V. SNiP SP16 2017 - Interaction check of a column
Design a column per the SP 16.13330.2017 code.
Details
A 6.78m tall, simply supported column has a European HE600B section. The column is subject to a 310 kN axial load along with a uniformly distributed load of 50 kN/m in the local Y axis. The steel used has a modulus of elasticity of 206,000 MPa and a Ry = 239 MPa. γc = 1, γm = 1.05
Validation
Ry = Ryn/ γm = 223.8 MPa
Rs = 0.58×Ry/ γm = 129.8 MPa
Shear force at support:
Q = qx × L / 2 = 171.8 kN
Mx = qx × L2/ 8 = 295.0 kN·m
Bending moment:
Mx = qx × L2 / 8 = 171.8 (6.78)2 / 8 = 295.0 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,
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 = 0.2144
(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) ) |
= | ||
= | ||
= |
From Table 7, α = 0.03 and β = 0.06.
(Cl. 9.2.5) |
= | ||
= | ||
= | ||
= | ||
= |
Therefore,
So, the ratio is
Calculate Cmax Per Annex E.1
(F.(E.1) ) |
= | ||
= | ||
= | ||
= | ||
= | ||
= | ||
= |
As per Table E.6, α = 0, β = 0
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\Russia\SNiP SP16 2017 - Interaction check of a column.std is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 02-Sep-20
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 6.87 0;
MEMBER INCIDENCES
1 1 2;
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 EUROPEAN
1 TABLE ST HE600B
****************************************
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 -310
MEMBER LOAD
1 UNI GX 50
********************************
PERFORM ANALYSIS
*********************************
PARAMETER 1
CODE RUSSIAN
TB 1 ALL
ENSGR 1 ALL
GAMM 2 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 HE600B PASS SP cl.9.1.1 0.28 1 3.100E+02 C 2.950E+02 0.000E+00 3.435E+00 1 I HE600B PASS SP cl.9.2.2 0.24 1 3.100E+02 C 2.950E+02 0.000E+00 3.435E+00 1 I HE600B PASS SP cl.9.2.4 0.38 1 3.100E+02 C 2.950E+02 0.000E+00 3.435E+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 = 6.87E+00 Gross Area = 2.70E-02 Net Area = 2.70E-02 x-axis y-axis Moment of inertia (I) : 171.E-05 135.E-06 Section modulus (W) : 570.E-05 902.E-06 First moment of area (S) : 321.E-05 696.E-06 Radius of gyration (i) : 252.E-03 708.E-04 Effective Length : 6.87E+00 6.87E+00 Slenderness : 273.E-01 970.E-01 DESIGN DATA (units -kN,m) SP16.13330.2017 Axial force : 310.0E+00 x-axis y-axis Moments : 295.0E+00 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)= ( 310.0E+00/ 2.7E-02+ 295.0E+00* 3.00E-01/ 1.71E-03+ 0.000E+00* 1.50E-01/ 1.35E-04+ 0.000E+00* 2.49E-01/ 1.10E-05)/( 223.8E+03* 1.00E+00) = 2.83E-01=<1 cl.9.2.2 m_ef=eta*mx= 1.42E+00* 4.51E+00= 6.41E+00 F.(109) N/(FIe*A*Ry*GammaC)= 310.0E+00/( 2.14E-01* 2.70E-02* 223.8E+03* 1.00E+00) = 2.39E-01=<1 F.(112) c=beta/(1+alfa*mx)= 1.01E+00/(1+8.75E-01* 4.51E+00)= 2.04E-01 c_max= 4.00E-01 F.(111) N/(c*FIy*A*Ry*GammaC) = 0.31E+03/( 0.20E+00* 0.66E+00* 0.27E-01* 223.8E+03* 1.00E+00) = 3.80E-01=<1