V. SNiP SP16 2017 - I section with axial force and Bi-moment
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 an HE650A 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 and a uniformly distributed load of 2 kN/m in the local Y axis. The steel used has a modulus of elasticity of 206,000 MPa and a Ry = 235 MPa. γc = 1, γm = 1.05
Section Properties
D = 640 mm
B = 300 mm
tf = 26 mm
tw = 13.5 mm
A = 241.6 cm2
Ix = 175,200 cm4
Iy = 11,720 cm4
IT = 458 cm4
rx = 26.93 cm
ry = 6.97 cm
Validation
Ry = Ryn/ γm = 223.8 MPa
Rs = 0.58×Ry/ γm = 129.8 MPa
Shear force at support:
Qx = qx × L / 2 = 75 kN
Bending moment:
Mx = qx × L2 / 8 = 30 (5)2 / 8 = 93.75 kN·m
My = qy × L2 / 8 = 2 (5)2 / 8 = 6.25 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.
where= |
Therefore,
Evaluate η, the coefficient of the shape of cross section vertical element when 5 < m ≤ 20, Af / Aw ≥ 1, and 0 ≤ λ ≤ 5:
(Table Д.2, Note 1) |
So, [As per F.(110)]
(F.(106) ) |
= | ||
= | ||
= |
So, the ratio is
Design for Stability (Cl. 9.2.2)
From Table E.3, depending on conditional slenderness and reduced relative eccentricity:
ϕe = 0.203
(F.(109) ) |
Design for Stability (Cl. 9.2.4)
Calculate the stability of eccentrically compressed elements of constant cross-section, out-of-plane bending moment in the plan of maximum stiffness (Ix > Iy), coinciding with the plane of symmetry:
(F.111 ) |
= | ||
= | ||
= |
(F.114) |
= | ||||
= | ||||
= | ||||
= | ||||
= |
| |||
= | ||||
= | ||||
= |
Therefore,
So, the ratio is
Design for Stability (Cl. 9.2.9)
(F.111 ) |
= | ||
= |
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Ratio per Cl. 9.1.1 | 0.127 | 0.127 | none | |
Ratio per Cl. 9.2.2 | 0.073 | 0.0729 | negligible | |
Ratio per Cl. 9.2.4 | 0.102 | 0.099 | negligible | |
Ratio per Cl. 9.2.9 | 0.075 | 0.074 | negligible | |
mef | 7.18 | 7.16 | negligible | |
mx | 5.172 | 5.18 | negligible | |
C | 0.176 | 0.179 | negligible | |
ϕey | 0.333 | 0.33 | negligible | |
ϕexy | 0.198 | 0.199 | negligible |
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\Russia\SNiP SP16 2017 - I section with axial force and Bi-moment.std is typically installed with the program.
STAAD SPACE
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 EUROPEAN
1 TABLE ST HE650A
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 2 ALL
GAMM 2 ALL
ENSGR 1 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 I HE650A PASS SP cl.9.1.1 0.13 1 8.000E+01 C 9.375E+01 6.250E+00 2.500E+00 1 I HE650A PASS SP cl.9.2.2 0.07 1 8.000E+01 C 9.375E+01 6.250E+00 2.500E+00 1 I HE650A PASS SP cl.9.2.4 0.10 1 8.000E+01 C 9.375E+01 6.250E+00 2.500E+00 1 I HE650A PASS SP cl.9.2.9 0.07 1 8.000E+01 C 9.375E+01 6.250E+00 2.500E+00 MATERIAL DATA Steel = S235 EN10025-2 Modulus of elasticity = 206.E+06 kPa Design Strength (Ry) = 224.E+03 kPa SECTION PROPERTIES (units - m, m^2, m^3, m^4) Member Length = 5.00E+00 Gross Area = 2.42E-02 Net Area = 2.42E-02 x-axis y-axis Moment of inertia (I) : 175.E-05 117.E-06 Section modulus (W) : 548.E-05 781.E-06 First moment of area (S) : 307.E-05 603.E-06 Radius of gyration (i) : 269.E-03 696.E-04 Effective Length : 5.00E+00 5.00E+00 Slenderness : 186.E-01 718.E-01 DESIGN DATA (units -kN,m) SP16.13330.2017 Axial force : 800.0E-01 x-axis y-axis Moments : 937.5E-01 625.0E-02 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 2 CRITICAL CONDITIONS FOR EACH CLAUSE CHECK F.(106) (N/A+Mx*y/Ix+My*x/Iy+B*w/Iw)/(Ry*GammaC)= ( 800.0E-01/ 2.4E-02+ 937.5E-01* 3.20E-01/ 1.75E-03+ 625.0E-02* 1.50E-01/ 1.17E-04+ 0.000E+00* 2.50E-01/ 1.10E-05)/( 223.8E+03* 1.00E+00) = 1.27E-01=<1 cl.9.2.2 m_ef=eta*mx= 1.38E+00* 5.18E+00= 7.16E+00 F.(109) N/(FIe*A*Ry*GammaC)= 800.0E-01/( 2.03E-01* 2.42E-02* 223.8E+03* 1.00E+00) = 7.29E-02=<1 F.(114) c=c5(2-0.2*mx)+c10*(0.2*mx-1.0)= 1.82E-01*(2-0.2* 5.18E+00)+ 1.08E-01*(0.2* 5.18E+00-1.0)= 1.79E-01 c_max= 3.20E-01 F.(111) N/(c*FIy*A*Ry*GammaC)= 8.00E+01/(1.79E-01*8.26E-01* 2.42E-02* 223.8E+03* 100.E-02) = 998.E-04=<1 F.(117) FIexy=FIey*(0.6*c**(1/3)+0.4*c**(1/4))= 3.33E-01*(0.6*1.79E-01**(1/3)+0.4*1.79E-01**(1/4))= 1.99E-01 F.(116) N/(FIexy*A*Ry*GammaC)= 800.0E-01/( 1.99E-01* 2.42E-02* 223.8E+03*1.00E+00) =7.41E-02=<1