V. GB500017-2017 Tube section with Combined Axial and Bending
Verify the strength, stability, and slenderness of a tube section subject to combined axial and bending per GB50017-2017.
Reference
MOHURD. 2017. GB 50017-2017 Standard for design of steel structures . Beijing, China: Ministry of Housing and Urban-Rural Development
Problem
The section is a TUB 300x10.0 with a length of 4 m. The structure is a portal frame. Member #1 assigned with a tube section (TUB300x10.0) is designed per GB 50017-2017. The section has an unbraced length of 4 m in either direction. The governing load case #1 has the following ultimate loads on the member:
- Fx = 30.55 kN
- Fy = 25.06 kN
- N = 66.69 kN
- Mx = 83.44 kN·m (at member end)
- My = 122.2 kN·m (at member end)
The material is Q235 type steel.
- Design strength in tension, compression, and flexure: fy = 215 MPa
- Design strength in shear: fv = 125 MPa
Calculations
Section Properties
- Section depth, H = 300 mm
- Section width, D = 300 mm
- Wall thickness, t = 10 mm
- Cross-sectional area, A = 11,260 mm2
- Moment of inertia about x, Ix = Iy = 155,200,00 mm4
- Radius of gyration about x, rx = ry = 118.2 mm
- Section modulus about x, Wx = Wy = 1,035,000 mm3
Slenderness Ratio
The effective length is:
lox = μx×lx = 1.402 × 4,000 mm = 5,188 mm
loy = μy×ly = 2.0383 × 4,000 mm = 8,150 mm
The slenderness ratio is:
According to table 7.4.6 of Standard for design of steel structures, the allowable slenderness ratio of compression members is λclim = 150.
Ratio: λmax / λclim = 69.44 / 150 = 0.46According to table 7.4.7 of Standard for design of steel structures, the allowable slenderness ratio of tension members is λtlim = 300.
Ratio: λmax / λtlim = 69.44 / 300 = 0.23Steel Grade Correction Factor
The steel type is Q235. According to note 1 in table 3.5.1 of Standard for design of steel structures and table 1 of Standard for design of steel structures. Commentary 2.2, the steel grade correction coefficient is εk = 1.
Check Flange Width to Thickness Ratio of Compression Member
According to table 3.5.1, note 2 of Standard for design of steel structures, and the width thickness ratio of cross-section plate is grade S3, so the limit value of height thickness ratio is:
Plastic Development Coefficient
According to clause 8.1.1 of Standard for design of steel structures, and the width thickness ratio of cross-section plate is grade S3,
γx = 1.05
γy = 1.05
Check Member Strength
According to clause 8.1.1 of Standard for design of steel structures,
Ratio:
Check In-Plane Stability of Member
According to table 7.2.1-1 of Standard for design of steel structures, the section is "b" for this section.According to the formula (D.0.5) in Appendix D of Standard for design of steel structures, for the x-x direction:
Class b, so, the coefficients are α1 = 0.650, α2 = 0.965, and α3 = 0.300.
Since , then the stability factor in x:
According to the formula 8.2.1-8 of Standard for design of steel structures,
According to the formula 8.2.1-10 of Standard for design of steel structures,
According to the formula 8.2.1-12 and 8.2.1-5 note of Standard for design of steel structures,
According to the formula 8.2.1-12 of Standard for design of steel structures,
According to the formula 8.2.5, ϕby = 1.0.
According to the formula 8.2.1, η = 0.7.
According to the formula 8.2.5-1,
Check Out-of-Plane Stability of Member
According to table 7.2.1-1 of Standard for design of steel structures, the section is "b" for this section.According to the formula (D.0.5) in Appendix D of Standard for design of steel structures, for the y-y direction:
Class b, so, the coefficients are α1 = 0.650, α2 = 0.965, and α3 = 0.300.
Since , then the stability factor in x:
According to the formula 8.2.1-8 of Standard for design of steel structures,
According to the formula 8.2.1-10 of Standard for design of steel structures,
According to the formula 8.2.1-12 and 8.2.1-5 note of Standard for design of steel structures,
According to the formula 8.2.1-12 of Standard for design of steel structures,
According to the formula 8.2.5, ϕbx = 1.0.
According to the formula 8.2.1, η = 0.7.
According to the formula 8.2.5-2,
Shear Strength
Take the neutral axis as the calculation point of shear stress, calculate the area moment:
S = 417,605 mm3
According to clause 6.1.3 of Standard for design of steel structures, shear stress
τmax = 7.69 < fv = 125 N/mm2
Therefore, the ratio is:
Comparison
Result Type | Reference | STAAD.Pro | Difference | Comment |
---|---|---|---|---|
Compression Slenderness | 0.46 | 0.46 | none | |
Tension Slenderness | 0.23 | 0.23 | none | |
Flange width to thickness ratio | 0.70 | 0.70 | none | |
Web height to thickness ratio | 0.70 | 0.70 | none | |
Column Strength | 0.91 | 0.91 | none | |
In-plane stability | 0.64 | 0.64 | none | |
Out-plane stability | 0.83 | 0.83 | none | |
Shear Strength | 0.05 | 0.05 | none |
STAAD.Pro Input File
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\China\GB500017-2017 Tube section with Combined Axial and Bending.std is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 21-Aug-18
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 4 0; 3 6 4 0; 4 6 0 0;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+008
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-005
DAMP 0.03
TYPE STEEL
STRENGTH FY 253200 FU 407800 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY CHINESE
1 TABLE ST TUB30030010.0
3 TABLE ST PIP299X10.0
2 TABLE ST HN300X150
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 4 FIXED
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
2 UNI GY -10
JOINT LOAD
2 3 FX 30 FY -50 FZ 30
PERFORM ANALYSIS
FINISH
Chinese steel design parameters (.gsp file):
[[version=2207]
*{ The below data is for code check general information, please do not modify it.
