5 1212.49 0.67 58382.0 13.72 0.08 fl a nge2
113.96 5169.5 1214.84 0.67 57242.5 13.45 0.08 fl a nge2
113.98 5179.5 1217.19 0.67 56102.8 13.18 0.08 fl a nge2
114.00 5189.5 1219.54 0.68 54962.9 12.92 0.07 fl a nge2
114.02 5199.5 1221.89 0.68 53822.8 12.65 0.07 fl a nge2
114.02 5199.5 1221.89 0.68 53822.8 12.65 0.07 fl a nge2