V. SNiP SP16 2017 - Eccentrically Compressed Tube Section
Design a column subject to axial compressive force and biaxial moment per the SP 16.13330.2017 code.
Details
A 5 m tall, simply supported column has a TUB200X160X8 section. The column is subject to a 80 kN axial load along with a uniformly distributed load of 30 kN/m in the local X axis. The steel used has a modulus of elasticity of 206,000 MPa and a Ry = 562 MPa. γc = 1, γm = 1.05
Section Properties
D = 200 mm
B = 160 mm
t = 8 mm
A = 55.0 cm2
Ix = 3,191.2 cm4
Iy = 2,248.1 cm4
IT = 3,971.6 cm4
rx = 7.61 cm
ry = 6.39 cm
Validation
Ry = Ryn/ γm = 561.9 MPa
Rs = 0.58×Ry/ γm = 325.9 MPa
Bending moment:
Mx = qx × L2 / 8 = 30 (5)2 / 8 = 93.75 kN·m
Design for Strength (Cl. 9.1.1)
Ryn ≤ 440 N/mm2
τ = 0; i.e., < 0.5×Rs
So, as per Cl. 9.1.1, F.105 should not be checked. Rather F.106 needs to be checked.
(F.(106) ) |
= | ||
= |
So, the ratio is
Design for Stability (Cl. 9.2.2)
To satisfy F.109, mef ≤ 20, where:
(F.110) |
= | ||
= |
Thus, m > 20, so must review Section 8 for further checks.
Design for Stability for a Box Section (Cl. 9.2.10)
Check the stability of box bars with constant cross-section subject to compression on one or two main planes:
(F.120) |
As per this clause, for uniaxial bending in the plane of maximum stiffness (i.e., Ix > Iy, My = 0), ϕey should be replaced by ϕy.
λx = Kx × L / rx = 1.0 (500) / 7.61 = 65.70 | (Cl 10.4.1) |
λy = Ky × L / ry = 1.0 (500) / 6.39 = 78.25
The conditional slenderness, , is the larger of and . Thus,
From Table 7, ɑ = 0.03 and β = 0.06 for a tube cross-section.
(F.(9) ) |
Note that per Cl. 7.1.3, for section type a, the maximum value of ϕ is given as . Thus, take ϕ = 0.455.
( F.122) |
So the ratio for stability about x axis is:
(F.120) |
Check for Flexure
[Eqn. 41 of SNiP SP16.13330.2011] |
= |
Check for Shear
By inspection, the shear at the maximum moment location is zero under a uniformly distributed load.
[Eqn. 42 of SNiP SP16.13330.2011] |
= |
Check for Combined Shear & Flexure
[Eqn. 44 of SNiP SP16.13330.2011] |
= | ||
= | ||
= |
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Ratio per Cl. 9.1.1 | 0.549 | 0.549 | none | |
Ratio per Cl. 9.2.10 | 0.502 | 0.501 | negligible | |
ϕy | 0.455 | 0.455 | none | |
δx | 1.03 | 1.03 | none | |
Ratio per Cl. 8.2.1 (41) | 0.523 | 0.523 | none | |
Ratio per Cl. 8.2.1 (42) | 0 | 0 | none | |
Ratio per Cl. 8.2.1 (44) | 0.455 | 0.455 | none | |
σx (MPa) | 293.8 | 293.8 | none |
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Russia\SNiP SP16 2017 - Eccentrically Compressed Tube Section.std is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 05-Jan-21
END JOB INFORMATION
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 5 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+08
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-05
DAMP 0.03
