 # V. GB500017-2017 Pipe section with Combined Axial and Bending

Verify the strength, stability, and slenderness of a pipe 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 PIP299x10.0 with a length of 4 m. The structure is a portal frame. Member #3 assigned with a pipe section (PIP299x10.0) 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 = 24.45 kN
• Fy = 34.94 kN
• N = 93.30 kN
• Mx = -76.7 kN·m (at member end)
• My = 117.8 kN·m (at member end)

Material Properties

The material is Q235 type steel.

• Design strength in tension, compression, and flexure: fy = 215 MPa
• Design strength in shear: fv = 125 MPa

Section Properties

• Outside diameter, D = 299 mm
• Wall thickness, t = 10 mm
• Cross-sectional area, A = 9,079 mm2
• Moment of inertia about x, I = 94,902,00 mm4
• Area moment about x, S = 417,600 mm3

## Calculations

Slenderness Ratio

The effective length is:

lox = μx×lx = 1.297 × 4,000 mm = 5,188 mm

loy = μy×ly = 2.0383 × 4,000 mm = 8,150 mm

The slenderness ratio is:

$λ x = l 0 x i x = 5,188 102.2 = 50.73 < 150$
$λ y = l 0 y i y = 8,150 102.2 = 79.72 < 150$

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 = 79.92 / 150 = 0.53

According 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 = 79.92 / 300 = 0.27

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 Diameter to Thickness Ratio

$D t = 299 10 = 29.9$

According to table 3.5.1 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:

$93 ε k = 93$

Ratio: $29.9 90 = 0.33$

Plastic Development Coefficient

According to clause 8.1.1-2 of Standard for design of steel structures, and the width thickness ratio of cross-section plate is grade S3,

γm = 1.15

Check Member Strength

According to clause 8.1.1-2 of Standard for design of steel structures,

$σ=NAn+Mx2+My2γmWn=NA+Mx2+My2γmW$

Ratio: $σ f = 202.8 215 = 0.94$

Check Member Stability

According to table 7.2.1-1 of Standard for design of steel structures, the section is "a" for this section.

According to the formula (D.0.5) in Appendix D of Standard for design of steel structures,

For section x-x direction:

$λ n = λ y π f y E = 50.73 π 225 206,000 = 0.545$

Class a, so, the coefficients are α1 = 0.41, α2 = 0.986, and α3 = 0.152.

Since $λ n = 0.545 > 0.215$ , then the stability factor in x:

$ϕ x = 1 2 λ n 2 α 2 + α 3 λ n + λ n 2 - α 2 + α 3 λ n + λ n 2 2 - 4 λ n 2$
$= 1 2 × 0.545 2 0.986 + 0.152 × 0.545 + 0.545 2 - 0.986 + 0.152 × 0.445 + 0.545 2 2 - 4 × 0.545 2 = 0.914$

For section y-y direction:

$λ n = λ y π f y E = 79.72 π 225 206,000 = 0.857$

Class a, so, the coefficients are α1 = 0.41, α2 = 0.986, and α3 = 0.152.

Since $λ n = 0.875 > 0.215$ , then the stability factor in x:

$ϕ x = 1 2 λ n 2 α 2 + α 3 λ n + λ n 2 - α 2 + α 3 λ n + λ n 2 2 - 4 λ n 2$
$= 1 2 × 0.857 2 0.986 + 0.152 × 0.857 + 0.857 2 - 0.986 + 0.152 × 0.857 + 0.857 2 2 - 4 × 0.857 2 = 0.785$

So, ϕmin = 0.785

Equivalent Moment Factor

According to formula 8.2.4-6 of Standard for design of steel structures:

According to the note of formula 8.2.4 of Standard for design of steel structures:

M1x = -76.7 kN·m

M2x = 63.06 kN·m

M1y = 117.8 kN·m

M2y = -0.006 kN·m

According to formula 8.2.4-4 of Standards for design of steel structures:

$β x = 1 - 0.35 N N E + N N E W 2x W 1x = 1 - 0.35 × 93.3 2,905 + 0.35 × 93.3 2,905 63.06 -76.7 = 0.886$

According to formula 8.2.4-5 of Standards for design of steel structures:

$β y = 1 - 0.35 N N E + N N E W 2y W 1y = 1 - 0.35 × 93.3 2,905 + 0.35 × -0.006 117.8 63.06 -76.7 = 0.937$

According to formula 8.2.4-5 of Standards for design of steel structures:

β = βxβy = 0.886 × 0.937 = 0.830

According to formula 8.2.1-2 of Standard for design of steel structures:

According to the note of formula 8.2.4-2 of Standard for design of steel structures:

MxA = 63.06 kN·m

MyA = -0.006 kN·m

MxB = -76.7 kN·m

MyB = 117.8 kN·m

Mmax = 140.6 kN·m

According to the note of formula 8.2.4-2 of Standard for design of steel structures:

$NϕAf+βMγmW1-0.8NNEx'f$
$= 93.3 × 10 3 0.875 × 9,079 × 215 + 0.830 × 140.6 × 10 6 1.15 × 634,792 1 - 93.3 2,641 215 = 0.826$

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:

$τ f v = 7.89 125 = 0.06$

## Comparison

Table 1. Comparison of results
Result Type Reference STAAD.Pro Difference Comment
Compression Slenderness 0.53 0.53 none
Tension Slenderness 0.27 0.27 none
Diameter thickness ratio 0.33 0.33 none
Column Strength 0.94 0.94 none
In-plane stability 0.83 0.83 none
Out-plane stability 0.83 0.83 none
Shear Strength 0.06 0.06 none

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\China\GB500017-2017 Pipe 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
2 UNI GY -10
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]
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)=PIPE
Type(Member Type)=3
Principle(Principle Rules)=0
SteelNo()=Q235
Fatigue(Fatigue Calculation)=0
Optimization(Perform optimized design)=0
MaxFailure(Failure Ratio)=1
MinTooSafe(Safety Ratio)=0.3
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
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
DFF(Deflection Limit of Beam)=400
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)=3

## Chinese Steel Design Workflow Report 