[CodeCheck]
SeismicGrade=None
BeamBendingStrength=1
BeamShearStrength=1
BeamEquivalentStress=1
BeamOverallStability=1
BeamSlendernessWeb=1
BeamSlendernessFlange=1
TrussStrength=1
TrussStability=1
TrussShearStrength=1
ColumnStrength=1
ColumnStabilityMzMy=1
ColumnStabilityMyMz=1
PressedTrussSlenderness=1
TensionTrussSlenderness=1
ColumnSlendernessFlange=1
ColumnSlendernessWeb=1
BeamDeflection=1
SelectAll=0
GroupOptimize=0
FastOptimize=0
Iteration=0
SecondaryMembers=
SectCollectionOrder=0
[CheckOptionAngle]
PrimaryAxis=60.000000
SecondaryAxis=60.000000
ExtendLine=10.000000
*{ The above data is for code check general information, please do not modify it.
[GROUP=1]
Name(Parameter Name)=TUBE
Type(Member Type)=3
Principle(Principle Rules)=0
SteelNo()=Q235
SectionSlendernessRatioGrade(Section Slenderness Ratio Grade)=3
Fatigue(Fatigue Calculation)=0
Optimization(Perform optimized design)=0
MaxFailure(Failure Ratio)=1
MinTooSafe(Safety Ratio)=0.3
CheckLoadCase(Force Loads Case No.)=1
CheckDispLoadCase(Displacement Loads Case No.)=1
BeamBendingStrength()=1
BeamShearStrength()=1
BeamEquivalentStress()=1
BeamOverallStability()=1
BeamSlendernessFlange(b/t on beam)=1
BeamSlendernessWeb(h0/tw on beam)=1
TrussStrength(Axial Force Strength)=1
SecondaryMoment(Secondary Moment of Truss)=0
TrussStability(Solid-web Axial Compression Stability)=1
TrussShearStrength(Axial Shear Strength)=1
PressedTrussSlenderness(Pressed Member Slenderness)=1
TensionTrussSlenderness(Tension Member Slenderness)=1
ColumnStrength(Column Member Strength)=1
ColumnStabilityMzMy(Column Stability In-plane)=1
ColumnStabilityMyMz(Column Stability Out-plane)=1
ColumnSlendernessFlange(b/t on column)=1
ColumnSlendernessWeb(h0/tw on column)=1
CheckItemAPPENDIX_B11(Beam Deflection)=1
UseAntiSeismic(Use Seismic Adjusting Factor)=0
GamaReStr(Seismic Adjusting Factor of Load-bearing Capacity for Strength)=0
GamaReSta(Seismic Adjusting Factor of Load-bearing Capacity for Stability)=0
SLevel(Grade of Seismic Resistance)=0
lmdc(Slenderness Limit of Compression Member)=0
lmdt(Slenderness Limit of Tension Member)=0
Lmd831(Slenderness of Seismic Column)=0
Lmd841(Slenderness of Seismic Brace)=0
Lmd9213(Slenderness of Seismic Single-story Plant)=0
LmdH28(Slenderness of Seismic Multi-story Plant)=0
rz(Plastic Development Factor in Major Axis)=0
ry(Plastic Development Factor in Minor Axis)=0
gamaSharp(Plastic Development Factor of sharp side)=0
betamz(the equivalent moment factor in Major Axis plane)=0
betamy(the equivalent moment factor in Minor Axis plane)=0
betatz(the equivalent moment factor out Major Axis plane)=1
betaty(the equivalent moment factor out Minor Axis plane)=0
HasHorLoadZ(Has Horizontal Load in Z-Axis)=0
HasHorLoadY(Has Horizontal Load in Y-Axis)=0
DFF(Deflection Limit of Beam)=150
DJ1(Start Node Number in Major Axis)=0
DJ2(End Node Number in Major Axis)=0
Horizontal(Check for Deflection in Minor Axis)=0
Cantilever(Cantilever Member)=0
fabz(Overall Stability Factor in Major Axis of Bending Member)=0
faby(Overall Stability Factor in Minor Axis of Bending Member)=0
StressFeature(Select the Stress Feature to calulate stability factor of beam)=1
faz(Overall Stability Factor in Major Axis of Axial Compression Member=0
fay(Overall Stability Factor in Minor Axis of Axial Compression Member)=0
lz(Unbraced Length in Major Axis)=0
ly(Unbraced Length in Minor Axis)=0
miuz(Effective Length Factor for Column in Major Axis)=0
miuy(Effective Length Factor for Column in Minor Axis)=0
Lateral(Member in Frame Without Sidesway or not)=0
APZ(Gyration Radius Calculation as Z-Axis Parallel Leg)=0
rFlange(Limit Ratio of Width to Thickness for Flange)=0
rWeb(Limit Ratio of High to Thickness for Web)=0
BucklingStrength(Axis forced member bulking strength)=0
ZSectType(Section Type in Z-Axis)=0
YSectType(Section Type in Y-Axis)=0
HSectWebInTrussPlane(Web of H in Truss Plane)=0
rAn(Net Factor of Section Area)=1
rWnz(Net Factor of Resistance Moment in Z-Axis)=1
rWny(Net Factor of Resistance Moment in Y-Axis)=1
CapReduce(Seismic Reduction Factor of Load-bearing Capacity for Brace)=1
AngleReduce(Angle Strength Reduce)=0
LAglConSta(Connect Type of unequal single angle)=0
LAngleStrength(Reduction Factor of Angle Strength)=0
LAngleStability(Reduction Factor of Angle Stability)=0
rTrussSectReduce(Effective Factor of Axial Force Section)=1
Members(Member Number)=1