TYPE STEEL
STRENGTH FY 253200 FU 407800 RY 1.5 RT 1.2
END DEFINE MATERIAL
****************************************
MEMBER PROPERTY RUSSIAN
1 TABLE ST TUB200X160X8
****************************************
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FY MX MZ
****************************************
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
JOINT LOAD
2 FY -80
MEMBER LOAD
1 UNI GX 30
*1 UNI GZ 2
********************************
PERFORM ANALYSIS
***********************
PARAMETER 1
CODE RUSSIAN
TB 1 ALL
GAMM 2 ALL
SGR 18 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD.Pro Output
STAAD.PRO CODE CHECKING - (SP 16.13330.2017) V1.0 ******************************************** ALL UNITS ARE - KN METRE ======================================================================== MEMBER CROSS RESULT/ CRITICAL COND/ RATIO/ LOADING/ SECTION NO. N Mx My LOCATION ======================================================================== 1 TUB TUB200X160X8 PASS SP cl.9.1.1 0.55 1 8.000E+01 C 9.375E+01 0.000E+00 2.500E+00 1 TUB TUB200X160X8 PASS SP cl.9.2.10 0.50 1 8.000E+01 C 9.375E+01 0.000E+00 2.500E+00 1 TUB TUB200X160X8 PASS SP cl.8.2.1(41) 0.52 1 8.000E+01 C 9.375E+01 0.000E+00 2.500E+00 1 TUB TUB200X160X8 PASS SP cl.8.2.1(42) 0.00 1 8.000E+01 C 9.375E+01 0.000E+00 2.500E+00 1 TUB TUB200X160X8 PASS SP cl.8.2.1(44) 0.45 1 8.000E+01 C 9.375E+01 0.000E+00 2.500E+00 MATERIAL DATA Steel = C590 SP16.13330 Modulus of elasticity = 206.E+06 kPa Design Strength (Ry) = 562.E+03 kPa SECTION PROPERTIES (units - m, m^2, m^3, m^4) Member Length = 5.00E+00 Gross Area = 5.50E-03 Net Area = 5.50E-03 x-axis y-axis Moment of inertia (I) : 319.E-07 225.E-07 Section modulus (W) : 319.E-06 281.E-06 First moment of area (S) : 168.E-06 144.E-06 Radius of gyration (i) : 761.E-04 639.E-04 Effective Length : 5.00E+00 5.00E+00 Slenderness : 657.E-01 782.E-01 DESIGN DATA (units -kN,m) SP16.13330.2017 Axial force : 800.0E-01 x-axis y-axis Moments : 937.5E-01 0.000E+00 Shear force : 0.000E+00 0.000E+00 Bi-moment : 0.000E+00 Value of Bi-moment not being entered!!! Stress-strain state checked as: Class 1 CRITICAL CONDITIONS FOR EACH CLAUSE CHECK F.(106) (N/A+Mx*y/Ix+My*x/Iy+B*w/Iw)/(Ry*GammaC)= ( 800.0E-01/ 5.5E-03+ 937.5E-01* 1.00E-01/ 3.19E-05+ 0.000E+00* 8.00E-02/ 2.25E-05+ 0.000E+00* 0.00E+00/ 0.00E+00)/( 561.9E+03* 1.00E+00) = 5.49E-01=<1 F.(120) N/(FIy*A*Ry*GammaC)+Mx/(cx*DELx*Wx,min*Ry*GammaC)=-800.0E-01/( 4.55E-01* 5.50E-03* 561.9E+03*1.00E+00)+-937.5E-01/( 1.14E+00* 1.03E+00* 319.1E-06* 561.9E+03*1.00E+00)=5.01E-01=&lt;1 m_x =20.2E+00>20. F.(41) M/(Wn,min*Ry*GammaC)= 937.5E-01/( 3.19E-04* 561.9E+03* 1.00E+00= 5.23E-01=<1 F.(44) 0.87/(Ry*GammaC)*SQRT(SIGMx^2+3*TAUxy^2)= 0.87/( 561.9E+03* 1.00E+00)*SQRT(-293.8E+03^2+3* 0.000E+00^2)= 4.55E-01=<1 TAUxy/(Rs*GammaC)= 0.000E+00/( 325.9E+03* 1.00E+00)= 0.00E+00=<1